# Is this a reasonable approach to determine the relative importance of valuation factors?

I am trying to come up with a measure of relative importance of a number of valuation factors. I am wondering whether correlation coefficients can't be used for determining this.

More on the issue: My goal is to determine whether sectors are over or undervalued when comparing current valuation metrics with historical. For example, let's assume I have P/B and P/E metrics for the consumer discretionary sector and on a P/B basis, the sector is undervalued but on a P/E basis it is overvalued. I am trying to build a way to sort this out to come up with a over/undervalued determination when you have valuation metrics that are contradictory.

My thought is to use metrics in time t-1 and returns in time t. Using this data I am thinking I can find correlations and use the correlation coefficients as the relative weights when trying to build a mechanism to determine whether a sector is over or undervalued.

Is this a reasonable approach? Any recommendations you have would be helpful. Thanks!

## 2 Answers

Are you really interested in ranking different indicators, or do you just want to know how you should combine them to make the best predictor possible? Is there any reason you can't use several together?

Correlation coefficients would certianly be a reasonable starting point for this. You have two obvious problems that come up if you do it this way:

1. A correlation coefficient doesn't tell you how economically significant the relationship is, just how statistically significant. In other words, a certain variable might correlate very closely with returns, but the difference in the returns might be very small for different values of the variable. However, if you are comparing different predictors for the same population, there is a total amount of variability, and something with a higher correlation coefficient will explain more of it. But it might not be possible for you to realise all the information you have as gains. For example, being able to identify big losers and big winners could be much more valuable than sorting out the mass of small winners and small losers from each other.
2. You will find that your indicators are correlated with each other. How do you measure the contribution each makes to determining valuation? Typically if you have two variables, both together will predict better than either one on its own. You might want to do various linear regressions with different sets of parameters and use some way of deciding which is the best. Correlation coefficients are closely related to single-variable regression, so this approach is kind of a generalization of using corrlation coefficients.

Calibrating in time t-1 and using the results to predict time t is also a reasonable approach. You should be careful of overfitting. This is when you develop a model which doesn't have any real content, but just happens by coincidence to match exactly how well something has done in t-1 and so doesn't work in any other period. You can take further periods and look for something which works pretty well over all of them to try and get round this. Or you could use various techniques like log-likelihood to measure how complex your model should optimally be.

If you really want to compare different indicators taken in isolation, paper trading could be a good way, although it makes more financial sense than statistical sense. Formulate a similar strategy for each indicator, eg. buy the best 10% and short the worst 10%, and see which would have made the most money after a certain time. This will force you to decide what time scale you are going to look for returns over (or to develop some other way of choosing when to close out positions), which is critical for statistical strategies.

The approach you describe of looking at the valuation metrics in one period versus the returns in the next is similar to cross-sectional factor models, like Barra, or the Fama-Macbeth procedure. In these methods, instead of looking at the correlation, you do a cross-sectional regression of the returns (or excess returns or alpha) against whatever factors, such as valuation metrics, you want. The coefficients of the regressions represent the returns to the various factors. The expected return and volatility of these factors would determine their relative importance.