Answer-first summary for fast verification
Answer: 4.94%
B is correct. The first step is to find the expected excess return for each factor, which is calculated by subtracting the risk-free rate from the expected return as follows: for factor P it is 5.40% - 2.10% = 3.30%, for factor Q it is 6.80% - 2.10% = 4.70%, and for factor R: 3.00% -2.10% = 0.90%. Multiplying by the respective factor betas for stock BBZ provides the contribution to the stock's expected return from its factor exposures: 0.95 * 3.30% + (-0.40) * 4.70% + 1.20 * 0.90% = 2.34%. Then, to find the total expected return for stock BBZ, add the alpha and the risk-free rate to the stock's expected return from its factor exposures, to get 2.34% + 0.50% + 2.10% for a total expected return of 4.94%. A is incorrect. This choice forgets to add back the risk-free rate. C is incorrect. This choice uses the total returns for each factor instead of the excess returns before multiplying by the factor betas, and also forgets to add in the alpha. This choice and choice D also do not add in the risk-free rate at the end since it was already incorrectly captured three times through the use of the total returns. D is incorrect. This choice uses the total returns for each factor instead of the excess returns.
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A pension fund's equity analyst is assessing a potential investment in stock BBZ by using an internal three-factor model. This model evaluates stock performances based on three distinct market factors, each represented by an Exchange Traded Fund (ETF). Each factor in the model is represented by an ETF that has a factor beta of 1 for its own factor and 0 for the other factors. The table below provides the necessary data for the analysis:
| Factor | P | Q | R |
|---|---|---|---|
| Expected annual return of ETF factor | 5.40% | 6.80% | 3.00% |
| Factor beta for stock BBZ | 0.95 | -0.40 | 1.20 |
Considering the details provided, the annualized risk-free rate is 2.10%, and stock BBZ has an alpha of 0.50%. Using the given internal model, calculate the anticipated annual return on stock BBZ.
A
2.84%
B
4.94%
C
6.01%
D
6.51%
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