Final answer:
The fund's required rate of return is calculated using the Capital Asset Pricing Model (CAPM) and by determining the weighted average beta of the fund.
After calculating the weights and betas for each stock, the fund's weighted average beta is 0.825.
Using the CAPM with a market rate of return of 14% and a risk-free rate of 6%, the fund's required rate of return is found to be 12.6%.
Step-by-step explanation:
To calculate the fund's required rate of return, we can use the Capital Asset Pricing Model (CAPM), which is expressed by the formula: required return = risk-free rate + (beta × (market rate of return - risk-free rate)). The fund is a mixture of four stocks with different betas, so we need to calculate the weighted average beta of the fund first.
- Stock A: Weight = $400,000 / $4,000,000 = 0.10 and Beta = 1.5
- Stock B: Weight = $600,000 / $4,000,000 = 0.15 and Beta = -0.5
- Stock C: Weight = $1,000,000 / $4,000,000 = 0.25 and Beta = 1.25
- Stock D: Weight = $2,000,000 / $4,000,000 = 0.50 and Beta = 0.75
Weighted average beta = (0.10 × 1.5) + (0.15 × -0.5) + (0.25 × 1.25) + (0.50 × 0.75) = 0.825
Using the CAPM formula and the market rate of return (14%) and the risk-free rate (6%), we get:
Required rate of return = 6% + (0.825 × (14% - 6%)) = 6% + (0.825 × 8%) = 6% + 6.6% = 12.6%
Therefore, the fund's required rate of return is 12.6%.