• Stock Strategies
  • Quantitative Strategies for Selecting Stocks

    by Richard Tortoriello

    Quantitative Strategies For Selecting Stocks Splash image

    A few years ago, I was asked to develop a series of quantitative stock-selection models for the equity research department of Standard & Poor’s.

    In preparation for this project, we backtested more than 1,200 different investment strategies to determine which were predictive of future “excess returns.” (A backtest is simply a statistical look at historical data to determine whether employing a given investment factor, such as selecting stocks with low price-earnings ratios, results in excess returns over time; i.e., returns above a stock market benchmark.)

    My goal was to determine the basic factors that drive future stock market returns, from an empirical point of view, using only historical data as our raw material (balance sheet, income statement, cash flow statement, and pricing data). In short, I set out to create a quantitatively drawn “road map” of the equity markets. To do our research, we used a sophisticated data-analysis program and Standard & Poor’s Point in Time database, which contains more than 20 years of “as originally reported” (unrestated) data for about 150 data items and 25,000 individual companies.

    This data-intensive approach to investment analysis yielded clear results. Certain strategies consistently outperformed the market over the two-decade test period, while others consistently underperformed. The results of this research are published in the book “Quantitative Strategies for Achieving Alpha” (McGraw-Hill, 2009). In it, I present a wide variety of investment strategies that predict excess returns, and I show investors how to combine individual investment strategies into more complex screens and models. These can be used to generate strong potential investment ideas, create quantitative portfolios, or simply help investors better understand the market from a quantitative point of view.

    Looking for Factors

    In structuring our backtests, we kept in sight one basic principle: Numbers can lie. If a backtest is not constructed carefully, or if too few years of data are used, backtest results will be unreliable.

    Statistical bias can cause the results to be flawed. The two most common are look-ahead bias and survivorship bias. Look-ahead bias is when information that would not have been known or available during the period is analyzed. For example, reported fourth-quarter earnings are not available for most companies as of December 31 of any given calendar year. Because strong companies tend to survive and weak companies are often acquired at a discount or go out of business, a database that includes only the survivors will likely yield much stronger results for a backtest than if “non-survivors” were included. (Our database protected our tests from both look-ahead and survivorship bias.)

    Returns must be calculated consistently—we used a stock’s annual price change plus dividends and cash-equivalent distributions of value (such as spinoffs). And a clear backtest universe must be defined: Our universe consisted of the largest 2,200 stocks in our database selected by market capitalization, with a minimum share price constraint ($2, to keep out volatile penny stocks).

    Each test divided the companies in our backtest universe into quintiles (five equally sized groups) based on their rank on one or more investment factors. For example, a price-earnings ratio test put the 20% of companies with the lowest price-earnings ratios into the first quintile, the next 20% into the second quintile, all the way down to the 20% of companies with the highest price-earnings ratios, which would be put into the fifth quintile. Portfolios were formed every quarter over our test period, and the holding period for each portfolio was 12 months.

    Returns for all portfolios in each quintile were then calculated, averaged over the 20-year test period, and compared to the average return over the same period for the overall universe. A strategy was said to have investment value if the top first quintile significantly outperformed the universe, the bottom fifth quintile significantly underperformed, and the outperformance/underperformance was consistent over time.

    Combining Indicators

    I like to use the idea of a mosaic to describe the results of our quantitative tests. A mosaic is a picture or pattern made by putting together many small-colored tiles. In a real mosaic, each tile is meaningless when viewed alone. However, when put together by an artist, a beautiful pattern emerges. In our investment mosaic, each “tile” is a strategy that has investment value (it consistently outperformed or underperformed the market) and is understood by the investor (we know why it worked).

    The second point is critical. Data mining—the search for correlations between items in a database—can uncover investment strategies that work fabulously during the test period and fail to work thereafter. By basing the investment strategies we tested on sound investment theory, we ensured that the results represent fundamental principles and tendencies in the investment markets and not statistical anomalies. The goal was to put various investment strategies together to identify what characteristics to look for or to avoid in the stocks in which we plan to invest.

    The Seven Basics

    So, what can investors learn from quantitative analysis? One important discovery we made was that most investment strategies that are predictive quantitatively fall into seven major categories. I call these categories the basics, precisely because they are fundamental to achieving excess returns in the stock market. They consist of profitability, valuation, cash flow, growth, capital allocation, price momentum, and red flags risk. There are likely more basics than the seven we identified (and the seventh, red flags, is somewhat of a catchall), but investors looking for primary market drivers need look no further than these.

    From a quantitative point of view, valuation, cash-flow generation, profitability, and price momentum are the most important basics. In particular, valuation and cash-flow factors should be included in almost all quantitative models, screens and analysis. The relative valuation tests we used were simple (e.g., price to earnings or price to sales), but showed that low valuations generated strong excess returns that were consistent over time. It seems obvious, but investors often forget to check the price they are paying for an asset.

    EV-to-EBITDA Strategy

    One of the strongest valuation ratios we tested is enterprise value to EBITDA. Enterprise value (EV) is the theoretical price it would cost to buy the entire corporation. We calculated it as the market value of common stock (price times shares outstanding) plus the book value of long-term debt minus cash and equivalents. EBITDA stands for earnings before interest, taxes, depreciation, and amortization. Roughly speaking, it represents operating income before depreciation. To calculate it, begin with 12-month income from continuing operations and add back the items listed above.

    Generally speaking, companies with EV-to-EBITDA ratios of 8x or lower outperformed over our 20-year test period, and companies with EV-to-EBITDA ratios of 11x or higher underperformed. General Electric’s (GE) CEO Jeff Immelt affirmed our observation when he opined at an investor meeting: “I think if you pay beyond 10x EBITDA [for an acquisition] it is hard to make it pay.” GE had learned from hard experience what our test results found.

    Figure 1 shows the average excess returns (i.e., returns above or below the return for the entire universe) by quintile for the EV-to-EBITDA strategy over our 20-year test period. Companies in the first quintile have the lowest EV-to-EBITDA ratios, while companies in the bottom quintile have the highest ratios.

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    Cash ROIC Strategy

    Cash flow tests also generated strong and consistent excess returns. (Cash flow was defined as cash generated by operating activities, instead of cash generated by financing or investing activities, all of which can be found on a company’s cash flow statement.) Why is cash flow so important? One reason is that cash represents a reality—purchasing power—while accounting earnings are at least one step removed from that reality. Another is that a company with excess cash has financial flexibility; it can use that cash to expand its business, pay dividends, repurchase shares, acquire other businesses, and so on.

    One way to measure cash flow is to compare the so-called “free cash flow” a company generates in a year to the capital invested in the business. Cash return on invested capital (cash ROIC) compares free cash flow (12-month cash generated by operating activities less 12-month capital expenditures) to invested capital (total stockholders’ equity plus long-term debt). Companies with cash ROIC of 12% of more outperformed over the 20-year test period, while those with cash ROIC ratios of 4% or less underperformed.

    Figure 2 shows average excess returns by quintile for the cash ROIC strategy. Companies in the first quintile have the highest cash ROIC ratios, while companies in the fifth quintile have the lowest.

    Return on Equity Strategy

    When looking for stocks likely to outperform, the investor should also favor profitability factors. A company’s level of profitability provides investors with a measure of the quality of the company’s productive assets (whether those assets are manufacturing facilities, a strong brand name, an excellent customer list, or a talented work force).

    A good profitability ratio, and one that’s easy to calculate, is return on equity (income from continuing operations over the past 12 months divided by stockholders’ equity). Investors should favor companies that can generate return on equity of 16% or more, and avoid those with return on equity of 8% of less.

    Figure 3 shows average excess returns by quintile for the return on equity strategy.

    52-Week Price Range Strategy

    Finally, investors should consider a stock’s price momentum. Price momentum simply refers to the speed with which a stock goes up or down over a given period of time. To quote William O’Neil, founder of Investor’s Business Daily, “The great paradox in the stock market is that what seems too high and risky to the majority usually goes higher and what seems low and cheap usually goes lower.” Our research certainly found this to be true.

    A simple way to measure price momentum is to consider the proximity of a stock to its 52-week high or low. The formula I used for this was current price minus 52-week low divided by 52-week high minus 52-week low. Stocks that score 82% or higher on this formula tend to outperform, while stocks that score 41% or lower tend to underperform. Figure 4 shows average excess returns by quintile for the 52-week price range strategy.


    One major conclusion of our study was that fundamentals matter, valuations matter, and technicals (i.e., price momentum measures) matter. The investor looking to achieve strong stock market returns over a six-month to an 18-month investment horizon would do well to consider all three of these factors.

    The seven aforementioned basics presented provide investors with strategies that work in all three of these important areas. Another important conclusion is that quantitative analysis, qualitative analysis, and technical analysis were not only far from being unrelated subject areas, but form mutually complementary disciplines. Investors who learn the lessons taught by each are apt to increase their ability to make money consistently in stocks.

    To put this all together, I suggest running a screen that incorporates the four individual investment factors mentioned in this article. These four factors cover the basics of valuation, cash flow, profitability, and price momentum. They also consider key data points from a company’s income statement, balance sheet, and cash flow statement, as well as its market price. The four screening criteria would be:

    Enterprise Value to EBITDA <= 8

    Cash ROIC >= 12%

    Return on Equity >= 18%

    52-Week Price Range >= 82%

    Practical Tips

    Here a few suggestions for screening or analyzing a stock:

    • Make sure you understand each ratio you are using. Ideally, you should understand not only what the ratio represents, but how predictive it is.
    • Certain ratios work better than others with particular industries, so a more focused sector-based analysis may yield better results than a screen or analysis designed for use on the entire stock universe.
    • Avoid screening or conducting analysis on a single factor. It will provide too narrow a view of a company and its stock (keep in mind the idea of an investment mosaic, described here). Instead prefer complementary factors, particularly those that combine valuation with profitability, price momentum, cash flow, and/or growth.
    • Never look at growth without also considering valuation! Our research found that growth factors alone are not predictive. There are two possible reasons for this: 1) high growth rates are very difficult to maintain, and 2) investors tend to overpay for growth. The growth/value combination helps investors avoid the second pitfall and our research shows that it works.
    • If the screening tool that you are using does not allow sophisticated screening, substitute less sophisticated ratios for more sophisticated ones. For example, the price-earnings ratio can be substituted for enterprise value to EBITDA, and relative strength for 52-week price range.
    • When screening, use values for each ratio that provide a sufficient number of results, but be more restrictive with valuation ratios than with other ratios. Quantitatively, valuation ratios are most predictive and provide the strongest results.
    Richard Tortoriello is the aerospace and defense analyst in the equity research division of Standard & Poor's and has conducted numerous quantitative investment studies for the company. He is author of "Quantitative Strategies for Achieving Alpha" (McGraw-Hill, 2009).


    Patrick from MO posted over 6 years ago:

    You might be better served using PROFIT MARGIN rather than ROE, along with only stocks that are within 95 perdcent of their 52 week high

    Steve from SC posted over 5 years ago:

    Stock Selection - Tools and Rules

    At least ten hands shoot into the air as the discussion turns to stock selection. The speaker smiles, responds to each, and observes: "You really need to know the depth of the water, its temperature, tides, and currents before you dive into the river --- and then, what kind of predators are in there?"

    The investment planning stage is too often ignored by the young and the new, and too often over cooked by the older and beaten up. Most of the confused indecisiveness is due to constant media hype and an endless bombardment of data, news, software solutions, electronic tools, and expert opinions. But most actual investment errors are caused by invalid expectations, fear, greed, and lack of discipline.

    Here's an overview, and it is expected to provide structure and provoke thinking while skimming over most of the detail and explanation that can be found in the "Brainwashing" book.

    For the rest of the story: http://kiawahgolfinvestmentseminars.net/Inv/index.cfm/18351

    Steve Selengut
    Author of: "The Brainwashing of the American Investor: The Book that Wall Street Does Not Want YOU to Read"

    Dave from WA posted over 5 years ago:

    Does anyone know what Steve's point was?

    This comment just looks like an advertisement.

    I liked the article, even though after 30 years of doing it, I am fading out of the stock picking game for a safer indexing strategy, because frankly I'm just not convinced that even the "average" expert can get this right in the long run.

    Dan from TX posted over 5 years ago:

    I like this approach, which is confirmed by realistic backtesting. An important part of the analysis is that takes into account the dividends, spinoff values and cash payouts, which can be a significant part of the overall return, but which are not always reflected in many databases. This review confirms my belief that an investor makes his gain on the buy side; usually by recognizing an undervalued entry point for a quality company. Unfortunately, the ratios employed here are not obtainable in any of the simple stock screens I have at hand. Why not offer this method as one of the AAII model portfolios?

    Fred from PA posted over 5 years ago:

    I am in a similar situation as Dan from Texas. I would have a difficult time obtaining most of the ratios used in the article and would think it would be nice to see this method as an AAII model portfolio.

    Bruce from CO posted over 5 years ago:

    I am with Dave and Dan and would welcome an easy way to obtain these ratios.

    Nash from GA posted over 5 years ago:

    Like Dan, Fred, and Bruce I will need more help to capitalize on this artical.

    John from FL posted over 5 years ago:

    I also would like an easy referral source for ongoing updates for the data. AAII ?.

    Choudary from MO posted over 5 years ago:

    Can AAII add the above criteria in the model stock portfolio and help us in screening stocks.

    Donald from PA posted over 5 years ago:


    Nishesh from IL posted over 5 years ago:

    one question to author on 52 week price range strategy is that

    what will be the exit strategy after entering buy in this strategy

    can i constantly compute the ratio and continue hold it it dosent break 41%?

    Paul from OH posted over 5 years ago:

    There's always the X-Factor nothing is for sure, world events even national events, nature, management changes, new technologies and so on things change. Then there the unforseen surprizes that are in our favor.Controling risk is paramount. Don't concentrate in to few sectors of the economy.

    John from LA posted over 5 years ago:

    Mr Tortoriello's book is in my library along with many others that I have collected over the past 40 years.Investing professionally and personally for most of that period I can attest to the value of disciplined approaches such as the one outlined in this article.In my opinion there isn't one best way to solve the investing puzzle. Lots of things work. You just need to keep doing it. And keep it simple. In my group's professional operation,we spend a great deal of time and money testing strategies and methods.After all is said and done, however, much of our stock selection process is still driven by basic inputs similar to those in this article and which were developed decades ago based on accepted and time-tested analytical techniques.

    Melvin from VA posted over 5 years ago:

    Does someone have a simple Stock Investor Pro screen worked our for this concept? If so, please include in your response.

    John from FL posted over 5 years ago:

    I would be pleased to pay for this screen, if it is ever available as an AAII portfolio.

    John from MD posted over 5 years ago:

    Is this a "buy and hold" strategy. Probably not, so what criteria do you use to determine when to sell? I have some stocks where PM has dropped to .2(with, of course, resulting losses).

    Jim from CA posted over 5 years ago:

    C'mon. Can't someone at AAII come up with a model stock portfolio for these strategies??? What can I do to spur this on?

    Jean from IL posted over 4 years ago:

    We have added the screen criteria and custom fields for use in Stock Investor Pro to the companion First Cut column on the Tortoriello approach: http://www.aaii.com/journal/article/tortoriellos-quantitative-strategies (it's linked above on the right under Related Articles, or just search on Tortoriello).

    Charles from IL posted over 4 years ago:

    As Jean noted, we posted the criteria for creating a Tortoriello approach in our Stock Investor Pro program. The First Cut article (http://www.aaii.com/journal/article/tortoriellos-quantitative-strategies) explains what how we did it: If you just want to see the criteria, you can download the excel file at: http://www.aaii.com/objects/get/1931.xls -Charles Rotblut, AAII

    Dominick Sciola from WA posted over 4 years ago:

    Liked this article a lot.

    Hope this isn't too ignorant of a question, but does Tortoriello, great Italian name by the way, advise holding onto stocks that fit this criteria (and perhaps others for that matter) for approximately 1 year?

    I would assume that's the optimal holding period here since the portfolios formed over the course of the screen were held for 12 months.


    Benster from NY posted over 4 years ago:

    It would seem that price momentum and value are counterveiling measures, and almost mutually exclusive; e.g., how likely is it that a stock near it's 52-week high will still have a low relative valuation (measured, say, by P/E)?

    Charles Rotblut from IL posted over 4 years ago:

    Ben, if a stock has previously been out of favor with investors or has strong earnings growth, it can have both good momentum and a low valuation. It is more common than you might think. This said, at some point, upward momentum will drive the valuation higher, so you have to monitor the stock's price to ensure the P/E is still reasonable. -Charles

    James Hargreaves from GA posted over 4 years ago:

    The concept that value matters (although it isn't determinative) should NOT be a shock.

    As was rightfully pointed out Graham figured that out back in the 1940s (or was it earlier).

    Bart DiLiddo, PhD (in the 1980s) developed a VST (Value, Safety, Timing) model that was and is the basis of Vector Vest.

    Finally, the real problem is HOW does one determine value (as one of the key factors to stock picking).

    In the late 1990s, Copeland (et. al.) developed a new method of stock (company) valuation that focused on not just earnings but looked at cash flow. The Copeland model was widely adopted in the Financial Analytics community.

    Finally, to simple say that stock valuation methods should be based (derived from) the company's financials and cash flow statements MISSES a key point.

    Without making proper accounting adjustments to PUBLISHED (10K) financials, one is not able to make one to one (performance) comparisons between different companies.

    The accounting NOTES to a set of financials are where the "gold" is found in analyzing a company's financials. That "gold" (and it's uses) can only be understood by someone with a working knowledge of accounting (policies, choices and adjustments).

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