Question

Home assignment 4 Consider following information Probability of the state of economy Rate of return if state occurs StockA StockB boom normal a. b. c. 0.2 0.8 0.4 0.2 0.05 Calculate the expected return of Calculate the variance and standard deviation of each stock. Calculate the covariance between stock A and B returns and the correlation coefficient. Calculate the expected return of the portfolio (Portfolio!) consisting 40% of stock A and 60% of stock B. Calculate the variance and standard deviation of this portfolio. Based on CAPM calculate each stock beta if risk-free asset expected return is 2% and market risk premium is 5%. each stock. d. e. f. . Which stock has the lowest systematic risk? Which stock has the lowest total risk? Which stock is "safest"? Explairn What is the beta of the Portfolio1? h.

Answer 1

(a) Expected Return of Stock ER = ΣP_iR_i, where Pi is the probability and Ri is the return for economy state i

=> ER_A = 0.2*0.4 + 0.8*0.2 = 0.24

ER_B = 0.2*0.12 + 0.8*0.05 = 0.064

(b) Variance of stock = σ² = Σ P_i(R_i - ER)²

=> σ_A² = 0.2(0.4 - 0.24)² + 0.8(0.2 - 0.24)² = 0.0064

σ_B² = 0.2(0.12 - 0.064)² + 0.8(0.05 - 0.064)² = 0.000784

Standard Deviation = σ = sqrt (σ² )

=> σ_A = sqrt(0.0064) = 0.08

σ_B = sqrt(0.000784) = 0.028

(c) Covariance = Cov(A, B) = Σ P_i(R_iA - ER_A)(R_iB - ER_B) = 0.2(0.4 - 0.24)(0.12 - 0.064) + 0.8(0.2 - 0.24)(0.05 - 0.064) = 0.00224

Correlation = Cov(A, B) / σ_A σ_B = 0.00224/(0.08*0.028) = 1

(d) Expected Return of Portfolio = w_AER_A + w_BER_B = 0.40*0.24 + 0.60*0.064 = 0.1344