CP

Stand-Alone Risk 113

The Trade-Off between Risk and Return

The table accompanying this box summarizes the historical
trade-off between risk and return for different classes of in-
vestments from 1926 through 2000. As the table shows, those
assets that produced the highest average returns also had the
highest standard deviations and the widest ranges of returns.
For example, small-company stocks had the highest average
annual return, 17.3 percent, but their standard deviation of
returns, 33.4 percent, was also the highest. By contrast, U.S.
Treasury bills had the lowest standard deviation, 3.2 percent,
but they also had the lowest average return, 3.9 percent.
When deciding among alternative investments, one
needs to be aware of the trade-off between risk and return.
While there is certainly no guarantee that history will repeat
itself, returns observed over a long period in the past are a
good starting point for estimating investments’ returns in
the future. Likewise, the standard deviations of past returns
provide useful insights into the risks of different invest-

ments. For T-bills, however, the standard deviation needs to

be interpreted carefully. Note that the table shows that Trea-

sury bills have a positive standard deviation, which indicates

some risk. However, if you invested in a one-year Treasury

bill and held it for the full year, your realized return would

be the same regardless of what happened to the economy

that year, and thus the standard deviation of your return

would be zero. So, why does the table show a 3.2 percent

standard deviation for T-bills, which indicates some risk? In

fact, a T-bill is riskless if you hold it for one year,but if you in-

vest in a rolling portfolio of one-year T-bills and hold the

portfolio for a number of years, your investment income will

vary depending on what happens to the level of interest rates

in each year. So, while you can be sure of the return you will

earn on a T-bill in a given year, you cannot be sure of the re-

turn you will earn on a portfolio of T-bills over a period of

time.

Distribution of Realized Returns, 1926–2000

Small- Large- Long-Term Long-Term U.S.

Company Company Corporate Government Treasury

Stocks Stocks Bonds Bonds Bills Inflation

Average

return 17.3% 13.0% 6.0% 5.7% 3.9% 3.2%

Standard

deviation 33.4 20.2 8.7 9.4 3.2 4.4

Excess return

over T-bondsa 11.6 7.3 0.3

aThe excess return over T-bonds is called the “historical risk premium.” If and only if investors expect returns in the

future that are similar to returns earned in the past, the excess return will also be the current risk premium that is

reflected in security prices.

Source:Based on Stocks, Bonds, Bills, and Inflation: Valuation Edition 2001 Yearbook(Chicago: Ibbotson Associates, 2001).

affects the way risk should be measured. Then, in Chapters 4 and 5, we will see how

risk-adjusted rates of return affect the prices investors are willing to pay for different

securities.

What does “investment risk” mean?

Set up an illustrative probability distribution for an investment.

What is a payoff matrix?

Which of the two stocks graphed in Figure 3-2 is less risky? Why?

How does one calculate the standard deviation?

Which is a better measure of risk if assets have different expected returns: (1) the

standard deviation or (2) the coefficient of variation? Why?

Explain the following statement: “Most investors are risk averse.”

How does risk aversion affect rates of return?

Risk and Return 111