How the major asset classes compare on return and risk

What is the difference between historical and expected return?

Historical return is what an asset actually earned in the past. Expected return is what an investor anticipates earning in the future. In practice analysts often use the long-run historical mean as a stand-in for the expected return, but a single decade can look nothing like the long-run average, so the two should never be treated as the same number.

Expected return has a structure. It is the nominal return that would persuade the marginal investor to hold the asset, built from three layers: the real risk-free rate, expected inflation and a risk premium. Each layer is a growth factor, and the factors multiply.

$$1 + E(R) = (1 + r_{rf})\,\big[1 + E(\pi)\big]\,\big[1 + E(RP)\big]$$

Expected return of an assetcompound the three layers, do not add them

• Nominal risk-free rate Memorize what a short government bill pays
  • Real risk-free rate reward for postponing consumption; positive
  • Expected inflation protects purchasing power; negative only in deflation
• Expected risk premium Memorize extra return for bearing the asset’s risk; positive in most cases

The real risk-free rate is expected to be positive, because it rewards postponing consumption. Expected inflation is normally positive, except in a deflationary economy. The risk premium is the extra return for bearing the asset’s risk and is positive in most cases. The exceptions are assets that reduce a portfolio’s overall risk, which the diversification lessons return to.

How do nominal and real returns differ?

A nominal return is measured in current money. A real return strips out inflation and measures the gain in purchasing power. An asset class can look strong in nominal terms and poor in real terms when inflation is high, which is why long histories are compared in real terms.

$$r_{real} = \frac{1 + R_{nominal}}{1 + \pi} - 1$$

Risk premiums can be stated either way. The nominal risk premium is the nominal return on a risky asset minus the nominal risk-free rate. The real risk premium is the real return on the risky asset minus the real risk-free rate.

How have the major asset classes ranked?

Across long histories in the major markets, higher average returns came with higher volatility. That is the risk–return trade-off : in efficient markets, extra return over long periods cannot be had without accepting extra risk, so assets with more risk must offer more expected return.

Asset class	Average return	Volatility
Small company stocks	highest	highest
Large company stocks	high	high
Long-term corporate bonds	middle	middle
Long-term government bonds	a little lower	middle (interest rate risk)
Treasury bills	lowest	lowest

Higher average return came with higher volatilityranked from highest to lowest

• Small company stocks Memorize highest return, highest volatility
• Large company stocks Memorize high return, high volatility
• Long-term bonds Memorize middle return, middle volatility (interest rate risk)
  • Corporate a little more return, credit risk
  • Government a little less return, rate risk
• Treasury bills Memorize lowest return, lowest volatility

The order is the same in nominal and real terms and broadly the same across the major developed markets. Stocks beat bonds in most, but not all, countries and periods. Treasury bills are the only close-to-riskless rung. They have little interest rate risk and, because their yield resets quickly, little inflation risk. Long-term government bonds carry little default risk but their prices swing when yields move, so they can be as volatile as corporate bonds, or more.

Read the diagram in three parts. The ladder shows rank only, with no numbers: more return to the upper right, more risk to the right. The two histograms show why standard deviation is not the full story. The spread bars show a cost the return series hides.

Go deeper Why the historical mean is a noisy estimate of the expected return

A risky asset has no guarantee of earning its expected return in any one period, and the period needed for the average to settle is unknown: 10 years, 50 years, perhaps 100. A stock index can lose money over a whole decade and still have a clearly positive long-run record. Treating the historical mean as the expected return is a common and reasonable assumption, but only an assumption.

Risk behaves better than return. The volatility of an asset class changes little from decade to decade, so historical risk is a decent proxy for future risk.

Go deeper Combining markets can lower volatility

A broad world stock index has historically been less volatile than most of the national markets inside it, even though every one of those markets is risky. That is diversification at work, and the next lessons show why.

Why is standard deviation not the whole story?

Mean and variance describe a normal distribution completely. A normal curve is symmetric, its mean equals its median, and about 68% of outcomes fall within one standard deviation of the mean, 95% within two and 99% within three. If returns were normal, expected return and standard deviation would be all an investor needed.

They are not quite normal, in two ways.

• Skewness is asymmetry. A distribution is negatively (left) skewed when the long tail is on the left, with most outcomes bunched to the right. Equity returns tend to be negatively skewed: more large losses than large gains, which variance cannot see because it treats gains and losses alike.
• Kurtosis is tail thickness. A fat-tailed distribution produces extreme returns, in either direction, more often than a normal curve with the same standard deviation. So σ understates the chance of a crash.

Characteristics of an asset classmean and variance describe a normal distribution fully; real markets are not quite that

• Shape of the return distribution Memorize departures from the normal curve
  • Skewness asymmetry; equity returns lean negative (more big losses than big gains)
  • Kurtosis fat tails; extreme returns more often than a normal curve predicts
• Liquidity Memorize the cost of trading
  • Commission the broker’s fee
  • Bid–ask spread wider when trading is thin
  • Price impact how far a large order moves the price

Exam tip Negative skew and excess kurtosis together mean “more frequent large losses than a normal curve suggests”. Tools such as value at risk were built partly to capture the tail that σ misses.

What does liquidity cost?

Liquidity is how easily an asset can be traded without a big concession in price. The cost of trading has three parts: the brokerage commission, the bid–ask spread and the price impact . Liquidity drives the last two.

The spread is the gap between the price a buyer pays (ask) and a seller receives (bid). Compare it with the price, because what matters is its size relative to the price of the share.

$$\text{Spread} = \frac{\text{Ask} - \text{Bid}}{\text{Midpoint}}$$

Price impact is how far the price moves when you trade. A small order in a heavily traded share may not move the price at all. An order for a large part of a day’s volume forces the buyer to bid up the price to coax sellers. Large institutions feel this most, which is why a fund that holds small companies may not be able to grow beyond a certain size.

Liquidity is a bigger concern in emerging markets than in developed ones, and in corporate bond markets, especially lower-credit-quality issues, an individual bond may not trade for days or weeks.

Go deeper Why is the premium usually positive, and what are the exceptions?

Investors are risk averse, so they must be paid to hold risk and the premium on a risky asset is positive. The exception is an asset that pays off when the rest of the portfolio is doing badly, such as insurance or, historically, gold. Such an asset reduces total portfolio risk, so investors may accept a zero or even negative expected return on it. Lesson 4 returns to this.