Consider the following questions about CAPM: 1. What is the equilibrium relation
ID: 2820344 • Letter: C
Question
Consider the following questions about CAPM:
1. What is the equilibrium relationship between return and risk that must hold for every risky asset in a perfect market?
2. Define systematic and non-systematic risk.
3. Suppose that the annual returns on two stocks (A and B) are perfectly negatively correlated, and that rA = 0.05, rB = 0.15, A = 0.1, B = 0.4. Assuming that there are no arbitrage opportunities, what must the one-year interest rate be?
4. The expected return on the market portfolio, rm is 13%. The standard deviation of the market return, m, is 0.20. The covariance of a well-diversified portfolio with the market, mp, is 0.03. What is the expected return on the portfolio? Use the answer from part 3
Explanation / Answer
1.
Return=riskfree+beta*market risk premium
The required return according to risk should be equal to expected return or every investor should be compensated fairly in terms of returns-not more not less for the risk of the asset
2.
Systematic Risk-Risk applicable to all the firms or market risk and hence cannot be diversified
Unsystematic risk-Unique risk and arises from specific companies and can be diversified
3.
In case of perfect negative correlation:
standard deviaiton of portoflio=weight of asset A*standard deviation of asset A-weight of asset B*standard deviaiton of asset B
Risk free asset has standard deviation of zero
so we have to construct a portfolio with zero standard deviation
Weight of A*0.1-(1-weight of A)*0.4=0
weight of A=0.8
Returns of the portfolio=0.8*5%+(1-0.8)*15%=7%
hence, risk free rate or 1 year interest rate=7%
4.
Beta=Covariance of Portfolio with the market/standard deviaiton of the market^2=0.03/(0.2*0.2)=0.75
Retrun=riskfree+beta*(market return-risk free)=7%+0.75*(13%-7%)=11.5%