he following are estimates for two stocks. The market index has a standard devia
ID: 2786664 • Letter: H
Question
he following are estimates for two stocks.
The market index has a standard deviation of 23% and expected return of 7%. Risk free rate is 2%.
a. What are standard deviations of stock A and B.
b. What is the correlation coefficient between stock A and B.
c. Suppose we construct a portfolio with the 30% A and 40% B and 30% risk free rate. Compute the expected return, standard deviation, and beta for the portfolio.
Please explain in detail.
stock expected return Beta Firm-Specific standard deviation A 14% 0.8 20% B 19% 1.3 25%Explanation / Answer
ca). The standard deviation of each individual stock is given by
b) COV (RA,RB) = (0.14 - 0.07) x (0.19 - 0.07) = 0.0084
Correlation Coefficient = 0.0084/(0.14x0.19) = 0.32
c) The expected return of the portfolio = WiRi = 0.3x0.14+0.4x0.19+0.3x0.07 = 13.9%
The beta of the portfolio = WiBetai = 0.3x0.8+0.4x1.2+0.3x0.00 = 0.76
The expected variance of the portfolio = Wi2(ei)2 = 0.32x0.22 + 0.42x0.252 + 0.32x0 = 0.0136
Standard Deviation = SQRT(0.0136) = 11.66%
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