Question

A portfolio is made up of stocks a, b, c, and d in the proportion of 20%, 30%, 25%, and 25% respectively. the nondiversifiable risks of the stocks as measured by their betas are 0.4, 1.2, 2.5, and 1.75 for stock a, b, c, and d respectively. the expected returns of the stocks are 12%, 24%, 30%, and 28% respectively. measure the beta of the portfolio.

Answer 1

The portfolio beta would simply be the summation of the weighted average of each beta.

Where weighted average of each beta is calculated as:

Stock weighted average = Stock proportion * Individual beta

Therefore,

Stock A beta weighted average = 0.2 * 0.4 = 0.08

Stock B beta weighted average = 0.3 * 1.2 = 0.36

Stock C beta weighted average = 0.25 * 2.5 = 0.625

Stock D beta weighted average = 0.25 * 1.75 = 0.4375

The summation of all betas yield the overall portfolio beta:

Portfolio beta = 0.08 + 0.36 + 0.625 + 0.4375

Portfolio beta = 1.5025 ~ 1.5