The Risk-return Tradeoff

When you use the standard deviation, range of returns, and the beta coefficient to measure risk, you can get a better sense of investment risk and expected rates of return. However, you already know that choosing riskier investments does not necessarily mean that you will always receive greater returns. The risk-return tradeoff relates directly to your expected or required rate of return on the investments you purchase and hold. In order to invest in a riskier investment, you would expect a greater rate of return. The required rate of return is the minimum rate of return necessary to purchase a security. This minimum rate of return includes the rate earned on a risk-free investment, which is typically a Treasury security, plus the risk premium associated with that investment. The risk premium is the added return that is related to the risk for that particular investment:

Required rate of return = risk-free rate + risk premium

For example, you may require a 10 percent rate of return for all stock investments. If the risk-free rate is 3 percent, the risk premium for the stocks you purchased is 7 percent. Figure 5–1 shows that the stocks you are willing to purchase must have a beta coefficient equal to that of the market in order to obtain the 10 percent expected return (market beta is 1 multiplied by the risk premium of 7 percent plus the risk-free rate of 3 percent to equal the required or expected rate of return of 10 percent). If you purchased stocks with a beta coefficient of 1.5, the risk premium would be 10.5 percent (1.5 * 7 percent), which is one and a half times the market risk. The preceding equation on the required rate of return can be expanded to include the beta coefficient:

Required rate of return = risk-free rate + beta coefficient * (market rate - risk-free rate)

Historic returns for stocks, confirm the risk-return tradeoff. That is, over long periods of time, the greater the risk taken, the greater are the expected returns.

However, this rule may not always hold over short periods of time and in down markets. Large- and small-cap stocks had real average annual returns of 7.7 and 9.1 percent over a 74-year period respectively from 1926 to 2000 versus 2.2 percent for intermediateterm government bonds, as quoted by Ibbotson and Sinquefield (1994). Real rates of return are nominal rates minus the rate of inflation. Risk, however, is greatest for stocks of small companies, followed by large-company stocks, as evidenced by the standard deviations of returns.

Figure 5-1
Relationship between Risk and Expected Returns



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