Question

Assume the following statistics for Stock A and Stock B:

	Stock A	Stock B
Expected return	.015	.020
Variance	.050	.060
Standard deviation	.224	.245
Weight	40%	60%
Correlation coefficient	.50

1) What is the expected return of the portfolio that consists of stocks A and B

2) Calculate the variance of this two-security portfolio?

3) Recalculate the expected return and the variance for the portfolio of the two securities when:

- the correlation is = +1.

- the correlation = -1

- the correlation = 0

4) What do you conclude?

Answer 1

1) Expected return = 0.40 x 0.015 + 0.60 x 0.020 = 0.018 or 1.8%

2) Variance = (Variance_A)² x (Weight_A)² + (Variance_B)² x (Weight_B)² + 2 x Variance_A x Variance_B x Weight_A x Weight_B x Correlation_AB = (0.05)² x (0.40)² + (0.06)² x (0.60)² + 2 x 0.05 x 0.06 x 0.40 x 0.60 x 0.50 = 0.002416

3) Expected return will remain the same as it is not affected by correlation.

Correlation = +1

Variance = (0.05)² x (0.40)² + (0.06)² x (0.60)² + 2 x 0.05 x 0.06 x 0.40 x 0.60 x 1 = 0.003136

Correlation = -1

Variance = (0.05)² x (0.40)² + (0.06)² x (0.60)² + 2 x 0.05 x 0.06 x 0.40 x 0.60 x (-)1 = 0.000256

Correlation = 0

Variance = (0.05)² x (0.40)² + (0.06)² x (0.60)² + 2 x 0.05 x 0.06 x 0.40 x 0.60 x 0 = 0.001696

4) Conclusion : The expected return is equal in all the three four cases. However, variance is the lowest in case correlation is -1 and the highest when it is +1. Perfectly positive correlation +1 means the securites move in the same direction , i.e., if Stock A falls, then Stock B will also fall. Whereas perfectly negative correlation of -1 means the securities move in opposite directions.