In: Finance
Consider the following information on Stocks X and Y: State of Economy Probability of State of Economy Rate of Return if State Occurs Stock X Stock Y Recession 0.24 0.065 −0.29 Normal 0.69 0.365 0.21 Irrational exuberance 0.07 0.225 0.49 The market risk premium is 11.9 per cent and the risk-free rate is 4.9 per cent. a. Calculate the expected return, beta and standard deviation of stock X. (Do not round intermediate calculations. Enter the expected returns and standard deviations as a percentage. Round your answers to 2 decimal places (e.g., 32.16).) • Expected return of Stock X % • Beta of Stock X • Standard Deviation of Stock X% b. Calculate the beta and standard deviation of Stock Y. (Do not round intermediate calculations. Enter the standard deviation as a percentage without the % sign. Round your answers to 2 decimal places (e.g., 32.16).) Expected Return of Stock Y % Beta of Stock Y Standard Deviation of Stock Y % c. Which stock has the most systematic risk? Stock d. Which one has the most unsystematic risk? Stock e. Which stock is “riskier”? Stock
Please see the table below. The rows highlighted in yellow contain your answer. Figures in parenthesis, if any, mean negative values.Adjacent cells in blue contain the formula in excel I have used to get the final output.
Expected return = Risk free rate + Beta x Market risk premium
For X:
28.32% = 4.9% + beta x 11.9%
hence, beta = (28.32% - 4.9%) / 11.9% = 1.97
For Y:
10.96% = 4.9% + beta x 11.9%
hence, beta = (10.96%% - 4.9%) / 11.9% = 0.57
Stock X has higher systematic risk, since its beta is higher and beta is a measure of systematic risk.
Total risk of the stock is measured using standard deviation. Further total risk = systematic risk + unsystematic risk. Stock Y has higher standard deviation and hence higher total return. It has lowr beta and hence lower systematic risk. Hence, stock Y should have higher unsystematic risk (= total risk - systematic risk).
A stock with higher standard deviation is riskier. Hence, stock Y is riskier.