How to Calculate the Beta of a Portfolio

What is the beta of the portfolio composed of stocks A, B, C, D, and E?

Consider a portfolio with the following stocks:

Stock A: $4 million invested with a beta of 1.8

Stock B: $2 million invested with a beta of 1.6

Stock C: $2 million invested with a beta of 1.4

Stock D: $1 million invested with a beta of 0.8

Stock E: $1 million invested with a beta of 0.4

How do we calculate the beta of the portfolio?

Calculation of the Weighted Average Beta

To calculate the beta of the portfolio, we need to determine the weighted average beta. This can be done by multiplying each stock's beta by its corresponding amount invested and then summing these values.

The formula for calculating the weighted average beta is as follows:

Weighted Average Beta = (BetaA * AmountA + BetaB * AmountB + BetaC * AmountC + BetaD * AmountD + BetaE * AmountE) / Total Investment

In this case, the amounts invested are $4 million, $2 million, $2 million, $1 million, and $1 million for stocks A, B, C, D, and E, respectively. The betas are 1.8, 1.6, 1.4, 0.8, and 0.4 for stocks A, B, C, D, and E, respectively.

Calculating the weighted average beta:

Weighted Average Beta = (1.8 * $4 million + 1.6 * $2 million + 1.4 * $2 million + 0.8 * $1 million + 0.4 * $1 million) / ($4 million + $2 million + $2 million + $1 million + $1 million)

Simplifying the equation, we get:

Weighted Average Beta = (7.2 + 3.2 + 2.8 + 0.8 + 0.4) / $10 million

Weighted Average Beta = 14.4 / $10 million

Weighted Average Beta = 1.44

Therefore, the beta of the portfolio composed of stocks A, B, C, D, and E is 1.44.