Question

Considering the following information, calculate the required rate of return for the Global Investment Fund holding 4 stocks.

Market's required rate of return: 13.25%
Risk-free rate: 7.00%
Stock investments and betas:
a) $200,000, 1.50
b) $300,000, -0.50
c) $500,000, 1.25
d) $1,000,000, 0.75

Options:
a) 9.58%
b) 10.09%
c) 10.62%
d) 11.18%
e) 11.77%

Answer 1

To calculate the required rate of return for the Global Investment Fund, the weighted beta of the portfolio is calculated and applied using the CAPM formula. The total calculated weighted beta is 0.7125, and the final required rate of return is approximately 11.45%, with the closest given option being 11.18%, which is option "d".

Step-by-step explanation:

To calculate the required rate of return for the Global Investment Fund, we need to use the Capital Asset Pricing Model (CAPM). CAPM formula is given by: E(Ri) = Rf + [βi * (E(Rm) - Rf)], where E(Ri) is the expected return on the investment, Rf is the risk-free rate, βi is the beta of the investment, and E(Rm) is the expected return of the market. We will calculate the weighted average return of the stocks, also known as the portfolio beta, and then apply it to the CAPM formula.

First, we find the total value of the investment:

• $200,000 + $300,000 + $500,000 + $1,000,000 = $2,000,000

Next, we calculate the weighted beta for the portfolio:

• ($200,000/$2,000,000) * 1.50 + ($300,000/$2,000,000) * -0.50 + ($500,000/$2,000,000) * 1.25 + ($1,000,000/$2,000,000) * 0.75 = 0.7125

Finally, applying the weighted beta to the CAPM formula:

• Required rate of return = 7% + (0.7125 * (13.25% - 7%))
• Required rate of return = 7% + (0.7125 * 6.25%)
• Required rate of return = 7% + 4.453125%
• Required rate of return = 11.453125%

The closest option to our calculation is 11.18% which is option "d".