A Dash of Insight

Market Multiple Compression: Revisiting a 2004 Prediction

During 2004 a leading quantitative analyst predicted the the market multiple on the S&P 500 stocks would decline as interest rates increased, reflecting the Fed's tightening cycle.  Yesterday we invited readers to examine the scatter plot presented and form their own conclusions.  (Those who did not see the prior post may wish to look at it now.)

[click on this image and others to enlarge]

At the time of the research, the interest rate was about 4.2% and the P/E ratio about 17.  The researcher noted the downward slope of the regression line, showing the logical conclusion that PE multiples decline as rates rise.  On this basis, he reached a bearish forecast for U.S. equities.

Always Look at the Data

There are several things wrong with the analysis.  The errors should leap out for someone who understands both the methodology and the underlying data.  The problem stems from blindly applying the derived regression equation, probably the single most common error of researchers.

• The data, as plotted, do not really support the conclusion.  The current interest rate (at the time of the research, December, 2004) of 4.2% was not actually on the regression line.  It was below it.  Rates could rise to 4.8% and the implied multiple would still be 17.

• More importantly, the regression equation does not fit the data very well for rates below about 6.25 percent.  The overall fit of the model is excellent (R square of .79) but the plot shows heteroskedasticity.  This means that the variance changes for different ranges of the independent variable (suggested by the researcher to be interest rates).  Looking at the actual data shows that most of the observations in the 5% to 6% range are associated with multiples of about 20.

This is the VERY range where this researcher seeks to make a prediction!  It does not support the conclusion.

Quantitative methods should not substitute for thought and observation.  In this case, the actual observations do not fit the prediction because the model does not provide a good fit in the relevant range.  As I test, I showed the plot to a leading expert in research methods who had no special knowledge about this particular question.  His observation, drawn strictly from the data, was that one should expect the multiple to increase as rates moved from the 4% range to the 5% range.

• The chart notes that data for thirty months (January, 1999 to June, 2001) have been omitted.  It is often reasonable to exclude data that represent an extremely unusual event, especially one that is unlikely to be repeated.  It does raise the question about how the omitted data might have affected the result.

In our reconstruction of the research, we have been able to restore the missing period, showing the impact on both the plot and the regression model.

The plot shows that the "tech bubble era" data reflect even higher multiples when rates are in the 5% to 6% range.  The average P/E ratio is about 24.  If these data had been included in the regression modeling, something that the research team certainly tried, their conclusion of expected multiple compression would not have been supported either by looking at the data or by the regression equation.

The overall fit of the model actually is just as good as the example that omits the "bubble" data.  There is more of a curve in the equation (the result of the so-called quadratic term, the one that squares the interest rate), but the curve fits everything well, except for the cluster of data points in the 4% range.

The Anomalous Cluster

When first shown the original scatter plot I immediately circled the cluster of data in the 4% range.  This is where some knowledge of the data comes in.  As astute readers will have noted, this scatter plot is really just a different rendering of the Fed Model, which we have been studying.  The Fed Model looks at  the forward earnings yield, which is  E/P.  Most  market  gurus  (perhaps not liking fractions) talk about market multiples or P/E.

Anyone with knowledge of the data would have had the same immediate reaction as I did, highlighting the cluster of points that did not quite fit.  While there was nothing in the original research to prove it, I was quite confident in my assertion.  The next image shows the values from mid-2001 through the end of 2004 in pink and with triangle shapes.
The excellent graphics work by Renae, our office expert, actually replicates the line that I drew around the cluster on the original chart.  She has also added a curving line showing the PE multiple implied by the Fed model.

The plot thickens now!  We see that the research team, already committed by previous reports to a bearish stance on the market, left out one unusual cluster of data that did not support their viewpoint.   There may have been a good reason for this, but they included another cluster that seems just as aberrant.  We certainly do not believe that the researchers were attempting to mislead their clients.  It is the natural impulse when one is locked into a position.  It is also what happens where there is no peer review.

Suppose that one includes both of the unusual periods and derives a regression equation.  The result is depicted in the next image.

The regression equation fits the Fed Model line very closely!  Also, both the bubble era and the modern data, what we see as a period of misguided gloom, stand out as events that do not fit either model.

In fact, if the research team had done a careful job they would have highlighted an important observation -- that current data seemed unusual.  This would serve to focus the discussion on why this might be.

Epilogue

Since this story ended in 2004, we understand that readers may wish to know how it all turned out.  First, the research team abandoned the original conclusion and went on to discuss a brand new theory of how market multiples were determined.

Second, since the ten-year note has not increased as much as the Fed Funds rate, the assumption forming the basis for the original question was never met.  To satisfy reader curiosity, here is how the plot looked as last year ended.

The current anomaly, still represented in pink triangles in the plot, has persisted for two years.  This is the sustained period of under-valuation reflected in our prior look at the Fed Model.
Are there other explanations?  Of course!

(to be continued)

The Scatter Plot Challenge

About two years ago the research described here circulated widely.  Since it was not in the public domain, our review of the work went only to private clients seeking our opinion.  Proprietary research is not peer reviewed.  While many buy-side firms have staff capable of interpreting sell-side research, we wonder how many spotted the flaws in this analysis.

The work was done by a first-rate team from a major firm.  We do not have the underlying data, and we are not publishing their proprietary work.  Instead we have made a few minor changes.  We have substituted a different interest rate series, highly correlated with the one actually used.  Briefly put, this is our own analysis.  The chart depicted is a spitting image of the one that was circulated widely and repeatedly.  Take a careful look, and form your own conclusion about what you see.

The author, writing in late 2004, concluded that rising interest rates would lead to a reduced PE multiple for the market.  One can readily see that this conclusion is consistent with the derived regression equation.  Rates were about 4 percent, and (given Fed action) seemed to be moving higher, suggesting a lower multiple.

The scatter plot challenge to readers is to spot any problems with this research.  It is a difficult challenge.  We shall post our own answer tomorrow.

The Risk-Reward Challenge

There is no need to explain why analyzing risk and reward is the key to investing.  There are a number of potential risks in the market, but let us try to simplify a bit for this challenge.  We shall focus on the economy, recession chances, and the potential for a soft landing (or as we prefer, the Glide Path).

To do this properly, one needs to answer three questions:

1. What are the recession odds?
2. What would happen to stocks if a recession occurs?
3. What would happen to stocks if the glide path is achieved?

When you have a blended expectation, you can compare it to the interest rate of your choice.  The key element is to discover where one has the biggest exposure.

The answer might be different for individual investors (wanting to avoid big moves in either direction) and traders or fund managers (wanting to beat benchmarks).

At "A Dash" we suspect that most market participants focus on the probability of moves rather than the potential size of moves.

Have you done this analysis for your own portfolio?  What is your conclusion?

The Payroll Employment Challenge

How well can you predict this month's change in non-farm employment?

Your can test your forecasting skill at the Payroll Employment Game site.  We have added some new features this month. 

First, you can play the game using a hypothetical set of data for four important indicators -- last month's Leading Economic Indicators, Consumer Confidence, the ISM manufacturing report, and weekly jobless claims.

Next, you can try your hand using the actual data.  The four series actually provide reasonable predictions, as you can see from the chart area.

Finally, you can post your high score to show off your predicting skill.

The "Who's Driving?" Challenge

Who's driving this bus?

At "A Dash" we have noted that many market analysts are currently emphasizing the policy role of the Fed.  In particular, they suggest that there is a "myth" about a soft landing (we prefer the Glide Path), supporting this view with a handful of cases stretching back in time to cover ten or, twelve, or sixteen cases (if they decide to include the Great Depression).  The point is that the emphasis is on the Fed.

At the same time some of the same analysts endorse the Presidential Cycle.  Under this theory, the administration does something good for the economy in the time before an election, and the market responds.

Since the Fed does not follow any Presidential directive, most notoriously in the George H.W. Bush administration, there is a question of consistency here.

The challenge is twofold:

1. Find an analyst who has espoused both of these positions (there are many), and
2. See how they have reconciled the competing forces in past years.  Who was driving the bus in the 1974 era, for example?  This is one held up as a failure to achieve a soft landing.  Preliminary analysis might suggest that it had something to do with Vietnam, Watergate, wage and price controls, Whip Inflation Now buttons, and other factors, but some point at the Fed.

Happily for most of us, we can just look at the record of economic policy over the last twenty-five years.  It includes both parties in control of Congress and the Presidency.  It covers two market "bubbles" and crashes and a couple of modest recessions.  Owners of stocks made five-fold gains, as did the U.S. economy.

The challenge to those giving dire warnings to equity investors is to show why today is more like the 70's or 1987 than any time in recent history.