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

Part 1

Portfolio beta = Weighted average Beta

Stock	Value	Weights	Beta	Weighted Beta
E	50000	0.25	1.5	0.375
B	50000	0.25	0.8	0.2
C	50000	0.25	1	0.25
D	50000	0.25	1.2	0.3
Weighted Beta	1.125

Part 2

SML Return or CAPM Return = Rf + Beta ( Rm - Rf )
Rf =  Risk free ret
Rm = Market ret
Rm - Rf = Risk Premium
Beta = Systematic Risk

Stock A = 4.25 % + 0.7 (11% - 4.25 %)

= 4.25% +0.7(6.75%)

= 4.25% + 4.73 %

= 8.98%

Stock B = 4.25 % + 1.2 (11% - 4.25 %)

= 4.25% +1.2 (6.75%)

= 4.25% + 8.1%

= 12.35%

Difference in required rate of return = Stock B expected return - Stock A expected return

= 12.35% - 8.98%

= 3.37%

Part C

New Portfolio Beta = Old portfolio beta - (Beta of outgoing stock * weight of Outgoing stock) + ( Beta of incoming stock * Weight of incoming stock)

= 1.25 -( 1* 0.125) + (1.35* 0.125)

= 1.25 -0.125 + 0.1688

= 1.2938

Part 4

Required Retuern = Rf + Beta ( Rm - Rf )

So if the Beta is doubled the Risk premium will be doubled but not the risk free return, so the required return will not be doubled if the if the Beta is doubled

Part 5

Beta represents the systematic risk of a stock, for example if beta is 0.5, 10% change in market will effect the stock by 5%

if both the stock and market are moving in the same direction, the stock must be having positive beta

In the given scenario also both are moving in the sam edirection (Downwards)

Hence the stock is having positive Beta

Pls do rate, if the answer is correct and comment, if any further assistance is required.