Consider a portfolio consisting of the following three stocks: LOADING The volatility of the market portfolio is 10 % and it has an expected return of 8 %. The risk-free rate is 3 %. a. Compute the beta and expected return of each stock. b. Using your answer from part (a), calculate the expected return of the portfolio. c. What is the beta of the portfolio? d. Using your answer from part (c), calculate the expected return of the portfolio and verify that it matches your answer to part (b). a. Compute the beta and expected return of each stock. (Round to two decimal places.) Portfolio Weight (A) Volatility (B) Correlation (C) Beta (D) Expected Return (E) HEC Corp 0.28 10 % 0.48 nothing nothing% Green Widget 0.34 30 % 0.58 nothing nothing% Alive And Well 0.38 11 % 0.59 nothing nothing%

Explanation:

            Portfolio Weight  Volatility  Correlation and Market Portfolio

HEC Corp   0.28      10%          0.48

Green Widget   0.34             30%                 0.58

Alive And Well  0.38             11%                0.59

a. (i) Calculation of Beta

Coefficient of correlation = Covariance / (SD security*SD market)

HEC Corp: 0.28 = Covariance / (0.10*0.10)

Covariance = 0.0028

Beta of HEC Corp = Covariance / Market variance

                              = 0.0028 / 0.12² = 0.1944

Beta of HEC Corp = 0.19

Green Widget: 0.34 = Covariance / (0.30*0.10)

Covariance = 0.0102

Beta of Green Widget = Covariance / Market variance

                                     = 0.0102 / 0.30² = 0.113

Beta of Green Widget= 0.11

Alive And Well: 0.38 = Covariance / (0.11*0.10)

Covariance = 0.00418

Beta of Alive And Well = Covariance / Market variance

= 0.00418 / 0.11² = 0.345

Beta of Alive And Well = 0.35

(ii) Calculation of expected return

Expected return = Risk free rate + Beta(Expected return of market - Risk free rate)

HEC Corp = 3 + 0.19 (8-3) = 3.95%

Green Widget = 3 + 0.11 (8-3) = 4=3.55%

Alive And Well = 3 + 0.35 (8-3) = 4.75%

b. Expected return of Portfolio = (3.95 x 0.28) + (3.55 x 0.34) + (4.75 x 0.38) = 4.118%

Expected return of Portfolio = 4.12

c. Beta of portfolio = (0.19 x 0.28) + (0.11 x 0.34) + (0.35 x 0.38) = 0.2236

Beta of portfolio = 0.2236

d. Expected return of portfolio = Risk free rate + Portfolio Beta(Expected return of market - Risk free rate)

= 3 + 0.2236 (8-3) = 4.118%

Expected return of portfolio  = 4.12%

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