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.

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

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,

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

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