Introduction

• Risk capital is the cushion that provides protection against the various risks inherent in the business of a corporation so that the firm can maintain its financial integrity and remain a going concern even in the event of a near-catastrophic worst-case scenario. Risk capital gives essential confidence to the corporation’s stakeholders, such as suppliers, clients, and lenders (for an industrial firm), or claimholders, such as depositors and counterparties in financial transactions (for a financial institution).
• Risk capital is often called economic capital, and in most instances, the generally accepted convention is that risk capital and economic capital are identical (although sometimes economic capital is defined as risk capital plus strategic capital).

Risk Capital Versus Regulatory Capital

• We should not confuse the concept of risk capital, which is intended to capture the economic realities of the risks a firm runs, and regulatory capital.
  • First, regulatory capital only applies to a few regulated industries, such as banking and insurance companies, where regulators are trying to protect the interests of small depositors or policyholders.
  • Second, while regulatory capital performs something of the same function as risk capital in the regulators’ eyes, it is calculated according to a set of industry-wide rules and formulas and sets only a minimum required level of capital adequacy. It rarely succeeds in capturing the true level of risk in a firm, and the gap between a firm’s regulatory capital and its risk capital can be quite wide.
  • Furthermore, even if regulatory and risk capital are similar numbers at the level of the firm, they may not be similar for each constituent business line (i.e., regulatory capital may suggest that an activity is much riskier than management believes, or vice versa).
• The new regulatory capital requirements imposed by Basel III make it likely that for some activities, such as securitization, regulatory capital may end up much higher than economic capital. Still, economic capital calculation is essential for senior management as a benchmark to assess the economic viability of the activity for the financial institution. When regulatory capital is much larger than economic capital, it is likely that over time the activity will migrate to the shadow banking sector, which can price the transactions at a more attractive level.

Risk Capital Measurement

• Risk capital measurement is based on the same concepts as the value-at-risk (𝑉𝑎𝑅) calculation methodology. The choice of the confidence level and time horizon in the internal VaR models are key policy parameters that should be set by senior management (or the senior risk management committee) and endorsed by the board.
• Risk capital should be calculated in such a way that the institution can absorb unexpected losses up to a level of confidence in line with the requirements of the firm’s various stakeholders. No firm can offer its stakeholders a 100 percent guarantee (or confidence level) that it holds enough risk capital to ride out any eventuality. Instead, risk capital is calculated at a confidence level set at less than 100 percent—say, 99.9 percent for a firm with conservative stakeholders.
• The exact choice of confidence level is typically associated with some target credit rating from a rating agency such as Moody’s, Standard & Poor’s, and Fitch, as these ratings are themselves explicitly associated with a probability of default. It should also be in line with the firm’s stated risk appetite.

Emerging Uses Of Risk Capital Numbers

• Recently, risk capital numbers have been used to answer more and more questions, particularly in banks and other financial institutions. These include:
  • Performance measurement and incentive compensation at the firm, business unit, and individual levels – Risk capital can be plugged into risk-based capital attribution systems, often grouped together under the acronym RAPM (risk-adjusted performance measurement) or RAROC (risk-adjusted return on capital). These can be used to compare the economic profitability, as opposed to the accounting profitability (such as return on book equity) of different activities. At the same time, RAROC numbers can be used as part of scorecards to compensate the senior management of particular business lines, as well as the infrastructure group, for their contribution to shareholder value.
  • Active portfolio management for entry/exit decisions – The decision to enter or exit a particular business should be based on both risk-adjusted performance measurement and the “risk diversification effect” of the business. For example, a firm focused on corporate lending in a particular region is likely to find that its returns fluctuate in accordance with that region’s business cycle. Ideally, the firm might diversify its business geographically or in terms of business activity. Capital management decisions seek an answer to the question, “How much value will be created if the decision is taken to allocate resources to a new or existing business, or alternatively to close down an activity?”
  • Pricing transactions – Risk capital numbers can be used to calculate risk-based pricing for individual transactions, ensuring that a firm is compensated for the economic risk generated by a transaction. For example, a loan to a non-investment-grade firm in relatively fragile financial condition must be priced higher than a loan to an investment-grade firm. However, the amount of the differential can be determined only by working out the amount of expected loss and the cost of the risk capital that must be set aside for each transaction. Trading and corporate loan desks in many banks rely on the “marginal economic capital requirement” component in the 𝑅𝐴𝑅𝑂𝐶 calculation to price deals in advance and to decide whether those deals will increase shareholder value rather than simply add to the volume of transactions.
• One problem is that a single measure of risk capital cannot accommodate all the different purposes at the same time.

Importance Of Economic Capital For Financial Institutions

• Capital is primarily used in a financial institution not only to provide funding for investments (as for a manufacturing corporation) but also to absorb risk. The fundamental reason for this is that financial institutions can leverage themselves to a much higher degree than other corporations at a much lower cost without raising equity, by taking retail deposits or issuing debt securities. Their debt-to-equity ratio might be as high as 20 to 1 , compared to perhaps 2 to 1 for an industrial corporation.
• A bank’s target solvency is a vital part of the product the bank is selling. The primary customers of banks and other financial institutions are also their primary liability holders – e.g., depositors, derivatives counterparties, insurance policy holders, and so on. These customers are concerned about default risk on contractually promised payments. Customers make deposits with the expectation that the safety of their deposits does not depend on the economic performance of the bank. In over-the-counter markets, institutions are concerned about counterparty risk: a bank with a poor credit rating will find itself excluded from many markets. Maintaining good creditworthiness is therefore an ongoing cost of doing business for a bank.
• Traditional accounting based measures of performance at the consolidated level and for individual business units, such as return on assets (ROA) or return on book equity (ROE), fail to capture the risk of the underlying activity.
• RAPM (risk-adjusted performance measurement) is a generic term describing all the techniques used to adjust returns for the risk incurred in generating those returns. It encompasses many different concepts, risk adjustments, and performance measures, with RAROC being the form that is most widely used in the banking sector. These RAPM measures are not fully consistent with one another.
  • RAROC (risk-adjusted return on capital) = risk adjusted expected net income/economic capital. RAROC makes the risk adjustment to the numerator by subtracting a risk factor from the return – e.g., expected loss. RAROC also makes the risk adjustment to the denominator by substituting economic capital for accounting capital.
  • RORAC (return on risk-adjusted capital) = net income/economic capital. RORAC makes the risk adjustment solely to the denominator. In practical applications,
  • 𝑅𝑂𝑅𝐴𝐶 = 𝑃&𝐿 (Profit and Loss) / 𝑉𝑎𝑅
  • ROC (return on capital) = RORAC. It is also called ROCAR (return on capital at risk).
  • RORAA (return on risk-adjusted assets) = net income/ risk-adjusted assets.
  • RAROA (risk-adjusted return on risk-adjusted assets) = risk-adjusted expected net income/ risk-adjusted assets.
  • S (Sharpe ratio) = (expected return – risk-free rate)/ volatility. The ex post Sharpe ratio – i.e., that based on actual returns rather than expected returns – can be shown to be a multiple of ROC.
  • NPV (net present value) = discounted value of future expected cash flows, using a risk-adjusted expected rate of return based on the beta derived from the CAPM, where risk is defined in terms of the covariance of changes in the market value of the business with changes in the value of the market portfolio. In the CAPM, the definition of risk is restricted to the systematic component of risk that cannot be diversified away. For RAROC calculations, the risk measure captures the full volatility of earnings, systematic and specific. NPV is particularly well suited for ventures in which the expected cash flows over the life of the project can be easily identified.
  • EVA (economic value added), or NIACC (net income after capital charge), is the after-tax adjusted net income less a capital charge equal to the amount of economic capital attributed to the activity, times the after-tax cost of equity capital. The activity is deemed to add shareholder value, or is said to be EVA positive, when its NIACC is positive (and vice versa) .An activity whose RAROC is above the hurdle rate is also EVA positive.

RAROC For Capital Budgeting

• For capital budgeting purposes, RAROC is calculated as
  𝑅𝐴𝑅𝑂𝐶 =(𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑟𝑒𝑣𝑒𝑛𝑢𝑒𝑠 − 𝑐𝑜𝑠𝑡𝑠 − 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑙𝑜𝑠𝑠𝑒𝑠− 𝑡𝑎𝑥𝑒𝑠 + 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑟𝑖𝑠𝑘 𝑐𝑎𝑝𝑖𝑡𝑎𝑙± 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝑠)/(𝑒𝑐𝑜𝑛𝑜𝑚𝑖𝑐 𝑐𝑎𝑝𝑖𝑡𝑎𝑙)

  where
  Expected revenues are the revenues that the activity is expected to generate (assuming no losses).
  Costs are the direct expenses associated with running the activity (e.g., salaries, bonuses, infrastructure expenses, and so on).
  Expected losses, in a banking context, are primarily the expected losses from default; they correspond to the loan loss reserve that the bank must set aside as the cost of doing business. Because this cost, like other business costs, is priced into the transaction in the form of a spread over funding cost, there is no need for risk capital as a buffer to absorb this risk. Expected losses also include the expected loss from other risks, such as market risk and operational risk.

  Taxes are the expected amount of taxes imputed to the activity using the effective tax rate of the company.
  Return on risk capital is the return on the risk capital allocated to the activity. It is generally assumed that this risk capital is invested in risk-free securities, such as government bonds.
  Transfers correspond to transfer pricing mechanisms, primarily between the business unit and the treasury group, such as charging the business unit for any funding cost incurred by its activities and any cost of hedging interest rate and currency risks; it also includes overhead cost allocation from the head office.
  Economic capital is the sum of risk capital and strategic capital where
  
  𝑠𝑡𝑟𝑎𝑡𝑒𝑔𝑖𝑐 𝑟𝑖𝑠𝑘 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 = 𝑔𝑜𝑜𝑑𝑤𝑖𝑙𝑙 + 𝑏𝑢𝑟𝑛𝑒𝑑−𝑜𝑢𝑡 𝑐𝑎𝑝𝑖𝑡𝑎𝑙
  
  Risk capital is the capital cushion that the bank must set aside to cover the worst-case loss (minus the expected loss) from market, credit, operational, and other risks, such as business risk and reputation risk, at the required confidence threshold (e.g., 99 percent).Risk capital is directly related to the value-at-risk calculation at the one year time horizon and at the institution’s required confidence level.
  Strategic risk capital refers to the risk of significant investments about whose success and profitability there is high uncertainty. If the venture is not successful, then the firm will usually face a major write-off, and its reputation will be damaged. Burned-out capital refers to the idea that capital is spent on, say, the initial stages of starting up a business but the business may ultimately not be kicked off due to projected inferior risk-adjusted returns. It should be viewed as an allocation of capital to account for the risk of strategic failure of recent acquisitions or other strategic initiatives built organically. This capital is amortized over time as the risk of strategic failure dissipates.
  The goodwill element corresponds to the investment premium—i.e., the amount paid above the replacement value of the net assets (assets – liabilities) when acquiring a company. (Usually, the acquiring company is prepared to pay a premium above the fair value of the net assets because it places a high value on intangible assets that are not recorded on the target’s balance sheet.) Goodwill is also depreciated over time.
• This figure shows the linkage between a risk loss distribution and the RAROC calculation. It displays the expected loss of 15 basis points (bps), and the worst-case loss of 165 bps, at the desired confidence level (in this example, 99 percent) for the loss distribution derived over a given horizon, say one year. The unexpected loss is, therefore, the difference between the total loss and the expected loss, i.e. 150 bps at the 99 percent confidence level, over a one-year horizon. The unexpected loss corresponds to the risk capital allocated to the activity.
  
• Let us assume that we want to identify the RAROC of a $1 billion corporate loan portfolio that offers a headline return of 9 percent. The bank has an operating direct cost of $9 million per annum and an effective tax rate of 30 percent. We’ll assume that the portfolio is funded by $1 billion of retail deposits with a transfer priced interest charge of 6 percent. Risk analysis of the unexpected losses associated with the portfolio tells us that we need to set economic capital of around $75 million (i.e., 7.5 percent of the loan amount) against the portfolio. We know that this economic capital must be invested in risk-free securities, rather than being used to fund risky activities, and that the risk-free interest rate on government securities is 5 percent. The expected loss on this portfolio is assumed to be 1 percent per annum (i.e., $10 million).
  If we ignore transfer price considerations, then the after-tax RAROC for this loan is:
  
  This number can be interpreted as the annual after-tax expected rate of return on equity needed to support this loan portfolio.
• RAROC was first suggested as a tool for capital allocation on an anticipatory or ex ante basis. Hence, expected revenues and losses should be plugged into the numerator of the RAROC equation for capital budgeting purpose. When RAROC is used for ex post, or after the fact, performance evaluation, we can use realized revenues and realized losses, rather than expected revenues and losses, in our calculation.

RAROC For Performance Measurement – Time Horizon

• All of the quantities that we plug into the RAROC equation must be calculated on the basis of a particular time horizon, such as a one-year horizon or over the lifetime of a deal. Practitioners usually adopt a one-year time horizon, as this corresponds to the business planning cycle and is also a reasonable approximation of the length of time it might take to recapitalize the company if it were to suffer a major unexpected loss.
• For credit risk, there is a straightforward equivalence between the one-year VaR produced by credit portfolio models, such as CreditMetrics or KMV, and risk capital. The same is also true for operational risk: most internal models used by institutions have a one-year horizon. Therefore, for both credit risk and operational risk, there is no need for any adjustment in the one-year VaR to determine risk capital.
• However, this is not the case for market risk. For trading businesses, market risk is measured using only short-term horizons – one day for risk monitoring on a daily basis and 10 days for regulatory capital. Our task is to translate a one-day risk measure into one-year risk capital attribution?
• The purpose of Risk capital is to limit the risk of failure during a period of crisis, when the bank has suffered huge losses. If we use the “square root of time” rule by approximating the one-year VaR by multiplying the one-day VaR by the square root of the number of business days in one year (252 or 250 days), we would miss the point of risk capital.
• So this approach needs to be refined by considering that even in a worst-case scenario, the firm might not be able to reduce its risk beyond a core risk level so that it can run as a financially viable business for the rest of the year. To work out a meaningful one-year economic capital allocation, we need to analyze the business in question so that we can understand the time to reduce from the current risk position to the core risk level, which in turn reflects the relative liquidity of positions during adverse market conditions.
• Estimations of the time to reduce should not make the assumption that there will be a fire sale, but instead assume a relatively orderly unwinding of positions. This can take considerable time in some markets, as firms discovered to their cost in the 2007-2009 financial crisis.

RAROC For Performance Measurement – Default Probabilities

• This figure shows an example of the calculation of risk capital when the core risk level is lower than the current risk position.
  
• A point-in-time (PIT) probability of default (PD), which is the approach of KMV and other economic/structural approaches, is reasonable for calculating near-term expected losses (EL) and for pricing financial instruments that are subject to credit risk. A through-the-cycle (TTC) PD, which is largely the approach taken by the rating agencies, is more reasonable for calculating economic capital, current profitability, and strategic decisions regarding products, geographies, and new business ventures.
• The probability of a firm’s staying in the same rating when it is assessed using a PIT approach is smaller than when it is assessed using a TTC approach. The TTC approach therefore reduces the volatility of economic capital, compared to PIT approaches. It is useful on a periodic basis to compare the impact of using PIT PD versus TTC PD in the RAROC calculation for both a normal part of the economic cycle and the worst part of the cycle.

RAROC For Performance Measurement – Confidence Level

• As stated earlier, the confidence level in the economic capital calculation should be consistent with the firm’s target credit rating. For example, most banks today hope to obtain an AA credit rating from the agencies for their debt offerings, which implies a one-year probability of default of 3 to 5 basis points. This, in turn, corresponds to a confidence level in the range of 99.95 to 99.97 percent. We can think of this confidence level as the quantitative expression of the risk appetite of the firm.
• Setting a lower confidence level may significantly reduce the amount of risk capital allocated to an activity, especially when the institution’s risk profile is dominated by operational, credit, and settlement risks (for which large losses occur only with some rarity). Therefore, the choice of the confidence level can materially affect risk-adjusted performance measures and the resulting capital allocation decisions of the firm.

Hurdle Rate And Capital Budgeting

• The hurdle rate should be reset every six months or every year, or when it has changed by more than 10.0%. This hurdle rate is calculated as

  \( h_{AT} = \frac{[CE \times r_{CE}] + [PE \times r_{PE}]}{CE + PE} \)

  where 𝐶𝐸 and 𝑃𝐸 denote the market value of common equity and preferred equity, respectively, and 𝑟_𝐶𝐸 and 𝑟_𝑃𝐸 are the cost of common equity and preferred equity, respectively.
• The cost of preferred equity is simply the yield on the firm’s preferred shares. The cost of common equity is determined via a model such as the capital asset pricing model:

  \( r_{CE} = r_f + \beta_{CE}(\overline{R_M} – r_f) \)

  where \(𝑟_f\) is the risk-free rate, \(\overline{R_M}\) is the expected return on the market portfolio, and \(\beta\) is the firm’s common equity market beta.
• When a firm is considering investing in a business or closing down an activity, it computes the after-tax RAROC for the business or activity and compares it to the firm’s hurdle rate. In theory, the firm can then apply a simple decision rule:
  • If the RAROC ratio is greater than the hurdle rate, the activity is deemed to add value to the firm.
  • In the opposite case, the activity is deemed to destroy value for the firm and the activity should be closed down or the project rejected.
• However, one can show that applying this simple rule can lead to a firm’s accepting high-risk projects that will lower the value of the firm and rejecting low-risk projects that will increase the value of the firm. High-risk projects, such as oil exploration, are characterized by very volatile returns, while low-risk projects, such as properly risk managed retail banking, produce steady revenues with low volatility.
• To overcome this, adjusted RAROC is calculated so that the systematic riskiness of the returns from a business activity is fully captured by the decision rule.

Adjusted RAROC

• Ideally, we would like to adjust the traditional RAROC calculation to obtain a RAROC measure that takes into account the systemic riskiness of returns, and for which the hurdle rate (the critical benchmark above which a business adds value) is the same across all business lines. To correct the inherent limitations of the traditional RAROC measure, let’s adjust the RAROC ratio as follows:

  \( \text{Adjusted RAROC} = \text{RAROC} – \beta_E (R_M – r_f) \)

  where 𝑅 is the expected rate of return on the market portfolio, 𝑟 denotes the risk-free interest rate, and 𝛽 is the beta of the equity of the firm. The new decision rule is:
  • Accept projects whose Adjusted RAROC is greater than r_f Reject projects whose Adjusted RAROC is less than r_f
  • Reject projects whose Adjusted RAROC is less than r_f
• The risk adjustment, \( \beta_E (R_M – r_f) \) is the excess return above the risk-free rate required to compensate the shareholders of the firm for the non-diversifiable systematic risk they bear when investing in the activity, assuming that the shareholders hold a well-diversified portfolio. When the returns are thus adjusted for risk, the hurdle rate becomes the risk-free rate.

Diversification And Risk Capital

• The risk capital for a particular business unit within a larger firm is usually determined by viewing the business on a stand-alone basis, using the top-of-the-house hurdle rate that we discussed earlier. However, intuition suggests that the risk capital for the firm should be significantly less than the sum of the stand-alone risk capital of the individual business units, because the returns generated by the various businesses are unlikely to be perfectly correlated.
• Measuring the true level of this “diversification effect” is extremely problematic. As of today, there is no fully integrated VaR model that can produce the overall risk capital for a firm, taking into account all the correlation effects between market risk, credit risk, and operational risk across all the business units of a company. Instead, banks tend to adopt a bottom-up decentralized approach, under which distinct risk models are run for each portfolio or business unit.
• For capital adequacy purposes, running these business-specific models at the confidence level targeted at the top of the house, for example 99.97 percent, produces an unnecessarily large amount of overall risk capital, precisely because it neglects diversification effects (across both risk types and business activities). It is therefore common practice to adjust for the diversification effects by lowering the confidence level used at the business level to, say, 99.5 percent or lower – an adjustment that is necessarily more of an educated guess than a strict risk calculation.
• Let’s apply some boundaries around the problem. The aggregate VaR figure obtained by this approach should fall in between the two extreme cases of perfect correlation and zero correlation between risk types and across businesses. For example, ignoring business risk, reputation risk, and strategic risk, for illustrative purposes, suppose that we’ve calculated the risk capital for each type of risk as follows:
  Market risk = $200
  Credit risk = $700
  Operational risk = $300
  Then aggregate risk capital at the top of the house is
  • Simple summation of the three risks (perfect correlation) = $1,200

    OR
    

  • Square root of the sum of squares of the three risks (zero correlation) = $787
• We can say with some confidence, therefore, that any proposed approach for taking diversification effects into account should produce an overall VaR figure in the range of $787 to $1,200.
• While the simple logic of our boundary setting makes sense, these boundaries are pretty wide! They also leave us with the reverse problem: how do we allocate any diversification benefit that we calculate for the business as a whole back to the business lines? The allocation of the diversification effect can be important for certain business decisions, such as determining the performance of each unit.
• Logically, a business whose operating cash flows are strongly correlated with the earnings of the other activities in the firm should require more risk capital than a business with the same volatility whose earnings move in a countercyclical fashion. Bringing together countercyclical business lines produces stable earnings for the firm as a whole; the firm can then operate to the same target credit rating with less risk capital.
• Institutions continue to struggle with the problem of attributing capital back to business lines, and there are diverging views as to the appropriate approach. For the moment, as a practical solution, most institutions allocate the portfolio effect pro rata with the stand-alone risk capital.
• Diversification effects also complicate matters within business units. Let’s look at this and other issues in relation to an example business unit, BU, which comprises two activities, X and Y.
  
• When calculating the risk capital of the business unit, let’s assume that the firm’s risk analysts have taken into account all the diversification effects created by combining activities X and Y and that the risk capital for BU is $100. The complication starts when we try to allocate risk capital at the activity level within the business unit. There are three different measures of risk capital:
  • Stand-alone capital
  • Fully diversified capital
  • Marginal capital
• Stand-alone capital is the capital used by an activity taken independently of the other activities in the same business unit—that is, risk capital calculated without any diversification benefits. In our example, the standalone capital for X is $60 and that for Y is $70. The sum of the stand-alone capitals of the individual constituents of the business unit is generally higher than the stand-alone risk capital of the business unit itself (it is equal only in the case of perfectly correlated activities X and Y ).
• Fully diversified capital is the capital attributed to each activity X and Y, taking into account all diversification benefits from combining them under the same leadership. In our example, the overall portfolio effect is $30 ($60+$70-$100). The portfolio diversification effect is allocated pro rata with the stand-alone risk capital, $30×60/130 = $14 for X and $30×70/130 = $16 for Y, so that the fully diversified risk capital is $46 for X and $54 for Y.
• Marginal capital is the additional capital required by an incremental deal, activity, or business, taking into account the full benefit of diversification. In the example, the marginal risk capital for 𝑋 (assuming that 𝑌 already exists) is $30($100 – $70) and the marginal risk capital for 𝑌 (assuming that 𝑋 already exists) is $40($100 – $60). In the case where more than two activities are included in the business unit 𝐵𝑈, marginal capital is calculated by subtracting the risk capital required for the 𝐵𝑈 without this business from the risk capital required for the full portfolio of businesses. Note that the summation of the marginal risk capital, $70 in the example, is less than the full risk capital of the BU.
• As this example shows, the choice of capital measure depends on the desired objective.
  • Fully diversified measures should be used for assessing the solvency of the firm and minimum risk pricing.
  • Active portfolio management or business mix decisions, on the other hand, should be based on marginal risk capital, taking into account the benefit of full diversification.
  • Performance measurement should involve both perspectives: stand-alone risk capital for incentive compensation, and fully diversified risk capital to assess the extra performance generated by the diversification effects.
• However, diversification benefits should be dealt with caution. Correlations between risk factors drive the extent of the portfolio effect, and these correlations tend to vary over time. During market crises, correlations may shift dramatically toward either 1 or -1 , reducing or totally

RAROC Best Practices

• Economic capital is a key element in the assessment of business line performance, in the decision to exit or enter a business, and in the pricing of transactions. It also plays a critical role in the incentive compensation plan of the firm.
• In firms where RAROC has been implemented, business units challenge the risk management function about the fairness of the amount of economic capital attributed to them. The usual complaint is that their economic capital attribution is too high (never that it is too low!). Another complaint is that economic capital attribution is sometimes too unstable for purposes of trying to hit a target.
• The best way to defuse this debate is to be transparent about the methodology used to assess risk and to institute forums where the issues related to the determination of economic capital can be debated and analyzed. The VaR  methodologies for measuring market risk and credit risk that underpin RAROC calculations are generally well accepted by business units. The disagreement stems from the setting of parameters that feed into these models and the consequent sizing of economic capital.

RAROC Best Practices – Recommendations

1. Senior management commitment – Given the strategic nature of the decisions steered by a RAROC system, the marching orders must come from the top management of the firm. The CEO and their executive team should sponsor the implementation of a RAROC system and performance should be measured in terms of contribution to shareholder value. The message to the business lines is this: Amount of income generated, is less important, and how well the firm is compensated for the risks being taken, is more important.
2. 1.Communication and education – The RAROC group should be transparent and should explain the RAROC methodology to all stakeholders including business’s heads but also to the business line managers and the CFO’s office, in order to gain acceptance of the methodology throughout all the management layers of the firm.
3. Ongoing consultation – The firm should institute a “parameter review group” composed of key representatives from the business units and the risk management function, that periodically reviews the key parameters that drive risk and economic capital. This group will promotefairness in the capital allocation process.
   • For credit risk, the parameters that should be reviewed include probabilities of default, credit migration frequencies, loss given default, and credit line usage given default. These parameters evolve over the business cycle and should be adjusted as more data become available. An important issue to settle is the choice of a historical period over which these parameters are calibrated—i.e., should this be the whole credit cycle (in order to produce stable risk capital numbers) or a shorter period of time to make capital more procyclical (capital goes down when credit environment improves and goes up when it deteriorates)?
   • For market risk, volatility and correlation parameters should be updated at least every month, using standard statistical techniques. Other key factors, such as the core risk level and “time to reduce”, should be reviewed on an annual basis.
   • For operational risk, the risk measurement approach is currently more judgmental and, as such, more open to heated discussions!
4. Maintaining the integrity of the process – As with other risk calculations, the validity of RAROC numbers depends critically on the quality of the data about risk exposures and positions collected from the management systems (e.g., in a trading business, the front and back-office systems). Only a rigorous process of data collection and centralization can ensure accurate risk and capital assessment. The same rigor should also be applied to the financial information needed to estimate the adjusted-return element of the RAROC equation. Data collection is probably the most daunting task in risk management. There is almost a certain chance of failure in implementing a RAROC system if calculations are based on inaccurate and incomplete data. The RAROC group should be accountable for the integrity of the data collection process, the calculations, and the reporting process. The business units and the finance group should be accountable for the integrity of the specific data that they produce and feed into the RAROC system.
5. Combine RAROC with qualitative factors – A simple decision rule for project selection and capital attribution was described earlier- i.e., accept projects where the RAROC is greater than the hurdle rate. In practice, other qualitative factors should be taken into consideration. All the business units should be assessed in the context of the two-dimensional strategic grid shown in this figure. Priority in the allocation of balance sheet resources should be given to the businesses in the upper right quadrant. At the other extreme, the firm should try to exit, scale down, or fix the activities of businesses that fall into the lower left quadrant. The businesses in the category “managed growth,” in the lower right quadrant, are high-return activities that have low strategic importance for the firm. In contrast, businesses in the category “investment,” in the upper left quadrant, are currently low return activities that have high growth potential and high strategic value for the firm.
   
6. Put an active capital management process in place – Balance sheet requests from the business units, such as economic capital, leverage ratio, liquidity ratios, and risk-weighted assets, should be channeled to the RAROC group every quarter. Limits are then set for economic capital, leverage ratio, liquidity ratios, and risk-weighted assets based on the kind of analysis we’ve discussed in this chapter. The treasury group often reviews limits to ensure that they are consistent with funding limits. This limit-setting process is a collaborative effort, with any disagreements about the amount of balance sheet resources attributed to a business put to arbitration by the senior executive team. Leverage ratios may restrain management from growing the bank beyond a certain level, but this in itself makes it more important that banks work every dollar of capital hard – and RAROC analysis is one way to do this.

Conclusion

• Wherever risk capital is an important concern, RAROC balances the divergent desires of the various external stakeholders, while also aligning them with the incentives of internal decision makers, as illustrated in this figure. When business units (or transactions) earn returns in excess of the hurdle rate, shareholder value is created, while the allocated risk capital indicates the amount of capital required to preserve the desired credit rating.
  
• RAROC information allows senior managers to better understand where shareholder value is being created and where it is being destroyed. It promotes strategic planning, risk-adjusted profitability reporting and incentive compensation schemes, proactive allocation of resources, better management of concentration risk, and better product pricing.
• Because RAROC is not just a common language of risk, but a quantitative technique, we can also think of a RAROC-based capital budgeting process as akin to an internal capital market in which businesses are competing with one another for scarce balance sheet resources—all with the objective of maximizing shareholder value. This makes RAROC a useful tool for capital allocation, both for banks and for nonbank corporations.