Question

Your portfolio is comprised of 36 percent of Stock X, 18 percent of Stock Y, and 46 percent of Stock Z. Stock X has a beta of 1.19, Stock Y has a beta of 87, and Stock Z has a beta of 1.26. What is the beta of your portfolio?

a) 1.16
b) 1.18
c) 1.09
d) 1.13
e) 1.11

Answer 1

The portfolio beta is a weighted average of individual stock betas, but a likely typo in the beta of Stock Y raises the calculated portfolio beta to an unusually high number. Assuming a corrected beta for Stock Y, the beta of the portfolio is 1.16.

Step-by-step explanation:

The beta of your portfolio can be calculated by taking the weighted average of the betas of the individual stocks. To do this, you multiply the beta of each stock by its percentage composition in your portfolio and then sum up these values.

Here is the calculation:
Beta of portfolio = (Percentage of Stock X * Beta of Stock X) + (Percentage of Stock Y * Beta of Stock Y) + (Percentage of Stock Z * Beta of Stock Z)

Plugging in the numbers given:
Beta of portfolio = (0.36 * 1.19) + (0.18 * 87) + (0.46 * 1.26)

Calculating each term:
= (0.4284) + (15.66) + (0.5796)

Summing these up gives us the portfolio beta:
= 16.668

Looks like there is a typo in the beta of Stock Y, as a beta of 87 is extremely high for a stock and likely not intended. Assuming it's a typo and the intended beta for Stock Y is 0.87 (common for stocks), the correct calculation would be:
Beta of portfolio = (0.36 * 1.19) + (0.18 * 0.87) + (0.46 * 1.26)

Calculating again with the corrected beta:

= (0.4284) + (0.1566) + (0.5796)

Adding these values gives us:

= 1.1646

rounded to two decimal places:
The beta of the portfolio is 1.16 (assuming correction in beta of Stock Y).