(Lecture note chapter 7 pages 15 22 chapter 8 pages 16-18. Recitation lecture no
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(Lecture note chapter 7 pages 15 22 chapter 8 pages 16-18. Recitation lecture note pages 17-19 ) Stock X has an expected return of 7%. a standard deviation of return of 10% and a beta of 2. Stock Y has an expected return of 6%. a standard deviation of return of 20% and a beta of 1.5. The correlation coefficient between the two stocks is 0.5. If you invest 60% of your funds in stock X and 40% in stock Y. Assume risk free rate is 1% and market risk premium is 4% what is the expected return of your portfolio? what is the standard deviation of your portfolio? Calculate the Sharpe ratios for stock X. stock Y AND >our portfolio (0.5) what is the beta of your portfolio? (0.5) what is the expected return of your portfolio, according to CAPM?Explanation / Answer
a. Expected Return of the porfolio is W1*R1 + W2*R2
Where W1 is weight if stock X = 60% =0.6
R1 is the return of X =7% =0.07
W2 =Weight of Y = 0.4
R2 is the return of Y = 6% =0.06
Hence return is 0.07*0.6 + 0.06*0.4 = 0.066 = 6.6%
b. Porfolio Std. deviation is given by = sqrt(w1^2*sd1^2 + w2^2*sd2^2 + 2*w1*w2*corr*sd1*sd2)
w1 =0.6, w2 = 0.4, sd1 = 10% =0.1, sd2 = 20% =0.2. correlation = corr =0.5
Hence Std. deviation of the portfolio is sqrt(0.6^2*0.10^2+ 0.4^2*0.2^2+ 2*0.4*0.6*0.5*0.1*0.2) = 0.1216
Hence Std. deviation of the portfolio is 12.16%
c.Sharpe for X is (rx-rf)/std.dev(x) where rx is return of X which is = 7% = 0.07 and rf =0.01 and std.dev of X =10%=0.1
Hence Sharpe for X (0.07-0.01)/0.1 =0.6
Similarly Shape for Y is (0.06-0.01)/0.2 = 0.25
d.Beta of the portfolio is calculated in the same manner in which we calculate the portfolio return
so it would 2*0.6 + 1.5*0.4 = 1.8
e.As per CAPM
Retrun on portfolio= Rf + beta * market premium
= 0.01 + 1.8(0.04) = 0.082 =8.2%
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