Suppose that the S&P 500, with a beta of 1.0, has an expected return of 12% and

Question

Suppose 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 4%. 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 %

Explanation / Answer

Weight of S&P500 is 0:
Beta of portfolio=0*1+1*0=0
Return=0*12%+1*4%=4%

Weight of S&P500 is 0.25:
Beta of portfolio=0.25*1+0.75*0=0.25
Return=0.25*12%+0.75*4%=6%

Weight of S&P500 is 0.50:
Beta of portfolio=0.50*1+0.50*0=0.50
Return=0.50*12%+0.50*4%=8%

Weight of S&P500 is 0.75:
Beta of portfolio=0.75*1+0.25*0=0.75
Return=0.75*12%+0.25*4%=10%

Weight of S&P500 is 1.00:
Beta of portfolio=1*1+0*0=1
Return=1*12%+0*4%=12%

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