Question

谁帮我解决这道题吧，是公司金融的：

your investmnet porfolio of $15,000 invested in only one stock-Microsoft.Suppose the risk-free rate is 5%,Microsoft stock has an expected reurn of 12% and a volatility of 40%,and the market porfolio has an expected return of 10% and a volatility of 18%.Under the CAPM assumption
a.What alternative investment has the lowest possible volatility while having the same expected return as MS?what is the volatility of this investment
b.what investment has the highest possible expected return while having the same volatility as MS?what is the expected return of this investment?

Answer 1

很基本的题,就考了个对return和variance的理解
a. 5%*w1+10%*(1-w1)=12% ==> w1=-40% 15,000*-0.4=-6,000
short 6,000 risk-free asset and long 21,000 market portfolio will replicate the MS investment return.
Vol of risk free asset = 0
(1-w1)^2*Vol(market)=1.4^2*18%=35.28%, the vol of this investment is 35.28%

b. Similar, (1-w1)^2*Vol(market)=40% ==> w1=-50%
short 7,500 risk-free asset and long 22,500 market portfolio will have the same volatility of MS investment with highest return=5%*-0.5+10%*1.5=12.5%