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Financial Risk Manager Part 1

Financial Risk Manager Part 1

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Greystone Asset Managers' investment analyst argues that a company's Fama-French main dependencies are:

Value
HML−0.66
SMB1.36
Beta0.35

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 equities11.5%
SMB3.2%
HML0.0%
Risk free rate1.7%

The expected return of the company is closest to?

Other
Community
TTanishq

Explanation:

The expected return is calculated using the Fama-French three-factor model formula:

E(Rc)=α+βc,M[E(RM)−r]+βc,SMBE(SMB)+βc,HMLE(HML)E(R_c) = \alpha + \beta_{c,M} [E(R_M) - r] + \beta_{c,SMB} E(SMB) + \beta_{c,HML} E(HML)E(Rc​)=α+βc,M​[E(RM​)−r]+βc,SMB​E(SMB)+βc,HML​E(HML)

Where:

  • α\alphaα = 2.5% (company-specific alpha)
  • βc,M\beta_{c,M}βc,M​ = 0.35 (market beta)
  • E(RM)E(R_M)E(RM​) = 11.5% (expected market return)
  • rrr = 1.7% (risk-free rate)
  • βc,SMB\beta_{c,SMB}βc,SMB​ = 1.36 (SMB factor loading)
  • E(SMB)E(SMB)E(SMB) = 3.2% (expected SMB premium)
  • βc,HML\beta_{c,HML}βc,HML​ = -0.66 (HML factor loading)
  • E(HML)E(HML)E(HML) = 0.0% (expected HML premium)

Plugging in the values:

E(Rc)=1.7%+2.5%+0.35[11.5%−1.7%]+1.36×3.2%−0.66×0.0E(R_c) = 1.7\% + 2.5\% + 0.35[11.5\% - 1.7\%] + 1.36 \times 3.2\% - 0.66 \times 0.0E(Rc​)=1.7%+2.5%+0.35[11.5%−1.7%]+1.36×3.2%−0.66×0.0

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.

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