Calculate the Beta of the New Portfolio After Selling a Stock

What will be the beta of the new portfolio if you sell a stock with beta 0.7 and purchase a stock with beta 1.4?

a. 1.165

b. 1.235

c. 1.250

d. 1.284

e. 1.333

Answer:

The new beta of the portfolio will be 1.235.

Imagine you have a diversified portfolio with $10,000 invested in each of 20 different common stocks, totaling $200,000. The portfolio's beta is 1.2. Now, you decide to sell a stock with a beta of 0.7 for $10,000 and use the proceeds to purchase another stock with a beta of 1.4.

To calculate the new beta of the portfolio after this transaction, we need to consider the increment in beta. The formula for increment in beta is:

Increment in Beta = Investment × (Purchase Stock's Beta - Sell Stock's Beta) ÷ Total Investment

Putting the given values into the formula, we get:

Increment in Beta = [tex]\frac{10000*(1.4-0.7)}{200000}[/tex]

Increment in Beta = 0.035

Therefore, the new beta of the portfolio will be the current beta (1.2) plus the increment in beta:

New Beta of the Portfolio = 1.2 + 0.035 = 1.235

So, the correct option is b. 1.235.