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Set out how the main asset classes have performed historically in terms of risk and return

CFA® Level I · Portfolio Management · Portfolio Risk and Return: Part I · PM.8.c

The idea

Long runs of historical data show a consistent ordering. Small-company stocks have earned the highest average returns with the highest volatility, followed by large-company stocks, then long-term government bonds, with short-term Treasury bills lowest on both counts; bills have barely kept pace with inflation, so their real return has been close to zero. The trade-off holds on average over long horizons, not in every period, and a decade in which bonds beat equities does not overturn it. Several cautions apply when reading these figures. Nominal returns should be converted to real by (1 + nominal) / (1 + inflation) - 1. The geometric mean, which is what an investor compounds, falls below the arithmetic mean by more the more volatile the asset. Equity returns show fat tails and negative skewness rather than a normal distribution. And long records drawn from one successful market carry survivorship bias.

A practice question

From the question bank, with the reason each wrong option is wrong.

Which ranking of average returns from highest to lowest is consistent with long-run historical data?

  1. Small stocks, large stocks, bonds, bills — correct
  2. Large stocks, small stocks, bills, bondsWhy not: Reverses both pairs: small stocks have out-earned large, and bonds have out-earned bills.
  3. Bonds, large stocks, small stocks, billsWhy not: Puts long-term government bonds above equities, the reverse of the long-run record.

Higher average return has historically come with higher volatility: small-cap equity at the top, then large-cap equity, long-term government bonds and Treasury bills.

A harder one

Over one ten-year period, long-term government bonds outperformed equities. What is the best inference?

  1. Equities no longer carry a risk premium at allWhy not: Generalises from one period; a risk premium is an average that can be negative for years.
  2. Bonds are now riskier than equities areWhy not: Confuses realised return with risk; bonds' higher return says nothing about volatility.
  3. The long-run trade-off need not hold every decade — correct

The historical risk-return relationship is a long-run average. Because equities are risky, there will be periods, even long ones, in which they underperform safer assets.

The hardest tier

An equity index returned +40% in one year and -20% in the next. What was its geometric mean annual return?

  1. 10.00%Why not: This is the arithmetic mean, which overstates what an investor actually compounded.
  2. 5.83% — correct
  3. 20.00%Why not: Adds the two returns without averaging or compounding them.

Geometric mean = (1.40 x 0.80)^0.5 - 1 = 1.12^0.5 - 1 = 5.83%. The gap from the 10% arithmetic mean widens with volatility, which is why equities show the largest gap.

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