A$.$ Quantitative Analysis

The part involves quantitative analysis. It will familiarize you with the CAPM, the Fama$-$

French $3-$factor model, and the Fama$-$French$-$Carhart $4-$factor model, and it will help you

understand how to identify mis$-$pricing. To answer the questions in this part, use the data

uploaded on Canvas $($Excel File $"$FF Data.xlsx$").$ We will use the industry$-$sorted stock

portfolios, the Mkt$-$Rf$,$ SMB$,$ HML$,$ UMD portfolios, and the risk$-$free rate. Remember that

all returns in the file are monthly and expressed in percentage points.

Consider the following $5$ industry portfolios: non$-$durable goods $($e$.$g$.$ food$),$ durable

goods $($e$.$g$.$ appliances, furniture$),$ retail, health and utilities. For each industry port$-$

folio, build the time series of its monthly excess returns by subtracting the monthly

risk$-$free rate from its monthly return. Then,

Calculate the average monthly excess return, standard deviation of excess returns,

and the ratio of the two.

Identify whether any of those $5$ industry portfolios has been mispriced historically.

Since you don't know the true model of returns, try three well$-$known models: the

CAPM, the Fama$-$French $3-$factor, and the Fama$-$French$-$Carhart $4-$factor model.

We start from the CAPM:

To identify mispricing relative to the CAPM, run the CAPM regression for each

of the five industries. For convenience, annualize the monthly CAPM alpha by

multiplying it by $12.$ Do you see any mispricing relative to the CAPM that are

statistically significant?

Move on to the Fama$-$French $($FF$)$ model. This is a $3-$factor model: the factors are

Mkt$-$Rf$,$ SMB and HML$.$

To identify mispricing relative to the Fama$-$French model, run the FF$3-$factor

regression for each of the five industry portfolios. Again, annualize the monthly

FF $3-$factor alpha by multiplying it by $12.$ Do you see any mispricing relative to

the FF model $-$ any statistically significant FF alphas?

Lastly, we use the Fama$-$French$-$Carhart $($FFC$)$ four$-$factor model.

To identify mispricing relative to the Fama$-$French$-$Carhart model, run the $4-$

factor regression for each of the five industry portfolios. Again, annualize the

monthly FFC $4-$factor alpha by multiplying it by $12.$ Do you see any mispricing

relative to the FFC model $-$ any statistically significant FFC alphas?