Question

Steve Brickson currently has an investment portfolio that contains four stocks with a total value equal to $80,000. The portfolio has a beta (β) equal to 1.4. To earn higher returns, Steve wants to invest an additional $20,000 in a stock that has β equal to 2.4. After Steve adds the new stock to his portfolio, what will the portfolio's beta be?

Answer 1

if Steve adds the new stock to his portfolio, then, the portfolio's new beta will be 1.6.

The Beta of Portfolio equals the Weighted Average because the weights are based on the market value of each stock.

Given Information

Beta of the portfolio = 1.4

Value of the Portfolio = $80,000

New Stock Beta = 2.4

Stock Value = $20,000

• The formula for Beta of the New Portfolio is [(Existing Portfolio Beta x Existing Portfolio Value) + (New Stock Beta x New Stock Beta)] / Existing Value of Portfolio + Value of New Stock

Beta of the New Portfolio = ($80,000 x 1.4 + $20,000 x 2.4) / $80,000 + $20,000

Beta of the New Portfolio = ($112,000 + $48,000) / $100,000

Beta of the New Portfolio = 160,000 / 100,000

Beta of the New Portfolio = 1.6

Therefore, in conclusion, if Steve adds the new stock to his portfolio, then, the portfolio's new beta will be 1.6.

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