Security A is priced such that it has an expected return of 11%. The standard de
ID: 2790381 • Letter: S
Question
Security A is priced such that it has an expected return of 11%. The standard deviation of its returns is 15%. Its returns have a coefficient of correlation of 0.80 with returns on the market index or portfolio. Security B is priced such that it has an expected return of 5%. The standard deviation of its returns is 20%. Its returns have a coefficient of correlation of 0.25 with returns on the market index or portfolio. The standard deviation of returns on the market index or portfolio is 10%. The risk free rate is 3.00% and the expected market risk premium is 5.25%.
1) We can say that (NO calculation required):
A. Security A has greater total risk than does Security B.
B. Security A has less total risk than does Security B.
C. Security A and Security B have the same amount of total risk.
D. No statement can be made about the relative total risk of the two securities.
2) Security A has a beta of: 37. Security B has a beta of:
3)The equilibrium expected return on Security A should be:
4) The equilibrium expected return on Security B should be:
5) Which of the following is true, based on the Capital Asset Pricing Model?
A. Security A is overpriced and Security B is underpriced.
B. Security A is underpriced and Security B is overpriced.
C. Both Securities A and B are underpriced.
D. Both Securities A and B are overpriced.
Explanation / Answer
1)
Option B
Security A has less total risk than does Security B. As standard deviation of A is lower than standard deviation of B
2)
Beta = Corelation * (standard deviation of stock / standard deviation of market)
Beta A = 0.8*(15%/10%) = 1.2
Beta B = 0.25*(20%/10%) = 0.5
3 & 4)
Return on equity = risk free rate + Beta * Market risk premium
Ra = 3% + 1.2*5.25% = 9.3%
Rb = 3% + 0.5*5.25% = 5.625%
5)
Option B
expected return of 11% is higher than Ra (9.3%) = underpriced
expected return of 5% is lower than Rb (5.625%) = overpriced