Question

Pinulo retums? 1 0 capital asset pricing model given historical data 2. Consider Table 1. (%) 3.77 Table 1 Summary Statistics Alpha, Beta, Expected Return and Variance a/c to the Stocks Sample Single Index Model Covariance Residual and Return Alpha Beta with Market Expected Variance Variance Market (%) (%) Return (%) (%) 3.60 3.59 4.80 Market 4.20 0.00 8.70 (a) Consider Table 1. Using the single index model, calculate beta and alpha for stocks 1 and 2. Interpret your findings. (6) Consider Table 1. Using the single index model, calculate the expected return, variance of returns, systematic risk, non-market risk for stocks 1 and 2, and the covariance between the returns for stocks and 2. Interpret your findings. Consider Table 1. Form an equally-weighted portfolio of stocks 1 and 2. Using the single index model calculate the expected return and standard deviation risk of this portfolio Sketch the set of portfolios comprised of stocks 1 and 2 (d) Consider Table 1. Suppose a third risky stock exists with expected return of 5% and standard deviation risk of 3%. Further suppose stock 3 has a market beta of 0. Forma portfolio of stocks 1 and 3. How does a portfolio of stocks 1 and 3 compare to a portfolio of stocks 1 and 2?

Answer 1

Answer first 4 question including sub-part as per policy:

The concept of Single index model can be explained as :

R = 2; +B;Ry te

Security Co-variance as :

σ, = β.β,σ

Beta of stock ,

B =- Cou(Ri, Rm) Varm

Alpha of stock ,

a = R; - (3,7m)

answer a.1)

B1 – 7.35 Pi = = 0.845

5.05 B2 = 3.70 8.70 = 0.58

Answer a.2) Alpha ,

Q1 = 3.6 - (0.845 * 4.20) = 0.051

Alpha ,

ay = 4.8 - (0.58 * 4.20) = 1.164

Answer 2.1 ) Expected return using Single Index model:

%

R1 = 0.051 +0.845 * 4.2 +3.59 = 7.19

%

R2 = 1.164 +0.58 * 4.2 +3.77 = 7.37

Answer 2.2) Variance of return ,

o? = (R - E(R))

for stock 1,

o = (3.6 – 7.19)2 = 12.89

For stock 2, .

o = (4.8 – 7.37) = 6.61