Assume that the assumptions of the CAPM hold. The expected return and the standard deviation of...
Assume that the assumptions of the CAPM hold. The expected return and the standard deviation of the market portfolio are 7% and 14%, respectively. There are two individual stocks A and B:
Mean Return A: 4% Standard Deviation A: 18%
Mean Return B: 12% Standard Deviation B: 36%
Stock A has a correlation of 0.2 with the market portfolio.
A.What is the beta of stock A?
B.What is the risk free rate?
C.What is the beta of a portfolio with 40% in stock A and 60% in stock B?
D.What is the idiosyncratic volatility of the portfolio from part C?
Homework Answers
A.
Beta = Covariance(Stock returns, market portfolio returns)/Variance(Stock Returns)
Covariance(Stock returns, market portfolio returns) = Correlation(Stock returns, market portfolio returns)*Standard Deviation of Stock Returns*Standard Deviation of Market Portfolio
b.
Using CAPM
Expected Stock Return = Risk Free Rate +Beta*(Market Returns - Risk Free Rate)
Risk free rate = [Expected Stock return - Beta*Market Return]/(1 - Beta)
c.
Using CAPM
Beta = (Expected Return - Risk Free Rate)/(Market Returns - Risk Free Rate)
D.
Idiosyncratic Volatility = Total Variance - Market Variance
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