Suppose that the S&P 500, with a beta of 1, has an expected return of 18% and T-

Question

Suppose that the S&P 500, with a beta of 1, has an expected return of 18% and T-bills provide a risk-free return of 5%.

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) 0.25; (iii) 0.5; (iv) 0.75; (v) 1? (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 2 decimal places.)

On the basis of your answer to (a), what is the trade-off between risk and return, that is, how does expected return vary with beta?

Suppose that the S&P 500, with a beta of 1, has an expected return of 18% and T-bills provide a risk-free return of 5%.

Explanation / Answer

The expected return of the portfolio is equal to the weighted average of the returns on the S&P 500 and T-bills. Similarly, the beta of the portfolio is equal to the weighted of the S&P 500 and T-bills.

(i) weight in S&P = 0 , then BETA = 0

expected return = 0*18%+1*5%=5%

(ii) weight in S&P = 0.25 , then BETA = 0.25

expected return = 0.25*18%+0.75*5%=8.25%

(iii) weight in S&P = 0.50 , then BETA = 0.50

expected return = 0.50*18%+0.50*5%=11.5%

(iv) weight in S&P = 0.75 , then BETA = 0.75

expected return = 0.75*18%+0.25*5%=14.75%

(v) weight in S&P = 1 , then BETA = 1

expected return = 1*18%+0*5%=18%

b. For every increase of 0.25 in the of the portfolio, the expected return increases by 3.25%The slope of the relationship (additional return per unit of additional risk) is therefore 13%

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