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A Better Valuation Model for the Financial Markets

by Doug Oriard, 7/30/2008, updated 11/15/2010


In the July 26, 2008 “Thoughts from the Frontline” weekly newsletter from John Mauldin, John stated that in spite of bubbles and recessions, markets tend to revert to the mean. A quote from that letter:

“A theme in this letter for many years has been that over time markets of all descriptions revert to the mean. The classic definition of mean reversion is "the behavior of a variable in which the values for that variable move towards the long-run average value for that variable." Prices, indexes, and all types of economic variables tend to fluctuate around their long-term averages. “

The topic of this essay is to offer a quantitative model of what exactly the mean is that the markets will revert to. Note that it is not a predictor of future market performance (especially short term performance), but only a means to evaluate market valuation and indicate a target that the market will revert to.

Past Attempts to Value the Markets

In order to determine relative safety in the financial markets, many individuals and institutions attempt to evaluate whether the current equity market is over-valued, under-valued, or fairly-valued. Two of the most common ways to do this are through P/E ratios, especially for the SP500, and moving averages, often a 200-day average of the Dow Industrials or SP500. Both of these methods are subjects to short-term (even up to several years) economic and sentiment fluctuations and do not represents a true mean of the market.

Index P/E ratios essentially are a lagging indicator over the intermediate term (6-12 months).  P/E ratios fluctuate due to economic conditions which can change rapidly over a period of up to 2-3 years. Very high P/E ratios can be due to favorable economic conditions which in turn result in high market exuberance, or due to a recession where earnings drop dramatically.   Low P/E ratios can also be caused by poor economic conditions that may last 1-3 years. In both cases the markets tend to over-react and the true measure of companies' value is not accurately reflected in the P/E ratio.  The SP500 may drop 20-40% in a strong bear market, especially in a recession, and P/E ratios fluctuate greatly as well.   P/E ratios fluctuate due to both economic conditions affecting corporate profitability, and market sentiment (which results in mass buying or selling). The P/E ratio of the SP500 tends to revert to a mean of approximately 15 based on long-term averages, but it can deviate for many years before returning to the mean.   Can we say the market was really over-valued during that a recession or bear market, or was it just due to a dip in corporate profitability due to poor economic conditions? Even though the price of the SP500 index may have dropped 20-40% during the bear market, the P/E ratio made the market look over-valued. The real point to notice, as will be explained more below, is that the P/E ratio is subject to fluctuating economic conditions while the true trendline is not.   P/E ratios can not be used as a reliable valuation indicator except over the very long term, or by averaging the P/E ratios over several years to smooth shorter term fluctuations.  Averaging P/E ratios gives a better result but still does not give a measured "baseline" in the way the method presented below does.

Moving averages are one of the other methods for determining market valuation, especially long-term averages like the 200-day moving average or weekly and monthly charts. Moving averages are always looking in hindsight and are more of a trend indicator than a valuation indicator – there is no mean for the price graph to return to. They also don't indicate any baseline for the market indices to track. Below I will present a method of calculating the mean that is independent of any economic conditions or market sentiment.


The New Model of Market Valuation

Free markets can go for years being over-valued or under-valued, but will always return to the baseline presented in the model below. Therefore, this valuation model can be used to determine if the current valuation represents a good long-term buying opportunity. Markets can deviate for years from the mean of this model, but tend to revert more quickly and more accurately than a mean represented by P/E ratios. The reason for the markets always reverting to the mean is that human productivity and creativity does not stop during recessions, wars, or anything else. Corporate profits can fluctuate, but people are still developing new ideas that will later turn into products and services. The mean of the markets is ultimately based on human potential, not economic conditions, and that potential results in a steady long term performance of the equity markets. This mean can be plotted empirically and extrapolated

Part of the idea for this model was taken from the behavior of the tech industry models for computer processor performance doubling every 2 years, and other similar trends in technology. The financial markets have a similar type of evolution due to long-term corporate profitability, and partly due to gradual increases in profitability from human innovation and the increasing productivity as technology provides more and faster tools for business use.

A compounded return rate of 7% (or any fixed percentage) on a business or industry results in an exponential curve when plotted on a price chart, and as a straight line when plotted on a log-scale price chart. When applied properly, this result can be used as a valuation model for the financial markets. Markets deviate from their normal curve, sometimes even for several years, but they always return to the curve (mean), as long as the markets are operating in a free economy with sufficient natural resources and a good labor pool. When the plot is done on capitalization-weighted indices like the SP500, the result is helpful, but the best results come from applying the curve to price-weighted indices such as the Value Line Arithmetic index. Capitalization-weighted indices can deviate from the trendline for longer periods due to their heavier weighting on a small number of companies.  The P/E ratios also have larger swings on capitalization-weighted indices like the SP500 as compared to a price-weighted index like the Value Line Arithmetic index.  Chart 1 below shows a log-scale plot of the SP500 since 1950 (red) and a trendline (black) which represents the mean of the SP500 over time.  The blue lines indicate one standard deviation from the trendline.  Some experts say that the P/E ratio of 34.5 for the SP500 as of this writing (2/25/2009) indicates the SP500 is over-valued.  However, the plot below shows that the trendline valuation is about 1400, which indicates an under-valued market.  (Note: the 1400 number was taken from a linear scale plot where it was easier to read, or can be calculated from the trendline equation).  This is in line with the P/E ratio of 17.7 when the SP500 was near 1500 in June 30, 2007, before the recession started.  A P/E ratio of 17.7 is close to the historically accepted mean value of 15.

CHART 1 -- SP500 from 1950-2009 with trendline

SP500

 

Chart 2 below shows this mean (exponential curve fit) applied to the Value Line Arithmetic Index over the life of the index (the index was created in 1984). The Value Line Arithmetic index typically has narrower swings in the P/E ratio and the standard deviation around the trendline is lower.  The red line on the chart is the price plot of the Value Line Arithmetic Index since 1984. The black curved line is an exponential curve fit of the price graph. The blue lines show one standard deviation above and below the exponential curve fit. The extended curve fit is an extrapolation of where the mean of the curve will be in five years. To know how far the current market price is from the mean, just subtract the mean value from the current price. A positive number is an indication of over-valuation, and a negative number is an indication of a current low valuation. It is also helpful to use the number of standard deviations from the mean to give a better idea of how far over or under valued the market is. If the current price is below the exponential curve, then based on valuation only, the long-term risk in the market is less. Many investors will use short term technical indicators to improve short term performance. This method of calculating the mean will work in any free market (no dictatorship) with sufficient available raw materials and a good available labor pool.  

As shown in Chart 2, the current value of the Value Line Arithmetic Index is over four standard deviations below the mean, and less than 50% of the current mean value.   This indicates a tremendous opportunity in terms of valuation. When the stock market does turn around, the Value Line Arithmetic index may double within 2-3 years, as it did 2003-2004, which is a reversion to the mean.  Conversely, by looking at the P/E ratio of the SP500 for 12/31/2008 as-reported estimated earnings, as of 2/19/2009, the ratio was 34.53.  The stock market may quickly revert to the mean, but 25 years may not be enough to adequately predict the mean -- it may be necessary to curve-fit over a complete PE ratio low-high-low 34-year (approximately) cycle.  Price data on the VL index is only available since 1984.  Stock market performance varies greatly depending on whether the cycle is a secular bull cycle (starting from low P/E ratios) or a secular bear cycle (starting from high P/E ratios).  In Chart 3 near the bottom of the page, the SP500 is plotted on a log scale and shows the mean line and deviations.  On the SP500 chart today (November 15, 2010) we are about 22% below the mean, indicating modestly good valuations, not high valuations.  P/E ratios will revert to a mean of about 15, but when calculating over or under valuation, using the trendline method above makes it much easier to see an actual trendline price that the market will return to.  However, the price can deviate from the mean for many years, so timing is important -- it helps to use technical analysis to time buy-ins.  Getting a better idea of true market valuation in this way is very helpful though.  Using the curve-fit method on a 59-year graph, the "mean" for the SP500 is actually about 1530 today.  If this method of caluclating market valuation becomes understood and accepted by the masses, in could result in a reduction of long-term market volatility.  When price index fell much below the mean trendline investors would more easily recognize a buying opportunity.  If a index rose significantly above the trendline, recognition of the over-valued condition would slow down buing and smooth out market performance.

During poor economic times the SP500 P/E ratio may be well above 20 due to poor corporate profitability.   This is a bit of an apples-to-oranges comparison since the P/E ratio of the SP500 is far higher than the P/E ratio of the Value Line Arithmetic index but a look at the plot below shows the VL price graph to be about 4.2 standard deviations below the curve-fitted mean graph. The P/E ratio for the VL index as of February 20, 2009 is only 11.8 compared to 34.5 for the SP500.  That is a drop on the VL index from 15.2 on September 26, 2008 (25.38 for the SP500 on September 30, 2008). That may be another reason this method works so well on the Value Line Arithmetic index -- the P/E ratio on the VL index usually doesn't reach the extreme high levels of the SP500 and Dow.  It is interesting that the P/E ratio for the SP500 has risen over the past 6 months, but dropped for the VL index.  This would be a good time to buy on a valuation basis only, based on the premise of this essay, especially if you're buying small and mid-cap stocks.  

Some Economists argue that the stock market cannot appreciate faster than Gross Domestic Product growth, but I believe they are part of the same phenomenon. Gross Domestic Product also has a long-term steady rate of growth as long as there is a sufficient supply of raw materials and labor pool. Human creativity does the rest (in a free market society). GDP and the stock market will both have growth curves like the ones shown here. The real problem comes when government debt approaches the level of GDP or higher. Then there is a risk of longer-term ecomonic slowdown which could result in a slower growth curve of GDP and stocks.

In general, when the P/E ratio on the SP500 is very high as it is preceding a secular bear market, the returns over then next decade are likely to be much lower.  This method does not argue with that fact; however, P/E ratios are a lagging indicator over the intermediate term and during poor economic conditions P/E ratios give a misleading indication with respect to valuation.   The trendline method adds more exact information about where the true mean price is.  Having visibility to the trendline makes it easier to quantify where the market is at in the bull/bear cycle and how far deviated it is from the trendline. 

At the end of the 2002-2003 bear market (which ended in March 2003) the Value Line Arithmetic Index reached a low of about 3.5 standard deviations below the mean. If you used the P/E ratio of the SP500 in March, 2003 (which was about 28 for reported earnings), it would indicate a poor time to invest, based on P/E valuations. However, the mean used in this essay indicated a good time to invest, and the major US market indices proceeded to double in value over the next four years. P/E ratios are subject to intermediate term economic conditions and is not the best valuation indicator for making buy and sell decisions, especially during poor economic conditions. If P/E ratios are used, a better method would be to use the P/E ratio of a broad-based price-weighted index like the Value Line Arithmetic Index, and/or use some averaging applied to the ratio. 

Chart 2 -- Value Line Arithmetic Index since 1984



 

In Chart 2, above, the 25-year period price plot follows very closely to the exponential curve fit (mean), except for a few brief periods. One standard deviation was only 8.3% deviation from the mean until the end of 2008, when it jumped to 13%. The mean trendline of the SP500 in Chart 1 is useful too, but due to the capitalization-weighting, it strays farther and longer from the trendline.  Note that this is not an extrapolation of an index from any particular high or low point, like the "DOW 30,000" estimates we heard about in 1999.  An extrapolation from a high or low point would be mis-leading.  This is a curve-fit to a broad index over as many years as we have data for.  

Chart 3 below shows the same method applied to the Dow Industrials since 1950. With only 30 companies in the index, the price plot deviates from the mean much more (on a long-term basis). Even larger indices like the SP500 that are capitalization-weighted have a higher standard deviation due to the heavier weighting of a few very large companies. Notice that one standard deviation on the Dow chart is 27.4% vs 13.8% on the Value Line Arithmetic Index (the time frames are also different, so it's an approximated comparison).

A point to note is that the markets may be advancing not only at a fixed, compounded interest rate, but also that rate could be increasing over time (double exponential curve). This can be seen in the effective interest rate of the SP500 over a 50-year and 25-year time frame – since 1950 the SP500 has returned an average of 7.1%, but since 1980 the average return has been 9.9%. One could argue that this is due to long-term economic cycles, and some of it may come from that; but the fact that business productivity is driven by technology advances (computers and other machines do more work and make businesses more productive, and this trend is accelerating over time) and financial innovation supports the premise that the rate of return may be increasing over time. This may only be noticeable when looking over time segments of 30-50 years or greater. 



CHART 3 -- Dow Industials since 1934


 

Limitations


The primary known limitations of this method of equity market valuation comes from two sources:

  1. Choosing the minimum length of time on which to do the curve fit. 25 years of data on the Value Line Arithmetic Index may not be enough.  Only 25 years of data exists for the VL Arithmetic index, but if you look at the SP500 since 1950 some interesting facts appear.  In Chart 1 above, the SP500 index is plotted on a log scale.  On this chart the mean seems to revert to a 7.1% return, compared to a 9.0% average return on a curve-fit plot from 1984.  It may be necessary to have at least a full 34-year cycle of PE ratios going from low-high-low to get an accurate curve-fit.  This is the case on the SP500 chart, but I believe the results are best on a broad, price-weighted index like the Value Line Arithmetic index.
  2. The effective rate of growth of the curve may be gradually increasing over time (double exponential curve), but this will probably only be noticeable in curve-fitting increments of perhaps 35 years or more. 
  3. High levels of government debt approaching the level of GDP or higher could slow the growth curve for a decade or more.
  4. This method of valuating the market is not an economic model, but more of a technical indicator.

Part of these limitations are compensated for by the fact the curve is a “curve fit”, which means it will be self-correcting.  There may also be an optimum number of years over which the curve fit is chosen – too short and the short term conditions have to much effect and do not include a full secular bull/bear cycle; too long and the double exponential curve may cause unwanted error.