Question

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:

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If a stock's expected return plots on or above the SML, then the stock's return is -Select-insufficientsufficientCorrect 1 of Item 1 to compensate the investor for risk. If a stock's expected return plots below the SML, the stock's return is -Select-insufficientsufficientCorrect 2 of Item 1 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):

r_RF = 2%; r_M = 8%; RP_M = 6%, and beta = 1.3

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

%

If inflation increases by 2% but there is no change in investors' risk aversion, what is WCE's required rate of return now? Do not round intermediate calculations. Round your answer to two decimal places.

%

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

%

If inflation increases by 2% and risk aversion increases by 1%, what is WCE's required rate of return now? Do not round intermediate calculations. Round your answer to two decimal places.

%

Answer 1

Required rate of return is given by the following formula

ER; = R + Bi(ERM – Rp) where: ER; = expected return of investment R; = risk-free rate Bi = beta of the investment (ERM - Rj) = market risk premium

1) Plugging in all the values in above equation, we get the ER as follows

ER = 2% + 1.3 (8%-2%) = 9.8%

2) We adjust the given Rfr and market return rates for inflation of 2%

ER = (2%+2%) + 1.3 (10%-4%) = 11.8%

3) Increase in risk aversion is adjusted in the incremental risk free rate rate

ER = (2%+1%) + 1.3 (8%-3%) = 9.5%

4) In case both inflation and risk aversion are added, we adjust Rfr for both and market return for inflation

ER = (2%+1%+2%) + 1.3 (10%-5%) = 11.5%