This exercise asks you to apply the Fama$-$French $3$ factor model to evaluate how risk factor sensitivity is estimated at the portfolio level.

$R_{i,t}^e={}_i+{}_{i,M}{R}_{MKT}^e+{}_{i,SMB}SM{B}_t+{}_{i,HML}HM{L}_t+e_{i,t}$

To simplify notation in the regression notice that:

$R_{i,t}^e=R_{i,t}-R_{F,t}=$ is stock or portfolio $i^{th}$ excess return and $R_{MKT}^e=R_{Mt}-R_{F,t}=$ is the excess return on a "stock market portfolio".

SMB $=$ Small Minus Big, i$.$e$.,$ the return of a portfolio of small stocks in excess of the return on a portfolio of large stocks.

HML $=$ High Minus Low, i$.$e$.,$ the return of a portfolio of stocks with a high book$-$to$-$market ratio in excess of the return on a portfolio of stocks with a low book$-$to$-$market ratio.

Consider the monthly returns from Nov$-2008$ to October $2017$ produced by a popular mutual fund Fidelity Magellan $($FMAGX$).$ This fund seeks capital appreciation. The fund invests primarily in common stocks. It invests in either "growth" stocks or "value" stocks or both.

$\backslash$table$[[$DATE$,$MKT$,$SMB$,$HML$,$RETX$\_$FMAGX$],[2008$M$11.,-7\mathrm{.}86,-2\mathrm{.}99,-5\mathrm{.}94,-11\mathrm{.}36],[2008$M$12,1\mathrm{.}74,3\mathrm{.}59,-0\mathrm{.}24,4\mathrm{.}63],[2009$M$01,-8\mathrm{.}12,-0\mathrm{.}01,-11\mathrm{.}1,-7\mathrm{.}31]]$

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In the estimation of the model, choose heteroscedasticity$-$robust standard errors.

Question $4$: The estimated model is $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$:

$R_i^e=$

$q,+,-R^{e}q,SM{B}_t+q,HML$

a$.R_i^e=-2\mathrm{.}23+0\mathrm{.}01*R_{MKT}^e+0\mathrm{.}50*SM{B}_t-1\mathrm{.}99*HM{L}_t$

b$.R_i^e=-1\mathrm{.}44+1\mathrm{.}99*R_{MKT}^e+1\mathrm{.}40*S_{MB}^t-1\mathrm{.}12*HM{L}_t$

c$.R_i^e=-2\mathrm{.}01+3\mathrm{.}15*R_{MKT}^e+2\mathrm{.}90*SM{B}_t-0\mathrm{.}46*HM{L}_t$

d$.R_i^e=-0\mathrm{.}08+1\mathrm{.}03*R_{MKT}^e+0\mathrm{.}20*S_{MB}^t-0\mathrm{.}08*HM{L}_t$

$R_i^e=-2\mathrm{.}17+1\mathrm{.}03*R_{MKT}^e+3\mathrm{.}20*S_t-1\mathrm{.}43*HM{L}_t$

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