When dealing with factors information is important to go to the detail and get insight about how the factor is built. Ratios combination improves robustness.

When we read papers or studies about the Factor Premium of different factors we almost always come across with the problem of how to define those factors:

If we talk about Value Factor, we read in many papers that the factor is measured by the **Price to Book **Ratio, others decide that is better to use **Enterprise Value to EBITDA**, another… we could go on endlessly. The problem with this inconsistency is that depending on the measurement used you can reach slightly different conclusions.

Then, when you read quotes about the behaviour of a factor according to this or that author, you can read things like: “…the Factor Value behaved great during 2009…” We should ask, How is the factor built? What ratios have been used? Can we expect the same behaviour with factors created from different measurements, at least in the long run? The short answer is no. In fact, the results expected from a ratio/measurement may vary during the history, in some cases due to the popularity reached by the measurement among practitioners.

Let us see some examples of what we are describing above:

If we compare the deciles obtained ranking the **EBITDA to EV** and the **Book to Prices** over the **S&P 500** components in the period 1/1/2000 – 4/29/2022 it is clear that the first ratio performs much better in the top deciles and much worse in the bottom deciles.

Regarding the risk, **EBITDA to EV** also shows more shallow drawdowns in the top deciles than the **Book to Price**.

According to these results the premium of the value factor represented by EBITDA to EV would be more interesting. However, let us split up the simulation period and see what happens in the top deciles:

From 2000 to 2010, the results of the top decile show again that the EBITDA ratio performs better than the Book to Price:

However, look what happens if, based on the previous curves, we had decided to choose EBITDA To EV as our Value Factor representant:

The evolution of the top decile of ranked by Book to Price beats the EBITDA To EV one.

## How to be more robust?

A simple way to improve the robustness of a factor definition is simply combining several connected measurements. We should make sure that the structure of the ranking of the measurements be similar; we could calculate the kendall correlation to get a sense of this.

In the case at hand, we are going to **average **the two ratios *EBITDA To EV* and *Book to Price*. Before that, we must **normalize **the ratios so that they are in similar intervals. In this case we use the z-score.

Comparing the new Value Factor top decile with the results obtained with the individual ratios, we realise that, at some periods, the combined factor can even beat both of the ratios, and it cushions some of the worst results.

## Conclusion

- When dealing with factors is important to go to the detail and get insight about how the factor is built and what measurements are used.

- Same factors defined differently may produce quite different outputs.

- The combination of linked ratios/measurements to define a factor gives robustness to the expected outcomes.