Consider the following properties of the returns of stock 1, the returns of stoc
ID: 2815392 • Letter: C
Question
Consider the following properties of the returns of stock 1, the returns of stock 2 and the returns of the market portfolio (m):
Standard deviation of stock 1 1 = 0.30
Standard deviation of stock 2 2 = 0.30
Correlation between stock 1 and the market portfolio 1,m = 0.2
Correlation between stock 2 and the market portfolio 2,m = 0.5
Standard deviation of the market portfolio m = 0.2
Expected return of stock 1 E(r1) = 0.08
Suppose further that the risk-free rate is 5%.
a) According to the Capital Asset Pricing Model, what should be the expected return on the market portfolio and the expected return of stock 2?
b) Suppose that the correlation between the return of stock 1 and the return of stock 2 is 0.5. What is the expected return, the beta, and the standard deviation of the return of a portfolio that has a 50% investment in stock 1 and a 50% investment in stock 2?
c) Is the portfolio you constructed in part b) an efficient portfolio? Assuming the CAPM is true, could you build a combination of the market portfolio and the portfolio of part b) to increase the expected return of the market portfolio without changing the variance of the combined portfolio.(I want this answer)
Explanation / Answer
a) Capital Asset Pricing Model: E(Ri)=Rf+(SDc/SDm)*(E(Rm)-Rf) E(Ri)=Expected return of stock Rf=Risk free return SDc=Standard deviation of stock SDm=Standard deviation of market portfolio E(Rm)=Expected returnof market portfolio In this case , Rf=5%=0.05, E(R1)=0.08,SD1=0.3,SDm=0.2 0.08=0.05+(0.3/0.2)*(E(Rm)-0.05) E(Rm)-0.05=(0.08-0.05)/(0.3/0.2)=0.03/1.5=0.02 Expected Return on market portfolio=(0.05+0.02)= 0.07 Expected return of Stock 2=E(R2) E(R2)=0.05+(0.3/0.2)*(0.07-0.05)= 0.08 Expected return of Stock 2=E(R2) 8% Weight of Stock 1 in the portfolio 0.5 Weight of Stock 2 in the portfolio 0.5 Expected Return of the portfolio =0.5*8+0.5*8= 8% Beta of Stock 1=B1 Beta of stock 2=B2 Rs=Rf+Beta*(Rm-Rf) Rs=return of stock=8% Rf=risk free rate=5% Rm-Rf=7-5=2% 8=5+B1*2 B1=1.5,B2=1.5 Portfolio Beta=0.5*1.5+0.5*1.5=1.5 Correlation of retrn of stock 1 &2=0.5 Standard Deviation of stock 1=SD1=0.3 Standard deviation of stock 2=SD2=0.3 Correlation(1,2)=Covariance(1,2)/(SD1*SD2) Covariance(1,2)=0.5*0.3*0.3= 0.045 Portfolio Variance=(w1^2)*(SD1^2)+(w2^2)*(SD2^2)+2w1w2*Cov(1,2) w1=Weight of stock1 in the portfolio=0.5 w2=Weight of stock2 in the portfolio=0.5 SD1=Standard deviation of stock 1=0.3 SD2=Standard deviation of stock 2=0.3 Cov(1,2)=Covariance of return of stock 1and2= 0.045 Portfolio variance=(0.5^2)*(0.3^2)+(0.5^2)*(0.3^2)+2*0.5*0.5*0.045 Portfolio variance= 0.0675 Portfolio Standard Deviation=Square Root of Variance Portfolio Standard Deviation=Square Root(0.0675)= 0.259808 Vp=(w1^2)*0.09+(w2^2)*0.09+2w1w2*0.045 SDp=Square Root (Vp) Rp=w1*0.08+w2*0.08 w1 w2 Vp SDp Rp Rp/SDp Weight of Stock 1 in the portfolio Weight of Stock2 Portfolio Variance Portfolio Standard Deviation Portfolio Return Return/Risk 0 1 0.09 0.3 0.08 0.266666667 0.1 0.9 0.0819 0.286182 0.08 0.279542623 0.2 0.8 0.0756 0.274955 0.08 0.290957187 0.3 0.7 0.0711 0.266646 0.08 0.30002344 0.4 0.6 0.0684 0.261534 0.08 0.305887645 0.5 0.5 0.0675 0.259808 0.08 0.307920144 0.6 0.4 0.0684 0.261534 0.08 0.305887645 0.7 0.3 0.0711 0.266646 0.08 0.30002344 0.8 0.2 0.0756 0.274955 0.08 0.290957187 0.9 0.1 0.0819 0.286182 0.08 0.279542623 1 0 0.09 0.3 0.08 0.266666667 Portfolio Return isconstant at 0.08=8% Risk is lowest when weight of each stock is=0.5 (Return/risk) is highest at weight of each stock=0.5 Hence, this is the efficient portfolio of stock 1 and2