Factor Study with P123

Hi all,

Lately, there seems to be a lot of discussion inside and outside p123 about factors. Those who are familiar with my thoughts, whether from the forum or the p123 on-line strategy design course (available in the Support area) know I’m not a fan of conventional factors because they are not theoretically sound. There is no reason why lower P/E, for example, should be better than high P/E. It all depends on how other things shake out.

Since nobody out there is doing the kind of research that needs to be done in this area, I decided to start doing it myself.

Attached here is an initial draft. It’s not my complete data set and its written using jargon that would be relevant to p123 users. But at least I got some initial thoughts onto (digital) paper.

For those of you who know how I derive my key factors from the Dividend Discount Model (DDM), you can skip the early material and jump to page 6 (where I test prospective ranking systems for use as proxies for the G factor in the DDM.

Anyway, enjoy (so to speak). Comments are welcome.


Gerstein - P123 VSQ Factor Investing Study.pdf (115 KB)

Marc,
Nobody has any valid information as to which factors should provide the best returns, and under what circumstances. That has not stopped the ETF suppliers to launch a myriad of factor ETFs; even Vanguard has now joined them with 6 ETFs. I did some research and found that only one factor ETF had a higher return than SPY over the last four years. That is the iShares Momentum Factor ETF (MTUM).

When in doubt one can also buy multi-factor ETFs. Why should this be better than SPY?

Here is a good summary article: Are Factors Linked To Business Cycles?
https://www.advisorperspectives.com/articles/2018/03/08/are-factors-linked-to-business-cycles?%3Ftextlink=

The author concludes:
The bottom line is that the most prudent strategy is for investors to build portfolios that are strategically (as opposed to tactically) diversified across factors that show persistence in their premiums, have low correlation to other factors, are pervasive around the globe and across asset classes, have intuitive reasons to believe the premiums should persist (whether behavioral-based or risk-based) and are implementable (meaning they survive transaction costs).

Furthermore, in the study “Contrarian Factor Timing Is Deceptively Difficult,” which appeared in the 2017 special issue of The Journal of Portfolio Management, Cliff Asness, Swati Chandra, Antti Ilmanen and Ronen Israel found “lackluster results” when investigating the impact of value timing (in other words, whether dynamic allocations can improve the performance of a diversified, multistyle portfolio). They write: “Strategic diversification turns out to be a tough benchmark to beat.”

Marc -

I really like the article because it’s so clear about the valuation formulae and how the various components work. It clarifies what the possibilities are for the E, the R, and the G really well.

I do have two brief questions:

First, the P = D/(R-G) formula. What happens when G is bigger than R? Is that possible? If not, why?

Second, when you discuss substituting earnings for dividends, you comment, “A couple of generations ago, such a step might have seemed absurd.” Why?

  • Yuval

Because it’s a bogus question. As I explain and demonstrate in the paper, no “factor” per se ever relevant except as the answer to a data mining exercise studying a particular period.

And why should it stop them? If there are fees to be collected, when have you ever seen lack of merit stop any of those firms?

Not surprising. It was a liquidity-driven bull market. Of course investors were going to be rewarded for taking risk.

If one is going to approach factors naively, the way they’ve been approached so far, by relying on Fama-French style data mining exercises, then SPY is probably the better choice. On the other hand, if one really understands how the factors relate to one another in a unified whole, one can do a heck of a lot better. That’s what I tried to show in the paper I posted.

I stopped reading when I saw the name of the author. That guy is a complete moron. I asked the publisher of that straight out site why they keep publishing him so much; even they know he can be sloppy as hell in his research. I also asked them if he was paying for placement. He didn’t answer and moved the conversation to an other topic.

It’s not possible because you’d wind up with a negative fair price. That’s why it can’t be used literally as a formula into which you plug numbers. (Actually, in the early days of internet finance, one site really did offer a DDM “tool” and, of course, computed negative fair prices. Needless to say, that site has long ago ceased to exist.

DDM is a framework. It shows how P,or P/E, Interest rates, risk premium (the market attitude toward risk) and growth expectations interact in relation to pone another. It’s a strategic framework. As a formula, it can’t really work.

But that’s OK. We already know that no formula can ever work because if it were possible, everybody would be able to at least buy their own island, and maybe even a country or two. What DDM can do is give the framework for the art of strategic thinking, the way color theory, perspective, etc. provide a framework for an artist.

Oh goodness, you;'re bringing me back to the days when I had great knees, wore earth shoes, and looked really good in bright red bell bottoms. For most of the life of the stock market, collecting dividends was everybody’s main goal, except for a few whackadoo speculators here and there. It wasn’t until the powerful bull market of the '80s that it became mainstream to invest for capital gains and not care about income. But before then, the typical institutional investor was barred, as a matter of policy, from owning any non dividend stocks, all of which were deemed inherently speculative.

Marc,

How does one derive the DDM? Is it necessary that it is an infinite series?

Is it required that D, R, and G are fixed quantities?

I enjoyed reading. Thanks!

//dpa

It does start with an infinite series: see image. There rest of the derivation (starting with the infinite series) is in Wikipedia and is pretty straight forward. Link here.

I leave any further comments to Marc.

-Jim


Infinte series.png

Interesting reading, as always, Marc. I thought I’d list a few typos:

To screen for the Best bucket, I’ll use Rating(“xxx”)<34
PRussell 300 universe
probable probable
tour control

Thanks, Marc. A question. You wrote:

“By the way, a word about the so-called size factor: It’s a branch of the Quality factor. Size means economies of scale (better coverage of fixed costs) and typically better business portfolio diversification . . .”

The way I understand size is that smaller companies outperform larger ones over time. What am I missing?

Delete.

Marc, My mind really only works in concrete ways, so I’m wondering if you were to put numbers to R for average stock, what would that be? Am I thinking about it properly that R would be around 5.9% now? Seems way to low as I think about it a required rate of return, but I wanted to see if I’m thinking correctly.

R = RF + (B * RP) = 0.029 + (1.0*0.03)

Above, I’m just using 10yr treasury yield for RF, and 0.03 for risk premium, but have no idea if that’s what most investors would require. I’ve seen projections that the future expected returns based on CAPE10 perhaps project future 10yr US equity returns might imply a current 0 risk premium ( https://www.starcapital.de/en/research/stock-market-expectations/ ), so I realize it varies - but wondering what number would normally go there? If the risk premium is very low now (or 0) very high stock prices can be justified until that changes.

Also, for G, in the infinitely long run doesn’t G have to be limited to the growth rate of the economy (unless it’s a zero or negative growth company)? Do you think o.02 or so be fair to use in many cases?

I realize you’re using the model as a framework for thought, but I’m wanting to just put some hard numbers in there and understand what folks that use the model literally would use so that I have some sort of baseline. Thanks,

Spaceman, if you want to take a deeper dive on this I suggest taking a look at some of damodaran’s datasets

http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datacurrent.html

I’m glad Jim picked up on the details of the infinite series; that’s outside my wheelhouse.

As for D, R and G . . . in THEORY, you would plug in a specific number for each item; not sure if “fixed” is the right word. I’d prefer to think of them as independent variables.

In an alternate ideal world, we’d plug in the numbers, do the simple computations, and have our answer. 100% of the real-world problems come from the fact that we can’t readily come up with credible assumptions for what the independent variables should be.

We can get some of them; D (or E is we prefer) is an easy one. The RF component of R is likewise do-able. The RP component of R is absolutely undoable - historical study will produce any number anyone wants to get simply by whatever sample period one chooses to study. And we have to be sure we don’t pick periods in which it turns out to be negative (I’ve seen some who make confuse “expected” risk premium which logic says must be positive versus "realized risk premium, which can be negative because sometimes, life has a way of dashing one’s expectations). The B component of RP is a maybe – as I noted, company change tends to be evolutionary rather than revolutionary so many times the observable statistical report card on the past can be helpful, especially if you combine more than one sample period. But when one is developing stock strategies, one does have to be aware of how that number can go awry.

G is the biggest killer. To make the formula work, G absolutely positively must be small enough to be less than R and the only passable verbal way to justify that s to taker infinity very seriously . . . through infinity, every company will wind up with a very small . . . almost approaching zero growth rate (and there is the economic law of diminishing returns which goes further and says G will eventually go negative). That’s useless to those of us who just want to make money in the market. We can’t be bothered with philosophical discussions of infinity. We need to identify better growers from worse growers so we can recognize which stocks to buy and sell for a holding period that matches our rebalance choices, rather than infinity. (And during our finite horizons, G will often exceed R). This alone dooms literal plug-and-lay use of DDM and forces us to wing it or adapt.

Ouch. :frowning: Thank you for catching it.

Others who find typos are extremely welcome to point them out

This is actually one of the reasons I’m working on this project. There’s way too ouch out there that fails to distinguish between (1) tendencies that are attributable to inherent traits of stocks or certain kinds of stocks, versus (2) tendencies that were observed over the course of specific time periods that may or may not have anything to do with the inherent qualities of anything. Bear in mind that empirical stock research is a more dangerous exercise than in many other fields because the available samples tend to be incredibly biased. Due the way things turned out, and skewed by the periods when data became more available, much of what’s available as sample has come from bullish market conditions, and especially in the last 35 years or so, when the market was dominated by plunges in RF which pushed ideal P/E way way way up across the entire equity asset class.

The so-called small cap effect is an example of the second kind of tendency - one that has been observed over the course of specific, but very long - sample periods.

Small per se does not help or hurt returns. The default assumption for small is that Quality is lower, sales and earnings are apt to be more volatile (don’t underestimate what diseconomies of scale – weaker coverage of fixed costs – can do in this regard), and as a result, and stock price are likely to be more volatile. Whether that helps or hurts returns depends on the market’s attitude toward risk taking. The samples used by those who claim to have identified a small cap effect are ones dominated by periods in which the market was good and in which risk taking was rewarded.

Arguably, there is a long-term secular bias toward rising stocks and rewards for risk taking. Population growth, productivity growth, education growth, health care growth, etc. lead to a bias in favor of rising GDP which leads to rising sales, rising profits, etc. So again, we might reason from this to assume a secular tendency toward superior small cap performance.

But when we shrink down to the human investment horizons with which we work, we have to be alert to the potential for periods that will be off-trend, during which small caps will underperform. We might take the patient I’m-not-going-to-try-to-time-this approach as many do, and stick with risk-on/small caps anyway. But at least if you understand the whys and wherefores of small cap performance, you’ll be better able to make sensible decisions whichever way you go, rather than get caught up in the traumas of “Oh my, hs the small cap effect ended?”

Marc,

I have heard it as: a company cannot expand faster than the GDP for infinity and growth has to eventually equal the GDP (or less).

Put this way the alternative is to believe that the company will eventually crowd out the entire economy. You occasionally see the fantasy nightmare in science fiction movies. A drug so addictive or the price of immortality where nothing else matters. But even here the growth ends up equaling the GDP.

Back to the real world, I do not think even Apple will consume all of our dollars into the future.

-Jim

Somebody recommended checking Damodaran;s data. He’s pretty good for this sort of thing. My sense, though, is that you may want to take RP up to 4%-5%, which many tend to do (almost as a matter of investment community gentleman’s agreement). And, of course, stay alret for changes in RF.

Also while I like using the 10-year, many many prefer to use the shortest possible Treasury as a proxy for RF since they want to be free not only of credit risk but also market risk.

If you want to keep going along these lines, your next step may be to try to segment the market by size and/or sector and assign different betas for each.

From there, try to identify periods of risk-on versus risk-off and start varying your RP.

As to G, I’d say .02 is the maximum - look for something in line with global population growth perhaps

Marc,

I do not think you are giving the formula the full credit it deserves. While knowing future growth is hard, as you say, the formula is solid even for plugging in numbers, IMHO. When we give someone money (e.g., our brokers) we want to know how much we will get back (amount and growth of our returns), when we are getting it back (time discount) and the risk that something will happen so we will not get what we expect.

It is all in the formula.

You already mentioned long-tern (non-infinite) growth as a partial solution to the zero denominator problem. But the equation can be expanded for 2 stages (or more) of growth with the latter-stage growth being limited as you describe. See image (source Wikipedia). If you factor in inflation (the real returns) I think a zero denominator is seldom a problem.

Anyway, I think the formula is solid and probably belongs in the core of any sim or port. That is not to say that I don’t believe that a few statistics or backtests cannot help sort out what actually works within the framework of this excellent formula. Thanks for your expertise on this and finance in general!!!

And as alway the devil is in the details.

-Jim


Two points:

For those who want to see how one advisory company is calculating DCF valuation, including growth rates, risk-free rates, and terminal value, see this web page:

https://github.com/SimplyWallSt/Company-Analysis-Model/blob/master/MODEL.markdown#discounted-cash-flow-dcf

I think parts of this are great and parts are weird. I tried to reproduce this using P123 data but encountered a number of minor difficulties. But it’s an interesting read. Note that the “growth” number they work with has a minimum of 0 and a maximum of 0.2.

Regarding small caps outperforming large caps: I agree with Marc that this is a myth. The average small cap or microcap is more likely to fall dramatically in price than the average large cap. They’re far riskier investments, and so command a risk premium, which is why Marc put size in the “quality” portion of his outline. The advantage small caps and microcaps hold for the savvy investor is that they are more susceptible to fundamental analysis (perhaps they’re less subject to “noise”). See the first two paragraphs of Part II of my article here, along with the chart that follows it:

https://seekingalpha.com/article/4148763-problem-small-cap-value-indexes

This is part of the literature, and actually, it’s the bridge that takes us from pure DDM to DCF modeling. You’ll see it referred to as a 2-step, or 3-step, or multi-step approach. Damodaran uses it to value new or less-than-mature businesses.

Again, though, there is the estimation problem . . . and the extent to which the infinite-growth assumption that usually comes at the end influences the final answer.

Can somebody refresh my memory on this: Did the on-line strategy design course cover the RIM (Residual Income Model)? If not, I’ll need to do an add-on. The RIM is a version of DCF that dramatically reduces the number of required inputs and makes for much better credibility than DCF . . . and for which I created a screen on p123.

Does this ring a bell for anybody?