Question

​(Security market​ line)  You are considering the construction of a portfolio comprised of equal investments in each of four different stocks. The betas for each stock are found​ below:

Asset	Beta
A	2.30
B	1.05
C	0.45
D	−1.70

a.  What is the portfolio beta for your proposed investment​ portfolio?

b.  How would a 25 percent increase in the expected return on the market impact the expected return of your​portfolio?

c.  How would a 25 percent decrease in the expected return on the market impact the expected return on each​asset?

d.  If you are interested in decreasing the beta of your portfolio by changing your portfolio allocation in two​stocks, which stock would you decrease and which would you​ increase? ​ Why?

Answer 1

a.

As we are investing in all the assets equally our beta of the portfolio will be average of all the betas.

So Beta of Portfolio will be equal to Sum of beta of A,B,C,D/4

= (2.30 + 1.05 + 0.45 + (-1.70))/4

= 2.1/4

= 0.525

b.

As we know beta is the responsiveness of a stock or portfolio against the market. So if the market grows 25% then the stock will respond to it according to its beta. So the 25% growth in market will reflect in portfolio by 25% * 0.525

= 0.25 * 0.525

= 0.13125

= 13.125%

The Portfolio will grow by 13.125%

c. Similarly if the market will fall by 25% so the portfolio will by 13.125%

d. If I want to decrease the beta of portfolio then we would decrease the allocation of stocks with high beta so that the average falls. So We will decrease the proportion of Asset A and B in the portfolio.