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Author: howardroark Big red star, 1000 posts Feste Award Nominee! Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: of 18386  
Subject: Re: Ben Graham's Equation Date: 11/1/2001 12:57 PM
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Are you saying that (a) the Graham formula is not, in itself, a substitute for a proper DCF analysis, or (b) it's a tool that is so fundamentally wrong-headed as to be useless for any purpose? I've used it for a few years as a method of getting a first rough cut at stocks that look interesting, and I've had reasonably good results with it -- stocks that look expensive under the Graham formula seem to look expensive when you run the numbers, although I've found the reverse isn't as true. If your answer is (b), can you suggest a better quick-and-dirty formula for making a first cut? Thanks.

Well, for the record, I was really speaking to David's argument that DCF is of limited use because its methodology generally proscribes identifying undervalued companies, rather than Graham's formula itself, but (not surprisingly) I do have opinions on the issue.

I would absolutely agree with (a). I'd add that there's a fairly common tendency to take a sort of egalitarian approach to valuation, where every possible valuation model is viewed as just another "tool in the toolbox," with no single tool being inherently superior to any other. I think this is a big mistake, as a general proposition. Every tool is an attempt to quantify the definition of value. In some cases, such as EBO models versus DCF models, the tools are in fact (roughly)identical in accurately defining value, and thus it can be true that each is a tool that can be more or less useful depending on the situation, but neither is inherently superior. In others, there are clearly inferior short-cuts, such as P/E, Graham's Formula, PEG or Stable Excess Earnings models, which have other advantages such as ease and speed. This latter category of heuristics are sometimes reasonable but sometimes poor substitutes for quantifying the definition of value, and thus are rarely a good substitute for someone investing their hard earned money on a fundamental basis.

As for (b), I certainly wouldn't say that the formula is "useless for any purpose," though I would presonally use it. I think it helps to break down the formula in its constituent parts, and look at where it breaks from, or makes fixed assumptions about, the definition of value such that a user might be constrained. We know that almost all heuristics have these shortcomings, so it's important to make them explicit. The formula again, for convenience is the following:

P = EPS * (8.5 + 2g) * (4.4/AAA).

We can agree that a "correct" price generally equals EPS times the "correct" P/E (of course the "E" in PE is really EPS, such EPS cancels out and leaves you with PE. Thus, parantheticals in the formula can be characterized to mean this:

Correct PE: (8.5 + 2g) * (4.4/AAA).

I'd like to break the formula into its two implicit, constituent parts, which are also the two factors necessary to determine the "correct" (I put correct in quotes because I really mean correct given your forecasts and assumptions about the business) P/E in any valuation model, which are required return and expected growth. Start with required return. To control for this variable, I'm going to assume we have a no growth business (g = 0). For a no growth business, the formula can be restated as PE = 8.5*(4.4/AAA) (or, more concisely, PE = 37.4/AAA). We can compare that formula to the accurate formula for valuing a stream of inflows, which is the Gordon growth model: PE = 1 / Required Return.* Initially, it's pretty obvious that Graham's formula isn't actually much of a short-cut when it comes to zero growth companies, because it isn't really easier than the accurate model, except that it defines "required return" for you. Of course, if a heuristic isn't any easier than the most accurate model, it's not particularly useful. But it's still worth looking at the assumptions and method this part of the formula is employing to determine required return.

One way to view the formula is setting a universal required return of 11.76% (the reciprocal of an 8.5 PE), and then adjusting that return based on prevailing risk free rates. An immediate problem with this is that it prevents you from having a different required returns for different businesses, or, if you try to, you are forced to do it obliquely by using a larger margin or safety rather than expressly. Now, when the Risk Free rate is 4.4%, the formula assigns an equity risk premium of 7.36% with no distinction between companies, and arbitrary though not irrational number. But, if the Risk Free rate changes, the equity risk premium suddenly changes as well. For example, if long term bond rates rise to 8.8%, the "correct" P/E for a zero growth company under the formula is suddenly 4.25, a required return of 23.53% and suddenly an equity risk premium of 14.7%! That's an interest relation without much of a reasoned basis that I can see. Another way of saying this is that defining "required return," which most people agree is the risk free rate plus a risk premium (which also can be broken down into and equity premium plus a specific company premium), as 1/(37.4/AAA) is both importantly flawed and not particularly time reducing as compared simply expressly estimating your required return from the investment.

So with required return aside, the formula can be assessed as a heuristic for thumbnailing growth into a single metric. Clearly, growth cannot be accurately thumbnailed into a single metric unless it is constant into infinity, in which case the Gordon model is both the most accurate and quickest method to apply. But convenience is important, so the question whether Graham's growth model's convenience overcomes its assumption in a non-stable growth situation is important. The growth part of the formula, assuming the AAA yield is 4.4% to control for required return, is thus as follows:

PE = 8.5 + 2G.

This can be compared to another growth-based heuristic, the PEG formula, which sometimes posits that PE/G should equal 1, or:

PE = G.

Thus, Graham's version is theoretically much more optmistic than the PEG = 1 or PEG = 2 formula, except that Graham's threshold requirements (such as 7 to 10 year growth and a maximum PE of 2X AAA yield) strongly counterbalance that effect. We know that growth is an exponential phenomenon, not easily modeled by simple heuristics when unstable. We also know that the length of the growth period can be very important, but cannot easily be measured in a linear formula is it's not perpetual.

It's worth examining how the PE = 8.5 + 2.G compares to the "correct" answer, using varying asumptions about growth rates and time periods. Let's again control for Graham's required return issues and assume AAA =4.4 and required return is thus 11.76%. To further simplify, I'll assume that terminal growth is stable (zero) in all cases. Here is a chart showing the "correct" P/E, under a two stage DCF, that would emerge along a matrix of two variables: Growth rates (in %) and length of growth period (in years). I know that my growth period and growth rates may exceed Graham's caveats, but it's helpful to see how they apply to various scenarios (they don't exceed it as much as Pfizer's growth rate does).

3 5 7 9 11
4% 9.5 10.0 10.4 10.8 11.2
6% 10.0 10.8 11.6 12.3 12.9
8% 10.5 11.7 12.8 13.9 14.9
10% 11.0 12.6 14.2 15.7 17.2
12% 11.6 13.6 15.7 17.8 19.0

In those cases, Graham's formula would create the following PE ratios:

3 5 7 9 11
4% 16.5 16.5 16.5 16.5 16.5
6% 20.5 20.5 20.5 20.5 20.5
8% 24.5 24.5 24.5 24.5 24.5
10% 28.5 28.5 28.5 28.5 28.5
12% 32.5 32.5 32.5 32.5 32.5

Along with the absolute differences (which will change as assumption about terminal value change), it's also important to note the failure to distinguish appropriate between differing situations, such as differing growth rates and time periods. While there are many cases, especially if you start playing with the terminal growth rate, when Graham's formula will be a decent estimate, there are some striking examples of potential discontinuities.

So, to sum, I would say that it would be a needless exaggeration to call it "uttlerly worthless" and take more hubris than I have. In stable growth situations, however, I don't see any possible use, as its required return components is neither more simple nor close enough to accuracy to be of much use. In an unstable growth situation, I would personally (this is my answer to (c) rather keep simple one-page spreadsheet of appropriate P/Es under various two (or three, which we didn't even examine) stage DCF scenarios using differnt growth periods, rates, and required return, than subject even my quick and dirty valuation to large potential errors. But that's admittedly somewhat subjective subjective. I like to make my implicity assumptions as explicit as possible, if I can do it and still maintain convenience.

*For the purposes of this discussion, I'd like to assume equivalency of earnings and cash flow. The potential discrepancy can be an important issue unless in some cases, but I'm going to set it aside for the purposes of this post.






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