Question

further understanding with how beta a,b,c are actually computed. I dont unseratand how the answers given are calculated or is there a part of the calcualtion missing?

Mr. Geller collected information regarding the following stocks and portfolio Portfolio P1 Security A Security B EU 5 % 10% Standard Deviation 20% Weight Security A 40% Weight Security B 40% Weight Security C 20% Security C 3% 8% Mr. Geller also has information regarding the following variance-covariance matrix: Variance - Covariance Security A Security B Market Portfolio Security A 0.0064 Security B -0.005 0.04 Market Portfolio 0.05 0.025 Assume that the CAPM model is valid. Consider additionally that the expected return from the Market Portfolio is 18%. a) (1 point) Compute the expected return and volatility (standard deviation) for portfolio P1. Solution: E() = 0.4x0.05 +0.4x0.1 +0.2x0.03 = 6.60% Var[E(r)] = 0.42x0.0064 +0.4²x0.04 + 2x0.4x0.4x(-0.005) = 0.005824 Op1 = V0.005824 = 7.63% b) (1.5 points) Compute the expected return, volatility (standard deviation) and beta of a portfolio invested 20% in security A and 80% in portfolio P1. Solution: The portfolio mentioned is equivalent to: WA 52%, w 32% and wc 16% E(rp) = 0.52x0.05 + 0.32x0.1 +0.16x0.03 6.28% Var[ ] = 0.522x0.0064 + 0.3220.04 + 2x0.52x0.32X(-0.005) - Op. = V0.005824 = 6.45% 0.05 PA = 1.25 0.025 625 0.2=0.625 Be=0 Bp=> wifi = 0.52x1.25 +0.32x0.625 +0.16x00.85

Answer 1

In the solution posted, the answers are correct but the formula is wrong

Beta=Covariance with market/Variance of market

From Variance Covariance Table we see for column Market Portfolio and row Market Portfolio, the value of 0.04

Hence, Variance of market=0.04

Beta A=0.05/0.04=1.25
Beta B=0.025/0.04=0.625