Problem 2 (25 marks). Consider the following properties of the returns of stock
ID: 2821293 • Letter: P
Question
Problem 2 (25 marks). 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 Standard deviation of stock 2 Correlation between stock 1 and the market portfolio Correlation between stock 2 and the market portfolio Standard deviation of the market portfolio Expected return of stock 1 =0.30 2 0.30 ,m0.2 P2m0.5 o,n = 0.2 E(r)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 10 marks] 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? the market portfolio and the expected return of stock 2? [10 marks] FINA202 - Assignment 1 Cheng Zhang 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 [5 marks] variance of the combined portfolio.Explanation / Answer
1.
Beta of stock=Correlation of stock with market*Standard deviation of stock/Standard deviation of market
Hence, Beta of Stock 1=0.2*0.3/0.2=0.3
Beta of Stock 2=0.5*0.3/0.2=0.75
Expected returns of a stock=risk free+beta*(market return-risk free)
=>8%=5%+0.3*(market returns-5%)
=>market returns=15%
hence, market returns is 15%
Expected returns of Stock 2=5%+0.75*(15%-5%)=12.5%
2.
50% in Stock 1 and 50% in Stock 2:
Expected return of the portfolio=50%*8%+50%*12.5%=10.25%
Beta of the portfolio=50%*0.3+50%*0.75=0.525
Standard Deviation of portfolio=sqrt(weight of stock 1^2*standard devaition of stock 1^2+weight of stock 2^2*standard deviation of stock 2^2+2*weight of stock 1*weight of stock 2*correlation of stock 1 with stock 2*standard devaition of stock 1*standard deviation of stock 2)=sqrt(0.5^2*0.3^2+0.5^2*0.3^2+2*0.5*0.5*0.5*0.3*0.3)=0.259807621
3.
Let w be the proportion in market portfolio and 1-w be the proportion in portfolio in b)
Standard devaition of the combination of market portfolio and the portfolio in b)=sqrt(w^2*0.2^2+(1-w)^2*0.259808^2+2*w*(1-w)*0.2*0.525*0.2)
variance should be unchanged
hence,
sqrt(w^2*0.2^2+(1-w)^2*0.259808^2+2*w*(1-w)*0.2*0.525*0.2)=0.259808
=>w=1.41986
and 1-w=-0.41986
Hence, invest 141.986% in market portfolio and short -41.986% of portfolio in b)
Expected returns would become =1.41986*15%+(1-1.41986)*12.5%=16.05%
So, the returns increase with the same variance