Question

pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.5%. The probability distributions of the risky funds are: Expected Return Standard Deviation Stock fund (S) 15 % 32 % Bond fund (B) 9 % 23 % The correlation between the fund returns is 0.15. Suppose now that your portfolio must yield an expected return of 12% and be efficient, that is, on the best feasible CAL. a. What is the standard deviation of your portfolio? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

The standard deviation of the portfolio is 7.09%.

What is the proportion of stock in minimum risky portfolio?

= [(0.23)² - (0.32*0.23*0.15)] / [(0.32)² + (0.23)² - (2*0.32*0.23*0.15)]

= 0.31421708452

= 31.42%

What is proportion of bond fund in minimum risky portfolio?

= 1 - 0.31421708452

= 0.68578291548

= 68.58%

What is the expected return of minimum risky portfolio?

= 0.3142*15% + 0.6858*9%

= 0.04713 + 0.061722

= 0.108852

What is the standard deviation of your portfolio?

= ((0.6858)² * (0.23)² * (0.3142)² * (0.33)²) + ((2 * 0.6858 * 0.3142 * 0.32 * 0.23 *  0.15))^0.5

= (0.00026747972 + 0.00475776218)^0.5

= 0.0050252419^0.5

= 0.0708889406

= 7.09%

Therefore, the standard deviation of the portfolio is 7.09%.

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