Question 3 Suppose that the Index Model for stocks A and B is estimated from excess returns with the following results: R=2% +0

Ans) a)

The standard deviation of each stock can be derived from the following equation for R²:

Standard deviation of A = [(Coefficient of Rm)^2*(sigma_m)^2/(Ra)^2]^0.5 = (0.6² * 20²/ 0.20)^0.5

Standard deviation of A = 26.83%

For Stock B: following the same formula

Standard deviation of B = (1.1² * 20²/ 0.12)^0.5

Standard deviation of B = 63.50%

b)

Systematic (market) risk = Beta² x σ_M² and Firm specific risk = σ²(e_i) = (Residual standard deviation)²

^{For Stock A, Systematic Risk = (0.6^2) * (0.2^2) = 0.144
For Stock B, Systematic Risk = (1.1^2)*(0.2^2) = 0.0484}

c)

σ_A²= Beta_A² x σ_M² / R-squareA = 0.6² x 0.2² / 0.2 = 0.72

Hence, σ_A= 0.72^1/2 = 0.2683 = 26.83%

σ_B²= Beta_B² x σ_M² / R-squareB = 1.1² x 0.2² / 0.12 = 0.403

Hence, σ_B= 0.403^1/2 = 0.635 = 63.5%

The covariance between the two stocks = Cov (RA, RB) = Beta_A x Beta_B x σ_M² = 0.6 x 1.1 x 0.2² = 0.0264

Correlation coefficient = Cov (RA, RB) / (σ_A x  σ_B) = 0.0264 / (0.2683 x 0.403) =  0.244

d)

The covariance between STOCK A and the market index = Beta_A x σ_M² = 0.6 x 0.2² = 0.024

The covariance between STOCK B and the market index = Beta_B x σ_M² = 1.1 x 0.2² = 0.044