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Limitations of the PEG ratio in a rising interest-rate environment


Graham Osborn
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Hi folks, people always ask where the PEG comes from and what it means so I made an attempt to derive it from the dividend discount model.  It's a heuristic proof at best, but it does produce results that seem to align with experience.  I was frustrated for many years by my inability to reconcile the PEG ratio with the Gordon Growth Formula, but I came to realize that the formula is invalid for companies growing above the level of inflation for finite periods of time (which of course is the case for most companies of interest).

 

Hopefully this is helpful to those of you who were as confused as I was.  I think it also lends some theoretical clarity to the comments Buffett has made over the years about the effect of interest rates on the valuations of growth stocks.

 

[DERIVATION ATTACHED]

Limitations_of_the_PEG_ratio.pdf

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PEG really became a thing to justify dot-coms in the 1990s. Nonsensical.  It’s like joining PE and gross margin, or price to book with inventory turns—there is no relevant analysis there.  Looking at P vs E is relevant, and looking at G vs what you pay is relevant.  But a ratio implying indefinite term is silly.  Garbage in and out.

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http://www.valuewalk.com/wp-content/uploads/2014/06/David-Einhorn-Value-Investing-Congress-2005-PEG-ratio.pdf

 

Mr. Einhorn isn't doing so well lately, but I think his speech on the PEG ratio is spot-on.

 

Thanks for the Einhorn paper.  There is truth and untruth mixed in here..

 

1) Most people intuitively realize that there is a correspondence between operating multiples and sustainable organic growth rates.  Is it linear?  Of course not, or a company with flat-line revenue and great cash flow would be worthless.  The term “PEG” is unfortunate because it assumes the PE/ G term can be isolated, implying a linear relationship.  But that doesn’t mean it isn’t a useful approximation when the assumptions are understood.  It’s a bit too easy to rip the PEG without understanding that it does apply in special cases.  I illustrated in the “proof” that it works fairly well when (1) interest rates are zero (2) interest rate velocity is zero (3) retained earnings growth falls off at around 1% per annum.  Historically, the PEG was typically applied to high-growth companies where the interest-rate term was essentially negligible, meaning interest rates didn’t have to be zero at the time.  As the other poster noted, the tech high-flyers of the late 90s often had both limited/ nonexistent retained earnings after buybacks plus unsustainable growth rates.  That doesn’t make the dividend discount model wrong - it just means people plugged silly numbers into it.

 

(2) Einhorn’s citation of the Gordon Growth Formula is both theoretically and practically irrelevant.  Theoretically, GGF only applies when the growth rate is less than the long bond rate (otherwise the series would not converge).  Most of us don’t waste our time evaluating a growth company that can’t even beat inflation.  Practically, no company grows at any rate (including zero) forever, which is why the remainder term in most DCFs (which he lauds) produces systematic overvaluation of companies.

 

(3) His “quality of growth” argument also misses the point.  If you can’t say something positive about the reliability of retained earnings/ retained earnings growth for a business, you can’t value that business within a hemisphere by any means - DCF or otherwise.  Only the balance sheet will (sometimes) save you there.  As I practice it, the sustained growth rate is derived from the last 5 years’ (preferably more) compounded growth in retained earnings - assuming we have every reason to expect continuation of such growth in the future.  You can count the number of businesses where that sort of characterization can be made on the head of a pin.

 

(4) Einhorn suggests his gold standard of valuation is a DCF.  I would be curious whether anyone has ever done a study showing that DCF valuations led to improved investment returns.  In my experience, DCFs are riddled with assumptions (most notably the “magic” discount rate) that are at best wrong and at worst impossible to recognize by anyone except the author.  While I’ve constructed DCFs in the past, I can’t think of a time I actually bought or sold a stock based on one.  Buffett: “Spreadsheets never disappoint.” Buffett: “A good idea should hit you over the head with a baseball bat.”

 

So I didn’t see anything in his analysis that accurately contradicts the inequality I presented.  Again, the purpose is not to value a company but to establish in certain situations that a margin of safety may be quantitatively established.  Since the mathematics of discounted dividends and discounted FCFs are structurally equivalent, the results are derived from assumptions shared by Einhorn.

 

You’ll note that the changes to the formula generally result in a downward revision of acceptable valuations compared to the PEG result.  For example, Google (which recently traded at 36X normative earnings) deserves a PE of about 18 based on the PEG rule.  Using the rule outlined above with 18% growth, more normative 4% inflation, 1% growth decline per year, and 0.5% rate increase per year (aggressive perhaps), this would be:

 

P/ E > (g-r)/(vg + vr) = (18-4)/(1+0.5) = 14/1.5 = 9X

 

If you think 10-year AAA rates will stay closer to 3% with 0.5% growth decline and 0% rate increase, then:

 

P/ E > (18-3)/(0.5+0) = 30X

 

Bump up the rate increase 0.5%:

 

P/ E > (18-3)/(0.5+0.5) = 15X

 

Personally I’d be willing to start buying Google at 15-20X.  10X would be nice but probably won’t come unless growth slackens or inflation ramps up to the historic 4% annualized  level (1956-2016).

 

I continue buying a company growing at 20% last 5 years at about 7X earnings (which are pretty close to FCF):

 

P/ E > (20-5)/(1+0.5) = 10X

 

So I feel my margin of safety in this case is acceptable even if inflation goes wacko or the company starts slowing down.

 

All approximate, but based on dividend discounting.

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You’ve thought this through and find it useful.  That’s fine.  I’m not about telling people how they ought to be managing money.

 

I do see PEG as unnecessary, even dangerous, in my own practice.  It’s like technicals: May be some merit there, but the difficulty and ease of misuse means it better to avoid altogether.  I believe in thinking of value as the present value of future cash flows, but I am not smart enough to measure this via PEG. I like obvious; I like real assets not properly measured on a balance sheet; I like great businesses selling at a discount; I like management I trust.

 

I own Google, think it’s relatively cheap still, don’t think it’s at 36 time normalized earnings, and I have never assigned a long term growth rate to it. Don’t need to.

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There seems to be some sort of Peking order for quality - an unquantifiable variable. I mean, you can have an industrial or consumer company with a strong economic moat with 5% organic growth and will have a high PEG ratio - but it will stay that way short of a major calamity. Even then, it will go down in relation to lower quality stocks by similar quantities. So yeah, quality, industry, and leverage matter. But if all those variables check out , then PEG can be a 2nd filter of cheapness, in fact once the preconditions are checked off your list, PEG is better than PE because growth is a very important element of valuation. Without growth you tend to get the one pop value stocks or perhaps even value traps. However quality and a clean balance sheet are so important as engines of future growth, you rarely get an apple to apple comparison

 

 

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Just realized my math was messed up - in the generalized dividend discount model you have to multiply by the variable growth and interest rates for each individual cash flow.  There's no generalized way to express a formula relating growth and interest rates unless you assume exponential rather than linear trajectories.  Ugly math.

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ScottHall,

I've followed this thread with interest.

I understand your comment as a reminder to avoid over-reliance on mathematical models.

The quantitative is often put in opposition to the qualitative but is not reasonable to see them as complementary?

Do you suggest that value is only based on an ability to assess the balance between spontaneous bearish and bullish intentions?

Or simply to be better than the average subjective opinion?

 

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(4) Einhorn suggests his gold standard of valuation is a DCF.  I would be curious whether anyone has ever done a study showing that DCF valuations led to improved investment returns.  In my experience, DCFs are riddled with assumptions (most notably the “magic” discount rate) that are at best wrong and at worst impossible to recognize by anyone except the author.  While I’ve constructed DCFs in the past, I can’t think of a time I actually bought or sold a stock based on one.  Buffett: “Spreadsheets never disappoint.” Buffett: “A good idea should hit you over the head with a baseball bat.”

 

I made the same argument as you about DCF in the past.

 

"DCF to is sort of like Hubble telescope - you turn it fraction of inch and you're in different galaxy"

 

But I have changed my mind.

 

Any valuation work you do is based on DCF with the exception of relative valuation or valuation of options. Let me explain.

 

DCF does not mean you have to do spreadsheets. When you say a company is worth 10x earnings, you are doing a DCF valuation. The fact that you did not use a growth rate or discount rate or explicitly model cash flows, does not mean you are not making assumptions about these.

 

You have just assumed away all these variables. You do not even know what you have assumed away. When you do DCF you are forced to think through these and it gives you a chance to make sure they are reasonable and consistent. If you are honest with yourself, this can make the valuation more robust.

 

The fact that Buffett does not put this on paper should not mislead us into thinking we can do the same. He probably can model that in his head. Not so for most of us who have much less practice with DCF.

 

I think it would be helpful for most of us to do a few hundreds of DCF valuations before resorting to shortcut of multiples. It would give one an idea of how cash flows, reinvestment rates, return on reinvested capital, dividends, buybacks, debt, etc impact business value. This is very hard to get an intuitive understanding of these without putting them on paper and looking at the results.

 

These does not have to be complex. Actually these are much better if done by hand on paper at least for the first few.

 

Vinod

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Just realized my math was messed up - in the generalized dividend discount model you have to multiply by the variable growth and interest rates for each individual cash flow.  There's no generalized way to express a formula relating growth and interest rates unless you assume exponential rather than linear trajectories.  Ugly math.

 

Here's the corrected version.  These functions for changes in growth and interest rates become pseudolinear so long as the rate of change is not too great.

 

Again, I'm not bashing DCF/ DD theory - I'm just saying the practice is wrong.  That's why people bother with PEGs or PEs at all.  I wanted a tool that is better than the PEG, but is still simple enough that I don't have to bust out my spreadsheet to look at rate sensitivity on a growth stock.

 

Part of the reason I'm doing this is I looked at Depression-era valuations (where the typical growth stocks sold for around 10X earnings) and asked myself - is that rational?  And when you start playing around with the inputs in the formula you can see that it IS rational if growth is going way down or rates are going way up.  I think understanding those dependencies in an intuitive way is valuable - it helps me quantify how low these stocks might fall with small changes in expected growth and interest rates.

 

estimating_appropriate_PE_based_on_sustainable_growth_and_interest_rates.pdf

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To drive that point home, here is a graph of the Google example showing the effect of the pace of annual interest rate increases on the calculated (minimum) fair value for the company.  If you plug the formula illustrated into Desmos you can read the datapoints.  In order for Google to reach a PE of 10 we would need to be adding about 1.5-2% per year to the current rates of 3%.  So that would be a 1970s-type era.  I wonder if people in the Depression were forecasting massive inflation to bail out the banks?

Presentation1.pdf

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(4) Einhorn suggests his gold standard of valuation is a DCF.  I would be curious whether anyone has ever done a study showing that DCF valuations led to improved investment returns.  In my experience, DCFs are riddled with assumptions (most notably the “magic” discount rate) that are at best wrong and at worst impossible to recognize by anyone except the author.  While I’ve constructed DCFs in the past, I can’t think of a time I actually bought or sold a stock based on one.  Buffett: “Spreadsheets never disappoint.” Buffett: “A good idea should hit you over the head with a baseball bat.”

 

I made the same argument as you about DCF in the past.

 

"DCF to is sort of like Hubble telescope - you turn it fraction of inch and you're in different galaxy"

 

But I have changed my mind.

 

Any valuation work you do is based on DCF with the exception of relative valuation or valuation of options. Let me explain.

 

DCF does not mean you have to do spreadsheets. When you say a company is worth 10x earnings, you are doing a DCF valuation. The fact that you did not use a growth rate or discount rate or explicitly model cash flows, does not mean you are not making assumptions about these.

 

You have just assumed away all these variables. You do not even know what you have assumed away. When you do DCF you are forced to think through these and it gives you a chance to make sure they are reasonable and consistent. If you are honest with yourself, this can make the valuation more robust.

 

The fact that Buffett does not put this on paper should not mislead us into thinking we can do the same. He probably can model that in his head. Not so for most of us who have much less practice with DCF.

 

I think it would be helpful for most of us to do a few hundreds of DCF valuations before resorting to shortcut of multiples. It would give one an idea of how cash flows, reinvestment rates, return on reinvested capital, dividends, buybacks, debt, etc impact business value. This is very hard to get an intuitive understanding of these without putting them on paper and looking at the results.

 

These does not have to be complex. Actually these are much better if done by hand on paper at least for the first few.

 

Vinod

 

Hi Vinod, I agree with you probably more than you realize.  I distinguish between the theory of DCF (which I agree with 100%) and the practice of DCF (which I think has serious shortcomings).  Part of the reason I went through this exercise is to find a middle point between an all-stops-out DCF and the sort of ratios many of us use.  The former incorporates all the variables but usually suffers from incorrect inputs.  The latter is oversimplistic but, through its ease of calculation, enables the experienced investor to establish appropriateness in different situations.  Buffett often says he can decide whether he wants to buy a company in 5 minutes, which means he's using pattern recognition as you say.

 

I use probably 10-20 different ratios to value a stock.  The most important are MC/ Cash, Price/ Tang book, Debt/ Equity (more risk means less value) EV/ Rev, EV/ EBITDA, EV/ FCF, Operating PE, PE, ROA, ROE, ROIC, revenue growth, tang book growth.  But the most difficult thing is always figuring out how much value I should attribute to different levels of growth.  I have used the PEG in the past because it produces numbers that pass my "whiff test" based on experience, at least for growth rates in the 10%-30% range.  But I dislike the PEG because it's clearly a tool pulled out of thin air.

 

It seems like the formula:

P/ E > 2/(G+R)*ln(g0/r0)-1

 

provides a better estimate of the appropriate PE, so I plan to start using it rather than the PEG.

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To drive that point home, here is a graph of the Google example showing the effect of the pace of annual interest rate increases on the calculated (minimum) fair value for the company.  If you plug the formula illustrated into Desmos you can read the datapoints.  In order for Google to reach a PE of 10 we would need to be adding about 1.5-2% per year to the current rates of 3%.  So that would be a 1970s-type era.  I wonder if people in the Depression were forecasting massive inflation to bail out the banks?

 

On thing to note in this example, as someone pointed out to me on another thread, is that G is actually partly a function of R.  In other words, businesses with pricing power should growth faster when inflation is higher because they (ideally) just raise prices in proportion to rising costs.  Businesses with high fixed assets and commodity products or price controls may not be able to do this and so inflation has a much greater impact on their value.

 

Mathematically, in the expression:

 

P/E > 2/(G+R)*ln(g0/r0)-1

 

you can see that a business that can increase prices with inflation will actually be PE-neutral (the convention in his equation is that G is decline per annum in growth, so we DECREASE the rate of decline):

 

P/E > 2/[(G-d)+(R+d)]*ln(g0/r0) = 2/(G+R)*ln(g0/r0)-1

 

So businesses with pricing power tend to maintain their multiples better than businesses that don't.

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(4) Einhorn suggests his gold standard of valuation is a DCF.  I would be curious whether anyone has ever done a study showing that DCF valuations led to improved investment returns.  In my experience, DCFs are riddled with assumptions (most notably the “magic” discount rate) that are at best wrong and at worst impossible to recognize by anyone except the author.  While I’ve constructed DCFs in the past, I can’t think of a time I actually bought or sold a stock based on one.  Buffett: “Spreadsheets never disappoint.” Buffett: “A good idea should hit you over the head with a baseball bat.”

 

I made the same argument as you about DCF in the past.

 

"DCF to is sort of like Hubble telescope - you turn it fraction of inch and you're in different galaxy"

 

But I have changed my mind.

 

Any valuation work you do is based on DCF with the exception of relative valuation or valuation of options. Let me explain.

 

DCF does not mean you have to do spreadsheets. When you say a company is worth 10x earnings, you are doing a DCF valuation. The fact that you did not use a growth rate or discount rate or explicitly model cash flows, does not mean you are not making assumptions about these.

 

You have just assumed away all these variables. You do not even know what you have assumed away. When you do DCF you are forced to think through these and it gives you a chance to make sure they are reasonable and consistent. If you are honest with yourself, this can make the valuation more robust.

 

The fact that Buffett does not put this on paper should not mislead us into thinking we can do the same. He probably can model that in his head. Not so for most of us who have much less practice with DCF.

 

I think it would be helpful for most of us to do a few hundreds of DCF valuations before resorting to shortcut of multiples. It would give one an idea of how cash flows, reinvestment rates, return on reinvested capital, dividends, buybacks, debt, etc impact business value. This is very hard to get an intuitive understanding of these without putting them on paper and looking at the results.

 

These does not have to be complex. Actually these are much better if done by hand on paper at least for the first few.

 

Vinod

 

Hi Vinod, I agree with you probably more than you realize.  I distinguish between the theory of DCF (which I agree with 100%) and the practice of DCF (which I think has serious shortcomings).  Part of the reason I went through this exercise is to find a middle point between an all-stops-out DCF and the sort of ratios many of us use.  The former incorporates all the variables but usually suffers from incorrect inputs.  The latter is oversimplistic but, through its ease of calculation, enables the experienced investor to establish appropriateness in different situations.  Buffett often says he can decide whether he wants to buy a company in 5 minutes, which means he's using pattern recognition as you say.

 

I use probably 10-20 different ratios to value a stock.  The most important are MC/ Cash, Price/ Tang book, Debt/ Equity (more risk means less value) EV/ Rev, EV/ EBITDA, EV/ FCF, Operating PE, PE, ROA, ROE, ROIC, revenue growth, tang book growth.  But the most difficult thing is always figuring out how much value I should attribute to different levels of growth.  I have used the PEG in the past because it produces numbers that pass my "whiff test" based on experience, at least for growth rates in the 10%-30% range.  But I dislike the PEG because it's clearly a tool pulled out of thin air.

 

It seems like the formula:

P/ E > 2/(G+R)*ln(g0/r0)-1

 

provides a better estimate of the appropriate PE, so I plan to start using it rather than the PEG.

 

Hi Graham,

 

To me, once you have a fix on the moatiness of the company, usually the next most difficult issue is estimating the growth.

 

The way I approach is to estimate the the earnings 7 years down the line and put a multiple of those earnings at that time and then discount it back. The multiple would depend on what I conservatively estimate to be how the market would be valuing the company. A 14x multiple if the company is an average business that can grow somewhat in line with the economy, pass on inflation, a decent level of free cash flow conversion and low disruption potential. Adjusting the multiple up or down. But I bother with looking out 7 years only for those companies that have strong moats.

 

Vinod

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  • 4 weeks later...

 

Hi Graham,

 

To me, once you have a fix on the moatiness of the company, usually the next most difficult issue is estimating the growth.

 

The way I approach is to estimate the the earnings 7 years down the line and put a multiple of those earnings at that time and then discount it back. The multiple would depend on what I conservatively estimate to be how the market would be valuing the company. A 14x multiple if the company is an average business that can grow somewhat in line with the economy, pass on inflation, a decent level of free cash flow conversion and low disruption potential. Adjusting the multiple up or down. But I bother with looking out 7 years only for those companies that have strong moats.

 

Vinod

 

Hi Vinod, good to hear from you as always.  This sounds like a variant of the "terminal value" method - I am assuming you project the next 7 years cash flows manually.  One thing that has often concerned me about the terminal value method (including the Gordon Growth Formula) is that it assumes stable company growth and interest rates.  As the Coke example above illustrates, this can be used to establish some "worst case" valuations but could be problematic in terms of assigning an exact value to intrinsic value.

 

My personal bias in valuations on "moaty" businesses is to sum up the discounted earnings over the next 10 years and ignore anything after (this thread is mainly concerned with simplified assumptions).  Most analysts would have a cow over this method - but I prefer to systematically undervalue businesses.  Any time terminal value accounts for more than 30% of the "manual" valuation you are building a lot of assumptions "in the cloud" IMO.

 

Sincerely,

Graham

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Really appreciate this thread.

 

One thing I like is that, conceptually, over time, the PEG ratio (individual stock and in the aggregate) will tend to gravitate to one.

Pricing for growth is difficult and this has been a crowded market for quite some time.

Focus on the PEG ratio may underestimate valuation risk, specific business entity risk and leverage risk, meaning that the margin of safety concept may be stretched.

 

Given the assumption that we normally operate in non black-swan periods and for relatively recession-resistant and acyclical entities, somehow integrating a PEG component into calculations can be a useful exercise. Trying to stay away from pure mathematical models and long term forecasts.

 

Like to obtain a range of intrinsic values from various angles and one of the ways is:

-Evaluate (through industry dynamics assessment and expected sales/margins for the specific firm) what the earnings will be in 5 years (5 years is arbitrary but one has to balance the necessity for longer term perspective without falling into the trap of futuristic assumptions).

-Apply what you think to be an appropriate PE on those 5 years down the road earnings (subjective but again based on a compromise between moat now and terminal value later).

-Buy now if the expected price in 5 years fits with your expected return. So if your hurdle is 15%, go for it if expected value at 5 years is double of share price now.

 

As of today, this would potentially work out for: BRK, FFH, BAM, Gildan Activewear, Richelieu Hardware.

But of course, this is a multi-dimensional exercise and success, it seems, is related to the ability to say no most of the time. :)

 

Would appreciate even more if others here like Uccmal et al who seem to be good at pricing reasonable growth could pitch in.

 

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