Question

Suppose that the expected return and standard deviation of the market are 10 percent and 16 percent, respectively. Stock A has a standard deviation of 45 percent and a correlation with the market of 0.64. What would the expected return of a portfolio that is equally split between stock A, the market and a risk-free Treasury bill be if the risk-rate is 4%?

Answer 1

Given that,

Expected return on market Rm = 10%

standard deviation of market SDm = 16%

Standard deviation of stock A SDa = 45%

correlation of stock A with market Corr(a,m) = 0.64

=> Beta of stock A with market is Corr(a,m)*SDa/SDm = 0.64*45/16 = 1.80

Beta of market is 1

Beta of risk free asset T-Bill = 0

Risk free rate Rf = 4%

For a portfolio with equally split between stock A, the market and a risk-free Treasury bill, beta of portfolio is weighted average of its assets,

So, beta of portfolio is (Beta of stock A + Beta of market + beta of risk free asset)/3 = (1.8 + 1 + 0)/3 = 0.9333

So, expected return of the portfolio using CAPM is

E(p) = Rf + beta*(Rm - Rf) = 4 + 0.9333*(10-6) = 9.6%

expected return of a portfolio = 9.6%