Question

15% 0% TU) You are given Tollowing intornation: Market Scenario Probability cp) Stock A's Returns Stock B's Returns Market Index Returns 25% 0% 10.2 18% 10% 0.3 10% 8% 10.2 112% 10% 0.2 16% -4% Additional information: Standard Deviation: Stock A =10.67%; Stock B - 5%; Market Index - 6.02% Covariances: Cov(Stock A & Market Index) - 64.15 or 0.006415; Cov(Stock B & Market Index) = 30 or 0.003000; Cov(Stock A & Stock B) = -53.20 or -0.005320; Prote=27 a) Compute the expected returns for Stock A, Stock B, and the Market Index. [3+3+3 marks] b) Assume that you have $8,000 available for investment and decide to invest $3,000 in stock A and remaining in stock B, what will be the return in your portfolio. Also compute the standard deviation of your portfolio [3+4 marks] c) Compute the beta of Stock A and Stock B. [3+3 marks d) Identify whether the stocks are overpriced, underpriced or correctly priced assuming CAPM holds.[1+1 marks]

Answer 1

a) The expected return of a security is calculated from the following formula:

Expected return = p1*r1 + p2*r2 + ........pn*rn

Where, r is the expected return in a given scenario

p is the probability of return in a given scenario

Therefore, Expected return of stock A = 0.1*25 +0.2*18 + 0.3*10 +0.2*0 + 0.2*(-8)

= 7.5%

Expected return of stock B = 0.1*0 + 0.2*4 +0.3*8 + 0.2*12 + 0.2*16

= 8.8%

Expected return of market index = 0.1*15 + 0.2*10 + 0.3*6 + 0.2*0 + 0.2*(-4)

= 4.5%

b) Expected return on portfolio= (Return on Stock A * Weight of stock A) + (Return on Stock B* Weight of Stock B)

Weight of stock is calculated as stock value/Total investment

Expected return on portfolio = 7.5 *(3000/8000) + 8.8*(5000/8000)

= 8.3125 %

Standard deviation of portfolio is calculated as

Op = wi* oỉ + wź * oỉ +2* W1 * W2 * Cov1,2

Where, w1 is weight of stock 1

w2 is weight of stock 2

$\sigma _{1}$ is standard deviation of stock 1

$\sigma _{2}$ is standard deviation of stock 2

$\sigma _{p}$ is standard deviation of portfolio

Weight of stock A = 3000/8000 = 0.375

Weight of stock B = 5000/8000 = 0.625

Therefore standard deviation of portfolio AB =

(0.3752 +0.10672 + 0.62.5 +0.05 +2+ 10.375+10.525+(-10.0053 2015

= 0.94%

c) Beta of stock = E(rx)-rf / E(rm) - rf

Where, E(rx) is expected return of stock x

rf is risk free rate

E(rm) is expected return of market

Beta of stock A = 7.5-2 / 4.5-2

= 2.2

Beta of stock B = 8.8-2 / 4.5-2

= 2.72

d). Required return if CAPM holds = rf + Beta*(rm - rf)

Required return of stock A = 2 + 2.2*(4.5-2) = 7.5%

Stock A is correctly priced since its required return equals expected return

Required return of stock B = 2 + 2.72*(4.5-2) = 8.8%

Stock B is also correctly priced since its required return equals expected return