The Rule of 20 (fair PE = 20 minus inflation) is getting more popular as more and more investors get to know it and appreciate its simplicity and usefulness.

One concern some investors have is the use of the CPI as a proxy for inflation. Some say that inflation calculation methods have changed over the years; others claim that the CPI is manipulated and does not accurately represent true inflation. However, to the extent financial markets use the official CPI for their assessment of inflation, it remains the best benchmark as it represents the views of the vast majority of investors.

The impact that all the QEs are having on interest rates is more troubling. The CPI in the Rule of 20 is but a convenient proxy for a “real discount rate” to apply to equity valuation. As the Fed keeps managing interest rates down, below their free market level, should it have an impact on the discount rate investors use in their valuation?

David R. Kotok, Chairman and Chief Investment Officer, Cumberland Advisors, argues that equity valuation is positively impacted by the QE-induced low interest rates:

(…) Assume that the long-term interest rate, defined by the ten-year Treasury note, is going to be in the vicinity of two percent for the next five to ten years. What would you then use as an equity-risk premium so you could calculate the value of the US stock market? Let’s run some numbers to try to predict where the market is headed.

A traditional equity-risk premium calculation would be 300 basis points over the riskless rate. (…) If you use the ten-year yield and a two percent estimate, you will derive an equity-risk premium comparative interest rate of about five percent. That is two percent on the riskless piece plus three percent on the equity risk premium, for a total of five. This calculation leads you to the basic conclusion that the stock market is priced properly and at an equilibrium level at twenty times earnings. Twenty times earnings is not excessive under this set of assumptions. The market would be neither cheap nor richly priced.

Apply the twenty multiple to the earnings estimates that we have for 2013. (…) For the purpose of this counting exercise, I am going to use $90. Ninety times a PE of 20, which we derive from an equity-risk premium of 300 basis points over the ten-year Treasury yield, gives us an $1800 price target on the S&P 500 Index. (…)

Will the Fed stay in its present mode for that long? No one knows. Given the current concentration of intensity, effort, and communication on the employment situation in the US, you can easily guess that it will take four to seven years to achieve an unemployment rate low enough to warrant the Fed changing its policy stance. One Fed president has now called for continuation of this policy until the unemployment rate is 5.5 percent. Another Fed president has repeatedly called for this policy to continue until the unemployment rate falls below seven percent. (…)

Kotok is adding a 300 points “traditional” risk premium to interest rates. The inverse of that discount rate gives him a P/E of 20 (1/(2% + 3%)). Kotok is precisely playing Ben Bernanke’s tune. The Fed wants to keep rates low enough for long enough to push people into riskier assets, potentially creating a wealth effect that, if translated into more spending, would help pull the economy out of its morass.

As a direct result of the Fed’s actions, real interest rates are currently negative, a truly unusual situation.


Negative long term rates have happened sporadically before, but only during periods when inflation spiked. Currently, U.S. inflation is below 2%.


This is clearly an exceptional situation. Should we normalize interest rates or used them as currently manipulated? Kotok is willing to bank on current low rates on the justification that artificially low rates are to continue as far as the investing eye can see.

Kotok thus derives a 5% earnings yield (20x P/E) assuming 2% long term interest rates and a 300 points “traditional equity-risk premium”. However, the foundation for that “traditional premium” is not readily visible from the chart below:


There is more of a “tradition” in the ratio of EY to interest rates: the range of 0.7 and 1.4 times 10y Treasury yields is more stable if one excludes the two very fat tails in the chart below. On that basis, EY should now be ranging between 1.4% and 2.8%, justifying P/E multiples between 35 and 71.


Obviously, the market has not (yet?) embraced Kotok’s approach. Investors are in effect normalizing interest rates.

Inflation is not as easily manipulated. Its use in the Rule of 20 provides rationality in most exceptional circumstances. The chart below (click chart to enlarge) clearly shows how the Rule of 20 values have historically remained within the 15-25 range except in periods of exceptional greed and fear. The red markers on the blue line indicate actual market highs and lows.


Equity markets constantly oscillate between greed and fear. In fact, precious little time is actually spent at the median valuation level. There is mean reversion but also mean aversion!

The Rule of 20 captures these fluctuations using two basic statistics: the inflation rate and the P/E on trailing earnings. As the chart shows, there have been a few periods when valuations remained excessive for many years:

  • The “nifty fifties” resulted in overvalued equity markets between 1968 and 1973.
  • A very difficult recession, exceptionally high inflation and interest rates and uncertainties on the eventual success of the Volcker and Reagan medicines kept markets deeply undervalued between 1982 and 1986.
  • Wild speculation during the internet revolution brought valuations way above normal between 1998 and 2001.

Such exceptional periods of over and under-valuation have always brought claims of “new paradigms” and “this time, it’s different”, severely testing investors discipline.

With the exception of a brief period late in 2009 and early in 2010, the S&P 500 Index has been in undervalued territory for nearly 4 years, even though the Index has more than doubled during the period! Why is that?

  • Earnings have also more than doubled;
  • Inflation has remained subdued.

The Rule of 20 currently states that fair P/E is 18.3x trailing EPS of $98.69. That’s 1800 on the S&P 500 meaning 23% upside. David Kotok is thus partly right, but for the wrong reasons.

Should we take the plunge?

The macro risks are pretty well laid out in front of everybody to see:

  • Earnings seem to be peaking.
  • Revenue growth is near zero.
  • Profit margins are very high and flattening.
  • The U.S. economy is running on but one cylinder.
  • Europe is in as complex a mess as possible.
  • China is landing not so softly.
  • The U.S. fiscal cliff is straight ahead.
  • Nobody really credible is in charge just about anywhere one looks.

That said, I still remember 1982’s gloom and doom. Treasuries were yielding 13% then! The S&P 500 closed at 107 in July 1982, exactly its June 1972 level. Alas, nobody has a monopoly on lost decades.

That said, July 1982 marked the beginning of a powerful bull market that peaked at 330 in August 1987. If you had closed your eyes, pinched your nose and bought on the Rule of 20 reading until it crossed into overvaluation territory in the spring of 1987, you would have tripled your money taking virtually no valuation risk.

Is this time different?

The biggest risk is obviously tied to earnings. Since 1938, there have 13 periods of meaningful earnings decline. Equity markets nonetheless rose during 7 of these periods (see Banking (Betting) on Bankers?).

However, in all 7 cases, inflation declined along with EPS, further proof of the validity and importance of the Rule of 20. In effect, a 1.0% decline in the inflation rate can offset a 5% drop in trailing earnings. Just as important, however, was that investors expectations were lifted by declining interest rates and receding commodity inflation. We can’t expect interest rates to decline much from here, can we? Will the world economic slowdown offset the effect of QEs of all types and nationality on commodity prices?

I debated in September on the prospects for inflation in What If The Fed Has It All Wrong?, erring negatively, arguing that all the QEs in the world are merely pushing on strings while artificially boosting commodity prices and driving inflation upward as a result. Most central banks have squarely abandoned inflation targets, focused as they are on boosting growth.

Can we have our cake and eat it, too?

Perhaps, if oil prices decline.

Saudi Arabia has recently said that it wants lower oil prices. According to Bloomberg, the Saudis recently

chartered at least seven very large crude carriers to load a total of about 14 million barrels in October, compared with about four a month so far this year, according to data from Athens-based Optima Shipbrokers Ltd. Brokers report tanker bookings when the deals are provisional and charters are then sometimes canceled. (…)

A one-way journey to the U.S. Gulf from Saudi Arabia takes about 40  days to complete, according to Optima. That implies the cargoes will probably be discharged in the second or third week of December.

President Obama may decide this is too late for Christmas (and the elections?) and release some of the U.S. strategic petroleum reserves in sync with Europe.

A meaningful decline in oil prices would do wonders for world economies and equity markets:

  • world consumers would get an instant and much needed break;
  • businesses would also immediately benefit;
  • consumer inflation would decline;
  • lower producers costs would likely trickle down to consumer prices, lifting expectations of slow inflation for an extended period.


  • Israel-Iran: no end in sight.
  • Iran is helping Syria’s government;
  • Saudi Arabia is helping Syrian rebels;
  • Saudi Arabia’s budget needs €100 to balance.
  • Venezuelan production? Mexican production? Nigerian production? Etc…

This time is different!

  • This time, whole countries are bankrupt and in depression;
  • Big countries such as Italy and France are seriously teetering;
  • Austerity measures keep being piled on;
  • Eurozone politicians have lost control leaving Eurocrats in charge;
  • Technocrats are meeting endlessly seeking common grounds to 17 widely different agendas;
  • Many major banks are on artificial life support;

Briefly stated, Europe is a catastrophe in slow motion that nobody can confidently predict how nor when it will end;

  • The U.S. looks only a little better;
  • Not so for U.S. politicians;
  • China: landing? Hardly or softly?
  • Can China recover without pulling commodity prices, including oil, higher? 
  • Central banks are down to experimenting, having pushed aside their own rules and regulations as well as anything resembling monetary discipline;
  • Monetary stimulus is no substitute for fiscal stimulus. However, few countries, least of all Europe and the U.S.A. are in a position to provide the necessary fiscal medicine.

In all, the world is a mess with little visibility for a turnaround mainly because normal market forces are ineffectual, being relentlessly overruled by political and/or technocratic interventions.

Yet, inflation is not slowing. Eurozone inflation was 2.7% in September, up from 2.4% between May and July. U.S. inflation was 1.7% in August, unchanged from May-June but up from July’s 1.4%. Core CPI has slowed a little but median CPI has held steady at 2.3% since May and the last 2 months annualized rate was +2.4%. The US Daily Index at the Billion Prices Project @ MIT has been accelerating lately, rising at a 3.8% annualized rate since June.


The hope is that central bankers’ bets succeed and growth reappears without higher inflation. If the monetary experiments fail and growth remains slow or gets even slower, profits will decline. If inflation takes off at a rate faster than economic growth, valuation will suffer. Neither “ifs” are good for equities.

Prudently waiting for positive evidence on profits and inflation is a wise attitude. What opportunity cost there might be is offset by the risk avoided. The valuation gap is wide enough to leave ample upside if and when the skies begin to clear. Meanwhile, quality, good yielding stocks remain the safer bets.


10 thoughts on “P/Es, QEs & SAUDIS

  1. This is a very well written article. You cover a whole lot of ground here, and while I’m sure the lack of a solid conclusion may disappoint some… I prefer the “we have more questions than concrete answers” approach than “we definitately are heading in this direction” view.

    As I’ve said before, I think the Rule of 20 model works very well– except in times of massive interventions by the central banks, when interest rates tend to be artifically suppressed across the board.

    In the case of the U.S. Federal Reserve, if their efforts to induce growth by pushing investors into risky assets DOES NOT work… earnings expectations will push lower, with the only open question being “how much lower”?

    If the artificial asset reflation theme indeed DOES spur growth, then the Fed has already indicated it will likely be behind the 8-ball on inflation and will need to play catch-up on interest rates. As a result, negative real rates can move to highly positive VERY QUICKLY, especially when rates have been artificially suppressed for so long. Most investors don’t want to be in front of that train, understandably.

    In either scenario, those investors looking at current valuations are likely discounting future valuations with these themes in mind.

    Which gets to how one measures inflation. I’ve always wondered to what extent that the Rule of 20 would be useful if a forward looking proxy of inflation (inflation expectations) is used in place of CPI, which is frustratingly backward looking. The nice thing is, there are proxies for inflation expectations that ARE determined by market forces, and much less prone to any government/central banker manipulation than CPI.

    What you might find is that the current market “pricing” of inflation expectations is running quite a bit higher than the current trailing rate. That doesn’t mean that, for example, applying a 3% forward inflation rate vs. 2% currently will make much of a difference from a model standpoint– it might move the S&P target down from 1,800 to 1,500. But it does suggest that investors are likely discounting equity market P/E based on forward looking measures (inflation expectations) than from utilizing past/CPI measures.

  2. A different view: Shadowstats uses the 1980 method for calculating inflation. My point is that the charts/graphs above are not ‘normalized’ to a constant method for CPI. Why don’t you re-calcutate data for 1981(?) and forward using the 1980 method and then plot a chart.

  3. Tks Ray. (20-CPI) is really a proxy for the discount rate investors are using at any given point in time. Same as for real interest rates. The “generally accepted” measure for inflation is the CPI.

  4. Hi Denis,
    You mention that “the market has not (yet?) embraced Kotok’s approach. Investors are in effect normalizing interest rates”. Kotok gives a discount rate of 5% and derives the 20 P/E multiple. Whereas you mention that EY yield should be between1.4-2.4%,justifying P/E multiples between 35 and 71.
    Since market is not trading at 35-71 multiples, I assume higher 10y Trsy expectations is the reason for it to trade at a lower multiple. And I assume this is what you mean by investors normalizing interest rates.
    If today market were to adopt Kotok’s approach, then 10y Trsy yield is what it is today, no higher yield is expected in the future and 20X is fairly valued. But using ratio of EY(5%) to 10y interest rate, market becomes cheap. What do we need to look at here?

    • This is a risk/reward game. Probabilities of winning vs losing. I personally wish to eliminate as much subjectivity from the analysis as possible. Hence the emphasis on the Rule of 20 which only uses past data to set what fair value should be. Once the objective analysis is done, each investor needs to assess his own situation (risk aversion). I generally go with the Rule of 20 but this time around, the manipulation by the CBs, the extreme complexity of the situation and my inability to understand the actual economic and financial risks involved lead me to more prudence that usual.

  5. Great article. It gives to me, with quite bearish view about the future, clear counterargument that even we have had a great run with the markets (at least in USA, not so much in Europe from where I’m writing), it seems however that for example S&P could be in fact under valuated, when using the rule of 20. However, and even that seems to be the case right now, my feeling is that the markets are in life-support supported by Worlds central banks, and my fear is that their unconventional measures will end up very badly. We have some examples from history for example from Germany and Japan during the II World War, where the government tried to keep (and succeeded some time) the stock markets elevated, but eventually gravity won big time.

  6. Denis,
    I am a frequent visitor to your website and consider your news items and associated commentary most enlightening. And I have no doubts that the Rule of 20 has some value in predicting equity returns. However, your discussion here regarding how to treat a fall in earnings and the difficulty determining where the PE multiple is headed suggests that maybe we can do a bit better.

    So I’d be interested in your comments on the John Hussman approach. I’m sure you’re well aware of the point he makes about stocks not being a claim on one year of earnings, but rather a claim on a long stream of cash flows well into the future. This leads him to place more emphasis on ‘normalised earnings’ and average PEs when estimating likely returns over the next 10 years. The strong correlation between his expected returns and actual returns as he says, “as far back as you like to go” is strong evidence of the worth of that approach.

    When I apply Hussman’s method to the Oz market the correlation between expected returns and actual returns is even higher (86pc) but we only have reliable data back to the 1970s so it still requires a leap of faith. The problem of course here in Oz is trying to determine the long term trend in earnings. In the US you have no such problem with data going back to 1870.

  7. Tks Chris,
    I read and respect John Hussman very much. Same with Jeremy Grantham and many others. I also pay heed to the Shiller PE. There is no foolproof method, unfortunately. Hussman, Grantham and Shiller provide a good longer term backgrounds while the Rule of 20 has been more useful cyclically.

  8. Yes, we got Knightian uncertainty.

    My interest is in “animal spirits,” which I believe are largely driven by the difference between the current unemployment rate and its adaptation level, an exponential moving average over recent years. When unemployment moves above its adaptation level, confidence collapses. The adaptation level is currently 8.8 percent. I expect unemployment to move up to that level over the coming year or so as we hit multiple forms of drag, fiscal, trade and political for starters.

    We’re not likely to get another long cycle this time, so a recession in the next year or so strongly implies a bear market. After that I expect inflation to accelerate and the market to rally nominally, but not “really.”

    See http://animalspiritspage.blogspot.com/search/label/animal%20spirits%20update

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