To answer this question, we need to utilize the Capital Asset Pricing Model (CAPM), which is a financial model used to determine the theoretically appropriate required rate of return of an asset, given its risk as measured by beta, and assuming markets are well-functioning and investors want compensation for both time value and risk. The CAPM formula is:
Required Return = Risk-free Rate + (Beta * Market Risk Premium)
The risk-free rate in this question is provided as 6% (or 0.06 in decimal form), the market risk premium is 5% (or 0.05 in decimal form), and the beta for the index fund is 1.0.
Now, let's apply the CAPM formula using the provided data:
Required Return = 0.06 + (1.0 * 0.05)
Required Return = 0.06 + 0.05
Required Return = 0.11 or 11%
With the calculations done, let's evaluate the statements:
a. This statement says an Index fund with beta = 1.0 should have a required return less than 11%. This is not correct because we calculated exactly 11%.
b. This statement implies that the required return on a stock is directly proportional to the beta of the stock. However, doubling the beta of a stock does not double the entire required return, only the portion of the return that is over and above the risk-free rate. So, this statement is incorrect.
c. This statement says that if a stock has a negative beta, its required return must also be negative. Although a negative beta can theoretically indicate that the stock moves in the opposite direction of the market, it does not imply a negative required return because the risk-free rate component of the CAPM equation ensures that the required return remains positive. So, this statement is incorrect.
d. This statement is also incorrect, as we have established that the correct required return, based on the CAPM formula, is exactly 11%, not greater than 11%.
e. This statement correctly reflects our calculation using the CAPM formula that an Index fund with beta = 1.0 should have a required return of 11%.
Therefore, the correct answer is:
e. An Index fund with beta = 1.0 should have a required return of 11%.
