Question

Two stocks have the same return and risk (standard deviation): 10 percent return with 20 percent risk. You form a portfolio with 50 percent each of Stock 1 and Stock 2 to examine the effect of correlation on risk.

1 Calculate the portfolio return and risk if the correlation is 1.0.
2 Calculate the portfolio return and risk if the correlation is 0.0.
3 Calculate the portfolio return and risk if the correlation is –1.0.

Answer 1

When the correlation is 1.0, the portfolio return and risk remain the same as the individual stocks. When the correlation is 0.0, the portfolio return and risk remain the same as the individual stocks. When the correlation is -1.0, the portfolio risk becomes 0%.

Step-by-step explanation:

To calculate the portfolio return and risk based on the correlation between Stock 1 and Stock 2, we can use the formula:

Portfolio Return = (Weight of Stock 1 * Return of Stock 1) + (Weight of Stock 2 * Return of Stock 2)

Portfolio Risk (Standard Deviation) = sqrt((Weight of Stock 1)^2 * (Risk of Stock 1)^2 + (Weight of Stock 2)^2 * (Risk of Stock 2)^2 + 2 * (Weight of Stock 1) * (Weight of Stock 2) * (Correlation between Stock 1 and Stock 2) * (Risk of Stock 1) * (Risk of Stock 2))

Calculation with correlation 1.0:

Portfolio Return = (0.5 * 0.10) + (0.5 * 0.10) = 0.10 (10%)

Portfolio Risk = sqrt((0.5^2 * 0.20^2) + (0.5^2 * 0.20^2) + 2 * 0.5 * 0.5 * 1.0 * 0.2 * 0.2) = 0.20 (20%)

Calculation with correlation 0.0:

Portfolio Return = (0.5 * 0.10) + (0.5 * 0.10) = 0.10 (10%)

Portfolio Risk = sqrt((0.5^2 * 0.20^2) + (0.5^2 * 0.20^2) + 2 * 0.5 * 0.5 * 0.0 * 0.2 * 0.2) = 0.20 (20%)

Calculation with correlation -1.0:

Portfolio Return = (0.5 * 0.10) + (0.5 * 0.10) = 0.10 (10%)

Portfolio Risk = sqrt((0.5^2 * 0.20^2) + (0.5^2 * 0.20^2) + 2 * 0.5 * 0.5 * -1.0 * 0.2 * 0.2) = 0 (0%)