Stranger Coincidences

The Relative-To-GDP Model

October 11, 2018



In assessing valuation of US equities, there is a school of thought in which it is opined that the total market capitalization of US equities should grow roughly in line with that of US GDP (the “Buffett Indicator”).

The premise is that if US market capitalization substantially outpaces that of US GDP, equities (in aggregate) are considered over-valued.  Conversely, if market capitalization lags that of US GDP, equities are considered under-valued.

This intuitive concept may be simplified by comparing the value of the S&P 500 index itself to that of US GDP (divided by a constant).  Since the S&P 500 is a reasonable proxy for the majority of market capitalization of US equities (the calculation of the S&P index ensures that it remains proportional to the market capitalization of its constituent components), this assumption would seem reasonable, especially for large-cap stocks.  We employ this formula to compute the value used in our model:


Quite simply, RGDP is the ratio of the index to the latest GDP, multiplied by 100.

Let’s have a look at how RGDP performed historically.

The 1973-1974 Recession

In early 1973 the RGDP ratio peaked at nearly 10:


[The lower plot encapsulates the RGDP ratio, in green]

Once the recession took hold and equities retreated through 1974, the RGDP declined substantially, finally bottoming out under 5.

The early 2000’s “Tech Wreck”

Here is what the market looked like in the 1999-2001 lead-up to the Tech Wreck and the ensuing recession:


As the market peaked, you will observe the RGDP ratio hovered near 15.  As the recession commenced, RGDP started to decline, finally bottoming at about 7:


The 2008-2009 Financial Crisis and Great Recession

Taking another example, during the lead-up to the financial crisis, the RGDP ratio peaked at just over 10.  However, once the market deteriorated in late 2008 / early 2009, the RDGP ratio bottomed out about 5:

Valuations - 2009

Current Picture

Finally, looking at the current picture, we see the RGDP ratio stands again at almost 15:


All things being equal, our ratio at just under 15 appears to be at an elevated level at the present time.

Discussion Points

There are several points to note.

  • As mentioned, the RGDP ratio takes into account the market capitalization of S&P 500 companies.  It does not take into account the entire market capitalization of all equities in the United States.  This simplifying assumption is introduced to make RDGP easy to calculate and is believed to be a reasonable proxy of the Buffett Indicator.  Nevertheless, readers may find RGDP is more aptly suited to large-cap equities (since it is based on the S&P 500)
  • Readers should keep in mind that market conditions vary over time.  For example, the RDGP ratio tended to peak around 10 in the 1970’s – whereas, more recently, it seems to peak about 15.  It is difficult to explain with certainty the underlying cause, but it may be due to a number of factors, including:
    • The 1970’s was a highly inflationary environment; recent times have seen  inflation remain low and stable
    • The 1970’s saw bond yields in the high teens; recent times have seen yields extraordinarily low
    • Trading in the 1970’s was still a very manually-driven process, with some automation largely assisting human traders.  Conversely, technology and automated trading today is extraordinarily widespread, with the majority of trading being done in milliseconds by specialized software
    • Quantitative Easing programs recently introduced by the Fed and other central banks may have skewed normal market forces which did not exist in earlier times
  • All of that to say, readers are advised not to adapt a hard-and-fast approach, such as “buy when RGDP falls to 5 and sell when it rises to 15”.  Readers would be better served by comparing RDGP values today to observed ranges in the recent past (say, the last 10 years)
  • RGDP is a market valuation tool – it is not a market timing tool.  Although RGDP seems to indicate with some degree of precision whether a market is over-valued (under-valued), it cannot forecast when the downturn (upturn) will occur
  • As with any model, readers are advised to employ RGDP simply as one tool among many.  The idea is to use RGDP, along with other models, to get an overall impression of market valuation – any one model should never be used alone.


The Relative to GDP (RGDP) model is a simple model (based on principles similar to the Buffett Indicator) which compares the S&P 500 index value to US GDP.  It provides a rough sense of equity valuation, especially as applied to large-cap stocks.

With a value of nearly 15 today, the RGDP is suggesting that equities have reached valuations close to that of where they were just prior to the “Tech Wreck” bear market and recession of the early 2000’s.


Market Cap to GDP: And Updated Look at the Buffet Valuation Indicator,, retrieved October 11, 2018

Stock Market Capitalization to GDP Ratio,, retrieved October 11, 2018

How is the value of the S&P Calculated?,, retrieved October 11, 2018



The above discussion of financial conditions represent  the opinion of the author and should strictly be used for educational purposes only.  It is not an endorsement to buy or sell any security whatsoever, and does not constitute investment advice.  Individual security prices fluctuate and may result in financial loss.

While data contained therein is believed to be accurate, no express or implied warranty is provided with respect to data accuracy.

Always consult your professional investment advisor prior to making any investment decision.


The Simplified Fed Model

October 8, 2018



This article presents a simplified Fed Model which can be used by retail investors to get a sense of S&P 500 market valuation relative to bonds.

We begin with some definitions.

Definition: Earnings Yield

Most readers are probably familiar with the common price-earnings ratio:

PE = Price / EPS

Simply, the PE ratio takes a stock price and divides it by the annual earnings-per-share.  A higher PE value indicates a higher stock valuation.

The earnings-yield of a stock is simply the opposite:

EYIELD = EPS / Price

Suppose a certain stock is currently valued at $100 and reports earnings of $5 per share.  We say that the stock is yielding 5% in earnings at current price levels.  A portion of those earnings may be paid out in dividends with the balance being retained by the corporation.

An index, such as the S&P 500, has no price per se, nor does it generate earnings.  Nevertheless, an index has a value, and one may calculate “earnings per share” as an aggregate sum of earnings of the index’s constituent components.  In practice, we don’t need to do this manually; organizations (including Standard & Poors itself) often provide aggregate earnings for an entire index.

Therefore, we may re-write our formula for an index as a whole as:

EYIELD = Aggregate EPS / Index Value


Definition: The Fed Model

The “Fed Model” is a simple method of performing valuation of an index as a whole.  It is a relative valuation model in the sense that it compares the forward (i.e. expected) earnings yield for the S&P 500 to the yield you would receive if you invested in a risk-free, 10-year US benchmark government bond.  The rationale is, if one had to choose, the rational investor would prefer to invest in equities so long as they were expected to yield more than (by a certain margin – the risk premium) what would be expected to be yielded by a risk-free US 10-year government bond.  And vice-versa.

Taking a simple example, suppose we have:

  1. US 10’s are yielding 9% in interest
  2. The S&P 500 is expected to yield 2.5% in earnings

In this circumstance – admittedly quite contrived with respect to current conditions – a rational investor would probably prefer to accept the 9% in interest from risk-free government bonds rather than accept the 2.5% in earnings in more risky equities.

This is the basis of the Fed Model.


The Simplified Fed Model

In practice this can be challenging to implement, especially for retail investors (who do not have their own research department to forecast aggregate earnings).  Moreover, forecasts are just that – forecasts – and are subject to revisions.

Retail investors, then, may find it more convenient to use a simplified version the the Fed Model, the Simplified Fed Model.  It is very similar except that it employs current earnings rather than forecast earnings:

EYIELD = Aggregate (current) EPS / Index Value

Though simplified, I have found this model to be a useful tool in determining equity valuation.

Let us have a look at how the Simplified Fed Model has performed over the past several years.

The Lead Up to the early 2000’s “Tech Wreck”

Here is what the market looked like in the 1999-2001 lead-up to the Tech Wreck and the ensuing recession:

Valuations - 2000

[Looking at the middle plot, the US 10 Year is indicated in green, and the (current) earnings yield is indicated in blue]

As the market peaked, you will observe we had 10’s yielding 6 – 6.5% whereas S&P earnings were yielding less than 4%.  We have, then, a risk premium of about -2.5%.  A negative risk premium.

It seems evident that, for most people, accepting a 6.5% yield from risk-free government bonds would tend to outweigh a 4% earnings yield from the more risky equities.  And, indeed, a substantial decline did eventually ensue.

Let us turn our attention to post-2001.  As markets bottomed, and as the economy came out of recession, we have the following:

Valuations - 2002

As you will note, the model continued to suggest bonds were of relative value vis-a-vis equities, until about Spring of 2003, at which time earnings began to solidify.  Earnings continued to remain elevated through to 2004.  Indeed, this marked the beginning the next bull market.

This bull market continued in strength through to late 2007, as indicated below.  Earnings yields continue to outperform bonds until signs of weakness began to show late 2007 / early 2008 when earnings yields deteriorated.

Valuations - 2009

As the market bottomed in 2009, earnings yields advanced markedly, significantly outpacing bond yields.  This set the stage for a very protracted market recovery, which continues to this day.

Which brings us to the current picture:

Valuations - 2018

Equities continue to yield nearly 5%, compared to bond yields of near 3%.  A +2% risk premium still marks a somewhat attractive valuation, but not compellingly so.  Moreover (as I note below), there is a risk bond yields have somewhat artificially been skewed lower due to the extensive quantitative easing programs that have been in place since the end of the financial crisis and may rise.


Caveats of the Model

Equity index valuation is not an easy task, especially for retail investors.  There are several points to bear in mind.

  • Every investor has his or her own view as to what is an attractive risk premium.  If equities are yielding 8% and bonds are yielding 6%, we have a risk premium of 2%.
    • Should we buy equities with a risk premium of 2%?  It depends on the investor; there is no one clear answer.  Risk-tolerant investors might say yes, risk-averse investors might say yes.  Everyone has their own view.
    • Having said that, as risk premiums become more and more extreme, there are times (as history has shown) where it becomes very difficult to justify buying equities, even for  risk-tolerant investors.
  • The Simplified Fed Model uses current earnings, not future earnings.  This is a trade-off.  Current earnings are easier to obtain (especially for retail investors) and are less subject to revision.  But future earnings look forward to what the market is expected to yield, and may be a better indicator of intrinsic value.
  • Though current earnings are less subject to revision, but are not immune.  They can – and do – change over time.  It takes time for all 500 companies to report earnings, it takes time for Standard & Poors to aggregate these earnings, and it takes time generate and report them.
    • Obtaining earnings for a single company is (relatively) easy: companies are required, by law, to report earnings on a quarterly basis in their financial statements.
    • Obtaining earnings for the aggregate S&P 500 is more difficult.  At present, they are available in Spreadsheet format from S&P itself for free, and have been so for the past several years.
    • But this can always change.  S&P may decide not to publish aggregate earnings any longer, or may continue to publish them, but only for a fee.
    • Other web sites likely publish S&P earnings, too.  Moreover, if one can obtain the market PE ratio, one can then derive aggregate earnings using this formula (recall these figures are inverses of one another):

Aggregate EYIELD = 1 / Aggregate PE

  • But be careful.  Even if the PE ratio is published on a financial news site, there is often no guarantee of its accuracy.  Sometimes sites (notably Yahoo! Finance) exclude companies which report negative earnings, which would tend to skew the aggregate PE lower and thus the earnings yield higher. At other times, the method of calculating aggregate earnings may vary; it is entirely possible some sites may use an equal-weight method of calculating aggregate earnings rather than a market-capitalization weight method.  This would be incorrect.
    • I would recommend cross-checking market data across several sites prior to use.
    • Note that the US Federal Reserve publishes 10 year bond yields on its website for free, and this will probably continue indefinitely.
  • Quantitative easing has probably skewed government bond yields.
    • In response to the 2008 financial crisis, the US Federal Reserve undertook a program of purchasing mass quantities of US government bonds, pushing prices up and consequently pushing yields down.  Some argue that US government bonds have not been responding to typical market forces for some time, and this continues to this day.
  • Markets do not always behave as expected.  Equities can at times be significantly undervalued or significantly overvalued, and this can continue for long periods of time.
    • In other words, neither the Fed Model nor the Simplified Fed model attempt to dictate timing.  They simply attempt to give an indication of relative valuation.


In practice, there are many hurdles for retail investors in this domain.  Simply obtaining reliable data for free, or at least reasonably priced, is not an easy undertaking.  Data sources come and go.  It is critical to have consistent, accurate, and timely data for any model to work.

But even armed with a reliable and timely data source does not make valuation an easy task.  Interpreting the data, deciding on an appropriate risk premium, and many other factors are of critical importance to use models such as these successfully.

It is always preferred to base valuation conclusions using a number of models and not to rely just on one model alone.  When assessing market valuation I use the Simplified Fed Model as well as others (I discuss a Relative GDP model in my next article).

With all of this in mind, looking at the S&P market valuation using this model in isolation suggests fair-market value.  With a +2% risk premium I am not seeing substantial signs of over- nor under-market value.

But other models (such as the Relative GDP indicator) paint a bleaker picture.  Going forward, in the current environment I am expecting rather anemic growth for the S&P, at best.


The above discussion of financial conditions represent  the opinion of the author and should strictly be used for educational purposes only.  It is not an endorsement to buy or sell any security whatsoever, and does not constitute investment advice.  Individual security prices fluctuate and may result in financial loss.

While data contained therein is believed to be accurate, no express or implied warranty is provided with respect to data accuracy.

Always consult your professional investment advisor prior to making any investment decision.

Will the Yield Curve Invert?

October 3, 2018


Many pundits attest to the predictive power of the inverted yield curve.  It is in fact true: a yield curve which inverts (that is, short rates rise above longer rates) has a tendency to forecast economic recessions.

This is strikingly illustrated just prior to the 2008 Financial Crisis:



Figure 1: The Great Recession

[Note: The top plot is the S&P 500 index.  The middle plot is simply the difference between 10- and 2-year US treasuries.  Normally, in a healthy, growing economy, 10-year yields are higher than 2-year yields, sometimes substantially. 

When the difference between these two rates reaches (nearly) zero, we say the yield curve has flattened.  And once the difference actually turns negative, we say the yield curve has inverted. It is this inversion of the yield curve which is the topic of this paper.

The purple highlighting indicates the ensuing recession.]


Let us turn to history to see how this has played out in past recessions.

In 1988 the market was dusting itself off from the 1987 Market Crash.  Over the course of the next two years, equities struggled but finally managed to reach new highs around 1989.

However, during this time, the spread between 10- and 2-year yields dwindled, finally inverting during early 1989.


Figure 2: The 1990-1991 Recession

A recession did in fact ensue mid-1990 through to early 1991.

Another example: the early 2000’s “Tech Wreck”.



Figure 3: The 2001 Recession

The curve flattened, and then finally inverted decisively in early 2000, resulting in the 2001 recession accompanied by a steep decline in equities.

Where are we now?  We are here:



Figure 4: Today

Yields are nearly flat, but there is still a positive spread of about 25 basis points.  We have not inverted.  Yet.


To Invert or Not to Invert

But will we?  Will the curve invert, and will we suffer another ensuing recession?

There are several points to note.


1. A flattening yield curve does not always go on to invert

This in fact happened in 1984, and was followed by strong economic growth and equity performance:



Figure 5: Near Inversion: a False Positive


2. A curve inversion does not necessarily guarantee a recession (but it is not good news)

Although my data set (going back 1977) does not contain such an anomaly, there are cases throughout history in which an inversion is not followed by a recession.  But such cases are rare.  Moreover, every recession in modern times has been preceded by an inversion.

To put into scientific parlance, curve inversions are highly sensitive – if not always highly specific – of ensuing recessions.


3. A curve inversion does not forecast when the recession will commence nor how severe it will be. 

While it is probably true that a substantial inversion likely indicates a deep recession, there are no guarantees.  And sometimes markets can rally for a year or two after an inversion before the recession actually starts.


4. Although some claim the US Federal Reserve would never allow a curve inversion to happen, this is likely untrue

There are some who argue the Fed would not allow the yield curve to invert.  They argue that the Fed has the tools to prevent an inversion, and therefore, prevent a recession.

Publicly, the Fed denies it would ever allow a yield curve inversion (on its own) to affect monetary policy.

Nevertheless, there is little doubt they are watching the yield curve closely.  In fact, Fed officials themselves have repeatedly acknowledged the forecasting track record of the yield curve.  And although an inversion (in and of itself) would not likely alter Fed policy materially, it is possible it is one factor of many taken into consideration when adjusting policy (especially the pace of a tightening cycle).

At the end of the day the Fed may have little choice.  The Fed’s Congress-imposed mandate requires them to adjust policy so as to maximize employment in the context of a low and stable inflationary environment.  No part of that mandate allows them to wrecklessly foster economic growth at any cost using artificial means.  Giving pause to a rate-tightening cycle solely for the purpose of avoiding an inversion risks allowing inflation to remain unchecked, and would run counter to the Fed’s Congress-imposed mandate.


Market Forecast

Where are rates forecast to be headed?  Here is the “market forecast” of the 1-year US Treasury:

market forecast

Figure 6: Market Forecast

[Looking at the lower plot, the market forecast of the 1-year US Treasury is indicated in green, while the purple line is the current value of the 1-year US Treasury.]

As you will note, near the beginning of 2018 1-year rates were about 2%, with a 1-year market forecast of about 2.5%.

In late 2018, we can see 1-year rates did in fact rise to about 2.5% – as forecast – and the now-current market forecast rate sits at about 3%.

In other words, as of today, the market is forecasting short rates to rise by about 50 basis points within the next year.

What are the ramifications of short rates rising?  There are several possibilities.


1. The first possibility is that the rise in short rates is accompanied by a gradual rise in long rates.  As such, the curve remains nearly flat, and no inversion occurs.

For this to occur, and given where we are today with a spread of about 25 basis points, long rates would have to rise by at least 25 basis points (assuming a rise in short rates of 50 basis points) for no inversion to occur.

Many private economists concur, and peg a rise in long rates of about this amount (25 basis points or so) over the 2019 / 2020 forecast horizon.

It is felt this is the most likely scenario, and is the base case of this paper.


2. The second  possibility is that the rise in short rates is not accompanied by a rise in long rates. 

Since the 2- / 10- year spread today is only about 25 basis points, and since we are seeing a forecast rise in short rates of 50 basis points … then this scenario means we are in essence actually witnessing the forecast of a yield inversion.

This is entirely plausible.  Though not the base case,  given where we are in the Fed’s tightening cycle with several 25 basis point increases expected to come, one could easily argue that short rates will out-pace long rates, forcing an inversion.


3. The third possibility is that the forecast is wrong, and short rates do not rise as expected.  They either do not rise at all, and perhaps even fall.

Although obviously possible, an outright falling of short rates seems unlikely.  Unemployment in the US has now reached multi-decade lows, and signs of inflation appear to be budding, as evidenced through recent core CPI and wage growth figures.  Although short rates may linger at current levels for some time, an outright falling of short rates would seem to be a long shot.


Going Forward

Where does this leave us?  Will the curve invert?  Is the market forecast of a 50 basis point rise in short rates in fact a forecast of a curve inversion?

It is simply too soon to know for sure.  Recent figures coming out of the US have been stellar…but nonetheless yields are telling us we may soon see signs of hairline cracks in the US economy.  Simply put, it is too soon to say with any confidence whether this comes to pass.

The next year will be critical.  Most importantly, we should watch the 2- / 10-year spread and see how it evolves.  We should watch the market forecast of short rates.  We should watch the US employment figures and the CPI.  We should pay attention to the Fed’s policy statements and its “dot plot”.

I am cautiously optimistic that the Fed will continue its gradual, measured pace of rising short term rates, and that longer rates will follow suit – avoiding an inversion.

But even if an inversion is averted, this is not all good news.  It seems improbable that recent strong economic growth continues indefinitely.  The fiscal winds of the Trump administration are now largely behind us, short rates have nowhere to go but up (if gradually), and we are perhaps beginning to see the seeds of inflationary pressures building. Even if an outright inversion is averted, it seems probable that anemic economic as well as asset price growth lies ahead for the next several quarters.

Notwithstanding, the risk of an outright inversion is very real and not to be dismissed lightly.

Adjusting portfolio exposure accordingly would seem prudent at this juncture.



The above discussion of financial conditions represent  the opinion of the author and should strictly be used for educational purposes only.  It is not an endorsement to buy or sell any security whatsoever, and does not constitute investment advice.  Individual security prices fluctuate and may result in financial loss.

While data contained therein is believed to be accurate, no express or implied warranty is provided with respect to data accuracy.

Always consult your professional investment advisor prior to making any investment decision.

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