The beta of a portfolio...
Portfolio beta
calculation
The beta of a portfolio can be calculated if the information about
the beta of each stock in the portfolio and the amount invested in
each stock is known. The formula is a weighted average of the
individual stock beta coefficients
bP = S = Wibi i = 1
Where:
bP = Beta coefficient of the portfolio
m = Number of securities in the portfolio
Wi = Relative weight invested in each security
bi = Beta coefficient of security i
i = Each specific security
Example
To illustrate the use of the formula, suppose that a portfolio contains the following stocks
| Security | Amount Invested | Coefficient Beta |
| Stock A | $1,000 | 0.80 |
| Stock B | $2,000 | 0.95 |
| Stock C | $3,000 | 1.10 |
| Stock D | $4,000 | 1.40 |