Question

1a. If the covariance between Stock A and Stock B is 0.00196 and the standard deviation for Stock A and stock B are 20% and 10% respectively, what is the correlation between A and B?

1b. Assume Michael has a diversified portfolio that had an actual an actual return of 15% last year. During the same time, the market returned 12%. The risk-free rate of return for this period was 4%, and the beta for Michael’s portfolio was 1.55(or 25% more volatile than the market). Michael wants to know whether his portfolio performed well on a risk-adjusted basis.

Answer 1

Solution to part 1a

Covariance between Stock A & Stock B = 0.00196

Standard Deviation of Stock A = 20% or 0.20

Standard Deviation of Stock B = 10% or 0.10

Correlation between Stock A & Stock B =

= 0.098

Correlation between Stock A & Stock B = 0.098

Solution to part 1b

Portfolio Return = 15% or 0.15

Return of Market = 12% or 0.12

Risk free rate = 4% or 0.04

Beta = 1.55

As per Capital Asset Pricing Model,

Required Return of Portfolio = Risk Free Rate + (Return on Market - Risk Free Rate) * Beta

= 4% + (12% - 4%) * 1.55

= 4% + 12.40%

= 16.40%

Therefore Alpha = Portfolio Return - Required Return on Portfolio

= 15% - 16.40%

= -1.40%

Thus, the portfolio has not performed well on risk adjusted basis