Fama$-$French Three$-$Factor Model.

In this problem, you will analyze the risk$-$factors associated with stocks in a portfolio. To limit the

amount of work, consider a portfolio of five stocks that you would put into a portfolio. You may decide

their weight in a hypothetical portfolio.

Download the Excel spreadsheet Portfolio$\_$Returns.xlsx from Blackboard. The file contains the monthly

excess returns $R_i=r_i-r_f$ in percent for a wide range of stocks and for QQQ $($Nasdaq ETF$),$ IWM

$($Russell ETF$),$ and MCHI $($China ETF$).$ Additionally, the file contains the time series ExcMkt, SMB$,$ and

$HML,$ representing the excess market return, the small$-$minus$-$big return, and the high$-$minus$-$low return

these are the factors of the Fama$-$French Three$-$Factor model.

With data from the Excel file, solve the following problems:

a$)$ Calculate $,$ using the single$-$factor model for each of the five stocks by rung a regresion in

Excel.

b$)$ Estimate their risk $($systematic and firm$-$specific$)$ according to the single$-$factor model.

c$)$ Calculate the weights of the stocks in your portfolio. Remember, stocks you're selling short have

negative weights, and the weights need to sum up to one.

d$)$ Produce a return time series for your portfolio of the largest three stocks, using $R_P(t)=$

$w_1{R}_1(t)+w_2{R}_2+w_3{R}_3.$ Estimate your portfolio's sensitivity to Fama$-$French's three factors,

that is$,$ run the regression

$R_P(t)={}_P+{}_M{R}_M(t)+{}_{SML}SML(t)+{}_{HML}HML(t)+e_P.$

Remember: ${}_m$ is a proxy to how much market risk your portfolio carries; ${}_{SML}$ is your exposure

to small over big firms; ${}_{HML}$ is your exposure to firms with a high book value compared to their

market capitalization. These three betas are assumed to be non$-$diversifiable risk factors, and in

the long run investors should be rewarded for their risk of having greater betas.

e$)$ Analyze your results. This includes, but is not limited to: classifying your portfolio in terms of

aggressiveness, small vs large cap, value vs growth; identifying which of your holdings

potentially contribute to the portfolio classification how; using the expected values of

$R_M,SML,HML$ to compute the expected return of your portfolio in the coming month.