Suppose the return on portfolio P has the following probability distribution: Be
ID: 2644865 • Letter: S
Question
Suppose the return on portfolio P has the following probability distribution:
Bear Market
Normal market
Bull market
Probability
0.2
0.5
0.3
Return on P
-20%
18%
50%
Assume that the risk-free rate is 9%, and the expected return and standard deviation on the market portfolio M is 0.19 and 0.20, respectively. The correlation coefficient between portfolio P and the market portfolio M is 0.6.
Answer the following questions:
Is P efficient?
What is the beta of portfolio P?
What is the alpha of portfolio P? Is P overpriced or underpriced?
Bear Market
Normal market
Bull market
Probability
0.2
0.5
0.3
Return on P
-20%
18%
50%
Explanation / Answer
Expected return on Portfolio P = (0.2 x -20%) + (0.5 x 18%) + (0.3 x 50%) = 30%
Variance of P = 0.2 x (-20% - 30%)2 + 0.5 x (18% - 30%)2 + 0.3 x (50% - 30%)2
= 0.2 x 0.25 + 0.5 x 0.0144 + 0.3 x 0.04 = 0.05 + 0.0072 + 0.012 = 0.0692
Standard Deviation of P = Square root of Variance = 0.2631
(a) Expected Return on market portfolio is 19% but P's expected return is 30%. So P is not efficient.
(b), Beta of P = Correlation coefficient between Market and P x (Standard Deviation of P's returns / Standard Deviation of Market returns)
= 0.6 x (0.2631 / 0.20) = 0.7892
(c) Alpha of P = Excess return = 30% - 19% = 11%
(d) CAPM Return on P = Risk Free Rate + Beta x (Expected Return of Market portfolio - Risk Free Rate ) = 9% + 0.7892 x (19% - 9%) = 16.89%
Since CAPM Return < Expected return, P is overpriced.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.