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CAPM_examples_sol

# CAPM_examples_sol - portfolio is not efficient Efficient...

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1. The expected return on the market portfolio M is E(R M ) = 12%, the standard deviation of M is σ M = 16%, and the risk-free rate is R f = 4%. The CAPM is assumed to hold. a) Suppose that there is a portfolio with an expected return of 16% and variance of 0.04. Is this possible under the CAPM? If so, is this an efficient portfolio? The Sharpe ratio of the market is: S(M) = E(Rm-Rf)/SD(Rm) = (0.12-0.04)/0.16 = 0.5 The Sharpe ratio of this portfolio is: S(P) = E(Rp-Rf)/SD(Rp) = (0.16-0.04)/sqrt(0.04) = 0.6 The CAPM says that the market has the highest Sharpe ratio, so it is not possible for this portfolio to exist under the CAPM. b) Suppose that another portfolio has a beta of 0.8 and a standard deviation of 16%. Is this possible under the CAPM? If so, is this an efficient portfolio? The expected return of the portfolio is: E(Rp) = Rf + bp*E(Rm-Rf) = 0.04 + 0.8*(0.12-0.04) = 0.104 The Sharpe ratio of this portfolio is: S(P) = E(Rp-Rf)/SD(Rp) = (0.104-0.04)/0.16 = 0.4 Since this is lower than the Sharpe ratio of the market, this is possible. But the

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Unformatted text preview: portfolio is not efficient. Efficient portfolios have the same Sharpe ratio as the market. 2. The expected market risk premium is E(R M-R f ) = 9%. The variance of the market is 0.0484. Assume that the CAPM holds. Suppose that an efficient portfolio P has a standard deviation σ P = 30%, and a correlation with the market portfolio of 0.55. Compute the beta and the expected risk premium of portfolio P. bp = Cov(Rp, Rm)/V(Rm) = Corr(Rp, Rm)*SD(Rp)*SD(Rm)/V(Rm) = Corr(Rp, Rm)*SD(Rp)/SD(Rm) = 0.55*0.30/sqrt(0.0484) = 0.75 E(Rp-Rf) = bp*E(Rm-Rf) = 0.75*0.09 = 0.0675 3. Assume that the CAPM holds. a) Is this situation possible under the CAPM: If two assets have the same beta, they must have the same risk premium under the CAPM. So this situation is not possible. b) Is this situation possible under the CAPM: For B, E(RB-Rf) = bB*E(Rm-Rf) = 0.45*0.07 = 0.0315 Since this is not equal to 0.0355, this situation is not possible....
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CAPM_examples_sol - portfolio is not efficient Efficient...

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