pose that the S&P 500, with a beta of 1.0, has an expected return of 12% and T-b

Question

pose that the S&P 500, with a beta of 1.0, has an expected return of 12% and T-bills provide a risk-free return of 3%. a. What would be the expected return and beta of portfolios constructed from these two assets with weights in the S&P 500 of (i) 0; (ii) .25; (iii) .50; (iv) .75; (v) 1.0? (Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediate calculations. Round your answers to 2 decimal places.) Expected return Beta (i) 0 % (ii) .25 % (iii) .50 % (iv) .75 % (v) 1.0 % b. How does expected return vary with beta? (Do not round intermediate calculations.) The expected return by % for a one unit increase in beta.

Explanation / Answer

Let w be the weight of S&P500, portfolio beta will be=w*1+(1-w)*0=w
Portfolio return=w*S&P500return+(1-w)*riskfree=w*12%+(1-w)*3%=w*9%+3%

w=0: Beta=0, Returns=0*9%+3%=3%
w=0.25: Beta=0.25, Returns=0.25*9%+3%=5.25%
w=0.5: Beta=0.5, Returns=0.5*9%+3%=7.5%
w=0.75: Beta=0.75, Returns=0.75*9%+3%=9.75%
w=1: Beta=1, Returns=1*9%+3%=12%

Portfolio's expected return=w*9%+3% and as beta=w, so portfolio expected return=portfolio beta*9%+3%

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