Gray & Carlisle Quality and price

In their book ‘Quantative Value: a practitioner’s guide to automating intelligent investment and eliminating behavioral errors’, authors Wesley Gray and Tobias Carlisle discuss some of the most popular quantitative investing screens and factors. For each model, they also present an alternative that outperforms the original model. One of the improved models is what they call ”Quality and Price”. This model is based on the same ranking method as the Magic Formula, but it uses a different quality and price factor. Gray and Carlisle got the idea to replace the factors based on 2 academic papers.


The Greenblatt Magic Formula uses return on capital (ROC) as a proxy of a stock’s relative quality. The problem with ROC is that it’s not a very clean measure of a firm’s profitability. A firm that quickly grows its sales by spending heavily on marketing or R&D will see its short term profitability impacted. Moreover, management can implement actions to increase short term profitability while putting long-term profit growth in jeopardy. In his paper ‘The Other Side of Value: Good Growth and the Gross Profitability Premium’ Robert Novy-Marx suggested to use gross profitability, which is a much cleaner measure of a firm’s true economic profitability. Find more about this measure in our glossary.


The Magic Formula uses EBIT/EV as its price measure to rank stocks. The problem with this measure is that it can vary significantly from period to period. For this reason, Nobel price winner Eugene Fama and Ken French consider book to market capitalization to be a superior metric as it varies less. This is important to keep turnover down in a value portfolio. Find more about this measure in our glossary.

Backtesting results

In their tests, the quality and price model significantly outperformed the magic formula. Between 1964 and 2011, the quality and price model showed an average yearly compound rate of 15.31% compared to 12.79% for the Magic Formula. This model also had higher volatility and worse drawdowns, but on a risk-adjusted basis it was the clear winner.