Question

An investor invests 40 per cent of her funds in Company A's shares and the remainder in Company B's shares. The standard deviation of the returns on A is 20 per cent and on B is 10 per cent. Required: Calculate the variance of return on the portfolio assuming the correlation between the returns on the two securities is: 1) +1.0 2) +0.5 3) 0 4) -0.5

Answer 1

Solution.>

The standdard deviation of a portfolio is calculated by:

Variance = (Standard Deviation) ^ 2

Part 1.> When correlation coefficient is 1.

Variance = (0.4)(0.4)(0.2)(0.2) + (0.6)(0.6)(0.1)(0.1) + 2*(0.4)(0.6)(0.2)(0.1)(1)

Variance = 0.01 + 0.0096

Variance = 1.96%

Part 2.> When correlation coefficient is 0.5.

Variance = (0.4)(0.4)(0.2)(0.2) + (0.6)(0.6)(0.1)(0.1) + 2*(0.4)(0.6)(0.2)(0.1)(0.5)

Variance = 0.01 + 0.0048

Variance = 1.48%

Part 3.> When correlation coefficient is 0.

Variance = (0.4)(0.4)(0.2)(0.2) + (0.6)(0.6)(0.1)(0.1) + 2*(0.4)(0.6)(0.2)(0.1)(0)

Variance = 0.01 + 0

Variance = 1%

Part 4.> When correlation coefficient is -0.5.

Variance = (0.4)(0.4)(0.2)(0.2) + (0.6)(0.6)(0.1)(0.1) + 2*(0.4)(0.6)(0.2)(0.1)(-0.5)

Variance = 0.01 - 0.0048

Variance = 0.52%

Note: Give it a thumbs up if it helps! Thanks in advance!