A pension fund manager is considering three mutual funds. The first is a stock f

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 5.3%. The probability distributions of the risky funds are:

Expected Return Standard Deviation
  Stock fund (S) 14 % 43 %
  Bond fund (B) 7 % 37 %

The correlation between the fund returns is .0459.

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.)

  Standard deviation %

Explanation / Answer

As the % of the funds invested in each fund is not provided it is assumed that 50% of the fund is invested in stock fund and 50% of the funds are invested in bond funds.

Basing on the above assumption, the standard deviation of the portffolio is as follows:

formula for calculation of standard deviation of portfolio is = Square root{(W1 * standard deviation of expected returns of stock1)+ (W2 * standard deviaiton of expected returns of stock 2)+2*W1*W2 *Correlation coefficient between the rates of returns of Stock and Bond funds * Standard deviation of stock fund * Standard deviation of bond fund.

W1 is the % of funds invested in stock 1

W2 is the % of funds invested in stock 2

= square root(0.5 *0.43+0.5 * 0.37+2*0.5*0.5*0.0459 )

=Square root (0.42295)

=0.6503 = 0.6503 *100 = 65.03%

Therefore standard deviation of the portfolio is 65.03%

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