1. Explain the (i) rational and (implementation) of one smart beta strategy of your choice.
Value stocks trade at a low market value relative to their book value. Some research shows value stocks perform in the long run better than growth stocks, which are stocks that trade at higher prices relative to their fundamentals.
There is research supporting the claim that past winners tend to outperform past losers. The respective smart beta factor premium would be 'momentum premium'
Research has provided evidence that 'off-the-run Treasuries, earn on average higher returns than the more liquid counterparts, such as on-the-run Treasuries. Therefore，going long the less liquid assets and shorting the liquid ones gives rise to the smart beta premium 'liquidity premium'.
Credit: There exists research arguing that bonds with higher default risk tend to pay higher average returns. The respective smart beta premium is the 'credit risk premium'.
There is empirical research showing that selling options and hedging them in the spot market has on average earned a positive risk premium. The respective smart beta premium is the short volatility risk premium.
2. Write the Fama-French 3-factor model as a multi-factor beta model.
The Fama-French 3-factor model
$f_1 \equiv r_M - r_f \\f_2 \equiv r_{HML} \\f_3 \equiv r_{SIZE} \\\\ \lambda_F = \begin{pmatrix} f_1 \\ f_2 \\ f_3 \end{pmatrix} = \begin{pmatrix} E[r_M]-r_f \\ E[r_{HML}] \\ E[r_{SIZE}] \end{pmatrix}$
The Fama-French 3-factor model can be viewed as I-CAPM Equilibrium model.
$E[r_M]-r_f =⇒ E[r_{i,t}]- r_{f,t-1} = \alpha_i +\beta_{i,M} * E[r_{M,t}- r_{f,t-1}]$=⇒
$u^{dy}, u^{Term}, u^{Def}, u^{rf}$ stands for innovations in the dividend yield, term spread, default spread, risk-free rate.
The term $\lambda_{u^{Term}}$ stands for the market price of term spread risk.