Question

A client has a 1.2 million portfolio consisting of the following 4 stocks: 300k in a stock with beta of 1.1, 225k in a stock with a beta of 0.7, 405k in a stock with a beta of 0.3 and 270k in a stock with a beta of 1.3. What is the beta of the portfolio as a whole

Answer 1

To calculate the beta of the portfolio as a whole, we need to calculate the weighted average beta of the individual stocks based on their respective values in the portfolio.

Let's calculate the weighted average beta of the portfolio:

Beta of Stock 1 = 1.1

Value of Stock 1 = $300,000

Beta of Stock 2 = 0.7

Value of Stock 2 = $225,000

Beta of Stock 3 = 0.3

Value of Stock 3 = $405,000

Beta of Stock 4 = 1.3

Value of Stock 4 = $270,000

Total Portfolio Value = $1,200,000

To calculate the weighted average beta, we need to multiply the beta of each stock by its corresponding value in the portfolio, and then divide the sum by the total portfolio value.

Weighted Beta = (Beta of Stock 1 * Value of Stock 1 + Beta of Stock 2 * Value of Stock 2 + Beta of Stock 3 * Value of Stock 3 + Beta of Stock 4 * Value of Stock 4) / Total Portfolio Value

Weighted Beta = (1.1 * $300,000 + 0.7 * $225,000 + 0.3 * $405,000 + 1.3 * $270,000) / $1,200,000

Weighted Beta = ($330,000 + $157,500 + $121,500 + $351,000) / $1,200,000

Weighted Beta = $960,000 / $1,200,000

Weighted Beta = 0.8

Therefore, the beta of the portfolio as a whole is 0.8.