Question

4. Your rich uncle asks you for financial advice. He is currently holding a portfolio of 30% T-bills and 70% Microsoft stock. The beta of Microsoft is 1.2 and the standard deviation is 37.95%. You decide to base your advice on the CAPM. The T-bill rate is 5%. The market portfolio has expected return 15% and standard deviation 20%. (a) What is the expected return of your uncle's portfolio? (b) What is the standard deviation of your uncle's portfolio? (c) You decide to recommend to your uncle a portfolio that has the same expected return as his portfolio but the lowest possible standard deviation. What is this portfolio, and what is its standard deviation?

Answer 1

1.
return on Microsoft=risk free rate+beta*(market return-risk free rate)=5%+1.2*(15%-5%)=17%
Expected return=weight in Tbills*return on Tbills+weight in Microsoft*return on Microsoft
=30%*5%+70%*17%=13.40000%

2.
=weight of Microsoft*standard deviation of Microsoft
=70%*37.95%=26.56500%

3.
Let w be the weight in market portfolio
w*15%+(1-w)*5%=13.40000%
=>w=(13.40000%-5%)/(15%-5%)
=>w=0.84000000

84% in market portfolio and 16% in T-bills

Standard deviation=weight of market portfolio*standard deviation of market portfolio=84%*20%=16.80000%