Making Value Work

I also worry about the slight overlap between the two periods I was looking at. Using rankprev(52) along with EPS%TTM could easily be subject to period overlap with factors that change from week to week (as opposed to quarter to quarter). So that could explain why the analyst and price measures give me such superior results.

I was stumped for quite a while on how to get rid of this. RankPrev does not go above 52. And you can’t combine FHist with FRank, even if you put one in a custom formula.

But I came upon a solution: use a one-node ranking system consisting of FHist(“XXX”,65), and then use Rank in the screen rather than RankPrev. I just have to plug in the ranking factors one by one. So I’ll see how that works with the various factors. I’ll update you soon.


Great question!

First, I understand that you could be thinking a lot of different things when asking this question. And let me say, ahead of time, that I know I am probably missing the main point of your question. But it is a question worthy of discussion, I think. In the way of background let me quote Wes Gray from Quantitative Momentum:

"Classic value investors claim to earn their paycheck by timing the difference between fundamentals and market prices. But what if the market decides to never update their expectation about the intrinsic value of a firm (also known as a value trap)? Assuming free cash flow distributions are distributed in the distant future, a value investor won’t win in this situation. The value investor, like all investors, needs market expectations to change in their favor for the strategy to work.”

So one theory that is often expressed is that when you have identified a company as possibly having a market price below the true fundament price (using a P123 screen say) momentum might suggest that the market, as a whole, has noticed this and will begin buying–pushing the price to the true market price.

But the even simpler answer to your question is: interaction of the factors. This is a subject of one of your recent posts I believe—with regard to factors that interact with Market Cap.

You want a company that is undervalued AND will correct to its actual value. The value ratios, hopefully, increase the probability that the company is undervalued. The momentum factor increases the probability that the market will push the stock price to its true market price in your investing lifetime. So, as with most interacting variables, it is a conditional probability. If you assume the stock is indeed undervalued then we are interest in the conditional probability: p(the stock will correct to its true market value | the stock has momentum). Or in words, the probability that the stock will correct to its true market value given that it has momentum. Presumably this is a bit higher than the unconditional probably: p(the stock will correct to its true market value) with no momentum information.

But it is also true that the stock having momentum may be confirmation of your theory that the stock is undervalued. And one could write a conditional probably about this also: p(the stock is actually undervalued | the stock has strong momentum). This would reduce the number of assumptions required to make this a valid theory. But I thought I would stick close to Wes Gray’s work because……Well, because he is smarter than I am.

TO BE CLEAR, WES GRAY STATES ABOUT ONE MILLION TIMES MOMENTUM AND GROWTH ARE NOT THE SAME THING—constituting a substantial percentage of the total word length of his text. So this may not be pertinent Marc’s original post (and certainly does not argue against anything he said).

Of course, this is just theory and I am not claiming this will always work going forward. I am thinking of Tiny Titans when I write this. In fact, I am not advocating this strategy at all: Please consult with your financial advisor………

Just a short answer to the question of why one might use fundaments and momentum together. A question that fills the pages of at least two entire books by Wes Gray. Not a complete answer and probably not the most important aspect at that.


OK, I’ve redone my experiment, and yes, there was clearly some contamination going on. Adding a three-month cushion makes a big difference. Just to reiterate: I’m looking at the top 20% of stocks for each factor, waiting fifteen months (65 weeks), then looking at their EPS%ChgTTM and seeing how many of these stocks get over 15%.

Now there’s a HUGE surprise here, which, when you think about, shouldn’t be in the least bit surprising.

The NUMBER-ONE predictor of future earnings growth is LOW PROFIT MARGIN. I just happened across it accidentally, but it makes perfect sense. Companies with low profit margins have very strong sales and terrible earnings. So those companies are the most likely to experience earnings growth. Just use NPMgn%TTM with lower values being better.

In a VERY CLOSE SECOND PLACE is LOW ROA. This works for the same reason. I would think almost anything with net income in the numerator and something good in the denominator would work well here. These two factors beat all other factors by a mile.

Number three, lagging significantly behind those, is comparing the current quarter’s analyst EPS estimate with the same quarter last year.

Number four is comparing the current year’s analyst EPS estimate with last year’s.

Number five is the accrual ratio: subtract operating cash flow from net income and divide by total assets, with lower values being better.

And number six is balance sheet accruals: subtract last year’s net operating assets from this year’s and divide by average total assets for both years; lower values are better. You’re looking for companies with shrinking net operating assets.

A few other observations:

Using EPS%ChgTTM will give you worse results than choosing stocks at random. Companies whose growth has already increased a lot in the last twelve months will be unlikely to increase that much in the next twelve months.

Volume-weighted SMA (VMA(15)/VMA(210)) gives you pretty good results, even with a three-month break. It ties with operating income growth (most recent quarter to same quarter last year) for number seven of the factors I tried.

  • YT


Interesting observation! Without backtesting this, I am guessing this would be particularly useful near the bottom of a market drawdown.

Fisher already advocates Price to sales in down markets. The thinking being that a company may not be that profitable at the moment but when the economy improves the sales will translate into profits. And I think Marc may occasionally use Sales/EV under similar circumstances.

In theory, a company could develop a higher profit margin coming out of a recession for many reasons. They may be able to increase the price as the economy improves. Or maybe they are not operating at full capacity with their fixed costs contributing too much to their overall costs (keeping profit margins low).

I bet the backtest does very well near the bottom of the 2008 recession—possibly working well when combined with price to sales. I have not backtested my ideas but there is good reason to believe your observation is based on sound theory.


Conversely, NPM is likely to be at a peak when the economy is good and companies have pricing power or if they have a moat … err … a sustainable competitive advantage.

Try this in a custom series (w/ S&P 500 Universe); it looks for a decline in NPM (and not level) as a sign of trouble.




Thanks for running this. On a percentage basis, that makes sense since the company with low profits has a low base and thereby high operating leverage (i.e., profits increases more as a % for $1 increase in revenues).

I think normalizing for revenue growth would provide much cleaner results which then be converted in expected earnings growth via operating leverage.


On the contrary! There are a lot of theories as to why momentum might exist:
a. band wagon effect / greed & envy
b. leakage of privileged information (i.e., price leads fundamentals)
c. I will grossly over-simplify Wes Gray’s theory as “under-reaction to good news”
d. cognitive dissonance

But they are all just theories. There is no question as to what causes prices to rise or fall: supply and demand. Also, I think we know a lot about what causes supply. However, I don’t think anyone actually knows exactly what causes demand since it is predicated on both rational and irrational behaviors.

As for leading indicators of growth, a lot of this depends on the credit, business, and commodities cycles in addition to endogenous factors (e.g., incremental returns on invested capital; capital allocation vs budgeting decision; real opportunities; etc…).

In this interpretation, sector momentum might help to explain the correlation with growth. I’d even be willing to bet that there is no predictive power in individual security momentum that cannot be captured by sector/industry/peer-group momentum (somebody can test this, I’m sure).

As for a leading measure of endogenous growth, I would think that a good approximation might be: (the return on incremental capital) * (invested capital in excess of maintenance capital i.e., “growth capital”). But that all gets back to Marc’s point: we don’t know what these numbers are. Assuming that incremental returns = average returns ignores the concavity (i.e., the diminishing aspect) of returns. Also, while we know what was spent, we don’t know how closely DD&A approximates maintenance capital spending.

Analyst’s estimates can provide clues, but there’s also a lot of crowd-following among the analytical community and there are unfortunately too few value creators.



I think you got this exactly right. If you did not read Wes Gray’s book then you must be following his posts.

But if I did not miss your main point it was purely by accident. There are a ton of valid points (theories) that I did not address in my short post: and I do not really disagree with any of them. I do not even claim that my theory is one of the better ones.

The only point I would stand firm on is that factors can interact whether you can find a direct cause-and-effect relation between the factors (or a good post hoc story) or not. Remember, we are kind of doing finance but through the filter of a multifactorial regression/factor analysis/supervised machine learning method: completely automated to be sure. Call this automated system whatever you wish.

Multicollinearity AND CONDITIONAL PROBABILITIES end up affecting the final selection of factors that work in an historical backtest. The conditions (of the conditional probabilities) are are not always incorporated into the sim/port if they are even understood. And those conditions can change. So “lurking” variables or “confounding” variables are a potential problem and this is just the beginning of potential inefficiencies of an automated system. But if you fully understand the reasons your factors work in a sim/port then your are surely incorporating those “lurking variables” already—so “no worries.” But I refer people to David’s post on momentum as an indication of how certain one can be if you even make an attempt to incorporate these variables.

I am always happy to look for reasons why factors interact but I am not always right. And I am always happy to look for new factors that interact with all of my previous factors in a positive way. The number of interactions becomes quite large with even the smallest ranking system. The chance that I fully understand all of those interactions is zero. Which is to say there is no particular reason to listen to any of my post hoc explanations.

Which is also to say that I commend you on your skepticism and fully agree with all of your last post.

Much of this discussion assumes that value and momentum work together in a port: something that I am not willing to speculate upon for the near future. Remember the original post was about value and factors that work with value. If nothing else, Marc’s discussion of risk and rising interest rates (possible lurking variables) is to be taken seriously.



Just for fun, try these custom series where the universe is the S&P500;

UnivAvg(“Sector= Tech”,“NPMgn%TTM”)-UnivAvg(“True”,“NPMgn%TTM”)
UnivAvg(“Sector= FINANCIAL”,“NPMgn%TTM”)-UnivAvg(“True”,“NPMgn%TTM”)
UnivAvg(“Sector= Energy”,“NPMgn%TTM”)-UnivAvg(“True”,“NPMgn%TTM”)


Marc, this probably isn’t what you’re looking for re earnings growth, and this thought likely only applies to a small subset of companies - but…

One of my takeaways from the Buffettology book is the idea of predictability: that some companies have relatively predictable trendiness in book value and ROE, and also in sales and margins. Ideally these would be companies with a fairly tightly fitted trend in these variables. Both book/ROE and sales/margins can be utilized to forecast a future estimated eps in 3-5 yrs time - again, assuming the company is relatively predictable. Most companies aren’t stable enough for this, but some will be. I’ve used these methods in excel on results from some Buffett-inspired screens, and when both bvps growth/stable ROE + sales growth/stable margin coincide with future earnings projections at reasonable forward valuation levels it flagged companies for me to investigate further. I don’t know if it’s possible to do that in P123, but taking advantage of this kind of predictability was one of my takeaways from the book and found it useful in that context. The problem I had with it was within the past several years often there were just so few companies that would pass, and many that did had problems.

Stability is usually fairly priced by market + upside potential of such companies are usually limited + unexpected break in stability is harshly penalized by the market.
There are some rules that maybe helpful:
LoopStdDev(“OpMgn% (ctr, ann )”, 10 ,0,1,1) < 2
LoopSum(“ROE%(ctr, ann ) > ROE%(ctr+1, ann )”, 10 ,0,1,1)


Motivated by this discussion, I recently posed a question to Stack Exchange, “Are the causes of momentum uniform for various asset classes?”. I was surprised to find the lack of academic research of whether price leads fundamentals. I am aware of prevailing theories which link momentum to limitations in market efficiency and behavioral pattern. I am not, however, aware of much evidence which links prices changes to information asymmetry which is a violation of both strong and semi-strong forms of EMH.

So I did an initial experiment which regressed annual changes in return on assets versus annual logarithmic price changes over the same period over a ten year period. The population was stocks in the NYSE, NYSEMKT, and NASD universes. I am using the screener, so survivorship bias is present. The initial results are interesting, though I am not sure they are not conclusive.

The results of 10 year study:

firms included: 2143

Correlation coefficients between annual earnings growth and price returns:
Median: .32
Average: .28
Cap-weighted average: .21

For the cap-weighted average:
T-stat (T[null: rho !< 0]): 9.81
Fisher Z-transform (1 tailed): 9.73
Fisher p-value: 1.00

In other words, there is a 1 probability that the size-weighted correlation between price changes and changes in returns are not less than 0.

Interesting, yes. But there are few problems that I can see:

  • Survivorship bias
  • Limited time horizon (10 years is relatively small)
  • “Post ergo propter hoc” (correlation does not lead to causation). Just because price is correlated to fundamental shocks does not imply that price leads fundamentals. We just can’t tell until we a) look at quarterlies (which would presume fundamental information is not diffused before it is publicly released); and, b) introduce lags.

Someone with some greater statistical acumen can probably take this up and perform a Granger causality test or something like that. In the meantime though, I am pretty convinced that one cause of momentum involves the diffusion of accurate information regarding fundamental shocks.

I’m probably misunderstanding you but I just can’t conceive of a scenario in which changes in the price of a stock would lead to or cause changes in a company’s return on assets. They might ANTICIPATE such changes using analyst reports and close reading of other fundamentals that cause changes in a company’s earnings, but how could the price changes themselves possibly CAUSE changes in earnings? It seems to me that the question of causality is settled.

You’re right, Yuval. Poor word choice.

I meant to say that price changes anticipate fundamentals.

On a somewhat related note, I also think its possible for price changes to cause changes in fundamentals.

Take, for example, a capitally constrained and distressed firm. Higher prices lower the cost of capital, thus allowing the firm to refinance and fund growth projects. Tesla comes to mind. But, no, this was not what I intended by my former statement on causality.


I agree about correlation and this is what I was try to say in my own way—lurking variables being one possible explanation for correlation without causation.

BTW, as per Wikipedia: Post hoc ergo propter hoc (Latin: “after this, therefore because of this”) is a logical fallacy that states “Since event Y followed event X, event Y must have been caused by event X.” It is often shortened simply to post hoc fallacy. But whatever it means I agree with you on that too.

My apologies for focusing on only one potential cause for momentum: I am not married to any particular explanation.


Speaking of correlation.
Anyone notice that ALL equity markets are moving together right now?

An unintended consequence of globalization.

So much for global diversification…

Does this include negative earnings?

I’ve read in books/papers that profit margins are mean-reverting, but I didn’t expect profitability such as ROA to be. A problem I have with using these types of metrics is some companies, like software companies are consistently high profitability, while some companies that rely on heavy investment in machinery and manufacturing are consistently low profitability, but I could be wrong.

Did you use current ESP estimate minus previous ESP estimate? Or some other formula, such as a ratio? And did it result in higher is better?

I used EPS%ChgTTM, which measures earnings growth whether the earnings are negative or positive. So, yes, this definitely includes negative earnings.

The only difference between profit margin and ROA is that one has sales in the denominator and the other has assets. So they’re going to behave very similarly over time. What we’re looking at here is companies with strongly negative or low earnings and high sales or assets. Those are the companies whose earnings are going to grow the most.

No, I used current EPS estimate minus GAAP EPS divided by the absolute value of the latter. And yes, higher better.

Interesting. Have you checked this against trends in turnover?

Low/high margin by itself is not good or bad. Low margin combined with high turnover is just as good as high margin combined with low turnover. A benefit of ROA etc. is that these numbers combine margin and turnover.

That’s fundamentals and value. On the other hand, there’s the noise component of stock pricing. Turnover and its role is not nearly as widely understood as margin, so at times, the market may excessively favor high margins and neglect turnover plays.

I’d say yes, definitely. Some of the best opportunities I’ve encountered are among rotten companies becoming good companies, or even rotten companies working their way up to mediocrity. Also, shares of good or ok companies can do quite well as the market looks for them to move beyond temporary bad spells.

ROA etc. do tend to be mean reverting but very slowly and towards a norm that reflects the nature of a company’s business. So i think modeling based on this concept might be most productive if you think of ROA trending toward ROAInd, or something like that.

So, how do momentum factors affect real-world investing at P123 if you use value ratios too?

In other words: what is the effect of momentum–in the node of a ranking system–if you also use a value ratio?

Using momentum could have nothing to do with how momentum, by itself, affects stock returns in your system. Let me give a simple example to illustrate.

Suppose you use the ratio Earnings(TTM)/P in the rank for a port and stock XYZ pops up on you buy list for the first time because the E(TTM)/P ratio has increased (increasing the rank for that stock). Does your port recommend buying XYZ because E(TTM) has increased or is it because P has decreased?

You do not know right? Could be either. I understand this is not an actual formula at P123. Insert your own fundamental value for discussion.

What if you add close(0)/ Close(252) to your rank? The chance that XYZ’s earnings have increased over the last year—assuming your port still recommends this stock—just increased dramatically.

If your port, with momentum factors, is doing well it could be because momentum, by itself, is having a positive effect. Equally plausible is that your port is doing well because momentum is interacting with the value ratio. Maybe it is both. Specifically, the port now has you selecting stocks that have a high E(TTM)/P ratio when the ratio has increased because of improving fundamentals. Because price has increased over the last year the denominator (price) will be greater than last year–for the stocks your port selects–and the numerator (fundamental) is much more likely to have increased. Your port might be working only because you are buying stocks with increasing fundamentals—the fundamentals in your value ratio. Momentum may have nothing to do with it.

You are not doing just finance at P123—unless you are fully aware of how your factors are interacting in the ranking system. Even then there are some quirky things that can effect a linear regression/factor analysis/supervised machine learning automated system (that have nothing to do with finance).


Yuval, this may answer a major question I have had about testing emerging factors.
Have you found this method to be effective?