In their book “Quantitative Value”, Carlisle and Grey provide excellent insight into their vast research on quantitative value investing methodologies. They started with creating a portfolio based on Joel Greenblatt’s Magic Formula, described in his book “The Little Book That Beats The Market”. The Magic Formula ranks stocks based on a combined (average) metric of Valuation (cheap stocks rank higher) and Quality (stocks with high returns on capital rank higher). Carlisle and Grey have found that ranking stocks based on Valuation alone provides even better risk-adjusted returns than the averaged Valuation-Quality ranking. They also discovered that narrowing down the bucket of cheap stocks by selecting the highest quality issues among those cheap stocks, yield even better returns. 

The distinction between how Carlisle and Grey approach Valuation and Quality factors vs. how Greenblatt does, is nuanced yet important. Greenblatt’s Magic Formula ranks stocks twice. First, stocks are ranked and sorted based on valuation – the cheapest stocks get the highest rank (e.g. 100), the second cheapest get a lower rank (99.5 in our example), the next gets a 99, then 88.5 and so on. Then, the stocks are ranked again based on a Quality factor, Return on Capital. The highest-quality stock receives a rank of 100, the runner up gets a 99.5, then 90 and so on. Each stock now has two ranks, one which represents its Valuation and the other – its Quality. The ranks are then averaged to result in a single magic formula rank. Naturally, very cheap stocks (high Valuation rank) with high quality (high-quality rank) will rank highest overall and will be bought for the Magic Formula portfolio. But even very high-quality stocks with mediocre valuation may get a high enough combined rank to enter the portfolio. And so do cheap stocks with mediocre quality. Thus, a well-diversified magic formula portfolio will typically include a mishmash of cheap and not-so-cheap stocks, some with above-average quality and some with mediocre quality. 

In contrast, Carlisle and Grey’s QV model ranks the stocks only according to valuation. For example, the QV model ranks and selects the cheapest third or quarter of the universe of stocks. All other stocks are discarded. Yet the quarter of the universe may still consist of several hundreds of stocks (depending on the lower bound set for market capitalization). The QV model then ranks this set of cheap stocks according to a quality rank (build as a combination of multiple quality metrics) and selects only the highest-quality stocks for investment. 

In the Magic Formula, stocks are ranked in parallel for Quality and Value. In the QV model, stocks are first ranked for value, with the expensive stocks discarded, and only then the cheap ones are ranked and selected for quality. Carlisle and Grey have found the QV model to yield better results with lower volatility than the magic formula. We have reached similar results through our own testing. 

While Carlisle and Grey describe their QV model with unprecedented detail in their 300-page book, they do leave much room for an investor’s own experimentation and decision. Carlisle and Grey do not disclose several parameters which are necessary to mimic their results. What is their percentile which they use to screen their universe for value? What is the order of applying their screens and are they applied to the initial universe or on the recently trimmed universe? Grey and Carlisle do not disclose. 

We have experimented with length with QV-like models, and we list our results below. 

In addition, while Grey and Carlisle insist that the QV model is a simple one, we have found some of their formula to be challenging for implementation in retail platforms, such as Quantopian and portfolio123. Constructing a QV-like model using the latter required some math and heuristics to simplify the formulas and thus enable implementation. Our model thus deviates from QV but only in minor ways, we believe.

Here are some of our research results on Quantitative Value.  

The following histogram buckets our universe into deciles based on TEV/EBIT ranks, and averages the performance for each decile over our backtesting period June-30 1999 to June-30 2017 (positions are held for a year). The cheapest decile is on the right and the most expensive decile is on the left. 

We also tested an alternative Valuation ranking system. Follows is the performance for a composite rank consisting of 6 measures: P/E, P/B, P/FCF, EV/EBITDA, EV/Sales, Shareholder’s Yield. The composite rank was first introduced in Jim O’Shaughnessy’s “What Works on Wall Street”. We improved its performance a bit by giving slightly higher weight to the EV/EBITDA and EV/Sales metrics. 

The results in our testing period are much better than ranking according to EV/EBIT alone.  

We are challenged by the fact that Carlisle and Grey tested a composite rank proposed by O’Shaughnessy and did not find it to yield better results than TEV/EBIT. They write (Ch. 9):

 Against formidable opposition in the form of other widely used individual price ratios, long-term average “normalized” price ratios promoted by Graham, and composite price ratios suggested by O’Shaughnessy, the humble EBIT enterprise multiple stood out.

We believe that the difference in results stems from the difference in the testing period. While Carlisle and Grey’s tests are from 1974 to 2011, ours is 1999-2017. It is certainly possible that a composite rank worked better during the last 18 years while TEV/EBIT worked better over the 37 years in C&G tests.