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 Return Standard Deviation Stock fund (S) 17% 34% Bond fund (B) 11% 25% The correlation between the fund returns is 0.15.

Answer 1

Variance and covariance are used  in probability to determine the spread and relationship between variables

• The variance of stock S is 0.1156
• The variance of stock B is 0.0625
• The covariance of the stocks is 127.5

How to determine the variance of the stocks

The variance of stock S is calculated as

$\sigma^2_s = (34\%) * (34\%)$

$\sigma^2_s = 0.1156$

The variance of stock B is:

$\sigma^2_b = (25\%) * (25\%)$

$\sigma^2_b = 0.0625$

The covariance of the stocks

This is calculated as:

$Cov = r(s,b) * \sigma_s * \sigma_b$

So, we have:

$Cov = 0.15 * 34 * 25$

$Cov = 127.5$

Hence, the covariance of the stocks is 127.5

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