The Relationship between Risk and Rates of Return (2)
by MaestriThe required return for Stock i can be written as follows:
ri = 6% + (11% – 6%)(0.5)
= 6% + 5%(0.5)
= 8.5%.
If some other Stock j were riskier than Stock i and had bj 2.0, then its required rate of return would be 16 percent:
rj = 6% + (5%)2.0 = 16%.
An average stock, with b 1.0, would have a required return of 11 percent, the same as the market return:
rA = 6% + (5%)1.0 = 11% = rM.
As noted above, Equation 3-9 is called the Security Market Line (SML) equation, and it is often expressed in graph form, as in Figure 3-12, which shows the SML when rRF 6% and rM 11%. Note the following points:
- Required rates of return are shown on the vertical axis, while risk as measured by beta is shown on the horizontal axis. This graph is quite different from the one shown in Figure 3-9, where the returns on individual stocks were plotted on the vertical axis and returns on the market index were shown on the horizontal axis. The slopes of the three lines in Figure 3-9 were used to calculate the three stocks’ betas, and those betas were then plotted as points on the horizontal axis of Figure 3-12.
- Riskless securities have bi 0; therefore, rRF appears as the vertical axis intercept in Figure 3-12. If we could construct a portfolio that had a beta of zero, it would have an expected return equal to the risk-free rate.
- The slope of the SML (5% in Figure 3-12) reflects the degree of risk aversion in the economy—the greater the average investor’s aversion to risk, then (a) the steeper the slope of the line, (b) the greater the risk premium for all stocks, and (c) the higher the required rate of return on all stocks.14 These points are discussed further in a later section.
- The values we worked out for stocks with bi 0.5, bi 1.0, and bi 2.0 agree with the values shown on the graph for rL, rA, and rH.
Both the Security Market Line and a company’s position on it change over time due to changes in interest rates, investors’ aversion to risk, and individual companies’ betas. Such changes are discussed in the following sections.
Taken From : Five-Minute MBA – Corporate Finance
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