Designing a PE-based Value Strategy

PDF Version: P123 Strategy Design Topic 3A – Designing a PE-based Value Strateg

Value is the relationship between the price of a stock and the benefit of ownership you, as a shareholder, would get.  As with anything in commerce, the reasonableness of a price is determined based on that benefit. There is no inherent advantage or disadvantage to a high or low price per se. It’s all about the relationship between what you pay and what you get.

In the stock market, the measure of owner benefit starts with the theoretical idea as articulated by the Dividend Discount Model (DDM) model. Specifically, the ideal formula to compute benefit is Dividend divided by the difference between the required rate of return and the expected dividend growth rate.

But as discussed in Topic 1, this formula is good in theory only. It cannot be implemented in the real world. So we do the best we can by coming up with approaches that are more likely than not to push us closer to the DDM ideal. The general principle here is that at all times, we will compare price to an identifiable measure of wealth that bears a reasonable relationship to the present value of expected future dividends.

In practice, value is really dividend into two sub-fields: (i) Direct Valuation, and (ii) Relative Valuation.

  • Direct valuation tries to hammer out, assumption by assumption, many years worth of future results and then discount it back to a present value. If you come across DCF or Discounted Cash Flow, that’s what this is. It’s very hard to do well in real life because of the large number of forecasts that must be made and because so much of the final computation hinges on an assumed “terminal value” which suffers from many of the computation difficulties that afflict DDM. And it’s really hard to do on Portfolio123 unless you make an exorbitant number of naïve assumptions or go really crazy with ShowVar (though if there’s interest, I can show you how to pull this off).
  • Relative valuation is what we generally do on Portfolio123. It looks for stocks that are “better” valued relative to others. What we do here will be aimed at that.

We’ll discuss earnings-based valuation here. Then, other parts of Topic 3 will address Sales, Book Value and Cash Flow based approaches.



Dividends are paid from earnings. Hence a good relationship between the price and the present value of expected future earnings is more likely than not to push us closer to stocks that have favorable DDM valuations. To successfully work with Price/Earnings (PE) ratios, we have to address two issues: (i) how do we decide what makes a particular PE reasonable, and (ii) how do we measure earnings for use in a PE ratio.

What Makes For a Reasonable PE

As discussed in Topic 1, we can derive the formula for a “correct” PE from DDM. Here is the logic.

  • Start with DDM: P = D / (k – g) where D = dividend, k = required return, g = growth
  • We know that D = E * PR where D = dividend, E = earnings, and PR = payout ratio
  • Substituting E * PR for D: P = (E * PR) / (k – g)

Now we have a formulation for PE that is every bit as theoretically strong as pure DDM. But in deference to real-world observation, we know that shareholders often act as if the portion of E not paid as dividends (the portion of E reinvested in the business) is being used on their behalf. Hence the near-universally accepted fiction that E is every bit as much a part of shareholder wealth as is D. Accordingly, we can revise DDM as follows:

  • P = E / (k – g) where D = dividend, k = required return, g = growth

Now, let’s do some simple algebraic reshuffling:

  • P / E = 1 / (k – g) where E = earnings, k = required return, g = growth

There it is. That’s the formula for an objectively correct P/E. In reality, due to difficulties estimating k and g, this formula shares the same problems that bedevil any effort to use pure DDM. But it highlights important relationships that can guide our Portfolio123 modeling based on PE:

  • Higher interest rates reduce P/E ratios
    • The risk-free interest rate is an important component of k. Given that increases in k increase the denominator, that translates to reductions in P/E
    • We cannot control interest rates so for the most part, haven’t been concerned with this in our Portfolio123 modeling. But if you do choose to incorporate interest-rate items into your models (i.e. for market timing), be aware that increases in rates, all else being equal, depress P/E ratios and vice versa.
  • Increases in risk reduce P/E ratios
    • This is something many may not realize. Eliminating higher PEs may not succeed in models if you’re eliminating riskier companies that can deliver on expectations.
    • This works because increases in risk boost k (an item in the denominator) in two respects.
      • In a market sense, higher risk increases the “equity risk premium” investors demand above and beyond the risk-free rate
      • More important for stock-selection models, increases in risk are reflected in higher Betas, which translate to k. NOTE: Don’t use Beta rigidly – it has problems we’ll discuss later on. But be aware of the relationship between company-risk and P/E.
  • Increases in growth expectations raise P/E ratios
    • The g term is a negative within the denominator. Therefore, higher g means a smaller denominator and this, in turn, means a higher P/E
  • Notice we didn’t cite PEG.
    • PEG, the PE-to-Growth ratio, is pure folklore. It ignores risk and it ignores cot of capital. So don’t get upset if you try PEG and it doesn’t work. That said . . .
    • As folklore goes, PEG is probably better than most because it at least accounts for an important part of the theory; it sensitizes us to the relationship between PE and growth.
      • But it could be better; it should leave no room for doubt that it’s future growth we care about, not historic growth
    • PEG, as incomplete as it is, remains far better and more usable than completely seat-of-the-pants ideas that often find their way into investment folklore
      • We can even slip by using historic growth rates if the future turns out to be like the past. It’s not a great idea, but there are many worse things traders and investors do every day.

This has vital implications for Portfolio123 modeling. You cannot expect a P/E-based rank factor to succeed with live money if applied to a universe not filtered at all or filtered only on the basis of liquidity. If you have a P/E based rank factor that is not working for you, it doesn’t mean the market doesn’t care about PE. It means you are not capturing stocks whose PEs are reasonable in light of growth expectations and risk. To do this, a rank factor based on P/E will have to be accompanied by other rank factors and/or screening-buy rules that weed out incompatible risk-growth situations.

That low PE works all else being equal is universal and indisputable. It’s easy, however, very easy, to erroneously assume all else is equal when in the real world, it rarely is. Use of PE will succeed or fail based on how effective you are in addressing “all else.”

What Should We Use For E

On Portfolio123, we have several pre-packaged choices. But they are not equal in terms of potential effectiveness. Some are better than others, and some should not ever be used. Before addressing individual items, let’s go back, as we always will, to our core theory and consider why we’re looking at PE; a process that will always point us in a good direction.

  • We consider PE as a real-world usable tool that can push us closer to stocks that are well priced in terms of ideal DDM valuation.
  • DDM, whether in its pure form or in a jerry-rigged real-world form, always thinks in terms of an expected future stream of money
  • Therefore, the item we use (earnings in the case of PE) should be as representative as possible of the future stream
    • As the base upon which all DDM-type computation would be built if we were to actually do them, we know with complete certainty that our computation would be thrown off, possibly very badly, if we were to use a base that is unreasonable
    • In applying real-world DDM workarounds, we have more than enough occasions to approximate with spit-and-chewing gum. That’s never great, but often it’s the best we can do. So at the very least, it’s in our best interest to avoid piling on more potential errors than absolutely necessary. We therefore have every incentive to try to pick an E that can be said to reasonably serve as a base upon which future-oriented expectations can be built.
  • We do this by trying to pick an identifiable EPS number that can reasonably be assumed to be representative of the company’s underlying sustainable earning power in the present or the very near future.
    • Much of the classic Graham-Dodd text on Security analysis is devoted to this topic. The analyst is NOT expected to simply take the latest reported number. Graham and Dodd work hard to coach readers to make appropriate choices among and adjustments to reported numbers in order to come up with a figure that is reasonably representatives of underlying earnings power.

Now, we’re in apposition to consider the various pre-packaged E factors.

  • EPSInclXor– Never, never, never, never, ever use this in a value model. Because it includes extraordinary items, it is, by definition, unsuitable. It might be usable in a model designed to pick up stock market “noise,” but even there it is unlikely to be effective since the accounting-profession regulators have, by now, pretty much defined Xor out of existence. Items the typical investor assumes are extraordinary are, by accounting rule, put in what we refer to as Special Items (SpcItems) which are included in all historic EPS and Net Income figures. Therefore . . .
  • EPSExclXOR– In much of on-line finance, this is the default figure. In its favor, it’s real; it’s what the company actually earned. Arguing against it, however, is the fact that it will often be dirtied (rendered inappropriate for valuation purposes) by the presence of SpcItems. This is not to say it’s completely unusable. Many companies do not report SpcItems all the time. And in a market where might makes right (flow of funds), the fact that so much of the investment community uses it can cause it to almost behave as if it works (i.e. the value modeling can benefit from an unseen “noise” effect). So I won’t say you should not use it. Just be aware of its limitations and be prepared to encounter situations that sharply vary from the spirit of the law of your models unless you use other rank factors and/or screening rules to limit their presence. (This is one example of why more ranking factors can be better than fewer, even though in other quant disciplines, less can be better.)
  • CurFYEPSMean– Perhaps the single best pre-packaged EPS item available in our database. It’s a forecast so it lacks the definiteness of EPSExclXOR. But it’s a near-term forecast (which, depending on the calendar, may include some already-reported quarters) and is likely to be less tenuous than other forecasts. Moreover, and this is important, SpcItems are absent. Analysts don’t include these in their headline numbers. The biggest disadvantage to this number is that many companies are not covered by analysts and will, hence, be NA.
  • NextFYEPSMean – It has the same pros and cons as CurFYEPSMean, but it is one year further out, meaning there is more uncertainty and a possibility that more companies (with some halfhearted analyst coverage) will come out NA. On the other hand, if CurFY is unusual (recession or boom), NextFY gives us more of a chance to get away from the trees and see the forest.
  • (NetIncBXorTTM- (.65 * SpcItemsTTM)) – This is obviously not a pre-packaged item, but you might find it useful, assuming you will compare it with MktCap since it’s not a per-share item. The formula adjusts Net Income by factoring out the Special Item. It would be great if we had the after-tax SpcItems, but the accounting professions does us no favor by not requiring it; as a result, SpcItems is a pre-tax number so we must cope with the tax effect on our own. We could work with the actual corporate tax rate, but that is often thrown out of whack by many tings, often the special items itself. Across the board use of a 35% assumed tax rate is often fine.

If you are doing valuation, you must use a 12-month figure for whatever definition of earnings you choose. This is the way the financial community thinks and it makes sense considering that companies, suppliers, customers etc. organize their planning and activities around 12-month cycles. Our goal is to come up with an earnings number that can be representative of the company’s underlying earnings power and serve as a base for a theoretical DDM valuation. Multiplying any quarterly number by four won’t suffice because it introduces too much non-systematic (from company to company) volatility into the picture.

If a quarterly number can be useful at all, it would not be an aspect of valuation. It would come up when we address noise; i.e. fundamental/earnings momentum.

Actually, no single year is really good enough because there is always the danger it, too, won’t be representative of actual underlying earning power. Temporary business conditions could throw things off for better or worse. Hence the logic of the Shiller PE, which uses 10-years of data (he got the idea from Graham and Dodd). So you can certainly experiment with multi-year averages. It’s cumbersome and not essential (point in time PEs can work is properly articulated and used). But if you want to be creative in your quest for Alpha, this is an area you could explore. You may also want to experiment with other ways of defining earnings (beyond what we’ll do when we get to cash flows).

Let’s Build Some Strategies

I’m going to work with CurFYEPSMean as my definition of earnings, which means the PE we’ll be using is: ProjPECurFY.

Before doing anything, we start with an expectation. The item should work for us, since PE does push us in the direction of stocks whose ideal DDM valuations should be good and since CurFYEPSMean is a pretty good definition of earnings. Many companies don’t have the CurFYEPSMean data items, but I’m going to be working in the PRussell3000 universe, which should be reasonably well covered.

NOTE ON UNIVERSE SELECTION: I give myself a challenge.  Getting things to succeed in the All Fundamentals universe is too easy. Since I’m not interested in maxing out my tests or sims but am seeking good live-money returns, I hurt my efforts if I test within in a marshmallow universe. If I really want to invest in sub-PRussell3000 stocks, I can go back later and switch the universe and throw in some liquidity filters. But when developing the idea, toughen up; give Mr. Market a fighting chance to defeat you.

I’m going to start with stocks ranking in the best (lowest) quintile (20%) for ProjPECurFY. This is not going to be investable. I want a starting point to see where I am in terms of execution of theory. So here’s my first model:

Main Settings

  • Universe: PRussell3000
  • Benchmark: Russell3000 w/Div
  • Ranking System: No Ranking
  • Max No. Stocks: 0


  • Test Period: MAX (01/02/1999 – 11/02/2015)
  • Rebalance Frequency: 4 Weeks
  • Max No. Stocks: 0


  • ProjPECurFY >0 // Get rid of NAs
  • FRank(“ProjPECurFY”,#previous)<20

Direct Link:

Backtest Results:

  • Annualized Return: 16.30% vs. 5.60% for Benchmark
  • Standard Deviation: 17% vs. 15.46% for Benchmark
  • Max Drawdown: -69.81% vs. -55.66% for Benchmark
  • Sharpe: 0.70 vs. 0.29 for Benchmark
  • Sortino: 0.98 vs. 0.39 for Benchmark
  • Beta: 1.23
  • Annualized Alpha: 11.20%

Here’s where we stand:

  1. Given the logical connection between ProjPECurFY and DDM, we shouldn’t be surprised to see good results in our first backtest. It worked because it is supposed to work.
  2. The danger about which we had to worry was whether our quest for lower PEs would be sabotaged by inattention to growth and risk: Can we really count on all else being equal to such a degree as to allow lower PEs, viewed in isolation, to be better?
  3. In this large-portfolio (portfolios comprised around 470 stocks) test, we saw good results. Did we get lucky? Or is there something systemic in the market that is allowing us to let our guard down in terms of “all else?” We’ll come back to this. But for now . . .
  4. Assuming we decide that what we have now could work going forward, the strategy is not investable; there are too many stocks. So while ProjPECurFY basically has potential, we need to do more.

Just for the heck of it, let’s stay only with ProjPECurFY and really clamp down on number of positions. We’ll confine ourselves to the 10 stocks with the lowest metrics.

Keep the Same Rules

  • ProjPECurFY >0 // eliminate NAs
  • FRank(“ProjPECurFY”,#previous)<20

But change the final selections in Main Settings:

  • Ranking System: No Ranking
  • Quick Rank
    • ProjPECurFY
    • Lower is Better
  • Max No. Stocks: 10

Direct link:

We’re really on the edge now. We’re not just asking for low ProjPECurFY in general. Now, in addition to ignoring growth and risk, we’re looking for just 10 stocks, the lowest of the low in terms of ProjPECurFY. As I mentioned in Topic 2, I don’t usually like to push factor sorts this far. But again, what the heck: Let’s take a look.

Here are the results with the same backtest settings.

  • Annualized Return: 14.61% vs. 5.60% for Benchmark
  • Standard Deviation: 90% vs. 15.46% for Benchmark
  • Max Drawdown: -70.66% vs. -55.66% for Benchmark
  • Sharpe: 0.64 vs. 0.29 for Benchmark
  • Sortino: 0.89 vs. 0.39 for Benchmark
  • Beta: 1.21
  • Annualized Alpha: 9.52%

Interesting. The 10-stock version of low ProjPECurFY also works; the MAX backtest results are almost indistinguishable from what we saw with the 400-stocks plus version. And with 10 PRussell3000 stocks rebalanced every four weeks, it’s easily investable.

Why not stop here?

A favorable test is a favorable test, but it’s not the same as a strategy that truly makes sense. We did something not great (relying very heavily on a pure sort), and we did something clearly wrong (we chased low PE without considering growth or risk, two factors of critical importance in determining the reasonableness of any PE). Maybe the market – the big money – just chases low PEs and doesn’t care about getting it right. And when the dollars move, might makes right. So maybe we should simply brush the theoretical errors off as part of “noise.”

That could work, if we had reason to be confident. Let’s see if we are. We’ll do a MAX-period set rolling 4-week backtests. Here’s the outcome:

  • Average “excess” return per 4-week period: +1.40%
  • During Up periods: +3.26%
  • During down periods: -1.62%

Oops. Now we understand why we sort-of got away with ignoring “all else.” It worked dung good times, when concerns about bad growth (or even negative growth) recede, as do concerns about business risk. But during down periods, when such concerns arise, we got slammed.

Now we can easily see why a strategy that tests very well in the aggregate over a long time frame can blow up as soon as we commit live money. It’s all a matter of how lucky or unlucky we are with the economy and the market. If good times persist after launch, we’ll be patting ourselves on the back. But if we hit some economic or market turbulence, we’re very badly positioned and will likely get hammered as punishment fort not having done what we should have done (considered growth and risk).

P.S. Even if I go from 10 stocks to 20, my typical default choice, the down-period result is just as bad.

  • Average “excess” return per 4-week period: +1.38%
  • During Up periods: +3.26%
  • During down periods: -1.67%

Refining the Model Based on Theory

I’m going to stick with ProjPECurFY because that uses my first-choice EPS measure. As to growth and risk, there are countless ways you can put them into a model as you go back and forth between screen and rank. Here’s one approach:

Rules (all backtest and other setting are based on my aforesaid default choices):

  • ProjPECurFY >0 // eliminate NAs
  • FRank(“ProjPECurFY”,#industry)<20
    • Generally speaking we tend to think of companies in the same industry sharing a common set of risk and growth characteristics, so this covers a lot of ground. It’s not perfect; no set of industry classifications can ever be. But it’s reasonable enough to warrant testing.
  • FRank(“ROA%5YAvg”,#previous)>50
    • When it comes to measuring risk, I far prefer company-based metrics over price-based metrics such as Beta. The latter amount to nothing more than statistical report cards on what happened in a specific historic time interval. I’d prefer to rely on fundamentals that determine why earnings are what they are and by extension what prices are what they are. Use of fundamental measures gives us a much better chance of taking our risk model from Universe A, the past, into Universe B, the future.
    • Notice my rule is not stringent; I’m more interested in eliminating dogs than I am in picky the most conservative situations.
    • The specific metric I chose, and the threshold of acceptability, are both ripe for experimentation and testing – as many trials as you want – so long as you don’t automatically lock in on the highest backtest result and have a logical reason for the choice you ultimately make.

This gets us down well below 400 stocks, but still leaves us with too many (87 as of this writing). So to get down to 20, I’ll sort:

  • Top 20 stocks as per “Basic: Sentiment” ranking system
    • Here, too, you can test and experiment. I’m trying to get at growth expectations. In my experience, use of historic growth rates is, by itself, a remarkably bad predictor of future growth. I’d rather go with analyst sentiment, which is tied heavily to expectations of future growth that tend, often, to be adopted by the market

Direct link to screen:

Direct link to pre-set Portfolio123 ranking system

Let’s do the basic backtest:

  • Annualized Return: 16.34% vs. 5.60% for Benchmark
  • Standard Deviation: 05% vs. 15.46% for Benchmark
  • Max Drawdown: -63.47% vs. -55.66% for Benchmark
  • Sharpe: 0.67 vs. 0.29 for Benchmark
  • Sortino: 0.92 vs. 0.39 for Benchmark
  • Beta: 1.18
  • Annualized Alpha: 11.24%

As to the rolling backtest:

  • Average “excess” return per 4-week period: +0.97%
  • During Up periods: +1.36%
  • During down periods: +0.34%

The main backtest is fine, in line with the others. But the rolling backtest is the one that really shows what we accomplished by incorporating the full theory of PE.

  • We cut our upside, not surprising considering we added some measure of risk control (but it’s still fine)
  • We very dramatically improved our down-market performance going from an average 4-week loss of 1.62% to an average 4-week gain of +0.34%.

By adding theory, we reduced the extent to which we gamble on the market (reduce market risk but not eliminate it – as long as we’re in equities, we have to always expect to do better in up markets than down) and are now running a legitimate value strategy. That means we have more reasons to expect good live-money performance. And if we don’t do well, we’re better able to understand what’s happening and ride out cold periods (as opposed to jack-rabbiting from one strategy to another based on the recent past).

Other position-size holding-period protocols

Actually, a strong case can be made for stretching the holding period for this 20-stock model to three months:

Basic Backtest:

  • Annualized Return: 12.90% vs. 5.60% for Benchmark
  • Standard Deviation: 41% vs. 15.46% for Benchmark
  • Max Drawdown: -61.06% vs. -55.66% for Benchmark
  • Sharpe: 0.54 vs. 0.29 for Benchmark
  • Sortino: 0.78 vs. 0.39 for Benchmark
  • Beta: 1.20
  • Annualized Alpha: 8.03%

Rolling backtest:

  • Average “excess” return per 4-week period: +3.04%
  • During Up periods: +3.67%
  • During down periods: +1.97%

True the returns and the alpha are lower than for the 4-week test. But it’s just a test, not reality. So we shouldn’t get too picky about comparisons; an 8% alpha is still outstanding in the real world. The idea of reduced trading activity is appealing as is the narrowing of the gap between average up and down market performance.

For those who really like to stay on top of things, here’s another test with a 1-week rebalancing period and 10 positions (if we’re trading weekly, many would prefer to be dealing with fewer positions).

Basic Backtest:

  • Annualized Return: 18.83% vs. 5.60% for Benchmark
  • Standard Deviation: 00% vs. 15.46% for Benchmark
  • Max Drawdown: -62.36% vs. -55.66% for Benchmark
  • Sharpe: 0.70 vs. 0.29 for Benchmark
  • Sortino: 1.00 vs. 0.39 for Benchmark
  • Beta: 1.22
  • Annualized Alpha: 14.34%

The faster-turning model has more appealing numbers. And it’s not random. Reliance on price (an aspect of every Value model) and analyst data combine to make a case for staying as fresh as possible. Rolling one-week tests are not possible on Portfolio123 so we can’t really see if jack-rabbiting is hurting us in down markets. But you can test isolated bad-market periods on your own.


We now have a legitimate PE-based Value strategy. Is it the best we can come up with? Who knows? It’s never a good idea to assume any strategy is so good it can’t be improved upon – especially where, as here, there are countless ranking and screening possibilities addressed to risk and growth expectations. What’s important here is that we have something legit, and a framework for change for anybody who wants to be inventive on their own (as I hope everyone is).

Coming Attractions

Next, we’ll turn our attention to Sales-based valuation.


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