Final answer:
The portfolio beta can be calculated by taking the weighted average of the individual stock betas using the market value of each stock as the weight.
Step-by-step explanation:
To find the beta of a portfolio, we need to calculate the weighted average of the individual stock betas, using the market value of each stock as the weight. The formula is:
Beta portfolio = (Market Value of Stock A x Beta of Stock A + Market Value of Stock B x Beta of Stock B + Market Value of Stock C x Beta of Stock C) / Total Market Value of the Portfolio
Using the given information, we can calculate the portfolio beta as follows:
Beta portfolio = (19,000 x 2.04 + 20,000 x 1.08 + 9,600 x 1.21) / (19,000 + 20,000 + 9,600)
This simplifies to:
Beta portfolio = (38,760 + 21,600 + 11,616) / 48,600 = 1.95
The portfolio beta is found by taking the weighted average of the betas of the individual stocks in the portfolio, with each stock's market value acting as the weight. The calculated beta reflects the portfolio's risk relative to the market.
The student has asked how to calculate the portfolio beta of a mix of stocks with given market values and individual betas. The portfolio beta is calculated by taking the sum of the products of the market value of each stock and its beta, divided by the total market value of the portfolio. The formula used is as follows:
Beta_{Portfolio} = (Market Value_{A} \times Beta_{A} + Market Value_{B} \times Beta_{B} + Market Value_{C} \times Beta_{C}) / Total Market Value
In this case:
Beta_{Portfolio} = (($19,000 \times 2.04) + ($20,000 \times 1.08) + ($9,600 \times 1.21)) / ($19,000 + $20,000 + $9,600)
After doing the calculations, one would find the total weighted beta for the portfolio. This value is an indication of the portfolio's overall risk in comparison to the market (usually the market beta is 1).