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 4.8%. The probability distributions of the risky funds are:

  

	Expected Return	Standard Deviation
Stock fund (S)	18%	38%
Bond fund (B)	9%	32%

  

The correlation between the fund returns is .1313.

  

What is the expected return and standard deviation for the minimum-variance portfolio of the two risky funds? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

  

Expected return	12.62 ± 1% %
Standard deviation	26.01 ± 1% %

So 12.62 and 26.01 are the answers for expected return and standard deviation but I am having difficulty understanding how to get those answers. My classmates are struggling with this question as well. We can not use excel only formulas by hand. This is the 4th time I've posted this question with the answer either being wrong or the answer uses excel. So far no luck so far and I really want to understand how it works!

Answer 1

Return of Stock Fund (Rs) = 18%

Return of Bond Fund (Rb) = 9%

SDs = 38%

SDb = 32%

Correlation(s.b) R(s,b) = 0.1313

Cov(s,b) = R(s,b) * SDs * SDb

= 0.1313 * 38 * 32

= 159.6608

Optimum weight of Bond (Wb) =

=

= 1284.3392 / 2148.6784

= .5977 Or 59.77%

Weight of Stock Fund (Ws) = 100 % - 59.77% = 40.22%

Expected Return = Ws * Rs  + Wb * Rb

= .0.4022 * 18% + .5977 * 9%

= 12.62%

SD =

=

=

= 26.00%

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