Question

The table below gives the amount invested and betas for three stocks.

Stock      Amount Invested          Beta

GM            K10, 000                      1.2

IBM           K10, 000                      1.0

WMT        K20, 000                      0.7

REQUIRED:

1. Using the CAPM, if the expected return for the market is 6% and the risk-free rate is 1.5%, what is the expected return for each stock?   
2. What is the beta for this portfolio based on the invested amounts?
3. Using the CAPM, what is the expected return for this portfolio?       

Answer 1

A)

GM:

Expected return = Risk free rate + beta(market return - risk free rate)

Expected return = 1.5% + 1.2(6% - 1.5%)

Expected return = 1.5% + 5.4%

Expected return = 6.90%

IBM:

Expected return = Risk free rate + beta(market return - risk free rate)

Expected return = 1.5% + 1(6% - 1.5%)

Expected return = 1.5% + 4.5%

Expected return = 6.0%

WMT:

Expected return = Risk free rate + beta(market return - risk free rate)

Expected return = 1.5% + 0.7(6% - 1.5%)

Expected return = 1.5% + 3.15%

Expected return = 4.65%

B)

Total value = 10,000 + 10,000 + 20,000 = 40,000

Beta of portfolio = (10,000 / 40,000)*1.2 + (10,000 / 40,000)*1 + (20,000 / 40,000)*0.7

Beta of portfolio = 0.3 + 0.25 + 0.35

Beta of portfolio = 0.9

C)

Expected return of portfolio = Risk free rate + beta(market return - risk free rate)

Expected return of portfolio = 1.5% + 0.9(6% - 1.5%)

Expected return of portfolio = 1.5% + 4.05%

Expected return of portfolio = 5.55%