ECON_134b_-_Section_Problem_Solutions

ECON_134b_-_Section_Problem_Solutions - Q1 The expected...

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Q1. The expected return on a portfolio that combines the risk-free asset and the asset at the point of tangency to the efficient set is 25%. The expected return was calculated under he following assumptions: The risk-free rate is 5%. The expected return on the market portfolio of risky assets is 20%. The standard deviation of the efficient portfolio is 4%. In this environment, what expected return would a security earn if it had a correlation coefficient of 0.5 with the market and a standard deviation of 2%? There are many ways to solve this. This method pulls together our class discussion on the CML and the SML. We are given some security - call it 's' and we have to find its expected return. Ask - will this security plot on the CML? Explain that it will not - why? Because it is not efficient, but in THIS environment (for a given Rf and Rm) we can use the capm/sml to value it. CAPM equation: E(rs) = beta*(Rm-Rf) + Rf We know rf, rm and all the components of beta except sigma m. We can use the Sharpe ratio to calculate sigma m. Beta = p*sigma m*sigma s/sigma^2 m = 0.5*0.03*0.02/0.03^2 = (1/3) E(rs) = (1/3)*(0.20-0.05) + 0.05 = 0.10
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Q2, The following data have been developed for the Burnham Company. Variance of market returns = 0.04326 Covariance of the returns on Burnham and the market = 0.0635. The market risk premium is 9.4 percent. Assume that the return on Treasury bills is 4.9 percent. a. Write the equation of the security market line. b. What is the required return of Burnham Company? a) CAPM equation: E(Rb) = beta*(rm-rf) + rf Thus, E(Rb) = beta*(9.4) + 4.9 b) If we can calculate beta, we can use SML to calculate expected return Beta = Covar(b,m)/Var(m) = 0.0635/0.04326 = 1.47 E(Rb) = 1.47*9.4 + 4.9 = 18.70% Q3. Mila Kunis has a $900,000 fully diversified portfolio. She subsequently inherits Soviet Mamba Company (SMC) common stock worth $100,000. Her financial adviser provided her with the following information: Expected Return Standard Deviation Original Portfolio 0.67 2.37 SMC 1.25 2.95 Correlation of Original Portfolio with SMC = 0.4 a) What is the expected return of her new portfolio? b) What is the covariance of the SMC stock returns with the original portfolio? c) What is the standard deviation of her new portfolio which includes the SMC stock?
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Weights: Wop = 900k/1000k = 0.90, Wsmc = 100k/1000k = 0.10 a) E(Rnp) = Wop*E(Rop) + Wsmc*E(Rsmc) = 0.9*0.67 + 0.1*1.25 = 0.73 b) Covar(op,smc)=rho*sigma(op)*sigma(smc)= 0.4*2.37*2.95 = 2.80 c) Var(np) = Wop*sd(op) + Wsmc*sd(smc) + 2Wop*Wsmc*cov(op,smc) = (0.9*2.37) 2 + (0.1*2.95) 2 + 2*0.9*0.1*0.4*2.37*2.95 = 5.14 SD(np) = sqrt(5.14) = 2.27 Notice this is less than the weighted average of the standard deviations = 0.9*2.37 + 0.1*2.95 = 2.43
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This note was uploaded on 12/05/2011 for the course ECON 134b taught by Professor Johnhartman during the Fall '11 term at UCSB.

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ECON_134b_-_Section_Problem_Solutions - Q1 The expected...

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