Question

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​%

Answer 1

Step-by-step 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%