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

ID: 2778371 • Letter: 3

Question

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

The market index has an expected return of 16% and a standard deviation of 20%. Riskfree rate is 4%.

(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)

PLEASE SHOW WORK

d) Standard Deviation of stock = (Betaof stock2 * Standard Deviation of market2 + Firm specific standard deviation2)1/2

Standard Deviation of C = (0.62 * 0.202 + 0.242)1/2 = 26.83%

Variance of C = 0.26832 = 0.072

Variance due to systematic component =Betaof stock2 * Standard Deviation of market2 = 0.62 * 0.202 = 0.0144

Variance due to firm specific component = 0.242 = 0.0576

Standard Deviation of D = (1.12 * 0.202 + 0.352)1/2 = 41.34%

Variance of D = 0.41342 = 0.1709

Variance due to systematic component =Betaof stock2 * Standard Deviation of market2 = 1.12 * 0.202 = 0.0484

Variance due to firm specific component = 0.352 = 0.1225

e) The residuals of stocks C and D are assumed to be uncorrelated.

Hence, the covariance between the returns of C and D is calculated using the following formula

Cov (C, D) = Beta of C x Beta of D * Variance of Market = 0.6 * 1.1 * 0.22 = 0.0264

Correlation coefficient is given by
Corr (C,D) = Cov (C, D) ) / (SDC x SDD) = 0.0264/(0.2683 * 0.4134) = 0.238

f) Covariance between stock and Market = Beta stock of Stock * Variance of Market

Covariance between stock C and market = 0.6 * 0.22 = 0.024
Covariance between stock D and market = 1.1 * 0.22 = 0.044

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