# Predicting stock returns - in a panel data specification or by using portfolio formation strategies?

I'm working on an empirical analysis where I try to predict stock returns using weekly data. Ideally, I would like to use a panel data model like the following: $$Y_{it}=X_{it}'\beta+\varepsilon_{it}$$

(here presented in a very simple format - it will be more complex in the analysis)

Here $Y_{it}$ is a vector of weekly returns and $X_{it}$ is a vector of explanatory variables with coefficients vector $\beta$.

However, in much of the empirical literature this is not the standard approach. Standard approach involves the sorting of stocks into different portfolios and using portfolio formation strategies.

My questions are:

1) Why is the portfolio approach the standard approach?

2) What are the caveats from using a panel data model?

3) Can explanatory variables typically found in the literature on the prediction of stock returns (e.g. size, P/E ratio, P/B ratio and momentum for each company) also be used in a panel data model?

Both approaches can be useful. For stocks, sorting into quantiles is popular because

1. it's easy to understand and explain
2. it's a simple matter to build factor portfolios and track or backtest their performance, while the translation from expected returns to a portfolio is a bit more involved
3. more robust than a single-stock regression, because it is less affected by stock-specific effects which make a predictive regression very noisy
4. avoids the rigidity of a linear model, which is a good idea because there are sometimes interesting 'outlier effects' in the first and last quantiles

Regarding your second and third question: there are sector- and country-specific effects (e.g. the valuation of technology vs. finance stocks) which will be important. In a weekly model, the variables size, P/E and P/B will often only vary with 'P', which limits their use as independent variables.

• Thank you for your very useful comments. As I understand your answers, there is nothing wrong with using a panel data model besides some of the caveats you mention. You make a very good point with regards to the weekly variables P/E, P/B and size only varies with price. Do you have any suggestions as to variables that could be included instead? Do you know of any research that employs a panel data framework and no sorting of stocks into portfolios? – Sunv Sep 9 '14 at 17:54
• @Sunv you can use fundamental variables as you suggested, or switch to macroeconomic or statistical factors which will change your regression model. In your setting with the data panel, you could include balance sheet numbers, analyst revisions, ownership data etc., the choice is quite large. – Felix Sep 10 '14 at 9:41
• do you have suggestions to literature on the empirical analysis of stock returns that applies panel data models and e.g. balance sheet numbers, analyst revisions etc.? Or suggestions as to where I might find inspiration? Thanks again! – Sunv Sep 10 '14 at 11:39
• @Sunv try chapter 15 of Zivot & Wang "Modeling Financial Time Series with S-Plus", or chapter 8 of Fabozzi, Focardi & Kolm "Financial Modeling of the Equity Market" – Felix Sep 10 '14 at 15:16
• Thanks for your answer once again. I looked up the chapters you're referencing, but I didn't find anything on panel data models there. Or have I misunderstood something? – Sunv Sep 11 '14 at 9:29