Portfolio Beta and Required Return You hold the positions in the table below. Wh
ID: 2731891 • Letter: P
Question
Portfolio Beta and Required Return You hold the positions in the table below. What is the beta of your portfolio? If you expect the market to earn 12 percent and the risk-free rate is 3.5 percent, what is the required return of the portfolio?
Company Price #Shares Beta
GG 40.00 100 3
IceStone 30.00 150 1
Bridgerock 50 75 0.3
CT 20 200 0.4
This problem can be solved two different and equivalent ways. Both ways require the weights of the stocks in the portfolio. In one method, compute the required return for each stock and then use the weights to form the portfolio required return. The other solution uses the weights to compute the portfolio beta. This portfolio beta is used to compute the portfolio required return. How to solved using both different ways. Please show work.
Explanation / Answer
Total value of portfolio = 40 * 100 + 30 * 150 + 50 * 75 + 20 * 200
= $ 16250
Weight of GG = 40 *100 / 16250 = 0.25 (approx)
Weight of Icestone = 30 *150 / 16250 = 0.28 (approx)
Weight of Bridgerock = 50 * 75 / 16250 = 0.23 (approx)
Weight of CT = 20 * 200 / 16250 = 0.24 (approx)
Beta of Portfolio = 0.25 * 3 + 0.28 *1 + 0.23 * 0.3 + 0.24 * 0.4
= 1.195
Required rate of return = Risk free rate + Beta of porflio * ( Market return - risk free rate)
= 3.5 + 1.195 * (12 - 3.5)
= 3.5 + 10.1575
= 13.6575 %
Conclusion:-
Beta of portfolio 1.195 Required return of portfolio 13.6575 % i.e., 13.66 % (approx)