Question

Suppose you held a diversified portfolio consisting of a $7,500 investment in each of 20 different common stocks. The portfolio's beta is 1.31. Now suppose you decided to sell one of the stocks in your portfolio with a beta of 1.0 for $7,500 and use the proceeds to buy another stock with a beta of 0.97. What would your portfolio's new beta be? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

The new portfolio beta is 1.31 rounded off to two decimal places.

Step-by-step explanation:

The portfolio beta is a function of the sum of the weighted average betas of the individual stock's that form up the portfolio. The portfolio beta is calculated using the following formula,

Portfolio beta = wA * Beta of A + wB * Beta of B + ... + wN * Beta of N

Where,

• w is the weightage of each stock in the portfolio

The beta of the portfolio when one stock with a beta of 1 is sold is,

The sum of individual stock betas for 19 stocks is = 20 * 1.31 - 1 * 1 = 25.2

The new portfolio beta when one stock with a beta of 0.97 is added is,

Portfolio beta = (25.2 + 0.97) / 20

Portfolio beta = 1.3085 rounded off to 1.31