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 4.0%. The probability distributions of the risky funds are:

	Expected Return	Standard Deviation
Stock fund (S)	10%	32%
Bond fund (B)	7%	24%

The correlation between the fund returns is 0.1250.

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.)

Answer 1

First we Need to find out the weights of minimum variance portfolio for two riskey assets Using

W1 = (σb²-ρabσaσb) / (σa² + σb² – 2ρabσaσb

Where

σb = SD of bond fund = 24%

σa = SD of Stock fund = 32%

ρab  = Correlation between stock fund and bond fund = 0.1250

Now put tall the values

W1 = ( 242 - 0.1250 * 32 * 24) / ( 322 + 242 - 2 * 0.1250 * 32 * 24)

= ( 576 - 96) / ( 1024 + 576 - 192)

= 480 / 1408

W1 = 0.340

Therefore W2 = 1 - W1

    = 1 - 0.34

= 0.66

Now that we have got the Weights we will use the formula for Expected return

Expected return = W1 R1 + W2R2

Where

W1 =  0.34

W2 = 0.66

R1  = 10%

R2  = 7%

Put the values we get

Expected Return = 0.34 * 10 + 0.66 * 7

= 3.4 +4.6

Expected Return = 8.02%

Now In order to find out Standard deviation of the portfolio of these two riskey Assets we will calculate Variance of portfolio first which will help us to find out Standard deviation

σp2 = w12σa2 + w22σb2 + 2w1w2 ρ1,2σaσb

Put all the values we get

σp2 = 0.342  322 + 0.662 242 + 2 * 0.34 * 0.66 * 0.1250 * 32 * 24

= 0.1156 * 1024 + 0.4356 * 576 + 43.084

= 118.374 + 250.905 + 43.084

σp2 = 412.363

Therefore

Standard deviation = Square root of (Variance of portfolio)

= Square root of 412.363

Standard deviation  = 20.306%