7. (3+3+3+2) Your employer offers two funds for your pension plan, a money market fund and...

7. (3+3+3+2) Your employer offers two funds for your pension plan, a money market fund and an S&P 500 index fund. The money market fund holds 3- month Treasury bills, which currently offer a 3% safe return per year. The S&P 500 index fund offers an expected return of 10% per year with a standard deviation of 20%.

You want to achieve an expected return of 8% per year for your portfolio. What should be the composition of your portfolio? What is the standard deviation of its returns?
Now your employer adds an emerging-market fund to the two existing funds. The emerging-market fund offers an expected return of 10% per year, the same as the S&P 500 index fund, but with a standard deviation of 30%, higher than the S&P 500 index fund. Would you consider including the emerging-market fund as part of your portfolio? Explain.
The correlation between the S&P 500 index fund and the emerging- market fund is zero. Consider portfolio A, which consists of 80% in the S&P index fund and 20% in the emerging-market fund. Calculate portfolio A’s expected return and standard deviation.

If you mix portfolio A with the money-market fund to achieve an expected return of 8%, is it better than the portfolio in part (a) of this question? Explain

Expert Solution

A ) Linearity of expected returns requires: w_a×8%+(1−w)a×20% = 8%. Solving for w_a yields 28.6% in the risk free asset and 71.4% in the S&P. Sigma is given by 0.714 × 20% = 14.28%.

B) Even though the Emerging Markets fund has the same return and a higher standard deviation, its correlation with the S&P may lead to achieve lower levels of risk for the portfolio as a whole. If the correlation is sufficiently low, we may be able to diversify away some of the risk. We should certainly consider the Emerging Fund.

C) Portfolio A’s expected return is 10%. Portfolio A’s standard deviation is calculated as follows

σ ²= 0.82 × 202 + 0.22 × 302 + 2 × 0.8 × 0.2 × 0 × 20 × 30

σ² = 292

σ = 17.09%

D) The weights will be the same as in part a, i.e., 28.6% in the risk free asset and 71.4% in Portfolio A. The standard deviation of the new portfolio will be 0.7143 × 17.09% = 12.2%, which is lower than for the portfolio in part a. We are clearly better off: now we can achieve the same return with a lower level of risk.

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