CFA Level 1 · Module 02 Quantitative Methods · Chapter 2
The previous reading, Returns of Financial Assets and Instruments, built the machinery for measuring a return. This reading asks a different question: where does that return actually come from, and how does its shape change from one kind of investment to the next? A government bond, a growth share, a foreign bond, and a stock index all deliver return, but they deliver it in very different proportions, and understanding those proportions is what lets an investor build a portfolio on purpose rather than by accident.
The single learning outcome here is to calculate, compare, and interpret the different types of returns across financial assets, instruments, and indicators. In practice that breaks into three moves. First, see how the two return components, price change and cash distribution, split differently across asset types. Second, add the currency dimension that appears the moment you invest across a border. Third, step back and look at what a long span of market history says about which asset classes have paid the most, and why the ranking is not an accident but a reward for risk.
Very little arithmetic is heavy here. The marks, and the real-world judgment, come from comparison and interpretation: knowing which component dominates for which asset, translating a foreign return into your own currency, and reading a table of historical returns without drawing the wrong lesson from it.
Recall the two ways an asset pays. A price return comes from the asset’s value changing, and it is usually uncertain. A capital distribution return comes from cash the asset hands over while you hold it, and depending on the instrument it can be fixed, variable, or absent. The total return is the two together, a point covered in full in the previous reading. What matters now is that the balance between them is not the same for every asset, and that balance tells you a great deal about the investment.
An asset whose return is mostly price change behaves very differently from one whose return is mostly a steady distribution. The first offers the chance of large gains and the risk of large losses, with little to show along the way. The second pays you predictably but rarely surprises on the upside. Neither is better in the abstract; they suit different goals. An investor who needs regular income leans toward distribution-heavy assets, while one saving for a distant goal can tolerate the swings of price-heavy assets and let them compound.
The mix also shapes practical matters such as tax and timing. Distributions are typically received and often taxed in the year they are paid, whereas a price gain is unrealized, and untaxed, until the asset is sold. Two investments with the same total return can therefore leave very different amounts in the investor’s hands after tax and after cash-flow needs, which is why the composition of a return is not a technicality but a decision input.
| Asset type | Main return source | Nature of the distribution |
|---|---|---|
| Common equity | Mostly price change | Dividend, variable and not guaranteed |
| Debt (bond) | Mostly distribution | Coupon, usually fixed and scheduled |
| Hybrid (for example a convertible) | Both, depending on conditions | Fixed coupon plus equity-linked upside |
| Non-dividend share | Entirely price change | None |
Setup. Over one year, a share of Corvus Logistics is bought at 500 rupees, pays a dividend of 10 rupees, and ends at 560 rupees. A bond from Kaveri Cement is bought at 1,000 rupees, pays a coupon of 60 rupees, and ends the year at 1,010 rupees. Compare the composition of each total return.
Answer: the share returned 14% (mostly price), the bond returned 7% (mostly coupon). Same formula, opposite shape, which is exactly why the two assets play different roles in a portfolio.
Two assets can post the same total return while being completely different investments. Always look at how much of the return is price versus distribution, because that split drives the income the asset provides, the tax it triggers, and the risk it carries.
Take the main asset types in turn. Equities represent ownership. Their distribution is a dividend, which the company may raise, cut, or skip, so it is variable and uncertain. Some firms return cash to shareholders through share buybacks instead of dividends, which supports the price rather than paying income directly, so even the distribution can arrive disguised as price return. Over long horizons a large part of an equity’s total return has come from price appreciation, but reinvested dividends have added a meaningful and steadier layer that compounds quietly over decades.
Debt instruments represent a loan. Their distribution is a coupon, usually fixed and paid on a schedule, which is why bonds are prized for predictable income. A bond’s price still moves, mostly with interest rates, so price return is real but secondary for an investor who holds to maturity and collects the coupons. Not all debt pays a fixed coupon: floating-rate notes reset their coupon with market rates, so their distribution is variable, and zero-coupon bonds pay no coupon at all and deliver their entire return through price, accruing toward face value. For international debt, a third force enters, currency, which the sections below treat on their own.
Hybrid securities deliberately blend the two. A convertible bond pays a fixed coupon like debt but can be converted into shares, so it also carries equity-linked price upside; the holder gives up some coupon in exchange for that option. Preferred shares sit between as well, paying a more dependable dividend than common equity but ranking behind debt and usually lacking a claim on the company’s growth. The purpose of a hybrid is to occupy a chosen point in the middle of the risk and return range rather than sitting at either extreme.
Expect a question that describes an instrument and asks which return component dominates, or which investor it suits. Match the words: “fixed”, “scheduled”, and “coupon” point to distribution-driven debt; “growth”, “no dividend”, and “appreciation” point to price-driven equity; “convertible” or “preferred” signals a hybrid that carries both. A “floating-rate” note is still debt, but with a variable rather than fixed distribution.
An asset is the underlying claim; an instrument is the standardized, tradable form that lets investors exchange that claim efficiently in a market. Standardization is what turns a private loan into a bond that thousands of investors can buy, and an ownership stake into a listed share. The return an instrument delivers still traces back to the price and distribution of the underlying asset, but the tradability adds something: the ability to realize price return by selling to another investor rather than waiting for the asset to mature or pay out.
Pooled vehicles such as mutual funds and exchange-traded funds are instruments that repackage the returns of many underlying assets into a single tradable unit. Their return is the blended return of everything they hold, less the fees of running the vehicle, which is the gross-versus-net distinction from the previous reading. Derivatives are instruments whose return is derived from something else, such as a share, an index, or a rate, and their payoff can be shaped to rise or fall with the underlying in ways a direct holding cannot. For this reading the point is simply that an instrument inherits its return type from what it is built on, then reshapes it through its structure.
Financial indicators are observable numbers that signal value but cannot be owned directly: a stock market index, an interest rate, an exchange rate. You cannot hold “the index” the way you hold a share, yet its percentage change is measured exactly like a price return, and that change is what index funds and benchmarks track.
where Rindex is the price return of the index, I0 is the index level at the start of the period, and I1 is the level at the end. A price index captures only this change; a total return index also adds the income of its constituents.
The distinction between a price index and a total return index matters more than it first appears. A price index tracks only the level of its constituents. A total return index assumes the dividends or coupons of its constituents are reinvested, so it captures the distribution component too. Over long horizons the two diverge widely, because the reinvested income compounds. Interest rates and exchange rates are indicators as well; their changes are read through the instruments tied to them, a bond for an interest rate or a foreign asset for an exchange rate, rather than as a return you collect from the indicator itself.
Setup. The Meridian 50, a broad equity index, begins the year at a level of 20,000 and ends at 21,600. Its constituent companies also paid dividends worth 2% of the starting level. Find the price return and the total return the index represents.
Answer: price return 8%, total return 10%. The 2 percentage point gap is the income a price index quietly leaves out, and over many years that gap compounds into a large difference in reported performance.
The moment you invest outside your home currency, your return has two moving parts: how the asset did in its local currency, and how that currency moved against yours. A bond can perform well in its own market yet lose you money once it is translated home, if the foreign currency weakened. The home-currency return combines the two multiplicatively, not by simple addition.
where Rhome is the return in the investor’s home currency, Rlocal is the asset’s return in its own local currency, and Rcurrency is the change in the value of the local currency against the home currency (positive if the foreign currency strengthened).
Setup. Farah, based in India, holds a US-dollar bond. Over the year the bond returns 5% measured in dollars. Consider two cases: the dollar strengthens 4% against the rupee, and separately, the dollar weakens 4%.
Answer: 9.2% if the dollar strengthened, 0.8% if it weakened. For a foreign investor, the currency is not a footnote; it can matter as much as the asset itself.
Because the currency can swing the outcome so sharply, investors sometimes remove it. A currency hedge uses a forward or similar contract to lock in the exchange rate in advance, so the home-currency return collapses back toward the local return and the currency term drops out. Hedging is not free, and it can subtract as well as add, but it lets an investor separate the decision to own a foreign asset from the decision to be exposed to a foreign currency. Over short horizons the currency move can dominate the local return entirely; over long horizons currencies tend to matter somewhat less, though never nothing.
Adding the local return and the currency move instead of compounding them. Simple addition (5% + 4% = 9%) is close only when both are small, and it hides the interaction. Multiply the growth factors, then subtract 1, and the interaction term is captured correctly.
Currency questions turn on the direction of the move and on getting the growth factors right. Read carefully whether the foreign currency strengthened or weakened against the home currency, apply that as a plus or minus inside the second factor, and multiply rather than add. A favorite trap offers the simple-addition answer as a near miss sitting beside the correct compounded one, and another offers the result you would get if you moved the currency the wrong way.
Every return in this reading is ultimately judged against one reference point: the risk-free rate, the return available with no default risk, usually proxied by a short-term government bill. It is the floor. An asset that carries risk must offer more than the risk-free rate, or no rational investor would accept the extra uncertainty for no extra reward. The amount above the risk-free rate is the risk premium, introduced in the previous reading, and it is the lens through which the historical ranking of asset classes suddenly makes sense.
Short-term government debt is chosen for the proxy because it has negligible default risk and little price sensitivity, so its return is close to a pure payment for time. Longer or riskier instruments layer premia on top: a maturity premium for lending longer, a credit premium for accepting default risk, an equity premium for owning rather than lending. Those premia are exactly what the historical record puts numbers on.
Look across long stretches of market history in major economies and a consistent ordering appears. Equities have earned the most, followed by long-term corporate bonds, then long-term government bonds, with short-term government bills earning the least. This is a real, widely documented pattern, not a coincidence, and the reason is risk. Each step up the ladder carries more uncertainty, and investors have demanded, and on average received, more return for bearing it.
The table below is illustrative, using round hypothetical figures to show the shape of the relationship rather than any specific market’s record. The pattern it shows, higher risk paired with higher long-run return, is the durable lesson.
| Asset class | Illustrative average annual return | Relative risk |
|---|---|---|
| Equities | 10% | Highest |
| Corporate bonds | 6% | Moderate to high |
| Government bonds (long term) | 5% | Moderate |
| Government bills (short term) | 3% | Lowest |
Setup. Using the illustrative figures above, read the ranking as a stack of risk premia over the risk-free bill. What extra return did each step up the ladder pay?
Answer: each rung, 3% to 5% to 6% to 10%, is a premium for a specific added risk (maturity, then credit, then ownership). The ranking is not luck; it is the price of risk, paid out over the long run.
Reading a high historical average as a promise of future return. History shows that risk has been rewarded on average and over long horizons, not that equities beat bonds every year. Over any single year the ranking can and does invert, which is precisely the risk the premium pays for. Historical averages also depend on the period and the market chosen, so treat them as evidence of a tendency, not a guarantee.
The returns quoted so far are nominal, measured in ordinary money. To judge whether an asset class actually grew an investor’s purchasing power, strip out inflation to get the real return, using the division method from the previous reading. Doing this to the historical record sharpens the story considerably, because inflation does not treat the asset classes equally.
Equities, with the highest nominal returns, have generally delivered a solid positive real return over long periods, meaningfully ahead of inflation. Short-term bills, at the bottom of the nominal ranking, have often barely kept pace with inflation, leaving a real return close to zero or even slightly negative after tax. The lesson is blunt: the safest asset protects the number in your account but does little to grow what that number can buy, while the riskier asset has historically been the one that built real wealth over decades.
Setup. Using illustrative long-run figures, equities average 10% nominal and bills average 3% nominal, while inflation averages 4%. Convert each to a real return.
Answer: about 5.77% real for equities and about negative 0.96% real for bills. The nominal gap of 7 percentage points is really a gap between building wealth and merely preserving cash, which is why long-horizon investors accept equity risk.
Total return splits into capital appreciation and capital distribution, and over long horizons the split differs sharply by asset class. For equities, price appreciation typically leads, but reinvested dividends contribute a large, compounding share that is easy to overlook. For bonds held over their life, almost all of the return is the coupon, with price change netting out toward zero as the bond pulls back to face value at maturity. Bills are nearly all distribution as well, since their price barely moves.
| Asset class | Total return | From price | From distribution |
|---|---|---|---|
| Equities | 9.0% | 6.5% | 2.5% |
| Long-term bonds | 5.0% | 0.3% | 4.7% |
| Short-term bills | 3.0% | 0.0% | 3.0% |
Setup. Using Exhibit 3, express how much of each asset class’s long-run total return came from its distribution, as a share of the total.
Answer: distribution supplied roughly 28% of the equity return, 94% of the bond return, and all of the bill return. The further you move from ownership toward lending, the more of your return arrives as a scheduled payment rather than as price appreciation.
Reinvested income is the quiet engine of long-run equity return. A price chart of an index understates what a shareholder actually earned, because it omits dividends that, reinvested and compounded over decades, add a large slice to total return.
When historical returns are summarized, two averages appear, and the previous reading established the difference. The arithmetic mean is the simple average of the yearly returns; the geometric mean is the compound annual rate actually achieved. For any asset whose returns vary, the geometric mean is lower, and the gap between the two widens with the dispersion, the spread of the annual returns around their average.
Dispersion is also reported as a range, the distance between the best and worst years, and as a standard deviation, which the statistics readings develop. Equities show the widest range of annual outcomes, from large gains to steep losses, while bills barely move from year to year. That wide range is the visible face of equity risk, and it is why equities show the largest gap between their arithmetic and geometric averages, while bills show almost none.
Setup. Two assets each average 8% by the arithmetic mean over two years. Anvil Stable returns 8% then 8%. Anvil Volatile returns 28% then negative 12%. Compare their geometric means and see what dispersion does.
Answer: both average 8% arithmetically, but the volatile asset compounds at only 6.13% against the stable asset’s 8%. The 1.87 percentage point shortfall is the pure cost of dispersion, and it is why a volatile asset needs a higher average return just to match a steady one.
Which asset class has historically shown the largest gap between its arithmetic and geometric mean return, and why?
Equities. Their annual returns have the widest dispersion, and the geometric mean falls further below the arithmetic mean as dispersion rises. Bills, with almost no year-to-year variation, show almost no gap.
Few investors hold a single asset class. They blend them, and the return of the blend is simply the weighted average of the returns of its parts, each weight being the share of money allocated to that class.
where Rportfolio is the portfolio return, ri is the return on asset class i, and wi is the fraction of the portfolio allocated to it, with the weights summing to 1.
Setup. Blackwater Capital allocates 60% of a portfolio to equities, expected to return 11%, and 40% to government bonds, expected to return 4%. What is the expected portfolio return?
Answer: an expected portfolio return of 8.2%, sitting between the equity and bond returns as the weighted average. The return blends by simple weighting, but the portfolio’s risk is usually less than the weighted average of the two risks, because equities and bonds do not move in perfect step.
Portfolio return is a simple weighted average of the parts. Portfolio risk is not, because assets that do not move together partly offset each other. That asymmetry, return averaging while risk more than averages down, is the entire case for diversification, and it is developed formally in the portfolio mathematics reading later in this module.
A bond is bought at 1,000, pays an 80 coupon, and ends the year at 970. What is the total return, and how does it split?
Price return = (970 − 1,000) ÷ 1,000 = −3%. Income return = 80 ÷ 1,000 = 8%. Total return = −3% + 8% = 5%. The coupon carried the return while the price slipped, which is typical for a bond.
A euro-denominated investment returns 6% in euros over a year, and the euro falls 5% against your home currency. What is your home-currency return?
1 + Rhome = (1 + 0.06)(1 − 0.05) = 1.06 × 0.95 = 1.007. Home-currency return = 0.7%. A solid local return was nearly wiped out by the weaker euro.
A portfolio holds 70% equities returning 10% and 30% bonds returning 3%. What is the portfolio return?
0.70 × 10% + 0.30 × 3% = 7.0% + 0.9% = 7.9%.
An asset returns 12% in nominal terms during a year when inflation is 5%. Roughly how much did its real purchasing power grow?
Real return = (1 + 0.12) ÷ (1 + 0.05) − 1 = 1.12 ÷ 1.05 − 1 = 6.67%. The quick subtraction (12 minus 5 = 7%) is close but slightly too high, because it ignores the interaction between the two rates.
Because equity owners bear more risk than lenders. Shareholders are paid after everyone else and their dividends are not guaranteed, so they have historically demanded, and on average received, a higher return, the equity risk premium, to compensate for that greater uncertainty.
A price index tracks only the level of its constituents. A total return index assumes dividends or coupons are reinvested, so it also captures the income component. Over long horizons the reinvested income compounds, and the two versions diverge substantially.
Your home-currency return combines the asset’s local return with the change in the foreign currency against your own, multiplied together. A strong foreign currency adds to your return; a weak one subtracts from it, and can turn a local gain into a home-currency loss. A currency hedge removes this exposure.
Not directly, because you cannot hold an indicator. Their changes are measured like returns and drive the returns of the instruments tied to them, such as bonds for interest rates and foreign assets for exchange rates, but you do not collect a return from the indicator itself.
Because it has negligible default risk and very little price sensitivity, so its return is close to a pure payment for the time value of money. That makes it the natural baseline above which every riskier asset must offer a premium.
No. History shows that risk has been rewarded on average across long periods, not that the ranking holds every year. In any single year a riskier asset class can underperform a safer one, which is the very risk the long-run premium compensates.
Because safety in nominal terms is not the same as growth in real terms. Bills have historically barely kept pace with inflation, so they protect the number in your account while doing little to grow what it can buy. For long-horizon goals, that shortfall in real return is itself a risk.
Portfolio return is a weighted average because each rupee earns its own asset’s return. Portfolio risk is usually below the weighted average because the assets do not move perfectly together, so their ups and downs partly cancel. That gap is the benefit of diversification.
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