What is a selection factor?

A selection factor is a financial criterion (or extra-financial) used to select the portfolio securities. This test is for three categories of data: consensus (estimates of the balance sheet and income statement provided by the Sell Side financial analysts), book value (publication of firms) and market (stock market characteristics of the company listed).

We created a tool for historical simulation (backtest) which measures the discriminating power of a selection factor in calculating the performance of an active management strategy induced by this criterion. The performance of the strategy can be summarized as the performance of securities with the best rating using the criteria minus the performance of securities with low rating. The idea is to make each month a number of portfolios in an investment universe, such as five among the 500 largest market capitalizations in Europe. Securities are classified according to the selected factor, from highest rated (quintile 1) to Lowest Rated (quintile 5), then we calculate the performance of each quintile / portfolio as presented in the graph below (quintiles relative performance against the average of the sample).

If Quintile 1 and 2 consistently achieve superior performance to other quintiles and especially better than the Quintile 5 ... then we can say that the selection criterion is discriminating in selecting securities in a portfolio. We note, for example, that the profit on price factor was an effective factor in selection between 2000 and summer 2007 for European equities.

How do you compare the backtests?

In order to compare different backtests these statistics are used fairly simple:
performance gap between the extreme portfolios
volatility of the different portfolios
information coefficient of the strategy (correlation between the signal has on a certain date and the relative performance of the securities in the following period)
absolute and relative maximum loss of a portfolio

Comparison of backtests is key since it is through this analysis that can be combined in a second phase, different discriminating criteria for the final model ...

Can you make them more readable?

Yes, you just have to isolate the monthly portfolio performance induced by selection factors in the form of screening.

The screening is used to represent synthetically the performance of a selection factor. This is, for example, the criterion defined above to defer each month the green curve monthly performance (Q1: securities with good rating) minus the red curve monthly performance (Q5:securities with poor rating). This gives the performance of a long / short portfolio representing the selection factor.

Reading these tables is relatively easy over a year but can become tedious over a long period. On the other side its analysis must be made with caution as this method of representation gives pride to the extreme values (Q1-Q5 performance). A display performance of intermediate values such as the performance of a portfolio strategy (Q1 + Q2) minus the portfolios (Q3 + Q4) is more representative of the "average" discriminating power of the selection factor.

But it is possible to synthesize further the information in a backtest by resuming it in a risk / return ratio, conventionally used in asset allocation. Therefore, we can make an analogy between factors and asset classes: each performance factor is characterized by a risk / return ratio, it is then easy to represent and compare them on a risk / return chart.

How do you account for changes in the market system in the choice of selection factors?

The risk / reward analysis of selection factors helps to understand the behavior of factors depending on the market system ("Bull", ie. Bullish and "Bear", ie. Bearish). For example, for a risk / reward analysis in a "Bear" market, we only keep the "Bearish" months to calculate the risk / return. It is then the quality factor (return on equity) and the dynamic factor of earnings revisions that offer the best risk / reward ratios on the European stocks sector.

In a "Bull" market, the analysis changes: it is the discount factors (cash flow and price ratio and net asset value and price ratio) that offer the best risk / return. We also note that the price momentum factors must be avoided because of their inefficiency and high risk.

changes in the market are becoming more frequent, it is therefore necessary to combine diversifying factors to develop a selection model that presents an optimized risk / return profile for customers. Then of course we must test the robustness of the model by incorporating the costs and management constraints. To illustrate the interest of diversification, we tested three simple combinations: the first is a combination of the least risky factor in a "Bear" market and the least risky factor in a "Bull" market, that is to say the market capitalization (small / large) and return on equity. The second is a mixture of the most performing factor regime in a "Bear" market and the most performing factor regime in a "Bull" market, that is to say, the price momentum over 12 months and the ratio of cash flow over price.

The third is a combination of the factor with the best risk / return ratio in a "Bull" market and the one with the best risk / return ratio in a "Bear" market, that is to say, the net asset value over price and the revision dynamic of profits. On the chart, we have shown, for each combination, the risk / reward in steady downward (red), steady upward (green) as well as any regime (gray). In the latter case, performance and risk are calculated historically since 1995 regardless of the market regime.

There is an asymmetry related to the regime : according to the combination adopted, it is possible to promote a regime in relation to another. The first two combinations favor the bearish regime while the latter favors the bull regime. Promoting the bull regime is accepting to be less optimal in bearish period in order to be particularly effective in bull regime, ie, this choice reflects a bullish belief in the long term. In contrast, promoting the bear regime is like having a pessimistic vision for the "long term" horizon. We can also imagine combinations for which the three points coincide. In this case, no bias is taken, nor bullish, nor bearish. It’s sort of a combination of "off-road" that will make steady gains regardless of the regime.

In conclusion, we have seen that it is possible to make static combinations of factors to create a model for stock picking on a given universe. The next step is to "test" various methods of portfolio construction to retain the one that can transmit at best discriminatory power of the combination of factors in the performance of the portfolio against its benchmark.