Question

Stocks A and B have expected returns of 8% and 10%, and standard deviations of 12% and 18%, respectively. Calculate the expected return and standard deviation of equally weighted portfolios of the two stocks if the correlation between the two stocks is 0.5? Repeat the calculation for correlation of 0 and -0:5. If you could set the correlation between the two stocks, which of the three values would you choose? Explain.

Answer 1

Expected return = 0.5 ( 0.08) + 0.5 ( 0.1)

Expected return = 0.04 + 0.05

Expected return = 0.09 or 9%

Standard deviation when correlation is 0.5:

Variance = 0.5² * 0.12² + 0.5² * 0.18² + 2 * 0.5 * 0.5 * 0.5 * 0.12 * 0.18

Variance = 0.0036 + 0.0081 + 0.0054

Variance = 0.0171

Standard deviation is square root of variance

square root of 0.0171 is 0.130767

Standard deviation is 13.0767%

Standard deviation when correlation is 0

Variance = 0.52 * 0.122 + 0.52 * 0.182 + 2 * 0.5 * 0.5 * 0 * 0.12 * 0.18

Variance = 0.0036 + 0.0081 + 0

Variance = 0.0117

Standard deviation is square root of variance

square root of 0.0117 is 0.108167

Standard deviation is 10.8167%

Standard deviation when correlation is -0.5

Variance = 0.52 * 0.122 + 0.52 * 0.182 + 2 * 0.5 * -0.5 * 0 * 0.12 * 0.18

Variance = 0.0063

Standard deviation is square root of variance

square root of 0.0063 is 0.079373

Standard deviation is 7.9373%

We would choose -0.5 as it has the lowest standard deviation