# Do Fama-French factor portfolios require optimization?

I am going to perform crowding analysis for my dissertation and I am struggling to build factor portfolios from the S&P 500 in . I built my dataset from the S&P 500 and I am able to add a column that signal me for each stock and time if it is going to be in the long ptf, in the short ptf or neither of them. However when it comes to really build the portfolio I have some problem at optimizing in because I use very restrictive constraint.

I just wanted to be sure that this kind of problem requires optimization and not a simple weighted average. Could I come up with a portfolio beta-neutral and dollar-neutral just by summing stock returns according to some weight?

It is so not clear what you are trying to do, and I suggest you read Fama-French (1992, 1993) papers first before touching any data.(Read again if you have already, because you seem very confused).

Fama-French do not do portfolio optimization. They merely sort stocks based on characteristics, group them into portfolios and take the returns, and then run regressions of individual stock returns on those characteristics.

Anyways, here is what you need to do in order to construct Fama-French factors.

1. Calculate the Market Capitalization of each stock on the last trading day of June, every year. Use CPI index in order to inflation-adjust the market caps.
2. For every year, divide stocks into two groups: Big stocks (B), whose calculated market cap in (1) is higher than the Median NYSE market cap on that year. the ones lower than the median are Small (S) stocks.
3. Similar process follows for the Value factor. Sort the portfolios based on the Book to Market ratios. and then divide the stocks into three groups. (High (H), Medium (M), Low (L)).
4. You should have 6 portfolios now based on these two sorts. Calculate value-weighted monthly return of each portfolio for each month in the sample.
5. Construct the Value (HML) factor. It is a zero cost portfolio: The return of the HML is the average return of two High book/market portfolios (B/H and S/H) minus the average return of two low book/market portfolios (B/L and S/L).
6. Construct the Size (SMB) factor. It is a zero cost portfolio: Difference between the average return of three small portfolios (S/H, S/M, S/L) and three large ones (B/H, B/M, B/L)
7. It is a good practice to compare your return results to the factors returns available on Kenneth French Website.
8. Construct your MKT factor as well. and then regress your returns on these three portfolios. Your regression should follow $$R_{i,t} = \alpha_{i} + \beta_{MKT,i}MKT_t + \beta_{SMB,i}SMB_t + \beta_{HML,i}HML_t + \epsilon_{i,t}$$

in which $$i$$ represents your individual stock or portfolio. The $$\beta$$ s tell you how much your stock or portfolio is loaded on each factor.

P.S: There are lots of details in the empirical process. Refer to the papers to make sure your mimic process is accurate. Again, first read the papers and make sure you understand. Then go to data. Then refer back to papers to fill in the gaps.