Answer-first summary for fast verification
Answer: 11.98%
The expected return is calculated using the Fama-French three-factor model formula: $$E(R_c) = \alpha + \beta_{c,M} [E(R_M) - r] + \beta_{c,SMB} E(SMB) + \beta_{c,HML} E(HML)$$ Where: - $\alpha$ = 2.5% (company-specific alpha) - $\beta_{c,M}$ = 0.35 (market beta) - $E(R_M)$ = 11.5% (expected market return) - $r$ = 1.7% (risk-free rate) - $\beta_{c,SMB}$ = 1.36 (SMB factor loading) - $E(SMB)$ = 3.2% (expected SMB premium) - $\beta_{c,HML}$ = -0.66 (HML factor loading) - $E(HML)$ = 0.0% (expected HML premium) Plugging in the values: $$E(R_c) = 1.7\% + 2.5\% + 0.35[11.5\% - 1.7\%] + 1.36 \times 3.2\% - 0.66 \times 0.0$$ Step-by-step calculation: 1. Risk-free rate: 1.7% 2. Alpha: 2.5% 3. Market premium component: 0.35 × (11.5% - 1.7%) = 0.35 × 9.8% = 3.43% 4. SMB component: 1.36 × 3.2% = 4.352% 5. HML component: -0.66 × 0.0% = 0% Total: 1.7% + 2.5% + 3.43% + 4.352% + 0% = 11.982% ≈ 11.98% The calculation shows that option B (11.98%) is the correct expected return for the company.
Author: Tanishq Prabhu
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Greystone Asset Managers' investment analyst argues that a company's Fama-French main dependencies are:
| Value | |
|---|---|
| HML | −0.66 |
| SMB | 1.36 |
| Beta | 0.35 |
Because of its advantages over its competitors, the analyst believes the company can produce an additional 2.5% return every year. The market forecast is as follows:
| Expected return on equities | 11.5% |
|---|---|
| SMB | 3.2% |
| HML | 0.0% |
| Risk free rate | 1.7% |
The expected return of the company is closest to?
A
10.87%
B
11.98%
C
11.91%
D
15.5%