Question

A 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 ReturnStandard Deviation Stock fund (S) Bond fund (B) 15% 9% 32% 22% The correlation between the fund returns is 0.15. a. What would be the investment proportions of your portfolio? Investment Proportions Bonds b. Calculate the standard deviation of the portfolio which yields an expected return of 12%. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Standard deviation

Answer 1

Where Correlation between two securities is "-1<r<1", we can reduce the risk but "not to Zero".

However Investment shall be made at minimum variance portfolio.

Assume The name of Stock fund is "S" & Bond fund is "B" for convineience.

Investment in Stock Fund = (SD of B)² - r*SD of S * SD of B / [ (SD of S)² + (SD of B)² - 2 . r * SD of S * SD of B ]

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

= [ 0.0529 - 0.01104] / [ 0.1024 + 0.0529 - 0.02208 ]

= 0.04186 / 0.13322

= 0.3142 i.e 31.42 % in stock fund & 68.58% IN Bond fund.

Portfolio return is Weighted Average return of securities in that portfolio.

Let x be weight of investment in Stock fund S & 1-X be the weight of Investment in Bond fund

Particulars Weight Stock Fund x Bond Fund 1-x Return Weighted return 15%)0.15x 996] 0.09(1-x) Portfolio Return 0.06 X 0.09

Given portfolio Return = 12 %

Thus 0.12 = 0.09 + 0.06X

0.06X = 0.03

x = 0.03/0.06 i.e 50%

SD of Portfolio = Square root { (Ws* SD of S)² + (W_B* SD of B)² + 2 * r * Ws* SD of S * W_B* SD of B }

= Square root { (0.5* 0.32)² + (0.5* 0.23)² + 2 * 0.15 *0.5* 0.32 * 0.5* 0.23}

=Square root { (0.16)² + (0.115)² + 0.00552 }

=Square root { 0.0256 + 0.0132 + 0.00552 }

=Square root {0.0443 }

= 0.2106 i.e 21.06%

Portfolio SD = 21.06%

Pls comment, if any further assistance is required.