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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