3. A portfolio manager analyzes 100 stocks and constructs a mean-variance effici

Question

3. A portfolio manager analyzes 100 stocks and constructs a mean-variance efficient portfolio using these 100 securities. (13 points)

(c) Calculate alpha values for two stocks. (2 points)

(d) Break down the variance of each stock to the systematic and firm-specific components. (3 points)

(e) What are the covariance and correlation coefficient between the two stocks? (2 points)

(f) What is the covariance between each stock and the market index? (2 points)

Explanation / Answer

Standard Deviation = square root of (Probability x returns- avg returns) whole squared) Alpha can be computed by the formula = actual return - expected return For A For B Beta ß = SD of Security's Return      = 0.08/20 .14/20 SD of Market's Return 0.40 0.71 For A For B Expected Return = Rm + ß X (Rm- Rf) 16+.4X(16-4) 16+.71X(16-4) 20.80 24.52 Actual Return = 6.00 13 Alpha actual returns - expected returns -14.80 -11.52 Correlation and covariance Probability Stock A Weighted Returns variance Stock B Weighted Returns variance covariance 1 0.3 7% 2% 0.01% -9% -3% 1.39% 0.751 2 0.5 11% 6% 0.15% 20% 10% 0.28% 0.402 3 0.2 -10% -2% 0.49% 26% 5% 0.36% -0.004 Total 6% 0.64% 13% 2.03% 1.15 standard Deviation 7.99% 14.26% 1.07 covariance = SQUARE ROOT OF probability x (returns of stock A -average returns of stock A) X (returns of Stock B - average returns of stock B) covariance (A,B) 1.07 correlation (a,b) cor(X,Y)=cov(X,Y) / sd(X) X sd(Y) = 1.07 / ( 0.08 X 0.14 ) = 95.54

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