*Quantitative Value* is an investing strategy that selects for investment the highest-quality cheapest stocks using state-of-the-art computer algorithm. Our implementation of Quantitative Value has generated returns of about 14% per year on average, over 22 years, with relatively low volatility, and low asset turnover.

The *Quantitative Value* algorithm selects stocks through a three-step process:

- Establishing a universe of stocks to choose from, per an investor's market cap preferences. The algo also eliminates the riskiest stocks from the universe (based on insights from vast academic research).
- Sorting the universe for cheapness using TEV/EBIT valuation multiple and selecting the cheapest stocks
- Sorting the cheapest stocks based on composite Quality and Technical ranking system which include profitability and financial strength metrics, and selecting for investment the highest ranking stocks.

Our Quantitative Value algorithm prunes thousands of stocks and performs fundamental and technical analysis on a scale which no human can do manually. The rules of the algorithm are based on tens of academic research papers and practitioners' experience. We have tested the Quantitative Value model rigorously using state-of-the-art statistical techniques.

There are many ways to implement a Quantitative Value strategy. Our implementation achieved average yearly returns of about 14%, with relatively low volatility and asset turnover. The following figure is an example of a 30-stock portfolio simulation (backtest) spanning 20-years between June 30th, 1999, and June 30th, 2021. Stocks have a lower market cap limit of about $200M and are rebalanced once a year. Results are exclusive of taxes and transaction fees, and assume slippage of 0.5%.

In the simulation example above, a portfolio of 30 stocks selected through our Quantitative Value algorithms, returned 13.87% per year vs. the S&P 500’s 7.27% per year (including dividends). Over the span of 20 years, our portfolio turned $100,000 into $1,740,930 whereas an investment in the S&P 500 would have turned the same $100,000 into a mere $468,130. Our portfolio was less volatile than the market, and its max drawdown, i.e., its largest decline was lower than the S&P 500, -49.36% vs. -55.19% for the S&P.

## The Design of the *Quantitative Value* Model

In their book, Quantitative Value, + Web Site: A Practitioner’s Guide to Automating Intelligent Investment and Eliminating Behavioral Errors, researchers and fund managers Tobias Carlisle and Dr. Wesley Grey provide excellent insight into their vast research on quantitative value investing methodologies. They start by re-creating the famous “Magic Formula” portfolio which was introduced by Prof. Joel Greenblatt in his book The Little Book That Beats The Market. The Magic Formula ranks stocks based on a combined metric of valuation (cheap stocks rank higher) and quality (stocks with high returns on capital rank higher). The Magic Formula portfolio is then constructed by buying a basket of highly-ranked stocks based on the combination of valuation and quality. Carlisle and Grey have found that ranking stocks based on valuation alone results in even better risk-adjusted returns than the averaged valuation + quality ranking. They have 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 used the stock factors (often called smart-beta factors) of Valuation and Quality vs. how Greenblatt had, is nuanced, yet important. Greenblatt’s Magic Formula ranks stocks based on the average of their valuation and quality. On one end, stocks are ranked and sorted based on valuation – the cheapest stocks get the highest rank (e.g., 100), the second cheapest gets a lower rank (99.5 for example), the next gets a 99, then 88.5 and so on. On the other end, 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 average rank to enter the portfolio. And so do cheap stocks with average 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 Quantitative Value (QV) model ranks stocks for value and quality consecutively (i.e., in series). The first rank is based on valuation alone. The QV model ranks and selects the cheapest decile (10%) of the universe of stocks, using a TEV/EBIT multiple. All the other stocks are discarded.

TEV (Total Enterprise Value) = Market cap + book value of Debt – Cash & equivalents

EBIT = Earnings before Interest and Taxes (trailing twelve months)

The lower the TEV/EBIT figure, the cheaper the stock.

A “Rank” is similar to a grade – the higher the rank, the better. A high TEV/EBIT rank corresponds to a low TEV/EBIT figure and a cheaper stock.

The resultant cheap decile may still consist of several hundreds of stocks (depending on the lower bound set for market capitalization). The QV model then ranks the resulting set of cheap stocks for again, but in this second ranking, the rank is based on a combination of several quality metrics. The QV model then selects only the highest quality stocks for investment. In the Magic Formula, stocks are ranked once based on an average of 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 conclusions through our own testing.

## Our Proprietary Improvements to the QV Model

Can we do better than Carlisle and Grey’s QV model? We believe we can.

In the example below, we re-create Carlisle and Grey’s model as accurately as we can using the tools we have at our disposal. The universe is comprised of stocks with a market cap in the highest 40% percentile. The portfolio consists of 40 stocks, value-weighted, and rebalanced every year. However, we must note that we cannot perform a 100% accurate re-creation of the original QV model. While Carlisle and Grey describe their QV model with unprecedented detail throughout their 300-page book, they do leave much room for an investor’s own interpretation. Carlisle and Grey do not disclose several parameters which are necessary to mimic their results. Also, while Grey and Carlisle insist that the QV model is simple to implement, we have found the implementation of some of their formula to be challenging using retail platforms, such as Quantopian and portfolio123. Constructing a QV-like model using Portfolio123 required some math and heuristics to simplify the formulas and fit the platform’s constraints.

Following is the performance of our re-creation of the original Carlisle and Grey’s QV model (1999-2017):

As shown above, the average performance over the span of 19 years is quite good. The QV model handily beats the S&P 500, with average annual returns of 17.18% vs. 5.13% for the benchmark. Sharpe is 0.78. Asset turnover is high at 84.05%, meaning that nearly all positions will be replaced with every yearly rebalance. We shall now show how we improved the model. Volatility is high, at 19.15% since inception, vs. just 14.62% for the s&P 500. Max drawdown is -36.74%.

Carlisle and Grey’s performance, tested over a span of 38 years is shown below:Our goal in designing the proprietary modifications was maximizing returns with the lowest volatility and lowest asset turnover possible. High volatility is undesired. Even the most experienced investors will find it hard to digest. Volatility spurs emotions which are hard to control, causing investors to exit positions immaturely. Therefore, reducing a portfolio’ volatility has a direct effect or investors staying power.

A high rate of asset turnover is also undesired. Selling stocks involves transaction costs as well as increased tax bills (for taxed accounts). We wish to decrease the number of transactions (and turnover) to the necessary minimum and thus increase after-tax after-fees returns.

Our first improvement was to change the portfolio from being value-weighted to being equal-weighted. In value-weighted portfolios, the size of a holding is determined by its market cap, relative to the other stocks in the portfolio. Higher market-cap stocks will comprise a larger portion of the portfolio than smaller market-cap stocks. In contrast, an equal-weighted portfolio, each holding is initiated with equal weight, an equal portion of the portfolio. Equal-weighted portfolio makes more sense to us, as we do not know apriori which stocks has a better chance to perform well, compared to other stocks in the portfolio. We must as well give every stock an equal opportunity to influence the portfolio’s results. Also, academics claim that equal-weighted portfolios earn more than equivalent value-weighted portfolios since they are more exposed to the small stocks effect (SML), in which smaller stocks have a higher likelihood to perform better than larger stocks.

Our second improvement was to modify the ranking system, which is used for the third step of the algorithm, to include not only Quality criteria but also technical criteria. We’ve added the stocks’ historical beta and another measure of price smoothness to the ranking system mix. We rely on academic research showing that lower-beta stocks deliver higher returns and that stocks which are less jittery also perform better.

The last modification is to our Sell and Rebalance rules. Upon every yearly rebalance, instead of selling all the stocks which are not the highest ranking stocks based on quality, as did Carlisle and Grey, we sell stocks based on their TEV/EBIT valuation. If the stock TEV/EBIT rank is NOT in the cheapest three deciles (30% cheapest stocks of the universe) – we sell it. If the stock is still cheap compared to the universe (present in the 30% cheapest stock), we keep it. This rule reduces the asset turnover rate, which results in less tax liability and fewer transaction costs, contributing to after-tax after-fee returns.

Here are the results of the modified portfolio, consisting of 30 stocks with a market cap in the highest 60% percentile (>$200M), equal-weighted, rebalanced every year.Annual average returns are slightly higher, at 19.19% vs. 17.18%, yet the volatility was reduced considerably, now at 13.33% vs. 19.15% in the original model. Sharpe ratio thus increased from 0.89 78 to 1.26. Asset turnover was reduced from 84.05% to 31.67%. With the new sell rules, only a third of the portfolio is being replaced in every annual rebalance, corresponding to an average holding period of three years. These new rules contribute to reducing tax liability and transaction costs. They thus help to maximize after-tax after-fees returns.

Where our unique modified QV portfolio really shines is with smaller market-cap stocks. We will now look deeper into one such portfolio.

## A Deeper Look in *Quantitative Value* Performance

How would the QV model perform year-over-year? Month-Over-Month? What performance should we expect? Let’s dive deeper into the past performance of the QV model to search for clues.

**Qualitative value (QV) Screener Performance During The Last Year (March'20 - March'21)**

The following chart presents the performance of a quantitatively-selected portfolio of 30 QV stocks, with the market cap in the 40th percentile or larger. The smallest stock in the sample is LFVN, with a $102 M market cap, and the largest is MO with a $89B market cap.

All stocks were bought on April 1st, 2020, and held for exactly one year.

Quantitative Value had beaten the market during this year. It has returned 59% per year, on average, vs. the S&P 500’s 53.28%, including dividends.

The year since March'20 was a great time for all stocks, as they recovered from the bear market that followed COVID-19 outbreak. Nevertheless, QV stocks had done slightly better.

### Long-Term Performance of the Quantitative Value Screener

Since the guys at AlphaArchitect.com, led by Dr. Wes Grey. were the ones to popularize the Quantitative Value model, let's check how their main vehicle, the QVAL ETF, has fared since its inception.

If we look at Alpha Architect’ss QVAL ETF from inception in October 2014, we can see that the fund lagged the S&P 500 by a substantial amount, delivering a total return of 26.16% over the four and half years, compared to the S&P 500 with 96%.

I do not think for a second that QVAL or my implementation of Quantitative Value is inferior to investing in a market fund or a benchmark ETF. On the contrary. I believe that QV is one of the best strategies that an individual investor can utilize for beating the market over the long term. The fact that it had underperformed in the short-term is not only a necessary evil that one has to bear in order to achieve long-term over performance. Actually, it is the reason for why the strategy overperforms over the long term. It works (over the long term) because it doesn’t always work (in the short-term). More on that later in future articles.

The following chart presents the performance of my version of the QV portfolio over a 5-years period, June 30th, 2014, to June 30th, 2019. The reason I do all my long term backtests starting June 30th is two-fold: 1) to be consistent with academic research who uses such convention 2) to be consistent across all my publications, enable readers to compare all my backtests, apples to apples.

We can see that the performance over a 5-years period was on par with the S&P 500’s performance. The QV model was ahead of the benchmark for the larger part of the 5-years period and stumbled below it just at the very end.

Testing the strategy over 20 years starting June 30th, 1999, and ending on June 30th, 2019, tells a totally different story.

Quantitative value delivered astonishing average annual returns of 17.35% vs. 5.82% for the S&P 500. Over the long term, QV beats the benchmark (and any other strategy I am familiar with) heads over feet. Moreover, it has done so with lower volatility, as measured by the standard deviation of monthly returns. The standard deviation of the strategy came in 13.39% vs. 14.51% for the S&P 500, as can be seen in the following table. Sharpe ratio is at a super high level of 1.13x vs. 0.32x for the S&P 500. The correlation with the S&P 500 benchmark is a mere 68%. It means that only 68% of the months tested, the S&P 500 and the model both appreciated or both declined. In all other cases, when the market declined during a month, the model appreciated, and vice versa. Over the long term, Quantitative Value develops a healthy margin over the market and runs much higher.

It is also interesting to see, in the tables above, the contrast between the wild overperformance in the long term (table on the right) vs. the mild underperformance during the last three years (table on the left).

Looking at the yearly performance in the following table, we see that in most of the years during the last 20 years, the QV model delivers positive excess returns over the market. It had underperformed the benchmark in only 6 of the last 20 years. Unfortunately, two of those years were 2017 and 2019, falsely leading some investors to believe that Quantitative Value, or any Value Investing method in general, had lost its touch. Some even go as far as saying that Value Investing is dead.

### What Does The Future Hold For Quantitative Value?

et history should lead us to the exact opposite conclusion. The largest overperformance was achieved following the underperforming years. Following 1999, a disastrous year for Value Investing and a bad year for our model, lagging by more than 10%, came the year 2000 with a fantastic excess of 68% above the market. Following 2007, when QV lagged 6% after the benchmark, it gained 19.20% above the market in 2008. The under-performance of 2009 was fully covered and then some, during 2010 and 2011. And after mildly underperforming in 2012, came four years of significant overperformance. It is only reasonable that following the recent performance of value investing, nowadays, in 2017-2019, the future will be bright for Value investors.

The most telling graph I could find about the history of Value Investing a one taken from an article by Dr. Gray titled Alternative Facts About Formulaic Value Investing:

The chart shows the 10-year rolling returns (compounded annual growth rate, or CAGR) or Value vs. the S&P 500. Every point on the chart indicates the following: had you invested in a value portfolio (or the S&P 500) 10 years ago and held it until that date, what would have been your CAGR. We can see that during most 10-years periods starting the 1930’s, a Value portfolio had beaten the S&P 500. But there were four long periods where that was not the case. Those periods occurred in the late ’30s to early ’40s, during the late ’50s to early ’60s, during the late ’90s, and recently, since 2010. In those periods, Value Investing fell short of the benchmark, leading investors (different ones each time) to believe that Value Investing is dead. An important observation is that those periods of Value underperformance are long, prolonging for many years, even a decade.

Now, ask yourself, examining the historical trends for almost a century, do you believe that Value Investing will underperform forever? Where would you put your money? And if you, like I, believe that Value will re-emerge, as it always has, wouldn’t you want to be invested in the best-performing Value Investing strategy?