Question

Risk and Rates of Return: Security Market Line The security market line (SML) is an equation that shows the relationship between risk as measured by beta and the required rates of return on individual securities. The SML equation is given below: ​

If a stock's expected return plots on or above the SML, then the stock's return is (Pick one: sufficent / insufficient) to compensate the investor for risk. If a stock's expected return plots below the SML, the stock's return is (Pick one: sufficent / insufficient) to compensate the investor for risk.

The SML line can change due to expected inflation and risk aversion. If inflation changes, then the SML plotted on a graph will shift up or down parallel to the old SML. If risk aversion changes, then the SML plotted on a graph will rotate up or down becoming more or less steep if investors become more or less risk averse. A firm can influence market risk (hence its beta coefficient) through changes in the composition of its assets and through changes in the amount of debt it uses.

Quantitative Problem: You are given the following information for Wine and Cork Enterprises (WCE):

rRF = 3%; rM = 10%; RPM = 7%, and beta = 1.3

What is WCE's required rate of return? Round your answer to 2 decimal places. Do not round intermediate calculations. _______%

If inflation increases by 3% but there is no change in investors' risk aversion, what is WCE's required rate of return now? Round your answer to two decimal places. Do not round intermediate calculations. _______%

Assume now that there is no change in inflation, but risk aversion increases by 1%. What is WCE's required rate of return now? Round your answer to two decimal places. Do not round intermediate calculations. _______%

If inflation increases by 3% and risk aversion increases by 1%, what is WCE's required rate of return now? Round your answer to two decimal places. Do not round intermediate calculations. _______%

Answer 1

According to CAPM, expected return on the stock is given by:

Expected return = risk free rate + beta * market risk premium

a). Expected return = 3% + [1.3 x 7%] = 3% + 9.1% = 12.1%

b). If inflation increases by 3%:

Risk free rate, rf = 3 + 3 = 6%

r = 6% + [1.3 x 7%] = 6% + 9.1% = 15.1%

c). If risk aversion increases by 1%:

Market risk premium, rpm = 7% + 1% = 8%

r = 3% + [1.3 x 8%] = 3% + 10.4% = 13.4%

d). If inflation increases by 3% and risk aversion increases by 1%:

Risk free rate, rf = 3 + 3 = 6%

Market risk premium, rpm = 7% + 1% = 8%

r = 6% + [1.3 x 8%] = 6% + 10.4% = 16.4%