Question

A portfolio is made up of Stocks A, B, C, and D in the proportion of...

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.

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Answer #1

Solution:

The portfolio beta is 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 = 0.20 × 0.4 = 0.08

Stock B beta weighted average = 0.30 × 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 yields the overall portfolio beta:

Portfolio beta = 0.08 + 0.36 + 0.625 + 0.4375

Portfolio beta = 1.5025 = 1.5

Therefore beta of the portfolio = 1.5

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