FRM Part 2 Sample Questions with Detailed Solutions

Correct answer: C. 24.0%

Here the VaR is given and the volatility is missing, so the lognormal VaR formula has to be rearranged and solved for σ_R.

Start from the lognormal VaR formula:

VaR = P × (1 − exp(μ_R − σ_R × z))

Write the reported VaR as a fraction of the position value:

VaR / P = 21.016 / 80 = 0.26270

Substitute and get the exponential term on its own:

0.26270 = 1 − exp(0.09 − 1.645 × σ_R)

exp(0.09 − 1.645 × σ_R) = 1 − 0.26270 = 0.73730

Take the natural log of both sides:

0.09 − 1.645 × σ_R = ln(0.73730) = −0.30476

Solve for σ_R:

1.645 × σ_R = 0.09 + 0.30476 = 0.39476

σ_R = 0.39476 / 1.645 = 0.2400

The volatility implied by the reported VaR is 24.0%.

Check: run it forward to confirm. VaR = 80 × (1 − exp(0.09 − 1.645 × 0.24)) = 80 × (1 − exp(−0.30480)) = 80 × (1 − 0.73727) = 80 × 0.26273 = USD 21.02 million, which matches the report.

The one step to be careful with is the drift term. The exponent is μ_R − σ_R × z, so when you move things around to isolate σ_R, the +0.09 drift crosses over and adds to the +0.30476. Both end up on the same side. A student who forgets the drift term lands on the wrong volatility.

Why the other options are wrong

• A. Uses z = 2.326, the 99% value, instead of z = 1.645 for 95%. Solving 0.39476 / 2.326 = 0.170. The arithmetic is otherwise correct; the error is pulling the wrong confidence level off the z table.
• B. Forgets the drift term. Solves 1.645 × σ_R = 0.30476 without adding back the 0.09, giving 0.30476 / 1.645 = 0.185. The drift is easy to lose when the formula is rearranged.
• D. Uses z = 1.282, the 90% value, instead of z = 1.645 for 95%. Solving 0.39476 / 1.282 = 0.308. It is the same type of error as A in the other direction: the method is right and z is wrong.

Module

Market Risk Measurement and Management

Chapter

MR 1: Estimating Market Risk Measures: An Introduction and Overview

Learning objective

Estimate VaR using a parametric approach for both normal and lognormal return distributions

Correct answer: A. 250 observations support at most 250 distinct quantiles, so 500 slices force repeated or interpolated quantiles carrying no information. The remedy is to bootstrap from the sample.

A coherent risk measure of this kind is a weighted average of quantiles, with the weighting function chosen by the risk measurer and applied over the probability range. The average-quantile route to it is the one the team is using: select the weighting function, decide the number of probability slices, estimate the quantile at each slice, and take the weighted average with a numerical algorithm.

The machinery is sound where the risk measurer can choose the number of slices freely, but in a non-parametric setting that choice is not free. The number of slices is limited by the data set, and each quantile has to be read off an actual observation, so 250 observations give at most 250 distinct quantiles.

500 minus 250 = 250

Those 250 extra slices land back on quantiles that have already been used, or on interpolations between adjacent observations. Either way they carry no new information about the tail, and constraints of this kind limit the accuracy of the resulting risk measure. The estimate is not being computed at a finer resolution. It is being computed at the same resolution and reported with more decimal places, which is why it moves about when the junior analyst repeats it on subsamples.

The remedy is the bootstrap. Resampling with replacement from the 250 observations builds a much larger effective data set out of the same underlying returns, and a larger effective data set supports a finer set of distinct quantiles for the weighting function to act on.

Why the other options are wrong

• B. Correctly states that the weighting function has to be normalized but incorrectly makes that the binding constraint. Normalization holds at any slice count and does nothing about a sample that cannot resolve 500 distinct quantiles.
• C. Incorrectly requires a parametric distribution. The weighting function is chosen by the risk measurer over the probability range, and the quantiles it weights can be read off a purely non-parametric sample.
• D. Gives the correct diagnosis but incorrectly resolves it by lengthening the window, which reaches a further year back into data whose relevance to current market conditions is what is in doubt. Resampling enlarges the effective sample without reaching further into the past.

Module

Market Risk Measurement and Management

Chapter

MR 2: Non-Parametric Approaches

Learning objective

Apply the bootstrap historical simulation approach to estimate coherent risk measures

Correct answer: B. 4.032%

The peaks-over-threshold VaR is the threshold plus a scaled adjustment:

VaR = u + ( beta / xi ) × { [ ( n / N_u ) × ( 1 − alpha ) ]^(−xi) − 1 }

The first thing to settle is the ratio. It is total observations over exceedances, not the exceedance fraction. Here that is 1,000 / 60 = 16.667. Getting this the wrong way up is the single most destructive error available in this formula, because the term is raised to a negative power and inverting the base sends the answer off by a factor of four.

Work through it.

( n / N_u ) × ( 1 − alpha ) = 16.667 × 0.01 = 0.16667

0.16667^(−0.20) = 1.43100

Subtract 1: 0.43100

beta / xi = 0.85 / 0.20 = 4.25

VaR = 2.20 + 4.25 × 0.43100 = 2.20 + 1.832 = 4.032%

Check: VaR must exceed the threshold. The threshold is the level exceeded by 6% of the sample, and a 99% VaR is by construction deeper than that, so anything at or below 2.20% is wrong before the arithmetic is even examined.

Calculator: 0.16667, y^x, 0.2, +|−, =, then −1, × 4.25, + 2.2.

Why the other options are wrong

• A. 1.832% is the adjustment term without the threshold added back. It is the distance past the threshold, not the loss level, and it sits below the threshold itself, which makes it impossible as a 99% VaR on this book.
• C. 4.936% applies the formula at 99.5% rather than 99%. Correct method, wrong confidence level, and the 0.9 percentage point gap between the two shows how quickly the tail deepens once the tail index is positive.
• D. 7.589% applies the formula at 99.9%. Same error as the previous option, one step further out, and the gap between 99% and 99.9% here is worth more than three and a half percentage points of portfolio value.

Module

Market Risk Measurement and Management

Chapter

MR 3: Parametric Approaches (II): Extreme Value

Learning objective

Describe the peaks-over-threshold (POT) approach

Correct answer: D. The analyst is wrong, because the 95 percent refers to the decision rule for rejecting the model, while the 97 percent sets the tail probability of 3 percent at which exceptions are expected to occur.

These are two different numbers doing two different jobs, and they happen to be written in the same units.

The VaR confidence level fixes p. At 97 percent, exceptions should occur on 3 percent of days, so over T days a correct model produces 0.03T of them on average. That is the null hypothesis.

The test confidence level fixes how much departure from that null the validation team is willing to attribute to sampling variation before calling the model wrong. At 95 percent, the team wants to be 95 percent confident that the observed count differs from 0.03T for a reason other than chance.

Nothing links the two choices. A 97 percent VaR can be tested at 95 percent, and a 95 percent VaR can be tested at 97 percent. Under the supervisory framework a 99 percent VaR is tested with a rule whose Type 1 error rate sits near 11 percent, and the mismatch is deliberate rather than an oversight.

Why the other options are wrong

• A. The probability of an exception under the null comes from the VaR confidence level alone. The test confidence level then decides how far the observed count has to stray from that null before the model is rejected, which is a separate choice.
• B. There is no ordering requirement between the two levels in either direction. They can be equal, or either one can be higher, with no effect on the internal consistency of the test.
• C. This reverses the roles. The expected number of exceptions comes from the VaR confidence level, and the test confidence level does not enter that calculation at all.

Module

Market Risk Measurement and Management

Chapter

MR 4: Backtesting VaR

Learning objective

Evaluate the accuracy of a VaR model based on exceptions or failure rates by using a model verification test

Correct answer: C. USD 2.97 million

Principal mapping looks only at when the principal comes back. Coupons are stripped out and ignored. The portfolio is then treated as a single zero-coupon exposure sitting at the average maturity of the redemption payments.

Average maturity here is 3 years, so the whole USD 200 million is placed on the 3-year vertex and charged the 3-year risk:

VaR = USD 200 million × 1.4841 / 100 = USD 2.97 million

One step, one lookup, and that is the entire method. Its only virtue is that simplicity.

Why the other options are wrong

• A. USD 0.94 million puts everything on the 1-year vertex at 0.4696%. That is the shortest redemption date and it ignores the 5-year issue entirely.
• B. USD 2.70 million is the duration-mapped figure. It uses the portfolio duration of 2.733 years rather than the average maturity of 3 years, and requires interpolating the risk between the 2-year and 3-year vertices.
• D. USD 4.85 million puts the whole USD 200 million on the 5-year vertex at 2.4261%. That is the longest maturity in the portfolio, not the average maturity of the redemption payments, and it ignores the fact that half the principal comes back in one year.

Module

Market Risk Measurement and Management

Chapter

MR 5: VaR Mapping

Learning objective

Differentiate among the three methods of mapping portfolios of fixed-income securities

Correct answer: D. The series of portfolio value changes is recomputed from the option positions actually held whenever those positions change, rather than being read from the realized return history.

Everything turns on where the risk lives. Selling an out-of-the-money put earns a premium on almost every day and loses heavily on the rare day the option finishes in the money. A history of realized returns from such a strategy is a long string of small gains, so any measure computed from that history reports low risk. The measure is not broken. It has been fed a series that does not contain the exposure.

Now revalue the option positions the fund is holding right now through history. The historical dates on which the underlying fell hard produce very large negative value changes for a short put, and those entries land in the tail of the series. The risk appears, because the positions carrying it are now in the calculation.

The word dynamic is doing the work. Positions change, so the series has to be rebuilt each time they do. A series built once and left alone describes a book the fund no longer holds.

Why the other options are wrong

• A. Pushing further into the tail of the wrong distribution does not help. The realized return history of the fund contains almost no large losses, so no quantile of it, however extreme, will show the exposure that the sold puts create.
• B. A longer history helps only if the fund held the same positions through it, and a dynamic strategy by definition did not. The risk is in the positions held today, and no amount of history about different positions will surface it.
• C. Subadditivity is about how a measure behaves when portfolios are combined. It has nothing to do with whether the measure can see a position that is not in the data it was computed from.

Module

Market Risk Measurement and Management

Chapter

MR 6: Validating Bank Holding Companies' Value-at-Risk Models for Market Risk

Learning objective

Describe some important considerations for a bank in assessing the conceptual soundness of a VaR model during the validation process

Correct answer: B. 0.0556

Where the Kolmogorov-Smirnov test keeps only the single largest gap, this one keeps all of them. Every observation contributes a squared deviation and the statistic is the sum, plus a correction term.

W² = Σ [ z_j − (2j − 1) / (2n) ]² + 1 / (12n), summed over j from 1 to n

Two details do the damage on this calculation, and they are independent of each other. The comparison point is the midpoint (2j − 1) / (2n), not j / n, so for eight observations it runs 0.0625, 0.1875, 0.3125 and so on in steps of one eighth. And there is a correction of 1 / (12n) that gets added once at the end, not per observation.

Then add the correction: 1 / (12 × 8) = 0.010417. So W² = 0.045150 + 0.010417 = 0.055567, which rounds to 0.0556.

Check the sign pattern in the deviation column. The first three are positive and the last five are negative, which says the observed values start out above the uniform grid and fall below it from the fourth observation onward. In this eight-point sub-sample that is a mild inward squeeze, and the two largest squared contributions come from the middle-to-upper ranks. Eight observations cannot settle the shape of a distribution, which is why the formal verdict on this desk comes from the full 500-observation sample.

Why the other options are wrong

• A. This is the sum of squared deviations without the correction term added at the end. The correction is one over twelve times the sample size, which is 0.0104 here, so leaving it out understates the statistic by roughly a fifth on a sample this small.
• C. This uses j divided by n as the comparison point instead of the midpoint (2j − 1) divided by 2n. Borrowing the empirical CDF from the Kolmogorov-Smirnov calculation shifts every comparison point up by half a step, which more than doubles the sum of squared deviations.
• D. This divides the sum of squared deviations by the sample size and stops there, taking the description of the test as a mean squared deviation literally. The statistic is a sum rather than an average, and the correction term is still missing as well.

Module

Market Risk Measurement and Management

Chapter

MR 7: Beyond Exceedance-Based Backtesting of Value-at-Risk Models

Learning objective

Describe backtesting using PITs, and compare the various goodness-of-fit tests that can be used to evaluate the distribution of PITs: the Kolmogorov-Smirnov test, the Anderson-Darling test, and the Cramer-von Mises test

Correct answer: A. Buy puts on an index such as the Dow and sell puts on the individual stocks.

Another way to be long correlation is to buy index puts and sell puts on the individual stocks of that index. When correlation rises, the index moves more than the diversified sum of the individual names would suggest, so the long index puts gain relative to the short single-stock puts. Since correlation tends to rise when the market falls, this position also carries an indirect short-market tilt.

The structure captures the same exposure as paying fixed in a correlation swap: it profits when co-movement across the index increases.

Why the other options are wrong

• B. This reverses the legs. To be long correlation you buy the index puts and sell the single-stock puts, not the other way around.
• C. Index futures alone carry directional market exposure, not a correlation position. The correlation trade uses index versus single-stock puts.
• D. Buying calls on everything is a long-market, long-volatility position, not a targeted long-correlation trade. The correlation trade is long index puts against short single-stock puts.

Module

Market Risk Measurement and Management

Chapter

MR 8: Correlation Basics: Definitions, Applications, and Terminology

Learning objective

Describe the structure, uses, and payoffs of a correlation swap

Correct answer: D. 79.03%.

The mean reversion rate equals minus the slope of the regression:

a = -β = -(−0.7903) = 0.7903 = 79.03%

The regression form of the mean reversion equation is S_t - S_t-1 = aμ_S - aS_t-1, so the coefficient on the prior level equals -a. A slope of -0.7903 therefore gives a positive rate of 79.03%, and the rate lies between 0 and 1.

On average, 79.03% of a deviation from the long-term mean is removed within one month. A rate of 1 would pull the series back to its mean completely at every time step, and a rate of 0 would mean no mean reversion at all.

Each figure in the fitted line has its own meaning:

At 79.03%, equity correlations show very strong mean reversion. An upward spike in correlation is typically followed by a sharp decline in the next month, and a downward spike by a sharp rise.

Why the other options are wrong

• A. Incorrectly reads the intercept of 0.256 as the rate, where the intercept equals the rate multiplied by the long-term mean.
• B. Incorrectly keeps the sign of the slope, where the rate equals minus the slope and is reported as the positive 79.03%.
• C. Gives the lag-1 autocorrelation, 1 - 0.7903 = 20.97%, which is the complement of the mean reversion rate rather than the rate itself.

Module

Market Risk Measurement and Management

Chapter

MR 9: Empirical Properties of Correlation: How Do Correlations Behave in the Real World?

Learning objective

Calculate a mean reversion rate using standard regression and calculate the corresponding autocorrelation

Correct answer: D. It takes the two marginal probabilities, each between 0 and 1, and returns one joint probability between 0 and 1 that describes both names together.

A copula function takes n marginal probabilities, each on the interval from 0 to 1, and returns one number on that same interval. In symbols it maps [0, 1]^n into [0, 1], which is how an n-dimensional problem becomes a unit-dimensional one. That one number is the joint probability, so the copula is the device that joins several univariate distributions into a single multivariate distribution.

For the desk's two names, n = 2 and the routine runs as follows:

The standard normal values are an intermediate step. They are where the two marginals sit while the joint normal distribution combines them with the correlation of 0.4, and the calling code never receives them.

The correlation is a parameter of the function rather than one of its outputs. It decides how the two names are joined, so changing it moves the output while the inputs stay where they are. At a correlation of 0.6 the same two marginals of 6.51% and 23.83% go in and 4.61% comes out, a rise of 4.61% - 3.44% = 1.17 percentage points in the joint probability alone.

Why the other options are wrong

• A. Incorrectly treats the standard normal values as the inputs and a correlation as the output, when -1.5133 and -0.7118 are produced inside the routine and the correlation of 0.4 is supplied to it as a parameter.
• B. Incorrectly has the copula return two revised marginals, when it returns one joint probability and leaves 6.51% and 23.83% as they were supplied.
• C. Incorrectly runs the function backward from the correlation to the marginals, when the marginals are inputs estimated for each name and the correlation only decides how they are joined.

Module

Market Risk Measurement and Management

Chapter

MR 10: Financial Correlation Modeling: Bottom-Up Approaches

Learning objective

Explain the purpose of copula functions and how they are applied in finance

Correct answer: B. The data reject a one-for-one relationship, so the trader should sell USD 93.6 million.

A DV01-sized hedge is correct when the two yields move one for one, which is the hypothesis that the slope equals one. The regression output settles it.

The constant being indistinguishable from zero is the expected and desirable result. Over an extended window it would be odd for the corporate yield to drift up or down on days when the government yield does not move.

The slope is the operative test. One sits outside the interval 0.740 to 0.944, so the data reject a one-for-one relationship and the DV01-sized hedge is the wrong size. The regression hedge follows:

DV01-sized amount = 100 × 0.2124 / 0.1910 = 111.2

Regression hedge = 111.2 × 0.842 = 93.6

The trader sells USD 93.6 million rather than USD 111.2 million.

Why the other options are wrong

• A. Both halves are incorrect: one lies outside the interval 0.740 to 0.944, so the relationship is rejected, and the face amount that follows is the regression hedge rather than the DV01-sized amount.
• C. The verdict on the slope is correct but the face amount incorrectly keeps the DV01-sized 111.2 million, which is the hedge the rejected hypothesis would justify.
• D. The face amount is correct but the verdict incorrectly accepts a one-for-one relationship, which the interval on the slope rules out.

Module

Market Risk Measurement and Management

Chapter

MR 11: Regression Hedging and Principal Component Analysis

Learning objective

Calculate the regression hedge adjustment factor, beta

Correct answer: A. 1.0147

The replicating portfolio and the option have the same payoff in every state on date 1, so they must have the same price today.

The two legs net to:

520.6225 − 519.6078 = 1.0147

The value is small because the two large positions offset each other closely. The option pays 0 in one state and only 5.2217 in the other, so its replicating portfolio has a small net cost.

Arbitrage rules out any other price. If the option trades below 1.0147, a trader can buy the option and sell the replicating portfolio. The trader receives cash today and the future cash flows offset in both states.

If the option trades above 1.0147, the trader can sell the option and buy the replicating portfolio. The future cash flows again offset in both states.

The calculation is sensitive to errors because 1.0147 is the difference between two values above 500. A small error in either leg can change the option value materially.

Why the other options are wrong

• B. 2.5596 incorrectly averages the two option payoffs using probabilities of one half and discounts at the six-month interest rate. Investors do not pay the average of a risky payoff, and this route never uses the replicating portfolio, so it does not produce the arbitrage price.
• C. 2.6108 incorrectly averages the two payoffs without discounting. It is a date 1 expected payoff under the desk probabilities, not a price today.
• D. 5.2217 incorrectly reports the down-state payoff on date 1 as the option's price today. It is a future payoff in one state.

Module

Market Risk Measurement and Management

Chapter

MR 12: Arbitrage Pricing with Term Structure Models

Learning objective

Construct and apply an arbitrage argument to price a call option on a zero-coupon security using replicating portfolios

Correct answer: D. Two-year spot rate 4.7473%, one-year forward rate 5.5000%

The two-year zero-coupon bond is discounted through 4.00% for the first year and 5.50% for the second year.

1,000 / (1.04 × 1.055) = 1,000 / 1.0972 = 911.4109

The two-year spot rate is the constant annual interest rate that produces the same price:

1.0972^(1/2) minus 1 = 4.7473%

The one-year forward rate beginning one year from today is implied by the one-year and two-year zero-coupon bond prices.

The one-year zero-coupon bond price is:

1,000 / 1.04 = 961.5385

So:

961.5385 / 911.4109 minus 1 = 5.5000%

The one-year forward rate beginning in one year is 5.5000%.

Under certainty, this forward rate equals the future one-year interest rate. A two-year zero-coupon bond and a strategy that invests for one year and then reinvests for another year have the same certain two-year payoff, so their prices must be consistent. If the two prices differed, an investor could buy the cheaper position, sell the dearer one and collect a certain profit with nothing at risk. That possibility is what forces the forward rate to the expected future one-year interest rate under certainty.

Why the other options are wrong

• A. Incorrectly sets the forward rate equal to the two-year spot rate. The spot rate covers both years, while the forward rate applies only to the second year. The two rates agree only when the first-year interest rate already equals the spot rate, which is not the case when the first year is 4.00% and the two-year spot rate is 4.7473%.
• B. 4.7500% incorrectly takes the arithmetic average of 4.00% and 5.50%. The two-year spot rate comes from compounding and equals 4.7473%.
• C. Incorrectly reverses the two quantities. 5.50% is the one-year forward rate for the second year, not the two-year spot rate.

Module

Market Risk Measurement and Management

Chapter

MR 13: Expectations, Risk Premium, Convexity, and the Shape of the Term Structure

Learning objective

Explain the role of interest rate expectations in determining the shape of the term structure

Correct answer: B. 41.57 basis points per month and 144.00 basis points per year

Start with variance because variance, not standard deviation, scales directly with time.

The random variable in the process has variance dt. So the variance of the interest rate change over an interval dt equals annual variance multiplied by dt. Taking square roots, the standard deviation of the rate change equals annual volatility multiplied by the square root of dt.

The one-year standard deviation is simply the quoted annual volatility because the square root of one equals one. This is why quoting volatility as 144 basis points per year is useful. It is both the model parameter and the standard deviation of the one-year rate change.

Dividing by 12 instead of by the square root of 12 gives 12 basis points per month. If twelve independent monthly changes each had this standard deviation, annual standard deviation would be 12 multiplied by the square root of 12, or 41.57 basis points, far below the assumed 144 basis points.

Why the other options are wrong

• A. 12.00 basis points per month and 41.57 basis points per year incorrectly scale the monthly standard deviation in direct proportion to time, dividing 144 basis points by 12 instead of by the square root of 12. The annual figure then carries that wrong monthly value forward, 12 multiplied by the square root of 12, which equals 41.57 basis points rather than the 144 basis points the model assumes.
• C. 12.00 basis points per month and 144.00 basis points per year get the annual value right but scale the monthly figure by the time interval rather than its square root.
• D. 41.57 basis points per month and 41.57 basis points per year correctly calculate the monthly figure but incorrectly leave the annual figure unchanged.

Module

Market Risk Measurement and Management

Chapter

MR 14: The Art of Term Structure Models: Drift

Learning objective

Calculate the short-term rate change and standard deviation of the rate change using a model with normally distributed rates and no drift

Correct answer: A. The choice is defensible. Non-negativity is one property among several, and where negative rates barely affect the prices in question, a simpler model can be the better tool.

The question is whether a known flaw in a model disqualifies it, and the answer depends on whether that flaw touches the numbers being produced.

Each of the three views does work here. The first says the extra machinery of a level-dependent specification is not buying a better description of the current environment. The second says the region where the two model families disagree most, the low end of the rate distribution, carries almost no value for these instruments. The third says the simpler model is cheaper to build, to run and to explain, and that this has value of its own.

Taken together they say the cost of the flaw is small and the benefit of the simplicity is real. That is a defensible trade, and it is the same reasoning that governs the choice between time-dependent volatility and mean reversion: the purpose at hand decides.

The trade would go the other way for a different book. A desk holding long-dated options struck deep out of the money at low strikes would be pricing precisely the region where the normal specification puts mass below zero, and there the flaw is not marginal.

Why the other options are wrong

• B. A model can be wrong about something and still be the right tool, provided the thing it is wrong about does not affect the quantities being computed. Every model in use is misspecified in some way.
• C. The presence of options is not the dividing line. What matters is whether the value of the position depends on the part of the distribution where the specifications disagree, which is the region near and below zero.
• D. Implementation cost is only one part of the third view, which also covers the effort of calibrating and explaining the model. The trader is entitled to weigh it.

Module

Market Risk Measurement and Management

Chapter

MR 15: The Art of Term Structure Models: Volatility and Distribution

Learning objective

Describe the short-term rate process under the Cox-Ingersoll-Ross (CIR) and lognormal models

Correct answer: A. 3.8155%, 4.2971% and 5.4195%.

Each ending level equals the starting level plus that factor's monthly change.

The short-term interest rate change is:

−0.9242 × (0.0375 − 0.0460) / 12 = 6.5464 basis points

The short-term interest rate change carries no random term, so this mean reversion amount is the whole monthly change.

The medium-term factor change is:

−0.4621 × (0.0460 − 0.0520) / 12 + 124.0 × (0.285 × 0.242487 + 0.958528 × (−0.346410))

This equals:

2.3105 − 32.6039 = −30.2934 basis points

The long-term factor change is:

−0.0231 × (0.0520 − 0.0840) / 12 + 88.0 × 0.242487

This equals:

0.6160 + 21.3389 = 21.9549 basis points

The original ordering remains short below medium below long.

The distance from the short-term interest rate to the medium-term factor falls from 85 basis points to 48.16 basis points.

The distance from the medium-term factor to the long-term factor rises from 60 basis points to 112.25 basis points.

The short-term interest rate change uses only the medium-term factor. The medium-term factor change uses the long-term factor and both random variables, and the long-term factor change uses the long-run constant and the first random variable.

Why the other options are wrong

• B. The short-term and long-term values are correct, but 4.7088% takes the medium-term factor change as 2.3105 plus 124.0 × 0.285 × 0.242487, which omits the second random variable.
• C. The medium-term factor is correct, but the short-term and long-term changes are incorrectly subtracted rather than added.
• D. Incorrectly combines the omitted shock with the two sign errors.

Module

Market Risk Measurement and Management

Chapter

MR 16: The Vasicek and Gauss+ Models

Learning objective

Calculate changes in the short-term, medium-term, and long-term interest rate factors under the Gauss+ model

Correct answer: C. Both conclusions are correct, and the 27.00% at the USD 60.00 strike price is the highest implied volatility in the range.

The call option struck at USD 60.00 is priced using an implied volatility of 27.00%.

This is above the implied volatility near the middle of the strike range.

A higher implied volatility produces a higher option price.

So the market price of the USD 60.00 call is above the price generated by a single-volatility lognormal benchmark centered near the money.

The call pays only when the commodity ends above USD 60.00.

Its high market price therefore corresponds to more probability in the right tail than the lognormal benchmark assigns.

At the other end, the USD 40.00 strike has an implied volatility of 19.00%.

This lower implied volatility corresponds to a cheaper low-strike put and a lighter left tail.

So both of the analyst's conclusions are correct.

The upward-sloping pattern is the reverse of the usual equity skew.

Equity implied volatility falls as the strike price rises, which corresponds to a heavier left tail and a lighter right tail. A commodity with the opposite slope is a market paying more against a sharp rise than against a sharp fall.

Why the other options are wrong

• A. Incorrectly separates the price and distribution conclusions. The high price of the tail option is the evidence for the heavier tail.
• B. A rise in implied volatility raises the call price rather than lowering it.
• D. Incorrectly reverses both conclusions. An upward slope corresponds here to a heavier right tail and lighter left tail.

Module

Market Risk Measurement and Management

Chapter

MR 17: Volatility Smiles and Volatility Surfaces

Learning objective

Compare the shape of the volatility smile (or skew) to the shape of the implied distribution of the underlying asset price and to the pricing of options on the underlying asset

Correct answer: D. 35.70, which is 0.17 above the 99% value at risk of 35.53

The rates desk has a mean loss of 1.8 and a standard deviation of 14.5. The equity desk figures are not used.

For a normal loss distribution, the 99% value at risk equals the mean plus 2.326 standard deviations.

The 97.5% expected shortfall equals the mean plus 2.338 standard deviations.

The current framework measure is:

1.8 + 2.338 × 14.5 = 35.7010

The measure it replaces is:

1.8 + 2.326 × 14.5 = 35.5270

The difference is:

35.7010 − 35.5270 = 0.1740

Under normality, the two measures are almost equal.

The difference can also be written as:

(2.338 − 2.326) × 14.5 = 0.012 × 14.5 = 0.1740

So the mean does not affect the difference.

The figure 30.22 comes from:

1.8 + 1.96 × 14.5 = 30.22

This is the 97.5% value at risk, not the 97.5% expected shortfall.

Value at risk identifies a loss quantile. Expected shortfall averages losses beyond the quantile, so the expected shortfall multiplier is larger.

Why the other options are wrong

• A. The expected shortfall is correct, but it is incorrectly compared with the 97.5% value at risk. The replaced capital measure is the 99% value at risk of 35.53.
• B. 30.22 incorrectly uses 1.96, the 97.5% normal quantile, as the expected shortfall multiplier. The correct expected shortfall multiplier is 2.338.
• C. The expected shortfall of 35.70 is correct, but 30.22 is incorrectly treated as the reported measure. 30.22 is the 97.5% value at risk.

Module

Market Risk Measurement and Management

Chapter

MR 18: Fundamental Review of the Trading Book

Learning objective

Describe the changes to the Basel framework for calculating market risk capital under the Fundamental Review of the Trading Book (FRTB) and the motivations for these changes

Correct answer: B. Bramwell Steel

Insolvency and default must be tested separately.

Insolvency compares liabilities with assets.

Default asks whether a contractual obligation has been met.

Bramwell Steel is insolvent but not in default.

Its liabilities exceed assets by USD 55 million, but it continues meeting its obligations.

Ashby Mills is solvent but in default because it missed a coupon.

Corrowdale Foods is both insolvent and in default.

Denby Optics is neither.

An obligor that is insolvent while still paying remains a going concern, and creditors often keep dealing with one.

What the insolvency tells them is how little would be left if the payments stopped.

Why the other options are wrong

• A. Incorrectly reverses the two tests for Ashby Mills. It is solvent but in default.
• C. Corrowdale Foods is insolvent, but it is also in default because it missed a supplier payment.
• D. Denby Optics is neither insolvent nor in default.

Module

Credit Risk Measurement and Management

Chapter

CR 1: Fundamentals of Credit Risk

Learning objective

Explain the differences between insolvency, default, and bankruptcy

Correct answer: C. Incorrect. Guidelines carry carve-outs for exchange rate movement, and this limit should be expressed in EUR rather than in USD.

The transaction was within the limit at inception.

Initial reported exposure:

96,000,000 × 1.1500 = 110,400,000

Eight months later:

96,000,000 × 1.2800 = 122,880,000

The excess above the USD 120 million limit is:

122,880,000 − 120,000,000 = 2,880,000

The exposure exceeded the limit because the euro appreciated.

The originator did not choose to increase the underlying EUR 96 million exposure.

Guidelines can account for market variables such as foreign exchange movements.

A local-currency limit can separate the credit decision from currency management, which is often handled by the treasury function.

A deliberate breach remains serious because it means an employee chose to take more risk than authorized.

In most financial firms a deliberate breach leads to immediate termination of employment. No employee may take more risk than the board of directors has accepted.

That is different from a limit being crossed because a market variable moved after the transaction was approved.

So the right response here is a correction to the guidelines rather than a disciplinary case.

Why the other options are wrong

• A. Correctly calculates USD 122.88 million but incorrectly treats the foreign exchange movement as additional risk deliberately taken by the originator.
• B. Incorrectly invents a tolerance band around the exposure limit. A limit carries no allowance for a small excess, and the relief that applies here is a carve-out for the cause of the excess rather than for its size.
• D. Incorrectly assigns currency hedging responsibility to the originator rather than the treasury function.

Module

Credit Risk Measurement and Management

Chapter

CR 2: Governance

Learning objective

Discuss the following key principles underlying best practice for the governance system of credit risk: Guidelines, Skills, Limits, and Oversight

Correct answer: C. USD 61.6 million, giving an expected loss of USD 859,320.

Exposure at default estimates how much of the credit line will be outstanding when default occurs.

Borrowers approaching default may draw additional amounts from available facilities.

The undrawn balance is:

80.0 − 34.0 = 46.0

Expected additional drawdown is:

0.60 × 46.0 = 27.6

Exposure at default is:

34.0 + 27.6 = 61.6

Expected loss is:

0.0310 × 61,600,000 × 0.45 = 859,320

The full commitment is the ceiling rather than the expected exposure.

The bank's history indicates that defaulting borrowers draw 60% of the unused balance before default.

Why the other options are wrong

• A. Incorrectly uses only today's USD 34 million drawn balance.
• B. Incorrectly uses the undrawn balance rather than the amount expected to be outstanding at default.
• D. Incorrectly assumes the entire committed line will be drawn.

Module

Credit Risk Measurement and Management

Chapter

CR 3: Credit Risk Management

Learning objective

Identify and explain the components of expected loss and differentiate between expected loss and unexpected loss

Correct answer: A. Incorrect. Expected loss is absorbed by reserves and by loan pricing, so economic capital stands behind unexpected loss alone at USD 638.0 million.

Economic capital covers unexpected loss. Expected loss is handled separately through reserves and loan pricing.

A bank expects some credit losses over a stated period. Those losses are part of the normal cost of lending rather than a surprise. Loan loss reserves absorb them, and the bank recovers the expected cost through the interest rate charged on its loans.

Unexpected loss is the volatility of actual losses around that expected amount. Because the bank cannot know in advance how far actual losses will run above the expected amount, it cannot recover that volatility directly through the loan interest rate. Economic capital provides the cushion against this uncertainty.

The capital multiplier converts unexpected loss into the amount of capital required at the bank's chosen confidence level. In USD million:

88.0 × 7.25 = 638.00

The proposed amount is below the required capital. Adding expected loss and unexpected loss gives 129.6, but that sum is not the economic capital requirement because unexpected loss still has to be scaled to the chosen confidence level.

Why the other options are wrong

• B. Incorrectly adds expected loss to unexpected loss and then omits the capital multiplier that converts unexpected loss into economic capital.
• C. Correctly applies the capital multiplier but incorrectly applies it to expected loss as well as unexpected loss.
• D. Incorrectly treats unexpected loss itself as the capital requirement without applying the multiplier.

Module

Credit Risk Measurement and Management

Chapter

CR 4: Capital Structure in Banks

Learning objective

Evaluate a bank's economic capital relative to its level of credit risk

Correct answer: C. EUR 165.17, because the exposure is the balance outstanding at default and the loss rate is the part not recovered.

Expected loss equals the product of probability of default, exposure at default and loss given default. Probability of default means the likelihood that the borrower defaults during the relevant horizon. Exposure at default means the amount outstanding when default occurs. Loss given default means the proportion of that exposure that is lost after recoveries.

EL = PD × EAD × LGD

For a credit card, exposure at default is not automatically the approved credit limit because the outstanding balance changes through time. For a term loan or a bond the amount due at default is fixed by the contract and can be specified directly, while a revolving card account carries no such fixed amount. Exposure at default for the segment is estimated from the bank's own default history for that reason. The EUR 12,000 limit is the maximum amount available to the borrower. The estimated balance outstanding at default is EUR 7,400, so EUR 7,400 is the exposure at default.

Loss given default is the complement of the recovery rate.

LGD = 100% − 38% = 62%

So:

0.036 × 7,400 × 0.62 = 165.17

Using the approved limit would produce EUR 267.84. Treating the entire exposure as lost would produce EUR 266.40. These are different mistakes even though the resulting amounts are close.

Why the other options are wrong

• A. Incorrectly uses the approved limit as exposure at default instead of the balance outstanding when default occurs.
• B. Correctly uses the outstanding balance as exposure at default but incorrectly assumes a 100% loss, ignoring the 38% recovery.
• D. Correctly uses the outstanding balance as exposure at default but incorrectly applies the recovery rate where the loss rate belongs.

Module

Credit Risk Measurement and Management

Chapter

CR 5: Introduction to Credit Risk Modeling and Assessment

Learning objective

Describe quantitative measurements and factors of credit risk, including probability of default, loss given default, exposure at default, expected loss, and time horizon

Correct answer: B. Incorrect. External ratings indicate systematic risk well and support benchmarking, and relying on a single system across the 2,400 exposures may not be the best option.

Using only one credit scoring or rating system can leave important information unused. Combining systems developed from different data and different objectives can provide a broader view of credit risk.

Dunhollow's three-year record supports the internal model's stronger default prediction on its own portfolio. Research has also found that external agency ratings can be weaker default predictors than internal or financial models.

External ratings can still add information. They can provide useful indications of systematic risk, meaning risk arising from broad market shocks, and they offer an independent benchmark against which the bank can review its internal model.

The two systems use different information and can serve different purposes. A weaker default-prediction record does not remove the external system's value in other areas.

Why the other options are wrong

• A. Incorrectly settles the decision on cost and acceptance and discards the internal model that separated defaulters from non-defaulters better in each of the three years.
• C. Correctly notes that external ratings can be weaker default predictors but incorrectly concludes that the external source should be discarded.
• D. Incorrectly identifies external ratings as the stronger default-prediction model.

Module

Credit Risk Measurement and Management

Chapter

CR 6: Credit Scoring and Rating

Learning objective

Compare the credit scoring system to the credit rating system in assessing credit quality and describe the different types of each system

Correct answer: C. 2.86% and 1.34%, a difference of 1.52 percentage points.

Loss rate equals probability of default multiplied by loss given default, so probability of default is recovered by dividing the loss rate by loss given default.

1.26% / 44% = 2.86%

0.51% / 38% = 1.34%

2.86 − 1.34 = 1.52

The implied probability of default for the weaker band is 1.52 percentage points higher.

Retail portfolios are segmented into groups with similar loss characteristics. Score bands provide one way to create those segments.

The Basel Capital Accord requires this segmentation of retail portfolios, with each band corresponding to a risk level. The bank estimates the loss rate for a band from its own historical data and then infers the probability of default from an estimate of loss given default.

Probability of default and loss given default both increase as credit quality deteriorates in this example. They rise for separate reasons. Weaker borrowers default more often, and the same borrowers tend to be less well secured, so recoveries on them are lower. Reading the observed loss rate itself as probability of default would combine the two effects.

A bank that does so understates the default frequency in every band.

Because loss given default cannot exceed 100%, dividing by loss given default cannot produce an implied probability below the observed loss rate. Multiplying the two instead gives 0.55%, which is not a quantity the bank holds.

Why the other options are wrong

• A. Incorrectly multiplies the loss rate by loss given default, applying the severity factor twice.
• B. Incorrectly treats loss rate as probability of default and ignores loss given default.
• D. Correctly divides loss rate by loss given default but uses the wrong score bands. Both the loss rate and the loss given default are read one band lower than the question specifies.

Module

Credit Risk Measurement and Management

Chapter

CR 7: Credit Scoring and Retail Credit Risk Management

Learning objective

Discuss the key variables in a mortgage credit assessment and describe the use of cutoff scores, default rates, and loss rates in a credit scoring model

Correct answer: D. Aranthia under economic structure, because 44% of export earnings resting on one complex ties the economy to one price.

Country risk can be grouped into four sources, and each concern here belongs to a different category.

The first is the country's position in the economic growth life cycle. Early growth economies and younger companies generally have smaller reserves to absorb shocks, so they can grow faster in recoveries and decline more sharply in downturns. Corandia fits this description, with a median listing history of 6 years and a 51% decline in earnings.

The second source is political risk. It includes the form of government and the stability of leadership succession. Dumaria's 22 years without an election falls into this category.

The third source is legal risk. One part concerns whether property rights are protected. The other concerns how efficiently legal claims are enforced. A dispute that takes 39 months to reach judgment reflects weakness in legal-system efficiency, which is Belvaria's problem.

The fourth source is economic structure. Heavy dependence on one commodity, product or service exposes the broader economy to shocks affecting that activity. Aranthia earns 44% of export revenue from one copper complex.

A decline in demand for the product on which a concentrated economy depends affects more than the producer. Suppliers, retailers and banks can all depend on the same income stream. The exposure is therefore country-wide rather than industry-specific, which is why concentration is classified as a source of country risk.

Why the other options are wrong

• A. Incorrectly classifies the time required to reach judgment as economic structure rather than legal-system efficiency.
• B. Incorrectly classifies an early growth economy as a legal-risk problem.
• C. Incorrectly places unelected leadership under legal risk rather than political risk.

Module

Credit Risk Measurement and Management

Chapter

CR 8: Country Risk: Determinants, Measures, and Implications

Learning objective

Identify and explain the different sources of country risk

Correct answer: A. USD 1,185,000 before the default, reduced by USD 9,480.

A buyer pays the ask. Protection on all 125 companies at 158 basis points on USD 600,000 each costs:

0.0158 × USD 600,000 × 125 = USD 1,185,000 per year

When a company defaults, the investor receives the usual credit default swap payoff on that name and the annual payment falls by the share of the total that the defaulted name carried:

USD 1,185,000 / 125 = USD 9,480

Selling protection on the same amounts would run at the bid, 156 basis points, for USD 1,170,000 a year. The two-basis-point spread between the quotes is the market maker's, and the side of it that applies depends entirely on which way the investor is going.

The structure is worth holding onto because it explains what an index position actually is. It is not one contract on a portfolio. It is 125 separate exposures of USD 600,000 each, settled one at a time, and after a default the investor continues to pay the coupon on the principal applicable to those companies in the index that have not yet defaulted.

Why the other options are wrong

• B. Applies the bid of 156 basis points, which is the rate at which the market maker buys protection. An investor buying protection pays the ask.
• C. Prices the protection correctly and then divides the reduction by 1,250 rather than by the 125 names the index contains.
• D. Uses the bid rather than the ask and then divides the reduction by 1,250 rather than by 125, so both figures are wrong.

Module

Credit Risk Measurement and Management

Chapter

CR 9: Estimating Default Probabilities

Learning objective

Define a credit default swap (CDS) and explain its mechanics including the obligations of both the default protection buyer and the default protection seller

Correct answer: B. The expression can be multiplied by a maturity adjustment factor, which allows for a loan lasting longer than one year deteriorating without defaulting, so the longer loan attracts more capital.

The maturity adjustment factor distinguishes the seven-year loan from the eleven-month loan even when the other stated inputs are the same.

The risk horizon remains one year. For a loan with eleven months remaining, the one-year horizon covers the loan's remaining life. By the end of the year, the loan has either repaid or defaulted.

A seven-year loan remains outstanding after the one-year horizon. Its credit quality can deteriorate during the year without default, leaving the bank with a lower-value credit exposure that continues for several more years.

A default-only one-year calculation does not directly capture this deterioration. The maturity adjustment factor accounts for the additional risk associated with longer remaining maturity.

The other stated risk inputs can be identical while capital still differs because the maturity adjustment sits outside those inputs.

Why the other options are wrong

• A. Incorrectly replaces the one-year default probability with a seven-year default probability. The horizon remains one year and maturity is handled through a separate adjustment.
• C. Incorrectly changes the confidence level according to maturity. The supervisory confidence level remains fixed.
• D. Incorrectly concludes that the two loans must have identical capital because the listed inputs match. Remaining maturity creates an additional adjustment.

Module

Credit Risk Measurement and Management

Chapter

CR 10: Credit Value at Risk

Learning objective

Describe the application of the Vasicek's model to estimate capital requirements under the Basel II internal-ratings-based (IRB) approach

Correct answer: C. 6.12%

The default correlation between any pair of firms in this model is the joint default probability less the squared default probability, divided by the default probability multiplied by one minus the default probability:

ρ = (π_12 − π^2) / (π (1 − π))

The squared default probability is the joint probability the pair would produce under independence:

0.0200^2 = 0.0004, or 0.04%

So the numerator is:

0.0016 − 0.0004 = 0.0012

The denominator is the variance of the default indicator, which is the product of the two standard deviations once both default probabilities are the same:

0.0200 × 0.9800 = 0.0196

0.0012 / 0.0196 = 0.0612, or 6.12%

This is the general default correlation expression with the two default probabilities set equal to one another. The joint default probability arriving from the bivariate normal rather than from an estimate is what makes it a single-factor calculation: the model supplies the joint probability from the asset return correlation, and the default correlation is read back out of it.

The two quantities the calculation moves between are easy to run together. A joint default probability of 0.16% against an independent 0.04% looks like a fourfold effect, and the default correlation that produces it is 6.12%. A default correlation of a few percent and a joint default probability several times the independent value are the same statement about the same pair.

Why the other options are wrong

• A. Incorrectly divides by the standard deviation of the default indicator rather than by its variance. With both default probabilities equal, the two standard deviations multiply to the variance.
• B. Incorrectly divides by the default probability rather than by the default probability multiplied by one minus the default probability.
• D. Incorrectly omits the squared default probability from the numerator, leaving the joint default probability where the excess over independence belongs.

Module

Credit Risk Measurement and Management

Chapter

CR 11: Portfolio Credit Risk

Learning objective

Estimate the probability of a joint default of any pair of credits and the default correlation between any pair of credits using the single-factor model

Correct answer: D. Both parts are incorrect: only the new transaction has to be valued on each stored path, and a negatively correlated transaction is likely to reduce both adjustments.

The existing simulated market paths do not need to be rerun when a new trade is added, and a negatively correlated trade is likely to reduce both adjustments.

The market variables have already been simulated and stored. The incremental effect of the new transaction can be measured by valuing that trade on each existing path and adding its value to the previously stored portfolio values.

Exposure equals max(V, 0), where V is the net value of the transactions to the bank. A trade whose value is negatively correlated with the existing book tends to reduce V on the paths where the existing book has its largest positive values. This lowers exposure.

A partial unwind is an example. It reduces the magnitude of the netted portfolio value in both directions, so it tends to reduce the bank's positive exposure and the counterparty's positive exposure.

Credit valuation adjustment and debt valuation adjustment both depend on the distribution of the same netted portfolio value, viewed from opposite sides.

Pricing the incremental adjustment rather than a standalone adjustment allows the bank to quote a better price on a trade that reduces its existing exposure.

Why the other options are wrong

• A. Incorrectly requires the simulation to be rerun and incorrectly states that a partial unwind raises exposure.
• B. Correctly rejects the rerun but incorrectly states that a negatively correlated transaction increases exposure.
• C. Incorrectly requires a rerun and incorrectly gives opposite directions for the two adjustments even though both depend on the same netted portfolio value.

Module

Credit Risk Measurement and Management

Chapter

CR 12: Credit Risk

Learning objective

Assess the credit risks of derivatives

Correct answer: A. 3.9115s

A regular credit default swap premium is paid only if the reference entity survives to the payment date.

Each premium must therefore be multiplied by the survival probability and then discounted.

For year 3, the expected payment is:

0.9161s

Discounting three years at 5.5 percent gives:

0.9161s × 0.8479 = 0.7768s

So the present value of the five regular expected premium payments is:

3.9115s

Without survival weighting, the discounted five-year premium stream would be 4.2523s.

The difference reflects the possibility that Ashgrove defaults and future premium payments stop.

Solving for the spread on the regular stream alone overstates it. A smaller payment stream is then asked to cover the same expected payoff.

Why the other options are wrong

• B. Incorrectly includes the accrual payment when the question asks for the regular payment stream.
• C. Incorrectly discounts the premiums without survival weighting.
• D. Incorrectly gives only the accrual component.

Module

Credit Risk Measurement and Management

Chapter

CR 13: Credit Derivatives

Learning objective

Explain how to account for credit risk exposure in valuing a CDS

Correct answer: B. Correct. The USD 200 million payout falls due on a credit event at a bank in the seller's own market, so the exposure is largest when the seller is weakest.

The value of a credit default swap changes with the credit spread of the reference entity, while the large contractual payment occurs only after a specified credit event. The value therefore responds continuously to a market variable, but the protection payment is triggered by a credit event.

This makes the protection seller's credit quality particularly important. On an interest rate swap, movements in interest rates determine exposure but do not normally affect the counterparty's own credit condition. On a credit default swap, the reference entity and the protection seller can be exposed to the same credit environment.

The second row describes wrong-way risk, meaning the exposure becomes greatest when the counterparty is least able to perform. Buying protection on one bank from another bank makes this relation particularly strong because both institutions can come under pressure from the same market conditions.

Senior tranches of structured finance collateralized debt obligations created an even stronger version of this problem. The resulting demand was for protection sellers viewed as remote from default.

Why the other options are wrong

• A. Incorrectly treats the interest rate swap and credit default swap as equivalent because both can be valued at replacement cost. The credit default swap can link a large protection payment to conditions that also weaken a seller operating in the same credit market.
• C. Reaches the correct conclusion using a margin assumption that does not hold. A protection seller does not post the full notional as initial margin, and monolines and credit derivative product companies sold protection while sometimes posting no collateral.
• D. Incorrectly concludes that linking the payout to the reference entity removes the seller's credit quality from the analysis. The buyer receives the protection payment only if the seller can perform.

Module

Credit Risk Measurement and Management

Chapter

CR 14: Derivatives

Learning objective

Describe the features and use of credit derivatives and discuss potential risks they may create

Correct answer: B. USD 14.5 million

The derivative valuation equals the present value of receipts minus the present value of payments.

USD 86.4 million - USD 71.9 million = USD 14.5 million

The swap is worth USD 14.5 million to Lowell.

Because that value is positive, current exposure is also:

Exposure = USD 14.5 million

If the counterparty defaulted immediately, Lowell would lose its net claim of USD 14.5 million. Had the valuation been negative, Lowell would have had no exposure at all, because a party that owes on a net basis still has to pay and cannot gain from the default.

The USD 2.3 million payment due in two weeks is already included in the USD 71.9 million present value of payments and should not be added or deducted again.

The valuation is not an amount Lowell can demand immediately. It is the present value of future contractual exchanges.

Why the other options are wrong

• A. Incorrectly uses the next scheduled settlement even though it is already included in the present value. It is also an amount Lowell pays, and exposure is never negative.
• C. Incorrectly adds the next settlement to the valuation, counting the same USD 2.3 million twice.
• D. Incorrectly uses the gross present value of receipts without netting contractual payments.

Module

Credit Risk Measurement and Management

Chapter

CR 15: Counterparty Risk and Beyond

Learning objective

Describe credit exposure, credit migration, recovery, mark-to-market, replacement cost, default probability, loss given default, and the recovery rate

Correct answer: A. The 148 credit default swaps compress straightforwardly because they are fungible once bucketed by reference entity and maturity, and the second book needs a more advanced method because the fixed rates differ.

The credit default swaps can be compressed inside matching buckets because their standardized terms make them fungible, while the interest rate swaps require a more advanced approach because their fixed coupons differ.

Credit default swaps use standardized fixed coupons and scheduled termination dates. Contracts with the same reference entity and maturity can therefore be interchangeable inside a bucket, so 148 contracts across 12 reference entities sort into buckets and compress inside each one.

Interest rate swaps are different. A swap struck at par uses the fixed coupon that made its value zero when it was entered. Two swaps executed years apart can therefore have the same floating leg but different fixed coupons.

Those contracts cannot be replaced one for one without changing their economics. Standardization is not always available. Where a product is bespoke, compression reaches only what the algorithms can blend and the rest of the book stays as it is.

More advanced compression algorithms can sometimes create replacement trades that blend the coupons. Credit default swap terms were standardized partly to make compression work and partly to make central clearing work. Interest rate swaps went a different way because a variable fixed rate is how that market prices a swap at par.

Why the other options are wrong

• B. Incorrectly treats matching floating cash flows as sufficient. Different fixed coupons prevent simple interchangeability.
• C. Incorrectly separates compression from contract terms. A cycle that replaces contracts must preserve their economic effect.
• D. Incorrectly requires every original contract term to be identical before any compression method can operate. More advanced algorithms can create replacement positions.

Module

Credit Risk Measurement and Management

Chapter

CR 16: Netting, Close-Out and Related Aspects

Learning objective

Describe the mechanics of termination provisions and trade compressions and explain their advantages and disadvantages

Correct answer: A. GBP 0.

The exposure can rise without producing a margin call when the remaining shortfall is below the minimum transfer amount.

The combined trigger is:

22.0 + 18.5 + 4.0 = GBP 44.5 million

The exposure is GBP 44.0 million, so it remains below that level.

The shortfall calculation gives the same result:

44.0 − 22.0 − 18.5 = GBP 3.5 million

The GBP 3.5 million shortfall is below the GBP 4.0 million minimum transfer amount. The shortfall is a real uncollateralized exposure even though no margin is called. The exposure has risen by GBP 3.0 million and the uncollateralized amount has risen with it, and it stays uncollateralized until the shortfall grows past GBP 4.0 million.

The GBP 0.1 million rounding amount is irrelevant because no transfer is triggered.

Why the other options are wrong

• B. Correctly calculates the GBP 3.5 million shortfall but incorrectly transfers it without applying the minimum transfer test.
• C. Incorrectly calls the GBP 3.0 million increase in exposure rather than the actual collateral shortfall.
• D. Incorrectly treats the minimum transfer amount itself as the amount due.

Module

Credit Risk Measurement and Management

Chapter

CR 17: Margin (Collateral) and Settlement

Learning objective

Calculate the credit support amount (margin) under various scenarios

Correct answer: C. GBP 184 million, being 40% of the 460, and default fund contributions are revisited less often than initial margin, monthly in many cases.

The largest member contributes GBP 184 million because default fund contributions are allocated in proportion to initial margin.

Total average initial margin is:

480 + 360 + 240 + 120 = 1,200

The largest member's share is:

480 / 1,200 = 0.40

Its default fund contribution is:

460 × 0.40 = 184

The total size of the default fund is set using stress testing against extreme but plausible scenarios.

Those scenarios are defined in relation to the default of one or more members and the market conditions that would accompany such a default, and the fund is sized to cover the losses that would run above initial margin in those conditions.

The total is then allocated across members using a simpler rule, such as initial margin or position size, sometimes with a minimum contribution.

Initial margin is recalculated frequently because it tracks current portfolio risk. In practice that means a daily recalculation, because the portfolio it is measured against changes every day. A default fund contribution tracks a member's share of a total that was itself set by a stress test, so it is updated less often, monthly being a common interval.

Why the other options are wrong

• A. Gives the correct GBP 184 million contribution but incorrectly recalculates it daily. The default fund is revisited far less often than initial margin, monthly being a common interval.
• B. Correctly recognizes less frequent updates but incorrectly allocates the fund equally.
• D. Incorrectly allocates the fund equally and incorrectly treats equal contributions as a condition for mutualization. The allocation follows each member's risk.

Module

Credit Risk Measurement and Management

Chapter

CR 18: Central Clearing

Learning objective

Describe the application and estimation of margin and default funds under central clearing

Correct answer: B. The argument holds, because the ratio rises from 0.04 over 10 days to 0.45 over 5 years.

Drift grows in proportion to time, while volatility grows with the square root of time.

Drift accumulates period by period. Dispersion accumulates as variance rather than as standard deviation, which is where the square root comes from.

So drift becomes more important relative to dispersion as the horizon lengthens.

Ten days is:

10 / 250 = 0.04

The cumulative drift over ten days is:

1.8% × 0.04 = 0.072%

The standard deviation is:

9.0% x √0.04 = 1.80%

The ratio is:

0.072 / 1.80 = 0.04

Over five years, cumulative drift is:

1.8% × 5 = 9.0%

The standard deviation is:

9.0% x √5 = 20.12%

The ratio is:

9.00 / 20.12 = 0.45

At ten days, drift is small relative to dispersion.

Over five years, it becomes material.

A drift in a forward curve or a differential between two currencies can carry the expected future value a long way from the current value before any dispersion is considered.

Long-horizon exposure models therefore need to incorporate drift as well as transaction aging and future cash flows.

Over five years cash flows are paid, options are exercised, transactions terminate and margin is called. None of that happens inside a ten-day horizon.

The same portfolio can also need two sets of calculations, one built on a real-world drift for risk management and one on a risk-neutral drift for pricing.

Why the other options are wrong

• A. Incorrectly scales drift and volatility at the same rate.
• C. Incorrectly reverses which horizon makes drift important.
• D. Incorrectly scales the drift-to-volatility ratio with time rather than its square root, which turns 0.04 into 5.00 over five years.

Module

Credit Risk Measurement and Management

Chapter

CR 19: Future Value and Exposure

Learning objective

Compare the characterization of credit exposure to VaR methods and describe additional considerations used in the determination of credit exposure

Correct answer: C. It is incorrect, because each EUR 2.2 million coupon is at risk in full while each swap cash flow is only partly at risk, and the fraction at risk depends on the yield curve shape, forward rates and volatilities.

A bond coupon is a one-way payment. If the issuer defaults before the coupon is paid, the holder loses that payment apart from any recovery. The credit charge can therefore be built by discounting the promised cash flows for default and adding the value expected to be recovered.

A swap is different because payments run in both directions. On some dates the bank owes the counterparty and on others the counterparty owes the bank. At default, positive and negative values offset, so only the remaining positive exposure is at risk.

That is why a swap generally carries a smaller counterparty credit charge than a bond with the same notional and maturity.

The difficult part is that the future positive exposure cannot be read directly from the contract. It depends on the yield curve, the forward rates determining future floating payments, and the volatility of the underlying market variables.

So the charge must be built from a simulated exposure profile rather than from a simple discounted cash flow rule.

The lack of principal exchange on many swaps also reduces risk, but that is separate from the problem of measuring the future exposure.

Why the other options are wrong

• A. Incorrectly treats equal current values as implying equal counterparty risk. The relevant quantity is the future exposure at the time of default.
• B. Incorrectly uses notional as the main driver of the charge. Swap exposure is usually only a fraction of notional, while bond exposure is close to the full notional, so equal notionals do not imply equal charges.
• D. Correctly notes that the swap has no principal exchange but incorrectly treats current mark-to-market as the full basis of the charge. The charge depends on exposure over the remaining life.

Module

Credit Risk Measurement and Management

Chapter

CR 20: CVA

Learning objective

Explain the motivation for and the challenges of pricing counterparty risk

Correct answer: C. Spreads sat in a 12 to 30 basis point band and US$40 million is small against US$62 billion, and in the crisis spreads and exposures both swung widely together

Two conditions kept the adjustment quiet. Spreads on the main counterparties moved inside an 18 basis point band, and the adjustment itself was US$40 million against a US$62 billion portfolio, which is six hundredths of one percent of it. Check: 40 divided by 62,000 is 0.06%, and 30 less 12 is an 18 basis point band. A small number that does not move is not a risk management problem, and it was not treated as one.

The crisis broke both conditions at the same time. The spread range went from 18 basis points wide to 425 basis points wide, and exposure amounts on derivative transactions swung with the markets underneath them. The adjustment is a product of those two things, so when both move the result is not the sum of two moderate effects but something considerably larger: US$40 million became more than US$1.9 billion, a factor of close to fifty.

The direction of the surprise is the part usually forgotten. The crisis produced large losses on the adjustment and also large and unusual gains, since both spreads and exposures were swinging in both directions, and on a bilateral view a dealer whose own credit deteriorates records a gain on the liability side as well. A framework built for a quantity that only ever nudged had no answer for either, and the development of a proper risk management framework for the adjustment dates from that point. Regulatory capital followed, with a charge specifically for this source of risk.

Why the other options are wrong

• A. The adjustment was already being carried, which is why it stood at US$40 million in 2005. What changed was how much it moved rather than whether it had to be there, and no accounting change turns US$40 million into US$1.9 billion.
• B. The direction is reversed. The 12 to 30 basis point band is the definition of stable, and it is exactly why the adjustment was not seen as a live risk.
• D. Where the adjustment is managed is a real organizational question. Moving it does not explain a rise from US$40 million to US$1.9 billion.

Module

Credit Risk Measurement and Management

Chapter

CR 21: The Evolution of Stress Testing Counterparty Exposures

Learning objective

Explain the treatment of counterparty credit risk (CCR) both as a credit risk and as a market risk and describe its implications for trading activities and risk management for a financial institution

Correct answer: D. Foreclosure repays the senior bond earlier than anticipated and writes the junior bond down now, while extension spares the junior bond that writedown and leaves the senior bond facing a larger eventual loss

Foreclosure and extension affect senior and junior bondholders differently.

Foreclosing converts the property into cash immediately.

The realized loss is absorbed first by the junior tranche.

Extending the loan delays realization of the loss and preserves the possibility that collateral value recovers.

That benefits the junior tranche but leaves the senior tranche exposed to a potentially larger future loss and weaker credit enhancement.

The servicer may be required to maximize the present value of the loan, but the decision can still favor one class of investors over another.

No action available to the servicer is neutral between the two classes. That is what makes this a structural conflict rather than a question of diligence.

Why the other options are wrong

• A. Incorrectly assumes the senior bond absorbs the first loss. A USD 7,000,000 shortfall is absorbed inside the USD 52,000,000 junior bond.
• B. Incorrectly treats the eventual property loss as fixed regardless of the servicing decision.
• C. Incorrectly reverses the effects of foreclosure and extension.

Module

Credit Risk Measurement and Management

Chapter

CR 22: Structured Credit Risk

Learning objective

Identify the key participants in the securitization process and describe conflicts of interest that can arise in the process

Correct answer: A. As an incentive, with the 150 basis point increase making the call the rational choice but not a duty.

The issuer is not generally required to redeem the notes on the call date. The step-up raises the coupon if the notes remain outstanding, and it is there to give the issuer a strong economic incentive to refinance and exercise the call.

The increase is 235 - 85 = 150 basis points, and the additional annual interest cost is:

430,000,000 × 1.50% = GBP 6.45 million a year

So investors hold an expectation that the issuer will call, not a contractual promise. If refinancing becomes difficult or expensive, the issuer can leave the notes outstanding and pay the higher coupon, and the 150 basis points is what compensates investors for that extension risk. It fails where it matters most, because an issuer that cannot refinance at year five is an issuer whose credit or whose market has deteriorated.

Why the other options are wrong

• B. Treats the call as a mandatory redemption. If it were, the notes would have a maturity at that date and the step-up would be pointless.
• C. Incorrectly states that the higher note coupon increases excess spread. Raising the note coupon narrows the difference between the asset return and the note interest, so it reduces excess spread.
• D. Nothing is paid to the trustee. The step-up increases the coupon payable to the noteholders.

Module

Credit Risk Measurement and Management

Chapter

CR 23: An Introduction to Securitisation

Learning objective

Describe and assess the various types of credit enhancements

Correct answer: D. Statements 1 and 2 are correct, and statement 3 is incorrect.

Statements 1 and 2 are correct, and statement 3 misreads what the 2021 revision changed. Legal risk is included within operational risk, while strategic and reputational risk are excluded from the published definition.

The 2021 revision changed how strategic and reputational risks should be considered, but it did not change the definition. Where appropriate, operational risk management should consider strategic and reputational risks. Considering a risk within the operational risk function is different from including that risk in the definition of operational risk.

Regulators may have excluded strategic and reputational risk in order to make the measurement of operational risk as objective as possible. Both are harder to measure than an event with a recorded financial loss, so including them would make the resulting figures less objective.

In practice, the treatment of reputational risk is broader than the definition. Most financial organizations assess and manage reputational damage as part of their operational risk activities, and it appears in most of their impact assessment tables.

Why the other options are wrong

• A. Correctly accepts legal risk as part of the definition but incorrectly rejects the exclusion of strategic and reputational risk, even though the same published complement states that exclusion.
• B. Incorrectly rejects legal risk, even though legal risk is explicitly included within operational risk.
• C. Incorrectly treats the direction to consider strategic and reputational risk as a change to the definition. Consideration by the operational risk function does not place those risks inside the definition.

Module

Operational Risk and Resilience

Chapter

OR 1: Introduction to Operational Risk and Resilience

Learning objective

Describe an operational risk management framework and assess the types of risks that can fall within the scope of such a framework

Correct answer: C. (i) The change management process; (ii) a risk appetite and tolerance statement approved and periodically reviewed by the board; (iii) business continuity plans linked with the framework; (iv) public disclosures.

Finding (ii) falls short of the principle on risk appetite, not the principle on the framework. The principles expect the operational risk appetite and tolerance statement to be approved and periodically reviewed by the board. The last approval of Quarrington's statement was in 2021:

2026 − 2021 = 5

So the statement was approved by the chief risk officer rather than the board, and it has not been reviewed for 5 years.

Finding (i) fails on both parts of the change management principle. Only 1 of the 3 waves has resources:

1 / 3 = 33%

So the change is not adequately resourced, and with no document setting out how it will be carried out, it is not articulated either. The finding says nothing about whether the risks of the merger were identified. What it records is a change that was neither resourced nor planned, which is what the change management principle covers.

Finding (iii) is not the absence of a control, because the plans exist. The principle asks for business continuity plans that are in place and linked with the operational risk management framework, and the link is what is missing.

Finding (iv) is a gap against a principle in its own right. Public disclosure of the approach to operational risk management and of risk exposures is one of the 12 principles.

Why the other options are wrong

• A. Incorrectly treats the merger as a failure to identify risk and treats finding (ii) as a gap in the board's approval of the framework. The merger finding is about resources and planning, and the appetite statement has its own principle requiring board approval and periodic review.
• B. Correctly matches the merger to change management but incorrectly assigns finding (ii) to board approval of the framework and finding (iii) to the control environment. The appetite statement has its own principle, and the continuity plans fall short because they are not linked with the framework.
• D. Correctly matches findings (ii) and (iii) but incorrectly treats the merger as an identification failure and the missing disclosure as a monitoring gap. Public disclosure on the approach to operational risk management and on risk exposures is a principle of its own.

Module

Operational Risk and Resilience

Chapter

OR 2: Risk Governance

Learning objective

Explain the Basel regulatory expectations for the governance of an operational risk management framework

Correct answer: B. USD 27.5 million, and both belong in the non-financial impact, through the reputation channel and the regulatory enforcement channel.

The ORX impact taxonomy separates 3 kinds of impact at level 1, and the lost revenue and the reputational damage belong to different categories.

14.0 + 6.5 + 1.8 + 2.2 + 3.0 = 27.5

The provision counts even though nothing has been paid yet, because provisions are one of the direct financial items in the taxonomy. A provision is an amount recognized for an expected obligation or loss. The internal costs of the remediation team count too, since internal costs excluding legal expenses are a separate direct item.

The USD 9.0 million of revenue that never arrived is an opportunity cost, meaning a financial benefit forgone because of the incident. It is a financial effect, and it is indirect, so it stays out of the direct total. Revenue adjustment is a separate direct item, and none of the Radwell amounts is one, because the USD 9.0 million was never booked as revenue.

27.5 + 9.0 = 36.5

USD 36.5 million is the total financial impact, direct and indirect together. It is not the direct financial impact.

Neither the fall in the reputation score nor the enhanced supervision is a financial amount. Both are adverse consequences for the stakeholders of the firm, carried through the impact channels that the taxonomy lists under non-financial impact: reputation, and regulatory enforcement. In the reference taxonomy the indirect financial impact holds only opportunity costs, and reputation and enforcement are non-financial channels.

Why the other options are wrong

• A. Incorrectly adds the opportunity cost into the direct total and places reputation and enforcement under indirect financial impact, which holds only opportunity costs. The USD 9.0 million belongs in indirect financial impact, and reputation and enforcement belong in non-financial impact.
• C. Gets the direct total right but incorrectly places reputation and enforcement under indirect financial impact. They are non-financial impact channels rather than opportunity costs.
• D. Places reputation and enforcement correctly, but counts the USD 9.0 million opportunity cost in the direct total. Opportunity cost is an indirect financial impact.

Module

Operational Risk and Resilience

Chapter

OR 3: Risk Identification

Learning objective

Describe and apply an operational risk taxonomy and give examples of different taxonomies of operational risks

Correct answer: A. Gross loss USD 4.17 million, recovery USD 2.10 million, net loss USD 2.07 million

Regulators generally require only the losses that are directly identifiable as negative financial effects of the incident. The server write-off, the contractor fees and the legal fees for the rebuilding permits all arise from the flood itself and are paid out, so all three are direct losses.

The gross loss is:

3.40 + 0.65 + 0.12 = USD 4.17 million

The lost fee income is forgone revenue, which the bank's loss data policy excludes from the gross loss. Management time and attention is a non-financial impact rather than a negative financial effect directly identifiable in the incident, so it stays out of the regulatory loss figure as well.

The insurance settlement is a recovery. The Basel guidelines ask for the gross loss and any recoveries to be reported, so the record carries both, and the net loss is the gross loss minus the recovery:

4.17 − 2.10 = USD 2.07 million

Why the other options are wrong

• B. Shows 5.07 as both the gross and the net loss, because it adds the lost fee income and drops the recovery. The policy excludes forgone revenue from the gross loss, and the USD 2.10 million settlement must be recorded as a recovery.
• C. Correctly limits the gross loss to the three direct items but incorrectly leaves the insurance settlement out of the record. The settlement is a recovery, and recoveries are reported beside the gross loss so that the net loss of 2.07 can be measured.
• D. Correctly records the settlement as a recovery but incorrectly adds the USD 0.90 million of lost fee income, giving 4.17 + 0.90 = 5.07 and a net loss of 2.97. The loss data policy excludes forgone revenue from the gross loss.

Module

Operational Risk and Resilience

Chapter

OR 4: Risk Measurement and Assessment

Learning objective

Explain best practices for the collection of operational loss data and reporting of operational loss incidents, including regulatory expectations

Correct answer: D. 1 optimistic, 2 collective, 3 more of the same

The same-day sign-off is an optimistic control, the two-clerk check is a collective control, and the longer checklist is more of the same. Each is a recognized weak design, and each fails for a different reason.

Item 1 is a "tick-box" control. The time available per page, in minutes, is:

40 / 300 = 0.13

That is about 8 seconds a page. A sign-off like this would need exceptional ability or motivation to be effective, which is what makes it an optimistic control.

Item 2 is the common four-eyes check. The interviews show the weakness directly: each clerk trusts the other to be the careful one, so the attention each gives may be less rigorous than a single accountable person would give.

Item 3 responds to a checklist that managers already bypass by making the same checklist longer. The cause of the bypass, a process that is too cumbersome, is made worse, so the new pages are likely to be skipped as well. More controls do not necessarily mean less risk, and a poorly designed control can increase the vulnerability of the process it is meant to protect.

Why the other options are wrong

• A. Incorrectly calls the sign-off collective and the longer checklist optimistic. One person signs the pack, so accountability is not shared, and the longer checklist repeats a design that is already being bypassed.
• B. Correctly identifies the sign-off as optimistic but incorrectly labels the other two. The two-clerk check spreads responsibility, which makes it collective, and lengthening a bypassed checklist is the more-of-the-same response.
• C. Correctly identifies the longer checklist as more of the same but incorrectly labels items 1 and 2. The sign-off is a tick-box control by one person, and the two-clerk check is a collective control.

Module

Operational Risk and Resilience

Chapter

OR 5: Risk Mitigation

Learning objective

Describe control automation, internal control design, and control testing, including risks and challenges that arise in these processes and ways to make them more effective

Correct answer: C. P to the board risk committee, Q to the executive committee, and R to the business-line managers who own the risks.

Item P, the summary view of exposure, emerging risks, and increasing trends, is part of what the board risk committee receives, together with KRIs linked to the risk appetite, the frequency and severity of risk events, and the investigation of the causes of large events. Each audience has a different role in monitoring operational risk, so each needs a different type and level of information.

Item Q is the kind of information the executive committee (ExCo) needs. The ExCo oversees the proper and effective execution of the operational risk management framework, and every significant piece of information that shows the framework is working, or is not, has a place in its reporting. This includes risk events, action plans, the remediation status of issues, and culture and use test indicators, as well as risk trends and exposure.

Item R stays with the business-line managers and risk champions. Operational risk data is collected at the business operations level, where it is monitored most closely, and business-line managers typically monitor the status of their KRIs, the progress of their action plans, and the nature and severity of the events in their lines.

The colleague's "one place" design sends two very different items to the operational risk committee and sends the board-level summary to the audit committee. The audit committee oversees internal audit's assurance work and is not the body that monitors the firm's operational risk profile against appetite.

Why the other options are wrong

• A. Correctly keeps item R with the business-line managers but incorrectly routes item P to the audit committee and item Q to the operational risk committee. The summary view goes to the board risk committee, and culture and use test remediation goes to the ExCo.
• B. Routes items Q and R to the operational risk committee, although it sends item P correctly to the board risk committee. The ExCo oversees execution of the framework, and daily KRI monitoring belongs to the business lines.
• D. Correctly sends item Q to the ExCo but incorrectly sends the board-level summary to the audit committee and the daily data to the operational risk committee. The summary view belongs to the board risk committee, and daily monitoring stays with the business lines.

Module

Operational Risk and Resilience

Chapter

OR 6: Risk Reporting

Learning objective

Identify roles and responsibilities of different organizational committees, and explain how risk reports should be developed for each committee or business function

Correct answer: B. USD 83.4 million

The legal loss module forecasts all litigation-related losses over the stress horizon in three parts: expected immaterial bulk litigation, conditional expected losses on the current case load above the reserved threshold, and incremental future litigation cases, the unknown unknowns.

Bulk claims:

2,400 × 3,500 = USD 8.4 million

For the current case load, only the conditional expected loss above what is already reserved enters the forecast.

Case 1:

120 − 70 = USD 50 million

Case 2's conditional expected loss of USD 30 million is below its reserve of USD 45 million, so it adds nothing. The excess reserve is not released into the forecast as a gain.

The total is:

8.4 + 50 + 0 + 25 = USD 83.4 million

Litigation is a large share of overall operational losses for most banks, and supervisors expect legal costs, including expenses, judgments, fines, and settlements, to be estimated under baseline and stressful environments and broken out into their own subcategory where possible.

The module also faces a lag. Business practices that lead to litigation after a market crash may not turn into settlements until years later, so the forecast must build in lags between the factors driving it, such as macroeconomic variables and firm-specific factors like assets, and the losses themselves.

Why the other options are wrong

• A. Omits the USD 25 million for future cases not yet filed. Incremental future litigation, the unknown unknowns, is one of the module's three parts.
• C. Incorrectly nets Case 2's excess reserve of USD 15 million against the forecast. A case below its reserve adds nothing, and a surplus reserve is not a gain in the legal loss forecast.
• D. USD 183.4 million adds both cases at their full conditional expected loss, USD 150 million in total. This counts again USD 100 million already covered by reserves: 70 on Case 1 and the whole 30 on Case 2.

Module

Operational Risk and Resilience

Chapter

OR 7: Integrated Risk Management

Learning objective

Explain challenges and considerations when developing and implementing models used in stress testing operational risk

Correct answer: C. 1, 3 and 4 only

Elements 1, 3 and 4 are consistent with observed practice, and element 2 is not. Where regulators obtain non-public information, they share it with selected parties through informal meetings or other informal communication vehicles, to preserve the anonymity and confidentiality of the bank that was attacked, not with every bank through a formal circular that names it.

Information-sharing from regulators to banks runs through established channels and draws on what the regulator receives from banks and from other sources. In jurisdictions with clear guidance on this kind of sharing, such as Australia, China, Korea, Saudi Arabia, Singapore, Turkey and the US, information flows from the bank to the regulator, the regulator assesses the risk to the industry, and it shares with the industry as appropriate, based on that assessment.

The reason for the informal route in element 2 is trust. Preserving the anonymity of a bank hit by an attack maintains banks' confidence and trust in their regulator, and a formal circular naming the bank works against that.

Why the other options are wrong

• A. Element 1 is accepted correctly, but element 2 is the one inconsistent with practice, and this option accepts it while incorrectly rejecting 3 and 4. Non-public information about a named bank goes to selected parties informally, while sharing best practices and anonymizing sensitive details are both observed practice.
• B. Elements 3 and 4 are accepted correctly, but element 1 is incorrectly rejected. In jurisdictions with clear guidance, the regulator assesses the risk to the industry and shares as appropriate on the basis of that assessment.
• D. Correctly accepts elements 3 and 4 but incorrectly swaps element 1 for element 2. Sharing follows the regulator's own risk assessment, and non-public information about a named bank is shared with selected parties through informal meetings.

Module

Operational Risk and Resilience

Chapter

OR 8: Cyber-Resilience: Range of Practices

Learning objective

Explain and assess current practices for the sharing of cybersecurity information between different types of institutions

Correct answer: B. Both claims are incorrect: the NIST framework is voluntary, but regulation often makes a framework mandatory or strongly encouraged.

The NIST Cybersecurity Framework was developed by the National Institute of Standards and Technology at the US Department of Commerce, but the framework is voluntary. It gives businesses an outline of best practices to help decide where to focus time and money on cybersecurity protection. Adopting it does not turn its steps into law, so the first claim is incorrect.

The second claim runs the other way and overreaches. Cybersecurity frameworks are often mandatory, or at least strongly encouraged, for firms that want to comply with industry-related regulations. So a bank can still be expected to follow a framework by the regulation it is subject to, even though the NIST framework is voluntary in itself. Both claims are therefore incorrect.

The framework was originally intended to protect critical infrastructure, such as power plants and dams, from cyberattacks. Its use has since extended beyond that industry, and many financial organizations have adopted it to guide their cyber risk management. It is designed to help businesses of all sizes, so a bank of 1,400 staff is within its intended audience.

Why the other options are wrong

• A. Incorrectly accepts both claims. The NIST framework is voluntary, and a bank can still be expected to follow a framework under industry regulation.
• C. Correctly rejects the first claim but incorrectly accepts the second. Frameworks are often mandatory, or at least strongly encouraged, for firms that must comply with industry-related regulations.
• D. Correctly rejects the second claim but incorrectly accepts the first. Being developed by a US government agency does not make the NIST framework binding, and the framework is voluntary.

Module

Operational Risk and Resilience

Chapter

OR 9: Case Study: Cyberthreats and Information Security Risks

Learning objective

Provide examples of cyber threats and information security risks, and describe frameworks and best practices for managing cyber risks

Correct answer: D. Internal auditors, and external auditors where engaged, should evaluate whether ML/FT controls are effective and compliant with regulations.

The auditor proposal assigns the task to the right functions. Internal audit is the third line of defense, and it independently evaluates the risk management and controls through periodic assessments of how effectively the bank complies with its AML/CFT policies and procedures. In many countries external auditors also play an important role, evaluating internal controls and confirming compliance with AML/CFT regulations and supervisory practice.

Each of the other proposals moves a task to the wrong function. Day-to-day control of ML/FT risk inside a business belongs to that business. Contact with supervisors and financial intelligence units belongs to the chief AML/CFT officer. Setting monitoring parameters is part of running the control, and an auditor who set the parameters would then be auditing its own work.

Why the other options are wrong

• A. Setting monitoring parameters is part of running the control, not auditing it. An internal audit function that set them would then be auditing its own design.
• B. Incorrectly moves day-to-day control of ML/FT risk from the business lines to the chief AML/CFT officer. Identifying, assessing and controlling the risks of a business is the first line's task, while the chief officer monitors from the second line.
• C. Incorrectly makes the chief risk officer the contact point for supervisors and financial intelligence units. That role belongs to the chief AML/CFT officer.

Module

Operational Risk and Resilience

Chapter

OR 10: Sound Management of Risks Related to Money Laundering and Financing of Terrorism

Learning objective

Explain best practices recommended by the Basel committee for the assessment, management, mitigation, and monitoring of money laundering and financing of terrorism (ML/FT) risks

Correct answer: A. 60 contractors; the bank reviews all client files for the period, verifies client information, files suspicious activity reports and closes suspicious accounts where needed.

Zennor needs 60 contractors, and the lookback covers every client file for the period, not only the files that raised alerts.

The total review time is:

36,000 × 2.5 = 90,000 hours

With 1,500 productive hours per reviewer in the 12 months, the number of reviewers is:

90,000 / 1,500 = 60 reviewers

The in-house team of 25 is fully occupied with day-to-day monitoring, so it contributes no lookback hours. All 60 reviewers must be contractors. Subtracting the 25 in-house analysts would assume that they can review files they have no time for:

60 - 25 = 35, which leaves 25 x 1,500 = 37,500 hours of work unassigned

A lookback is a costly AML remediation program that follows regulatory findings. The bank must review all client files for a specified period, verify client information, file suspicious activity reports, as they are called in the United States, and even close suspicious accounts. Limiting the review to files that raised alerts would not meet that requirement, since the lookback covers all client files for the period.

The size of the task is also why lookbacks bring in contractors. Large spikes in workload with tight deadlines are common in AML remediation, and at USAA the failure to train contractors or ensure their qualifications was itself criticized.

Why the other options are wrong

• B. Correctly describes the lookback but incorrectly subtracts the 25 in-house analysts, who are fully occupied and contribute no hours. All 90,000 / 1,500 = 60 reviewers must be contractors.
• C. Correctly sizes the team but incorrectly limits the lookback to files that raised alerts. A lookback reviews all client files for a specified period, not only those that raised alerts.
• D. Incorrectly subtracts the fully occupied in-house team and incorrectly limits the lookback to alerted files. The lookback needs 60 contractors and covers every client file for the period.

Module

Operational Risk and Resilience

Chapter

OR 11: Case Study: Financial Crime and Fraud

Learning objective

Summarize the regulatory findings and describe the lessons learned from the USAA case study

Correct answer: C. Line 3 is correct, and lines 1, 2 and 4 are incorrect.

Only line 3 states its risk correctly. Each of the other three lines changes the element that carries the definition.

Compliance risk is measured against US law. It arises when the services, products, or activities of a service provider fail to comply with applicable US laws and regulations. A provider that follows every rule of its home country can still expose a US bank to compliance risk if the service breaks a US consumer protection or privacy rule.

Line 2 describes the trigger for country risk and gives it the wrong name. Concentration risk is about how many providers the bank relies on and where the services are located. A concentration can arise without any foreign provider involved.

Legal risk is about the institution's own exposure. Legal risk turns on whether the provider's actions expose the bank to legal expenses and possible lawsuits. A dispute between the provider and one of its other clients does not describe that exposure.

Why the other options are wrong

• A. Incorrectly accepts line 1. Compliance risk is measured against applicable US laws and regulations, not the laws of the country where the provider is located.
• B. Incorrectly accepts lines 2 and 4 and rejects line 3. A foreign-based provider is the trigger for country risk, legal risk concerns the bank's own exposure to legal expenses and lawsuits, and line 3 is the definition of country risk.
• D. Reverses the verdict on every line. Line 3 is the only line that matches its definition, and lines 1, 2 and 4 each change the defining element.

Module

Operational Risk and Resilience

Chapter

OR 12: Guidance on Managing Outsourcing Risk

Learning objective

Explain how risks can arise through outsourcing activities to third-party service providers and describe elements of an effective program to manage outsourcing risk

Correct answer: D. 1,400 seats can keep running if contracts and controls change to let offshore staff work remotely, which shows why cross-country contract management matters.

When the COVID-19 pandemic shutdowns hit, US and European banks that had call centers or other critical processes handled in countries such as India or the Philippines faced either rapidly moving these activities back to their home countries, or changing contracts and controls to allow offshore third-party employees to work remotely. Dunmere has already taken the first route for as many seats as its home center can hold.

Spare seats in the home center: 1,000 - 400 = 600

Seats left with the provider: 2,000 - 600 = 1,400

For the remaining 1,400 seats, the choice is between the second response and an outage. The contract change takes time, but it is the response that keeps the process running, and it comes with new controls over staff working away from the provider's offices.

This is why cross-country contract management adds another dimension to third-party management. A contract written for work in an offshore office may not allow that work to move anywhere else.

Why the other options are wrong

• A. 1,600 seats is 2,000 - 400, which subtracts the home seats already in use instead of the 600 spare seats. So 1,400 remain with the provider, although the remote-work response is right.
• B. Incorrectly subtracts the 400 seats in use rather than the 600 spare and also treats moving work home as the only response. 1,400 seats remain, and changing contracts and controls for remote work was the other response open to banks.
• C. Correctly computes the 1,400 remaining seats but incorrectly treats moving work home as the only response. Banks also changed contracts and controls so that offshore employees could work remotely.

Module

Operational Risk and Resilience

Chapter

OR 13: Case Study: Third-Party Risk Management

Learning objective

Explain how risks related to the use of third parties can arise and describe characteristics of an effective third-party risk management framework

Correct answer: B. Bullets 1 and 2 only

Bullets 1 and 2 belong on the slide, and bullets 3 and 4 do not. The Investor Protection Act established the committee that consults with the SEC about regulatory priorities surrounding new financial products, fee structures and trading strategies, and it granted whistleblowers increased protections.

The Volcker Rule and the Consumer Financial Protection Bureau (CFPB) are both part of the broader Dodd-Frank Act. They are attributed to the broader Dodd-Frank Act, but not to the Investor Protection Act itself.

The confusion is easy to make because "investor protection" describes the purpose of much of Dodd-Frank. Dodd-Frank regulates multiple aspects of investor protection, including OTC derivatives trading, but the Investor Protection Act is one component of it. A slide titled with the narrower act should list only what that act did.

Why the other options are wrong

• A. Correctly includes whistleblower protection but incorrectly adds the CFPB and drops the committee. The CFPB is attributed to the broader Dodd-Frank Act, not to the Investor Protection Act.
• C. Correctly includes the SEC consultation committee but incorrectly swaps whistleblower protection for the Volcker Rule. Whistleblower protection came from the Investor Protection Act, and the Volcker Rule is a separate part of Dodd-Frank.
• D. Incorrectly treats two other Dodd-Frank provisions as the Investor Protection Act. This is the answer reached by reading "investor protection" as a label for all of Dodd-Frank.

Module

Operational Risk and Resilience

Chapter

OR 14: Case Study: Investor Protection and Compliance Risks in Investment Activities

Learning objective

Summarize important regulations designed to protect investors in financial instruments, including MiFiD, MiFiD II, and Dodd-Frank

Correct answer: A. 37, counting models in development and recently retired, each variation that warrants its own validation, and the two spreadsheets.

Banks should maintain a comprehensive set of information for models implemented for use, under development for implementation, or recently retired. Four decisions settle the count.

19 + 7 + 11 = 37 entries

Any variation of a model that warrants a separate validation should be included as a separate model and cross-referenced with the other variations, which is why treasury's six models become seven entries. The spreadsheets are models by definition whatever the desk calls them, since they process input data into quantitative estimates using a financial formula.

While each line of business may maintain its own inventory, a specific party should be charged with maintaining a firm-wide inventory of all models, which should assist the bank in evaluating its model risk in the aggregate. So the business-line lists cannot just be added together as submitted.

Why the other options are wrong

• B. Incorrectly accepts the desk's label and leaves out the two spreadsheets. They produce quantitative estimates from a pricing formula, so they are models, and the count is 37.
• C. 29 counts only the models currently in use and ignores the treasury variation, 14 + 6 + 9 = 29. The inventory also covers models under development for implementation and those recently retired.
• D. 38 adds the model treasury retired four years ago. The inventory covers recently retired models, and a retirement four years ago is not recent.

Module

Operational Risk and Resilience

Chapter

OR 15: Supervisory Guidance on Model Risk Management

Learning objective

Describe elements of an effective model risk management process

Correct answer: D. Tools 2 and 3 only

Tools 2 and 3 are models. The current consensus treats a model as any estimation method that uses data and relies on a set of assumptions to generate an uncertain estimate or forecast. The emphasis is on the uncertain nature of the output rather than on the method or technique used to produce it.

Tool 1 adds up numbers that are already known. The total of 420 agreed prices is arithmetic, not an estimate, so there is nothing uncertain for the tool to get wrong except the arithmetic itself.

Tool 2 has qualitative inputs, but it still uses data, the officers' ratings, and relies on assumptions about how those ratings relate to default. What it produces is a probability of default, which is an uncertain estimate.

Tool 3 is not a financial tool, but the definition does not ask what the forecast is about. It uses data, relies on an assumption that the historical weekday pattern continues, and produces a forecast that can be wrong.

Tool 4 reports what has already happened. Nothing in it is an estimate.

Why the other options are wrong

• A. Incorrectly includes the loan sale list and excludes the scorecard. The loan list totals agreed prices, so it produces no uncertain estimate, while the scorecard produces an uncertain probability of default from data and assumptions.
• B. Correctly includes the call volume forecast but incorrectly adds the dashboard and drops the scorecard. The dashboard shows realized results with no estimate in them, and the scorecard produces an uncertain probability of default.
• C. Incorrectly treats every tool with a financial output as a model and excludes the call volume forecast. The loan list and the dashboard report known figures, and the forecast is a model whatever its subject.

Module

Operational Risk and Resilience

Chapter

OR 16: Case Study: Model Risk and Model Validation

Learning objective

Define a model and describe different ways that financial institutions can become exposed to model risk

Correct answer: A. 6.9 times; the haircuts reached only the trading book while most sovereign exposure sat in the banking book, and the thin disclosure kept the market from checking.

The Irish need was EUR 24 billion against a CEBS total of EUR 3.5 billion for all seven failing banks:

24 / 3.5 = 6.86, or about 6.9 times

So the capital found for four Irish banks alone was almost seven times what the CEBS test had asked of the whole group of 91.

Two features of the CEBS design left its result open to doubt. First, the stress on sovereign debt was applied through haircuts on bonds in the trading book, while the bulk of the sovereign exposure was in the banking book, so most of the banks' sovereign exposure sat outside the haircut. Second, the disclosure was thin. Loss rates by firm came only for overall retail and overall corporate, whereas the SCAP had released loss rates by major asset class such as first-lien mortgages, credit cards and commercial real estate. With so little detail, the market could not check the results for itself.

Markets reacted benignly to the CEBS results at first, but the reaction changed when Ireland requested assistance from the EU and the IMF, and every Irish bank that needed capital had passed. To help close the credibility gap, the Irish exercise disclosed far more than any stress test to that date, and bank and Irish sovereign credit spreads tightened.

Why the other options are wrong

• B. 6.9 times is the correct multiple, but the Irish banks were not outside the test. All of the Irish banks that later needed capital had passed the CEBS test, so they were in it.
• C. Gives the correct explanation with the wrong multiple. Dividing the per-bank averages, EUR 6 billion against EUR 0.5 billion, gives 12 times, while the question asks for the Irish need against the entire CEBS raise.
• D. Incorrectly says no sovereign haircuts were applied and uses the per-bank multiple. The CEBS test did impose haircuts on trading book sovereign bonds; its weakness was that most sovereign exposure sat in the banking book.

Module

Operational Risk and Resilience

Chapter

OR 17: Stress Testing Banks

Learning objective

Describe the evolution of the stress testing process and compare the methodologies of historical European Banking Association (EBA), Comprehensive Capital Analysis and Review (CCAR), and Supervisory Capital Assessment Program (SCAP) stress tests

Correct answer: C. Statements 1 and 2 only

Statements 1 and 2 are correct, and statements 3 and 4 are incorrect.

Regulatory capital applies only in the few industries where regulators protect small depositors or policyholders, which is statement 1. It is computed from industrywide rules and formulas and sets only a minimum level of capital adequacy, which is statement 2. Risk capital is built to capture the economic realities of the risks the firm itself runs. Because regulatory capital comes from industrywide rules, it rarely captures the true level of risk in a firm, and the gap between the two can be quite wide.

Statement 3 fails because equal totals for the whole bank say nothing about the business lines. Regulatory capital may suggest that an activity is much riskier than management believes, or the reverse, so the two measures can differ line by line even when the totals match.

Statement 4 fails in the direction it asserts. The Basel III requirements make it likely that for some activities, securitization being the example, regulatory capital ends up much higher than economic capital. Being a minimum does not stop a rule-based number from exceeding a risk-based one.

When regulatory capital is much larger than economic capital, the activity is likely to migrate over time to the shadow banking sector, which can price the transactions at a more attractive level. Economic capital is still calculated in that case, because senior management needs it as the benchmark of the activity's economic viability.

Why the other options are wrong

• A. Correctly accepts statement 2 but incorrectly accepts statement 4 and drops statement 1. Basel III is expected to push regulatory capital well above economic capital for some activities, securitization among them.
• B. Correctly keeps statement 1 but incorrectly accepts statements 3 and 4 and drops statement 2. Totals that match for the whole bank can still hide large differences between business lines.
• D. Correctly accepts statement 2 but incorrectly accepts statement 3 and drops statement 1. Regulatory capital does apply only to regulated industries, and similar firm-level totals do not imply similar line-level numbers.

Module

Operational Risk and Resilience

Chapter

OR 18: Risk Capital Attribution and Risk-Adjusted Performance Measurement

Learning objective

Define, compare, and contrast risk capital, economic capital, and regulatory capital, and explain methods and motivations for using economic capital approaches to allocate risk capital

Correct answer: B. The corporate share rises from 60% to 68.2%, so the confidence level changes how each book looks on risk-adjusted performance measures.

Moving from 99% to 99.9% raises the corporate book's share of capital from 60% to 68.2%. The farther out in the tail of the loss distribution the capital is measured, the more relative capital goes to concentrated exposures.

The corporate book's share at each level is its contribution divided by the total:

At 99%: 60 / (60 + 40) = 60 / 100 = 60.0%

At 99.9%: 150 / (150 + 70) = 150 / 220 = 68.2%

The retail share falls from 40.0% to 31.8% over the same move. The two books do not scale by the same factor: the corporate book's capital rises 2.5 times and the retail book's 1.75 times.

150 / 60 = 2.50 and 70 / 40 = 1.75

So the choice is not a scaling decision. The choice of risk measure and confidence level heavily influences the relative capital allocated to individual exposures or portfolios, and this can have a strategic impact: a portfolio can look better or worse on risk-adjusted performance measures than it would under an alternative choice. At 99.9% the corporate book is charged for more capital and its risk-adjusted return falls relative to retail.

The confidence level also depends on the question being answered. High confidence levels reflect the view of creditors, rating agencies and supervisors, who want enough capital to minimize bankruptcy risk.

Why the other options are wrong

• A. Correctly computes the rise to 68.2% but incorrectly reverses its effect on performance. The corporate book takes a larger share of capital at 99.9%, so the move makes the corporate book look worse, and retail better, than they did at 99%.
• C. Correctly computes the rise to 68.2% but incorrectly concludes that relative performance cannot change. The shares move from 60% and 40% to 68.2% and 31.8%, so the relative charge, and with it relative risk-adjusted performance, changes.
• D. Incorrectly assumes both books scale by the same factor. The corporate book grows 2.5 times and the retail book 1.75 times, so the corporate share rises to 68.2%.

Module

Operational Risk and Resilience

Chapter

OR 19: Range of Practices and Issues in Economic Capital Frameworks

Learning objective

Within the economic capital implementation framework, describe the challenges that appear in: Defining and calculating risk measures, Risk aggregation, Validation of models, Dependency modeling in credit risk, Evaluating counterparty credit risk, Assessing interest rate risk in the banking book

Correct answer: D. 1: robust internal controls; 2: effective loss-estimation methodologies; 3: solid resource-estimation methodologies; 4: effective governance

Finding 1 is a failure of robust internal controls, finding 2 of effective loss-estimation methodologies, finding 3 of solid resource-estimation methodologies and finding 4 of effective governance. Each finding matches the wording of one of the seven principles of an effective capital adequacy process.

Finding 1 is two control failures: model validation and independent review, and policies and procedures. Both sit in robust internal controls.

Finding 2 is about aggregation, and the loss-estimation principle names aggregating estimated losses across the BHC in its own wording.

Finding 3 fails the resource-estimation principle twice, because the principle asks both for a clear definition of available capital resources and for an effective process for estimating them.

Finding 4 is a governance failure. Governance covers regular review of limitations and uncertainties and approval of capital decisions, and the board approved a capital decision without the review.

Why the other options are wrong

• A. Correctly maps findings 1 and 3 but incorrectly files aggregation under capital adequacy impact assessment and board approval under capital policy. Aggregating losses across the BHC is part of the loss-estimation principle, and approval of capital decisions is part of governance.
• B. Correctly maps findings 2 and 4 but incorrectly files finding 1 under governance and finding 3 under foundational risk management. Model validation and policies are internal controls, and the definition of available capital resources is the resource-estimation principle.
• C. Misfiles all four findings. Each one sits under a principle whose wording does not cover it, for example model validation under governance rather than under robust internal controls.

Module

Operational Risk and Resilience

Chapter

OR 20: Capital Planning at Large Bank Holding Companies

Learning objective

Describe the Federal Reserve's Capital Plan Rule and explain the seven principles of an effective capital adequacy process for bank holding companies (BHCs) subject to the Capital Plan Rule

Correct answer: C. RWA of EUR 770 million and minimum total capital of EUR 61.6 million

Harrowgate's EUR 1,500 million of book assets carry EUR 770 million of risk-weighted assets, and the 8% total capital minimum on that base is EUR 61.6 million.

Each asset is multiplied by its Basel I weight and the products are summed. The mortgages with a full guarantee from the OECD central government are the item to watch: an instrument carrying a full guarantee from an OECD government sits in the 0% category with the government itself, not in the 50% category for uninsured residential mortgages.

The claims on OECD public sector entities, here the municipality, share the 20% weight with claims on OECD banks:

20% × 150 + 20% × 50 = 30 + 10 = 40

The total capital requirement is 8% of RWA:

8% × 770 = EUR 61.6 million

Of that, Tier 1 capital must be at least 4% of RWA:

4% × 770 = EUR 30.8 million

EUR 30.8 million is the Tier 1 floor within the total, not the total requirement.

Why the other options are wrong

• A. 830 comes from weighting the government-guaranteed mortgages at 50%, which adds 50% × 120 = 60 of RWA. A full guarantee from an OECD government puts the claim in the 0% category, so RWA is 770 and not 830.
• B. Correctly computes RWA of 770 but reports the 4% Tier 1 floor as the total requirement. Total capital must reach 8% of RWA, which is 61.6.
• D. Makes both errors. It weights the guaranteed mortgages at 50%, giving RWA of 830, and then applies the 4% Tier 1 ratio in place of the 8% total ratio, giving 4% × 830 = 33.2.

Module

Operational Risk and Resilience

Chapter

OR 21: Capital Regulation Before the Global Financial Crisis

Learning objective

Explain the calculation of risk-weighted assets and the capital requirement per the original Basel I guidelines

Correct answer: A. USD 3,847.4 million

Basel 2.5 market risk capital adds two terms. Each term is the larger of the latest value and a multiple of the 60-day average, and both VaR and stressed VaR are 10-day, 99% measures:

MR = max(VaR(t-1), m(c) × VaR(avg)) + max(SVaR(t-1), m(s) × SVaR(avg))

So only the 99.0% row enters the charge. The 95.0% and 99.9% rows describe the same book at other confidence levels and play no part in the calculation.

The multiplied average VaR is:

3.4 × 371 = 1,261.4

It exceeds the latest VaR of 402 and sets the VaR term at USD 1,261.4 million.

The multiplied average stressed VaR is:

3.0 × 862 = 2,586.0

It exceeds the latest stressed VaR of 915 and sets the stressed VaR term at USD 2,586.0 million.

The charge adds the two terms:

1,261.4 + 2,586.0 = USD 3,847.4 million

The latest values are above their own 60-day averages, but in both terms the multiplied average is well above them. The latest value takes over only when a single day's VaR is more than the multiplier times the recent average, which requires a sudden jump in risk.

Why the other options are wrong

• B. Swaps the two multipliers, applying 3.0 to the average VaR and 3.4 to the average stressed VaR. This gives 1,113.0 + 2,930.8 = USD 4,043.8 million, which overstates the charge by USD 196.4 million.
• C. Uses the wrong row, 99.9%, where the terms are 3.4 x 497 = 1,689.8 and 3.0 x 1,158 = 3,474.0. The sum of USD 5,163.8 million uses the wrong confidence level, since both measures in the charge are set at 99%.
• D. Incorrectly adds the latest VaR and the latest stressed VaR, 402 + 915, without comparing either with its multiplied average. The max function in each term stops capital from falling below a multiple of the recent average.

Module

Operational Risk and Resilience

Chapter

OR 22: Solvency, Liquidity, and Other Regulation After the Global Financial Crisis

Learning objective

Describe and calculate the stressed VaR introduced in Basel 2.5 and calculate the market risk capital charge

Correct answer: B. Measures 2 and 4 belong to the December 2017 reforms, and measures 1, 3 and 5 belong to the initial phase.

Measures 1, 3 and 5 come from the initial phase of Basel III, and measures 2 and 4 come from the reforms finalized in December 2017.

The initial phase strengthened the framework in six ways. It improved the quality of regulatory capital, with a greater focus on Common Equity Tier 1 (CET1) capital. It raised the level of capital requirements. It revised the areas of the risk-weighted framework that proved acutely miscalibrated, such as market risk, counterparty credit risk and securitization. It added macroprudential elements: capital buffers built up in good times and drawn down in stress to limit procyclicality, a large exposures regime, and a buffer for systemically important banks. It set a minimum leverage ratio. And it introduced the Liquidity Coverage Ratio and the Net Stable Funding Ratio to limit liquidity risk and maturity transformation.

The December 2017 reforms complement those improvements. They aim to restore credibility in the calculation of risk-weighted assets (RWA) and to improve the comparability of capital ratios.

Measure 2 is easy to misplace. The minimum leverage ratio was set in the initial phase, but the buffer that G-SIBs must hold on top of it was added in December 2017.

Why the other options are wrong

• A. Incorrectly moves the large exposures regime into the December 2017 package. That regime was one of the macroprudential elements of the initial phase, built to address interlinkages across institutions and concentrated exposures.
• C. Incorrectly places the liquidity ratios and the large exposures regime in the December 2017 package and the leverage ratio buffer in the initial phase. The liquidity ratios came first, while the G-SIB leverage ratio buffer is a 2017 addition to the minimum leverage ratio.
• D. Incorrectly treats the PD and LGD input floors as an initial-phase measure and moves the liquidity ratios and the large exposures regime into 2017. The input floors are part of how the 2017 reforms constrain internal models.

Module

Operational Risk and Resilience

Chapter

OR 23: High-Level Summary of Basel III Reforms

Learning objective

Explain the motivations for revising the Basel III framework and the goals and impacts of the December 2017 reforms to the Basel III framework

Correct answer: D. 725

The SC takes the larger of other operating income and other operating expenses, and adds the larger of fee income and fee expenses. Nothing is netted.

The two operating lines need adjusting before the comparison. Income from operating leases is excluded from other operating income, and losses from operational loss events that were not provisioned in previous years belong in other operating expenses.

The operating term is:

max(65, 115) = 115

The fee term is:

max(610, 205) = 610

So the SC equals:

115 + 610 = 725

The adjustments matter only on the operating line, because the fee income of 610 dominates the fee expenses whatever the outsourcing fees are. On the operating line the fines turn the expense side into the larger of the two, and the larger side enters the SC.

Why the other options are wrong

• A. Leaves both operating lines as booked. The comparison is then max(90, 70) = 90, and 90 + 610 = 700.
• B. Correctly removes the operating lease income but incorrectly leaves the unprovisioned fines out of other operating expenses. The comparison becomes max(65, 70) = 70, and 70 + 610 = 680.
• C. Nets each pair instead of taking the larger item. The netted figures |65 - 115| = 50 and 610 - 205 = 405 add to 455, which is not how the SC is built.

Module

Operational Risk and Resilience

Chapter

OR 24: Basel III: Finalising Post-Crisis Reforms

Learning objective

Explain the elements of the new standardized approach to measure operational risk capital, including the business indicator, internal loss multiplier, and loss component, and calculate the operational risk capital requirement for a bank using this approach

Correct answer: A. The proportional spread should be 2.40%, but the cost of liquidation of USD 180,000 is correct.

The proportional spread is measured against the mid-market price, which is halfway between the bid and the offer:

(24.70 + 25.30) / 2 = 25.00

0.60 / 25.00 = 0.0240

So the reported 2.43% is incorrect. Dividing by the bid price gives a larger figure:

0.60 / 24.70 = 0.02429

The cost of liquidation equals the proportional spread multiplied by the mid-market value of the position, divided by 2:

0.0240 × 600,000 × 25.00 / 2 = 180,000

The analyst's two errors cancel. He used a proportional spread that is too large, but he multiplied it by a value that is too small by the same factor:

0.02429 × 14,820,000 / 2 = 180,000

Both routes reduce to the number of shares multiplied by the dollar spread, divided by 2:

600,000 × 0.60 / 2 = 180,000

So the cost figure stands, but the spread figure does not. This matters whenever the proportional spread is used on its own, for example to compare the liquidity of two assets or to apply a spread estimate to a position valued at the mid-market price.

Why the other options are wrong

• B. 182,186 applies the bid-based spread of 2.43% to the position valued at the mid-market price. 0.02429 multiplied by USD 15,000,000 and divided by 2 overstates the cost, and the spread itself should be 2.40%.
• C. Incorrectly accepts the 2.43% spread. The spread is measured against the mid-market price of 25.00, which gives 2.40%.
• D. Correctly computes the 2.40% spread but incorrectly applies it to the position valued at the bid. 0.0240 multiplied by USD 14,820,000 and divided by 2 gives 177,840, which mixes two conventions.

Module

Liquidity and Treasury Risk Measurement and Management

Chapter

LR 1: Liquidity Risk

Learning objective

Explain and calculate liquidity trading risk via cost of liquidation and liquidity-adjusted VaR (LVaR)

Correct answer: C. USD 170 million

Larkfield must pay out USD 170 million, USD 50 million to its investors under the gate and USD 120 million to its repo lender. A hedge fund faces liquidity risk all through its capital structure, and this quarter it is hit from both sides at once.

The gate caps the payment to investors:

10% × 500 = USD 50 million

The repo loan before and after the haircut increase:

800 × (1 − 0.25) = USD 600 million

800 × (1 − 0.40) = USD 480 million

The cash the fund must hand back to the lender:

600 − 480 = USD 120 million

The total paid out:

50 + 120 = USD 170 million

Hedge fund capital, unlike the equity of a corporation, can be withdrawn at agreed intervals, quarterly as a rule. Gates permit a suspension or limitation of withdrawal rights when investors collectively ask for more than some limit, so the gate holds the first drain to USD 50 million and leaves the other USD 100 million of requests unmet this quarter. A gate does nothing for the asset side. Hedge funds typically have no access to wholesale funding and rely on collateral markets, short positions and derivatives to take on leverage, so when a lender raises a haircut, the fund must find the cash or cut the position.

Larkfield can meet both demands from its USD 300 million of cash, which leaves it with USD 130 million. Any further redemptions it has to meet, or any further rise in haircuts, would draw on the same cash.

Why the other options are wrong

• A. USD 140 million incorrectly applies the 15-point rise in the haircut to the USD 600 million loan, giving 90, instead of to the USD 800 million value of the bonds. The haircut is a share of the collateral's value, so the loan falls from 600 to 480 and the fund repays 120.
• B. USD 50 million counts only the gated redemptions, as if the gate protected the fund as a whole. The gate limits withdrawals of capital, while the higher haircut is a separate demand on the funding of the assets that adds USD 120 million.
• D. USD 270 million incorrectly pays the full USD 150 million of redemption requests and ignores the gate the fund has invoked. With withdrawals limited to 10% of net asset value, investors receive USD 50 million this quarter, so the total is 170.

Module

Liquidity and Treasury Risk Measurement and Management

Chapter

LR 2: Liquidity and Leverage

Learning objective

Differentiate between sources of liquidity risk and describe specific challenges faced by different types of financial institutions in managing liquidity risk

Correct answer: B. Signals 3 and 4 sit outside the bank, and signal 2 is a Wall Street signal that originates within the bank.

Signal 2 is observed in a financial market, but it is a verdict on the bank alone. Repo lenders charged this bank 3 percentage points more in haircut:

7% − 4% = 3 percentage points

while the haircuts they charge peer banks did not move. A move that the market applies to one bank and not to its peers measures that bank's own condition, so signal 2 sits in the within-the-bank row on the Wall Street side. It sits beside the grid's own example for that cell, increased debt spreads, which are also quoted in the market and also measure the bank's own standing. Typical industry lists also carry the repo haircut among the bank-specific liquidity metrics.

The other three place directly. Signal 1 is deteriorating asset quality in the bank's own loans, a main street signal from within the bank:

2.9% − 1.8% = 1.1 percentage points

Signal 3 is a change in the wider economy, outside the bank on the main street side:

5.1% − 3.9% = 1.2 percentage points

Signal 4 is a funding market event across the industry, outside the bank on the Wall Street side.

Keeping both rows on the dashboard matters because liquidity events can start within the bank, or can be driven by the environment the bank operates in, so a sound suite strikes a balance between the two.

Why the other options are wrong

• A. Correctly places signals 3 and 4 and the row of signal 2 but incorrectly puts signal 2 on the main street side. A repo haircut is set in a financial market, so it belongs on the Wall Street side.
• C. Incorrectly puts signal 2 outside the bank because it is set in a market. The haircut moved for this bank alone, so it measures the bank's own standing and originates within the bank.
• D. Incorrectly limits the within-the-bank row to the loan book. Signal 2 is a market measure of this bank alone, so only signals 3 and 4 sit outside the bank.

Module

Liquidity and Treasury Risk Measurement and Management

Chapter

LR 3: Early Warning Indicators

Learning objective

Evaluate the characteristics of sound Early Warning Indicators (EWI) measures

Correct answer: D. 61.5%

Money market instruments reach maturity within one year, and capital market instruments have remaining maturities beyond one year. The dividing line is the time a security has left to run, so a Treasury note issued with a five-year life joins the money market group once it is inside its final year.

The money market total is:

35 + 15 + 10 + 20 = 80

The full portfolio is:

35 + 20 + 15 + 10 + 30 + 20 = 130

The money market share is:

80 / 130 = 61.5%

The tax-anticipation note is a short-term municipal obligation. A county issued it, but its 9-month maturity places it in the money market group alongside commercial paper and Eurocurrency deposits. The agency note goes the other way: federal agency securities are listed among money market instruments, but the one-year rule still decides, and this note has 15 months to run, so its remaining maturity places it in the capital market group.

Why the other options are wrong

• A. 34.6% comes from classifying the positions by original maturity, which drops the Treasury note and leaves 15 + 10 + 20 = 45 of 130. With only 8 months left to run, the note belongs in the money market group today.
• B. 76.9% counts the agency note as a money market holding even though it still has 15 months to run. Its remaining maturity is beyond one year, so adding its 20 to reach 100 of 130 overstates the share.
• C. Treating the tax-anticipation note as a capital market instrument because a county issued it gives 70 of 130, or 53.8%. Short-term municipal obligations are money market instruments, and this note matures in 9 months.

Module

Liquidity and Treasury Risk Measurement and Management

Chapter

LR 4: The Investment Function in Financial-Services Management

Learning objective

Compare various money market and capital market instruments and discuss their advantages and disadvantages

Correct answer: C. Bond sales raise fewer liquid funds and the losses cut earnings, and borrowing costs more, with some lenders refusing to lend at all.

Liquidity management is exposed to two risks: interest rate risk, the risk that interest rates will change, and availability risk, the risk that liquid funds will not be available in the volume needed. Both act on Thornbury here. The rate rise cuts the value of the bonds and raises the cost of borrowing, and on the borrowing route some forms of borrowed liquidity may no longer be available, while some lenders refuse to lend at all.

On the asset route, the rate rise works through prices. The bank planned to sell bonds to raise cash, and a bond's market value falls when interest rates rise. The bonds carried at USD 50 million now raise only:

50 × (1 − 4%) = 48

So the same sale leaves USD 2 million of the deficit uncovered, and the realized loss comes out of earnings as well:

50 − 48 = 2

On the liability route, the rate rise and the lenders' view act together. Borrowed liquidity costs more as interest rates rise. A lender who believes the bank is more risky than before charges a higher interest rate to compensate, and some lenders will simply refuse to make liquid funds available at all.

Why the other options are wrong

• A. Correctly describes the borrowing route but incorrectly claims the bond sale raises more funds. Rising yields mean falling bond prices, so the sale raises fewer funds and realizes losses.
• B. Correctly describes the bond sale but incorrectly makes borrowing cheaper. Higher interest rates and a riskier view of the bank raise the cost of borrowing and can lead some lenders to refuse to lend at all.
• D. Reverses both routes. Rising interest rates lower bond prices and raise borrowing costs, and lenders who see more risk lend less.

Module

Liquidity and Treasury Risk Measurement and Management

Chapter

LR 5: Liquidity and Reserves Management: Strategies and Policies

Learning objective

Calculate a bank's net liquidity position and explain factors that affect the supply and demand of liquidity at a bank

Correct answer: B. EUR 58 million, because the balance is part of the compensation the bank provides for the correspondent's services.

Banks manage the cash they place in correspondent bank accounts to a target average monthly balance, as part of the compensation provided to the correspondent for its banking services. The target is an average over the month, so the shortfall of the first 20 days must be made up within the remaining 10.

The month needs this total of daily balances:

50 × 30 = 1500

The first 20 days supplied:

46 × 20 = 920

The remaining 10 days must supply:

(1500 − 920) / 10 = 58

The target exists because of compensation, not regulation. Historically banks managed their balances down to the minimums called for by two things: reserve requirement regulations, which applied at their Federal Reserve accounts, and compensation arrangements for services provided by correspondent banks. A nostro account at a correspondent falls under the second. Nostro balances are replenished or drawn down daily, and on any given day the account can act as a source or a use of intraday liquidity.

Why the other options are wrong

• A. Correctly finds EUR 58 million but incorrectly attributes the target to reserve requirement regulations. Reserve requirements applied at Federal Reserve accounts, while a correspondent balance is managed as compensation for the correspondent's services.
• C. Incorrectly recovers the shortfall only once and incorrectly attributes the target to reserve requirements. The required average is EUR 58 million, and the target is part of the compensation for the correspondent's services.
• D. Correctly states the purpose of the balance but incorrectly adds the EUR 4 million daily shortfall only once, giving EUR 54 million. The shortfall built up over 20 days must be recovered in 10, so it is doubled to EUR 8 million a day.

Module

Liquidity and Treasury Risk Measurement and Management

Chapter

LR 6: Intraday Liquidity Risk Management

Learning objective

Identify and explain the uses and sources of intraday liquidity

Correct answer: A. Item 1 fixed; Item 2 fixed; Item 3 behavioral.

The payout on a one-touch option is a sum set by the contract. Ashcombe receives EUR 2 million when the index breaches the barrier, so the amount follows directly from the contract's terms. What is unknown today is the moment the barrier is touched. So the cash flow is fixed in amount and stochastic in time.

Drawdowns on a line the bank has received are also fixed in amount. The amount depends on a choice made by the bank itself, and it can be taken as some level between zero and the line's limit, chosen according to the bank's needs. The timing is stochastic because the bank's own liquidity needs can arise at any moment until the line expires.

Drawdowns on a line the bank has granted belong to a different category. The amount now depends on a decision made by the client, which can only be loosely predicted. So the amount is behavioral, uncertain within the limits of the line. The timing is again stochastic.

Why the other options are wrong

• B. Correctly treats the client's drawdowns as behavioral but incorrectly classifies the other two items. The one-touch payout is a set sum, and the bank's own drawdowns follow the bank's choice rather than a client's behavior.
• C. Correctly treats the one-touch payout as fixed but incorrectly swaps the two credit lines. The bank decides how much it draws on a line it has received, and the client decides on a line the bank has granted.
• D. Incorrectly treats the one-touch payout as indexed/contingent and the client's drawdowns as fixed. The one-touch pays a set sum, and a client's drawdowns depend on the client's own decisions.

Module

Liquidity and Treasury Risk Measurement and Management

Chapter

LR 7: Monitoring Liquidity

Learning objective

Differentiate between deterministic and stochastic cash flows and provide examples of each

Correct answer: A. USD 30.00 million

A haircut is the part of the collateral's market value that the repo lender does not lend. At a 15% haircut, each USD 100 of bonds supports a loan of USD 85, so the USD 170 million loan was secured by bonds worth:

170 / (1 − 15%) = 170 / 0.85 = USD 200 million

Kestrel sells the bonds at 30% below that value:

200 × (1 − 30%) = USD 140 million

It recovers USD 140 million of the USD 170 million it lent, so its loss is:

170 − 140 = USD 30 million

Check: the cushion of USD 30 million absorbs the first USD 30 million of the USD 60 million fall in the value of the bonds, and Kestrel bears the remaining USD 30 million.

Lending cash in repo exposes the dealer to the risk that the borrower fails to perform on the loan. The haircut, which reflects the risk or liquidity of the securities, mitigates that performance risk. It protects the lender to some degree from fluctuations in the market value of the collateral, but only up to the size of the cushion. A fall in value larger than the haircut leaves the lender with a loss.

Why the other options are wrong

• B. USD 33.15 million treats the haircut as a markup on the loan, 170 x 1.15 = 195.5, then 195.5 x 0.70 = 136.85 and 170 - 136.85 = 33.15. The haircut is a share of the collateral's market value, so the bonds were worth 170 / 0.85 = 200.
• C. USD 25.50 million is 170 x (30% - 15%). Incorrectly applies the excess of the price fall over the haircut to the cash lent, when both percentages apply to the bonds' market value of USD 200 million, which gives 200 x 15% = 30.
• D. USD 60.00 million is 200 x 30%, the full fall in the value of the bonds. Incorrectly ignores the USD 30 million haircut cushion, which absorbs the first part of the fall before the lender loses anything.

Module

Liquidity and Treasury Risk Measurement and Management

Chapter

LR 8: The Failure Mechanics of Dealer Banks

Learning objective

Compare and contrast the major lines of business in which dealer banks operate and the risk factors they face in each line of business

Correct answer: D. Neither is fully right: the test measures funding liquidity risk, but asset liquidity still counts because it affects what asset sales can raise.

Neither director's position is supported in full. The objective of the liquidity stress test is to measure the amount of liquidity the institution must maintain to keep meeting its financial obligations under stressed conditions. For that purpose "liquidity" means funding liquidity risk, the risk that the institution will not have adequate capacity to fund its obligations without incurring unacceptable economic losses.

Asset liquidity risk is a different risk: the risk of incurring losses because assets are difficult to convert into cash. It is not the objective of the test. It must still be carefully considered inside the test, because it affects how much funding can be made available from the sale of assets.

A simple illustration shows why it cannot be left out. Suppose USD 100 million of securities can be sold under stress only at a 6% discount. The cash they raise is:

USD 100 million × (1 − 6%) = USD 94 million

A model that ignores asset liquidity would count USD 100 million of funding from these securities, which overstates the funding available by:

USD 100 million - USD 94 million = USD 6 million

Why the other options are wrong

• A. Incorrectly takes asset liquidity risk as the objective of the test. The test measures funding liquidity risk, and selling or pledging securities is one source of the funding it measures.
• B. Incorrectly makes asset liquidity the objective and moves funding liquidity outside the test. Measuring funding capacity under stress is the test's own objective, and its results provide a foundation for the contingency funding plan.
• C. Correctly identifies funding liquidity risk as the objective but incorrectly leaves asset liquidity out. Asset liquidity must be considered in the test because it affects how much funding asset sales can raise.

Module

Liquidity and Treasury Risk Measurement and Management

Chapter

LR 9: Liquidity Stress Testing

Learning objective

Differentiate between various types of liquidity, including funding, operational, strategic, contingent, and restricted liquidity

Correct answer: B. 90.0%; these count as short-term liabilities, so moving them into fixed-term or notice accounts would improve the metrics

Total retail deposits are:

140.0 + 1,120.0 + 12.0 + 34.0 + 76.0 + 18.0 = 1,400.0

Current accounts and rolling deposits together are:

140.0 + 1,120.0 = 1,260.0

So their share is:

1,260.0 / 1,400.0 = 90.0%

For regulatory purposes, current accounts and rolling deposits are treated as short-term liabilities and do not assist the bank's regulatory liquidity metrics, which emphasize long-term funds. The local regulator may allow the bank to treat overnight balances as longer term if they can be shown to be acting as such in behavioral terms, but that treatment must be demonstrated and is not automatic.

So it can be worthwhile for the bank to run a marketing exercise to see whether customers would move deposits into fixed-term or notice accounts. Any increase in those accounts improves the bank's liquidity metrics.

Why the other options are wrong

• A. 80.0% is the rolling deposits alone, 1,120.0 / 1,400.0. Incorrectly leaves out the GBP 140.0 million of current accounts, which are also short-term liabilities for regulatory purposes.
• C. 80.0% leaves out the current accounts, and the conclusion incorrectly treats rolling deposits as long-term funds. Both current accounts and rolling deposits count as short-term liabilities, so 90.0% of the book does not help the regulatory metrics.
• D. Correctly computes 90.0% but incorrectly treats rolling deposits as long-term funds. For regulatory purposes current accounts and rolling deposits are short-term liabilities, unless the regulator accepts behavioral evidence that they act as longer-term funds.

Module

Liquidity and Treasury Risk Measurement and Management

Chapter

LR 10: Liquidity Risk Reporting and Stress Testing

Learning objective

Compare and interpret different types of liquidity risk reports

Correct answer: C. The CFP could leverage controls and processes already established, raising its effectiveness and its consistency with the rest of the firm.

The contingency funding plan, or CFP, is not a stand-alone tool. It is an integrated part of the bank's liquidity risk management framework and of its firm-wide risk management frameworks, which include enterprise risk management, capital management, and business continuity and crisis management. Integrating the CFP with these other components increases its effectiveness and consistency, because it can leverage and reference controls and processes that are already established.

Ingleby's stand-alone plan shows the cost of the opposite. In a crisis, two call lists and two approval paths would compete, and the people running the business continuity plan would not know the CFP's escalation contacts.

Integration does not make the CFP disappear into another plan. The CFP keeps its own scenarios, menu of contingent actions and escalation levels, and the other frameworks supply the controls, protocols and links it relies on.

Why the other options are wrong

• A. Incorrectly has the CFP give up its escalation levels inside the capital plan. Capital management is one framework the CFP integrates with, and integration does not merge the CFP into the capital plan.
• B. Incorrectly has the CFP replace the business continuity plan. Linking the two reinforces operational and communication protocols in a crisis, and each plan still does its own job.
• D. Incorrectly limits the value of integration to smaller banks. Smaller institutions have typically included their CFPs in broader business continuity plans, but integration with the broader frameworks is a design consideration for every sound CFP.

Module

Liquidity and Treasury Risk Measurement and Management

Chapter

LR 11: Contingency Funding Planning

Learning objective

Describe best practices in the design of a sound contingency funding plan

Correct answer: B. USD 4 million, and the funding is likely to be more stable, because the CD normally will not be withdrawn until it matures.

The net result of a CD sale is often a simple transfer of funds from one deposit to another inside the same institution, and the bank still gains loanable funds. While the money sat in checking, 10% of it had to be held as legal reserves. As a CD it carries no reserve requirement. So that slice is released for lending.

Reserves held against the checking balance before the move:

USD 40 million × 10% = USD 4 million

Reserves held against the CD after the move:

USD 40 million × 0% = USD 0

Stability is also likely to improve. Checkable deposits can be withdrawn at any time, while the CD normally stays until it matures. Negotiable CDs can be sold in the secondary market to provide corporate customers with liquidity, and a sale changes only who holds the CD, while the CD itself normally will not be withdrawn from Rexley until it matures.

The drawback is interest rate sensitivity. The interest rates on the largest negotiable CDs are sensitive to market conditions. So the bank must work harder to combat volatile earnings and make aggressive use of rate-hedging techniques.

Why the other options are wrong

• A. USD 40 million is the size of the CD. Incorrectly counts the full transfer as new loanable funds, although only the USD 4 million of released reserves is new lending capacity.
• C. USD 40 million counts the transfer as new money, and the option also incorrectly treats secondary market sales as early withdrawals. The gain is USD 4 million, and the CD normally stays until maturity.
• D. Correctly finds USD 4 million but incorrectly treats negotiability as a threat to the bank's funding. A secondary market sale changes who holds the CD, and the funds stay with Rexley until maturity.

Module

Liquidity and Treasury Risk Measurement and Management

Chapter

LR 12: Managing Nondeposit Liabilities

Learning objective

Distinguish between the various sources of non-deposit liabilities at a bank

Correct answer: A. Call for USD 1.4 million of additional collateral, restoring USD 50.0 million of collateral against the USD 47.5 million loan

Fenwick lends USD 47.5 million against USD 50.0 million of notes, so the haircut gives it USD 2.5 million more collateral than it has lent. The haircut is set at the start. The margin call keeps that protection in place as prices move, and through it the borrower of cash supplies extra collateral in a declining market.

The fall in the value of the notes is:

USD 50.0 million - USD 48.6 million = USD 1.4 million

So the borrower posts USD 1.4 million of additional collateral, and Fenwick again holds USD 50.0 million of collateral against its USD 47.5 million loan.

The analyst's argument treats the haircut as a buffer to be used up. The haircut exists for the case where the borrower defaults at the same time as the collateral falls, and with no call Fenwick would enter that case with USD 1.1 million of protection rather than USD 2.5 million.

The mechanism also works the other way. In a rising market the borrower may withdraw collateral.

Why the other options are wrong

• B. USD 2.5 million is the original haircut, not the fall in value. Incorrectly asks for the cushion in full when USD 1.1 million of it is still in place, so Fenwick would hold USD 51.1 million of collateral.
• C. Correctly notes that USD 48.6 million still exceeds the loan but incorrectly treats the haircut as a buffer that may be used up. The call restores the USD 2.5 million of excess collateral the agreement set.
• D. USD 1.33 million equals 1.4 x 95%. Incorrectly applies the haircut to the margin call, which leaves the collateral at USD 49.93 million rather than USD 50.0 million.

Module

Liquidity and Treasury Risk Measurement and Management

Chapter

LR 13: Repurchase Agreements and Financing

Learning objective

Describe the mechanics of repurchase agreements (repos) and calculate the settlement for a repo transaction

Correct answer: A. USD 712,500, crediting the stable part at the three-year premium and the volatile part at the overnight premium.

Demand deposits are hot or volatile money and indeterminate-maturity products, and they can be withdrawn at any time without notice. Pooled and modeled over time, though, a portion is rarely withdrawn and forms a stable, or core, part, while the rest is the hot or volatile part. Better practice credits the core more, using its modeled behavioral maturity, and credits the volatile part less; here the volatile part behaves like overnight money, so it takes the overnight premium.

The core balance and its credit are:

65% × USD 600 million = USD 390 million

USD 390 million × 0.0018 = USD 702,000

The volatile part and its credit are:

USD 210 million × 0.00005 = USD 10,500

USD 702,000 + USD 10,500 = USD 712,500

Applying the matched-maturity approach mechanically to the contractual maturity would credit every demand deposit at the overnight premium, which is likely very close to zero. The bank would obtain the funding cheaply, and units would be discouraged from raising it.

Why the other options are wrong

• B. USD 30,000 incorrectly credits the full balance at the overnight premium, from the contractual maturity. This ignores the modeled core and discourages units from raising demand deposits.
• C. USD 891,000 incorrectly credits the volatile part at the 9 bps average, USD 702,000 + USD 210 million x 0.0009. The volatile part behaves like overnight money, so under matched-maturity pricing it earns the overnight premium; crediting it the 9 bps average mixes in an approach that ignores maturity and overpays volatile funding.
• D. USD 540,000 incorrectly falls back on the average cost of funds. The average makes no distinction between core and volatile funding, which is the distinction better practice draws.

Module

Liquidity and Treasury Risk Measurement and Management

Chapter

LR 14: Liquidity Transfer Pricing: A Guide to Better Practice

Learning objective

Compare the various approaches to liquidity transfer pricing (zero cost, average cost, and matched-maturity marginal cost)

Correct answer: C. Foreign claims rose to 3.4 times their starting level, an increase of 240%, with growth accelerating; for some European banking systems, dollar and other non-euro positions were more than half the rise in foreign assets.

The multiple of the starting stock is:

34 / 10 = 3.4

The percentage increase is the multiple minus one:

(34 − 10) / 10 = 240%

The rise was large even when scaled by global economic activity, and it accelerated: annual growth went from around 10% in 2001 to close to 30% by mid-2007. It took place during a period of financial innovation, which included the emergence of structured finance, the spread of universal banking combining commercial banking with investment banking and proprietary trading, and strong growth in the hedge fund industry, to which banks offer prime brokerage and other services.

Much of the increase for some European banking systems reflected greater intra-euro area lending after the single currency arrived in 1999. But their estimated US dollar and other non-euro positions accounted for more than half of the overall increase in their foreign assets between end-2000 and mid-2007. So a large part of the expansion was in dollars and other non-euro currencies, and the dollar assets it created had to be funded.

Why the other options are wrong

• A. Correctly computes the multiple and the increase but incorrectly makes intra-euro area lending the main source of the European rise. Dollar and other non-euro positions accounted for more than half of it.
• B. Incorrectly reads 3.4 times as a 340% increase and incorrectly makes intra-euro area lending the main source of the European rise. A stock that rises to 3.4 times its starting level has increased by 240%, and dollar and other non-euro positions were more than half of the rise for some European systems.
• D. 340% is the multiple of 3.4 read as an increase. A stock that rises to 3.4 times its starting level has increased by 240%, so 340% counts the starting stock as part of the increase.

Module

Liquidity and Treasury Risk Measurement and Management

Chapter

LR 15: The US Dollar Shortage in Global Banking and the International Policy Response

Learning objective

Identify the causes of the US dollar shortage during the Great Financial Crisis

Correct answer: D. USD 1.1218 per euro, 218 forward points, because the forward rate equals the spot rate multiplied by (1 + 3.0%) / (1 + 1.0%)

CIP is the no-arbitrage condition that interest rates on two otherwise identical assets in two currencies are equal once the foreign currency risk is hedged. With S as the spot rate in US dollars per unit of foreign currency, r as the US dollar interest rate and r* as the foreign currency interest rate, it reads:

F / S = (1 + r) / (1 + r*)

So the forward rate is:

1.1000 × 1.03 / 1.01 = 1.1218

The forward points are the forward rate less the spot rate, expressed in units of USD 0.0001:

(1.12178 − 1.1000) / 0.0001 = 218

The euro trades at a forward premium against the dollar because the dollar pays the higher interest rate. A party that swaps dollars into euros gives up the 3.0% dollar rate and earns only the 1.0% euro rate, and the higher dollar price at which it sells the euros back forward makes up the difference.

Why the other options are wrong

• A. Incorrectly treats a hedged position as one with no forward points. CIP sets the forward rate so that the hedged returns are equal, and that requires a forward rate different from spot whenever the two interest rates differ.
• B. Incorrectly inverts the interest rate ratio. With S quoted in US dollars per euro, the dollar interest rate belongs in the numerator, so the currency with the higher interest rate trades at a forward discount.
• C. 220 points comes from the linear shortcut S x (r - r*). It incorrectly skips the division by (1 + r*), which takes the CIP points down to 218.

Module

Liquidity and Treasury Risk Measurement and Management

Chapter

LR 16: Covered Interest Parity Lost: Understanding the Cross-Currency Basis

Learning objective

Differentiate between the mechanics of foreign exchange (FX) swaps and cross-currency swaps

Correct answer: D. The bonds carry price risk, which hurts if interest rates rise; the maturing loans carry reinvestment risk, which hurts if interest rates fall.

Price risk arises when market interest rates rise. The market values of most bonds and fixed-rate loans then fall, so an institution that wishes to sell them must be prepared to accept capital losses. Halsworth intends to sell its bonds in six months, so a rise in interest rates before then would force the sale at a loss.

Reinvestment risk arises when market interest rates fall. Incoming funds must then be invested in lower-yielding earning assets, which lowers expected future income. The USD 250 million of maturing loans returns cash that will be lent again at whatever interest rates prevail, so a fall in interest rates would cut the income on that money.

The two risks move in opposite directions. A rise in interest rates helps the reinvestment and hurts the sale, and a fall does the reverse. So a large part of managing assets and liabilities consists of finding ways to deal effectively with both forms of risk.

Why the other options are wrong

• A. Incorrectly swaps the two labels while keeping each position's direction, so each risk is paired with the wrong move. A rise in interest rates hurts the bond sale, and that is price risk, not reinvestment risk.
• B. Correctly names both risks but incorrectly reverses both directions. Bond prices fall when interest rates rise, and reinvestment income falls when interest rates fall.
• C. Swaps the two labels and carries each label's direction with it, so the bonds are said to lose from a fall and the loans from a rise. The bonds being sold lose market value when interest rates rise, and the maturing loans lose income when interest rates fall.

Module

Liquidity and Treasury Risk Measurement and Management

Chapter

LR 17: Risk Management for Changing Interest Rates: Asset-Liability Management and Duration Techniques

Learning objective

Discuss how asset-liability management strategies can help a bank hedge against interest rate risk

Correct answer: B. -1.75%; investors accept an expected return below zero because the asset pays off when the market crashes, which makes it valuable to hold.

The asset's beta is its correlation with the market multiplied by its volatility, divided by the market's volatility:

-0.5 × 20% / 16% = −0.625

The security market line then gives:

2% + (−0.625) × 6% = −1.75%

A negative expected return is a legitimate result of the capital asset pricing model, or CAPM, not an error. Assets that pay off when the market tanks are valuable to investors who already hold a diversified portfolio. They have low betas and very large diversification benefits, so investors need little compensation to hold them. If the payoffs in a falling market are high enough, investors are willing to pay to hold the asset rather than be paid, and its expected return falls below zero. Gold and, at times, government bonds are often given as examples of low or negative beta assets that pay off when the stock market crashes.

The opposite case shows the same rule from the other side. An asset that falls when the market falls has a high beta and must offer a high expected return before investors will hold it.

Why the other options are wrong

• A. Incorrectly treats negative beta as zero beta. A correlation of -0.5 is systematic co-movement with the market, which the CAPM prices as a negative premium.
• C. 5.75% drops the sign of beta and adds 3.75% to the risk-free rate. The asset's own volatility does not set its premium; its negative co-movement with the market does.
• D. Correctly computes -1.75% but incorrectly calls the asset overpriced. Low enough betas produce negative expected returns in equilibrium, because investors value the payoff in bad times.

Module

Risk Management and Investment Management

Chapter

IM 1: Factor Theory

Learning objective

Explain the implications of using the CAPM to value assets, including equilibrium and optimal holdings, exposure to factor risk, its treatment of diversification benefits, and shortcomings of the CAPM

Correct answer: C. About 20.2%; the colleague is wrong, because the common value component cannot be diversified away, so it must be priced.

The rational story of value starts from the fact that value stocks move together after controlling for market exposure. Holding many of them shrinks the firm-specific part of the risk, but it leaves the common part untouched.

The variance of a single stock equals the common variance plus the firm-specific variance:

0.20 × 0.20 + 0.30 × 0.30 = 0.13

so a single stock has a volatility of about 36.1%.

In an equally weighted portfolio of 100 independent firm-specific components, the firm-specific variance is divided by 100, while the common component is held in full:

0.04 + 0.09 / 100 = 0.0409

The square root gives the portfolio volatility:

0.0409 ^ 0.5 = 0.2022

The common component carries about 98% of the portfolio's variance, 0.0400 out of 0.0409. Some value risk can be diversified by building portfolios, but a large amount of value movement cannot. In the context of the arbitrage pricing theory, or APT, risk that cannot be diversified away must be priced in equilibrium, and that gives a value premium. The colleague is therefore wrong. Fama and French use this same common movement when they construct the high minus low, or HML, factor.

Why the other options are wrong

• A. 3.6% divides the single-stock volatility of 36.1% by 10, shrinking the common component along with the rest. Only the independent firm-specific part shrinks with the number of stocks, and the common value component stays in full.
• B. Correctly computes 20.2% but incorrectly sends the remaining risk to the market factor. The common value component is independent of the market in this model, so it is a separate source of risk that must earn its own premium.
• D. 36.1% is the volatility of a single stock, reported as if diversification did nothing. The firm-specific components are independent, so their contribution falls from 0.0900 to 0.0009 in the portfolio.

Module

Risk Management and Investment Management

Chapter

IM 2: Factors

Learning objective

Describe the process of value investing and explain why a value premium may exist

Correct answer: A. 0.78

The information ratio, or IR, equals the average excess return over the benchmark divided by tracking error, the standard deviation of those excess returns. The first step is the yearly excess return, portfolio minus benchmark.

The average excess return is the alpha:

Alpha = 0.025 / 5 = 0.0050

Tracking error uses the sample standard deviation, dividing by five minus one:

Tracking error = (0.000166 / 4)^0.5 = 0.00644

The IR follows:

IR = 0.0050 / 0.00644 = 0.78

The beta column plays no part in this calculation. The IR here measures active return against the benchmark as given, so the yearly betas, which average about 0.90, are extra data.

Why the other options are wrong

• B. 1.09 divides the average portfolio return by the average benchmark return. 0.0638 / 0.0588 = 1.09 compares return levels and contains no risk measure at all.
• C. 0.90 is the average of the five betas. It describes market sensitivity and is not a ratio of return to risk.
• D. Incorrectly divides by the volatility of the portfolio's own returns. Their sample standard deviation is 0.0132, and 0.0050 / 0.0132 = 0.38 measures active return per unit of total risk, not per unit of tracking error.

Module

Risk Management and Investment Management

Chapter

IM 3: Alpha (and the Low-Risk Anomaly)

Learning objective

Define and calculate alpha, tracking error, the information ratio, and the Sharpe ratio

Correct answer: B. The constraints act partly as a safeguard against unreasonable and noisy inputs, and the same protection can be pursued more directly by refining the alphas before optimizing.

Implementation schemes are, in part, safeguards against poor research. A sophisticated set of constraints moves the portfolio toward the benchmark and away from the bets that unreasonable or noisy alphas would otherwise create.

Any constrained procedure can be replaced by a simpler one. A process that first refines the alphas and then runs a simple unconstrained mean/variance optimization reaches the same active positions. So the constraints are a reason to look at the inputs. They are not proof that the inputs are good.

Implementation must answer two questions:

Many of the procedures used in portfolio construction are indirect methods of coping with noisy data. The direct attack is either to refine the alphas first, which is preprocessing, or to design the implementation so that it openly acts as an "input moderator."

The consultant is correct and the chief investment officer is not. A long constraint list says that the process is compensating for something. It does not say that the alphas going into it can be trusted.

Why the other options are wrong

• A. Incorrectly reverses which problem is harder. Handling perfect data is the easier dilemma, and the constraints address noisy and unreasonable inputs rather than transactions costs.
• C. Incorrectly denies the equivalence. Any constrained portfolio can be reached by an unconstrained optimization run on modified alphas with an appropriate risk aversion.
• D. Incorrectly reverses the role of the constraints. They protect the portfolio most when the alphas are noisy, so dropping them and optimizing raw forecasts exposes the portfolio to the errors they were containing.

Module

Risk Management and Investment Management

Chapter

IM 4: Portfolio Construction

Learning objective

Describe the inputs to the portfolio construction process and explain challenges faced when using these inputs

Correct answer: D. EUR 2.206 million.

The diversification benefit equals undiversified value at risk, or VaR, minus diversified VaR. Both start from the individual VaR of each sleeve.

For the equity sleeve:

2.326 × 16% × 40 = 14.8864

For the bond sleeve:

2.326 × 7% × 25 = 4.0705

Undiversified VaR adds the two:

14.8864 + 4.0705 = 18.9569

Diversified VaR combines them with the correlation, and the cross term carries a factor of two:

√(14.8864² + 4.0705² + 2 × 0.35 × 14.8864 × 4.0705) = 16.7508

The benefit is the difference:

18.9569 − 16.7508 = 2.2061

The benefit is modest because the bond sleeve is small and the correlation is positive. A lower correlation would widen the difference between the two VaR figures, and a correlation of 1 would remove it completely, since diversified VaR then equals the sum of the individual VaRs.

Why the other options are wrong

• A. Incorrectly treats the two sleeves as uncorrelated. Diversified VaR becomes the square root of 14.886² + 4.071², or 15.433, which overstates the benefit at 3.524.
• B. Incorrectly drops the factor of two on the cross term. The variance then contains only 0.35 x 14.886 x 4.071, diversified VaR comes out at 16.105, and the benefit is overstated at 2.852.
• C. 16.751 is the diversified VaR, not the benefit. The benefit is the difference between undiversified and diversified VaR.

Module

Risk Management and Investment Management

Chapter

IM 5: Portfolio Risk: Analytical Methods

Learning objective

Define, calculate, and compare the following portfolio VaR measures: diversified and undiversified portfolio VaR, individual VaR, incremental VaR, marginal VaR, and component VaR

Correct answer: C. II and III only

Statements II and III are correct, and statements I and IV are incorrect.

Statement I is incorrect. Risk budgeting is spreading fast as a best-practice method, but like VaR, the concept itself is not new. Like VaR, its main advantage is to provide a top-down, comprehensive and practical method to manage risk.

Statement II is correct. The process compares each unit's current risk profile with the budget set for it.

Statement III is correct. A manager inside its risk guidelines can execute new transactions without senior approval, so the approach avoids micromanaging the investment process.

Statement IV is incorrect. The class budget is a diversified VaR. When two managers' returns are less than perfectly correlated, the managers' individual budgets sum to more than the class budget, because part of their risk offsets inside the class.

Why the other options are wrong

• A. Incorrectly accepts statement I. Like VaR, the concept is not new; what is recent is its spread as a best-practice method.
• B. Incorrectly rejects statement III. Avoiding micromanagement of the investment process is one of the stated advantages of the approach, provided managers stay within their risk guidelines.
• D. Incorrectly accepts statement IV. Manager budgets add up to more than the class budget whenever the managers' returns are less than perfectly correlated, because the class budget already reflects diversification.

Module

Risk Management and Investment Management

Chapter

IM 6: VaR and Risk Budgeting in Investment Management

Learning objective

Define risk budgeting

Correct answer: D. 0.53. The fact sheet divided the fund's excess return over the risk-free interest rate, 10.4%, by the residual standard deviation.

On the committee's definition the reward is alpha, the return above what the capital asset pricing model, or CAPM, predicts for the fund's beta, and the risk is residual standard deviation.

The fund's alpha is:

13.4 − (3 + 0.90 × (11 − 3)) = 3.20

The information ratio is:

3.20 / 6 = 0.533

The fact sheet's 1.73 comes from a looser definition that some practitioners use: excess return, rather than alpha, per unit of nonsystematic risk. Excess return here is the fund's return over the risk-free interest rate:

(13.4 − 3) / 6 = 1.73

The two versions differ by the return the fund earned for bearing market risk, 0.90 x 8 = 7.20%. The looser version credits that return to the manager, even though an index position would have delivered it, and divides it by a risk measure that leaves market risk out. Terminology in the profession is not uniform: some writers use "appraisal ratio" for alpha over residual risk and keep "information ratio" for the excess-return version. Checking which definition a document uses comes before comparing two quoted figures.

Why the other options are wrong

• A. Correctly explains the fact sheet's 1.73 but incorrectly computes the committee's ratio as 0.23 by dividing alpha by the total standard deviation of 13.96%. Total risk includes the systematic risk that an index position already carries, and only the residual 6% belongs in the denominator.
• B. Incorrectly accepts the quoted 1.73 as alpha over residual risk. Alpha is 3.20%, and 3.20 / 6 gives 0.53, so the 1.73 must use the full 10.4% excess return.
• C. Correctly computes 0.53 but incorrectly explains the fact sheet's figure. Alpha over total standard deviation gives 3.20 / 13.96 = 0.23, not 1.73, and only the 10.4% excess return divided by 6% reproduces the quoted figure.

Module

Risk Management and Investment Management

Chapter

IM 7: Portfolio Performance Evaluation

Learning objective

Describe risk-adjusted performance measures, such as Sharpe's measure, Treynor's measure, Jensen's measure (Jensen's alpha), and the information ratio, and identify the circumstances under which the use of each measure is most relevant

Correct answer: A. USD 36.48, or about 3.6% of the convertible.

Income from a convertible hedge comes from four flows: the coupon received, plus interest on the short sale proceeds, minus the dividend paid to the stock lender, minus the stock borrow cost. The last three are computed on the short sale proceeds, not on the face value.

The shares the bond converts into have a value of:

18 × 50 = 900

The short position is 60% of that:

900 × 60% = 540

30.00 + 16.20 − 8.10 − 1.62 = 36.48

36.48 / 1,000 = 3.6%

The income rises if the arbitrageur leverages the investment, and two or three times leverage is common. Hedging interest rate risk or credit risk reduces it.

Why the other options are wrong

• B. Incorrectly charges the dividend on the full USD 900 conversion value, giving USD 13.50. Only 540 of stock is sold short, so the dividend paid is USD 8.10.
• C. USD 52.68 incorrectly adds the dividend as income. The fund is short the stock and pays the USD 8.10 dividend to the lender, so adding it overstates income by twice that amount.
• D. Incorrectly charges the borrow cost on the USD 1,000 face value, giving USD 3.00. The borrow cost applies to the USD 540 of short proceeds, so it is USD 1.62.

Module

Risk Management and Investment Management

Chapter

IM 8: Hedge Fund Investment Strategies

Learning objective

Compare different types of arbitrage strategies and describe the mechanics of convertible arbitrage strategies

Correct answer: B. USD 620 million, most of it collateralized by the funds' securities and cash.

A multiple of NAV is assets per unit of equity. Borrowing equals assets less equity, so each fund borrows its multiple minus one times its equity.

For the relative value fund:

200 × 3.0 − 200 = 400

For the macro fund:

200 × 2.1 − 200 = 220

Total borrowing is:

400 + 220 = 620

On how the borrowing is secured, the vast majority of hedge fund leverage is collateralized by assets. The lender is usually secured by all of the securities in the portfolio together with cash, or by cash posted as collateral on derivative contracts. So although notional leverage can be very large, uncollateralized borrowing within the industry is relatively small.

Typical leverage runs from 40% to 60% for many equity long/short strategies to over 200% for relative value strategies and well over 500% for some fixed income arbitrage strategies. The amount used depends greatly on the underlying portfolio risk, including the types of assets and whether the portfolio holds long and short positions expected to be highly correlated.

Why the other options are wrong

• A. USD 1,020 million is the total of assets, not the borrowing. The USD 400 million of equity is part of those assets and must be subtracted.
• C. Incorrectly reports total assets as the borrowing and incorrectly calls it uncollateralized. Borrowing is USD 620 million, and most hedge fund borrowing is secured.
• D. Correctly computes USD 620 million of borrowing but incorrectly calls most of it uncollateralized. Hedge fund borrowing is mostly secured by the portfolio's securities and cash, and large notional leverage does not change that.

Module

Risk Management and Investment Management

Chapter

IM 9: Risk, Regulation and Organizational Structure

Learning objective

Describe different risks faced by investors in hedge funds

Correct answer: C. High-yield market of about USD 2.8 trillion, and deployed private credit of about USD 1.6 trillion.

If private credit equals about three-quarters of the high-yield market, the high-yield market is private credit divided by 0.75:

2.1 / 0.75 = 2.8

The USD 2.1 trillion combines loans already made with capital investors have committed but managers have not yet deployed. Removing the dry powder gives:

2.1 − 0.5 = 1.6

High yield is a useful yardstick because it is a more mature but similarly risky market. Private credit has grown to a comparable scale, but it remains unrated, rarely traded and lightly regulated.

The dry powder matters for risk as well as for size. A large stock of committed but uninvested capital can add to the pressure on managers to deploy, and that pressure can push down risk premiums and weaken covenants.

Why the other options are wrong

• A. Incorrectly multiplies by three-quarters and incorrectly treats the full USD 2.1 trillion as deployed. Both halves of the pair are wrong.
• B. Correctly separates the dry powder but incorrectly multiplies by three-quarters, 2.1 x 0.75 = 1.6. Private credit is three-quarters of the high-yield market, so high yield is the larger figure.
• D. Correctly computes the high-yield market but incorrectly treats the full USD 2.1 trillion as deployed. The total includes USD 0.5 trillion of undeployed commitments.

Module

Risk Management and Investment Management

Chapter

IM 10: The Rise and Risks of Private Credit

Learning objective

Explain the return profile and growth profile of the private credit asset class, and compare the historical returns of private credit to those of other asset classes

Correct answer: C. USD 44 million, recycled during the investment period.

Capital called to pay fees and expenses is not invested in companies. During the investment period the management fee is:

2% × 400 × 5 = USD 40 million

The organizational expenses at their cap are:

1% × 400 = USD 4 million

So the capital left to invest from commitments alone is:

400 − 40 − 4 = USD 356 million

This is 89% of the commitment. To invest USD 400 million, the fund must reinvest:

400 − 356 = USD 44 million

Recycling is allowed only during the investment period. At the end of that period the fund may not make new investments, although it can reinvest in existing assets if necessary.

Why the other options are wrong

• A. Incorrectly charges the 2% fee on commitments for all ten years. Recycling is allowed only during the investment period, so only the fees charged in that period matter here, and the fee on committed capital is usually scaled down after it.
• B. Correctly computes USD 44 million but incorrectly places the recycling in the divestment period. New investments stop at the end of the investment period, so recycling must happen before it ends.
• D. Incorrectly leaves out the USD 4 million of organizational expenses. Those expenses are also paid from called capital, so 40 + 4 = USD 44 million must be recycled.

Module

Risk Management and Investment Management

Chapter

IM 11: Private Markets Investing

Learning objective

Describe different investment structures that can be used to invest in private assets and compare their characteristics

Correct answer: A. IV only

Only finding IV justifies rejection now. Findings I, II and III are infrastructure that a newly launched fund of this kind may reasonably lack.

The heavy focus on operations, credit risk and liquidity has made it possible for investors to overemphasize parts of due diligence. An investor can stress operational due diligence so much that it ends up choosing managers with great controls that add little return. The answer is a balance between the investment opportunity and the fund's risk profile, kept in place by a set of minimum standards, or bright lines. The bright lines stop the balance tipping the other way, toward great strategies with poor controls.

Independent administration, audits and top-tier service providers are generally not negotiable. Infrastructure and business models, however, should be strategy and life cycle specific. Elmstead is the case in point. A recently launched equity variable bias fund in the United States may not need multiple prime brokers, real-time disaster recovery, and a hot backup or succession plan, certainly not all on day one.

So rejecting Elmstead for findings I to III would overweight infrastructure in the way investors are warned against. Investors invest to increase return and reduce risk, and that purpose can easily be forgotten.

Why the other options are wrong

• B. Incorrectly treats a single prime broker as grounds for rejection. Multiple prime brokers are among the items a recently launched equity variable bias fund may not yet need.
• C. Incorrectly treats the missing disaster recovery site and succession plan as grounds for rejection. Both are infrastructure matched to the fund's strategy and life cycle, unlike independent administration.
• D. Incorrectly treats every finding as a bright line. A new U.S. equity variable bias fund may not need multiple prime brokers, real-time disaster recovery, a hot backup or a succession plan on day one.

Module

Risk Management and Investment Management

Chapter

IM 12: Performing Due Diligence on Specific Managers and Funds

Learning objective

Explain elements of the due diligence process used to assess investment managers