Question

5. You are provided data on the three companies listed in Alternative Investments Market in the UK. Assume the risk free rate and market index return is 3% and 5% respectively. A. Use the Capital Asset Pricing Model (CAPM) to calculate the required rate of returns on the companies. (5p) B. Assuming that the three stocks are equally weighted in your portfolio, calculate the beta of portfolio (4p) Stock Beta Abbey plc 0,4 1PM plc 1,8 32 Red plc 0,9

Answer 1

The formula for calculating the expected return of an asset given its risk is as follows:

​ERi​ =Rf​+βi​(ERm​−Rf​ )

where:

ERi​=expected return of investment

Rf​=risk-free rate = 3%

βi​=beta of the investment

(ERm​−Rf​)=market risk premium​ =(5% - 3%) = 2%

So accordingly in question :

CAPM			ERi
Abbey Plc	3% + 0.4 (5%-3%)	3% + 0.8%	3.80%
1PM Plc	3% + 1.8 (5%-3%)	3% + 3.6%	6.60%
32 Red Plc	3% + 0.9 (5%-3%)	3% + 1.8%	4.80%

Beta of Portfolio Formula :

To calculate the beta of a portfolio, you need to first calculate the beta of each stock in the portfolio. Then you take the weighted average of betas of all stocks to calculate the beta of the portfolio.

so in our case BETA of all stock :

0.4 + 1.8 + 0.9 = 3.1/3 =1.0333333 or 1.03 Beta of Portfolio