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 investments 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 Treasury 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 invest 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 return 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?

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Responses

  • hal
    What was the average return for the tbills between 2000 2011?
    7 years ago
  • terry
    How does risk aversion affect rates of return on securities?
    7 years ago
  • mathias
    Is there a tradeoff between risk and return?
    6 years ago

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