Question

An investor can design a risky portfolio based on two stocks, The standard deviation of return on stock A is 24% while the standard deviation on stock B is 14%. The correlation coefficient between the return on A and B is 0.35. The expected return on stock A is 25% while on stock B it is 11%. What is the proportion of the minimum variance portfolio that would be invested in stock B?

When solving this problem, make sure you use at least 4 decimal places when completing the calculations and round your answer to 2 decimal places. Please input your final answer as a percentage with 2 decimal places without the percent sign. For example, 47.27.

Answer 1

A minimum variance portfolio represents a diversified portfolio that consists of assets that have varying levels of individual risk, which are combined in an appropriate ratio to obtain the lowest possible risk for the rate of expected return.

One needs to invest in low risk securities or a combination of volatile investments with low correlation to each other, in order to build a minimum variance portfolio.

The data is illustrated as below:

The covariance matrix is illustrated as follows:

The proportion of Stock A that should be invested in the minimum variance portfolio is calculated as below.

Applying the formula, we substitute the values:

[ (0.14)^2 - (0.35) * (0.24* 0.14) ] / [(0.24)^2 + (0.14)^2 - {2(0.35) * 0.24 * 0.14}]

= [0.0196 - {0.35 * 0.0336}]/[ 0.0576 + 0.0196 - (0.70 * 0.24 *0.14) ]

= [0.0196 - 0.01176] / [ 0.0576 + 0.0196 - 0.02352]

= 0.00784 / 0.05368 = 0.146051 or

Hence, the proportion of Stock B = (1- 0.146051) = 0.8539 or 85.39%