Question

Ally holds a RM200,000 portfolio consisting of the following stocks. The portfolio's beta is 0.875.

Stok [Stock] Pelaburan [Investment] (RM) Beta

A 50,000 0.50

B 50,000 0.80

C 50,000 1.00

D 50,000   1.20

Total 200,000

1. If Ally replaces Stock A with another stock E, which has a beta of 1.50, what will the portfolio's new beta be?

2. Company A has a beta of 0.70, while Company B's beta is 1.20. The required return on the stock market is 11.00%, and the risk-free rate is 4.25%. What is the difference between A's and B's required rates of return?

3. Suppose you hold a portfolio consisting of a RM10,000 investment in each of 8 different common stocks. The portfolio’s beta is 1.25. Now suppose you decided to sell one of your stocks that has a beta of 1.00 and to use the proceeds to buy a replacement stock with a beta of 1.35. What would the portfolio’s new beta be?

4. If a company’s beta were to double, would its required return also double? Explain

5. A stock had a 8.47% return last year, a year when the overall stock market declined. Does this mean that the stock has a negative beta and thus very little risk if held in a portfolio? Explain

Answer 1

1.

Stocks	Investment Amount	Weight	Beta	Weighted Beta
A	50000	0.25	0.50	0.125
B	50000	0.25	0.80	0.20
C	50000	0.25	1	0.25
D	50000	0.25	1.2	0.30
TOTAL	200000	1		0.875

If Ally replaces Stock A with another stock E, which has a beta of 1.50, the portfolio's new beta will be:-

Stocks	Investment Amount	Weight	Beta	Weighted Beta
E	50000	0.25	1.5	0.375
B	50000	0.25	0.80	0.20
C	50000	0.25	1	0.25
D	50000	0.25	1.2	0.30
TOTAL	200000	1		1.125

The portfolio new beta will be 1.125.

2. Difference between A's and B's required rate od return

rA= 4.25%+(11%-4.25%) *0.7= 8.975%

rB= 4.25%+(11%-4.25%) *1.2= 12.35%

Difference= 12.35-8.975= 3.375%

3. Change in portfolio beta= Weight *(change in security beta)= 0.125 *(1.35-1)= 0.4375

New portfolio beta= 1.25+ 0.4375= 1.29375

4. If a company's beta is doubled then its required rate of return would not be doubled because the risk free rate od return is also a component of CAPM( Required return= Risk free rate+ Beta(Market return- risk free rate ) for calculating the desired result.

5.When as stock has negative beta it means that its returns would have to go up in the future when other stocks' return were falling. Assuming that in one year the stock's return increase when market declined, it doesn't mean that the stock has a negative beta. So, it does not mean that if a stock has a negative beta, there is very little risk if it were to be held in a portfolio.