A Market Valuation Gauge That Works

Originally Published March 15, 2016 in Advisor Perspectives

In my previous article, I examined many popular metrics that all show that U.S. equities have been overvalued for over 20 years. The conventional explanation is that the overvaluation and its unusually long duration is a statistical outlier. But those aberrations were observed in only 15% of the data population (20 out of 134 years) and are unlikely to be statistical outliers. The root cause is not yet known. Until the anomaly is better understood, naively equating the lack of mean reversion with overvaluations will lead to misguided valuations and ill-advised investment strategies.

A decade ago, I began searching for a valuation indicator that is immune to possible mean-reversion malfunction. The challenge proved to be much more difficult than anticipated. I ultimately had to abandon my search and developed my own valuations gauge, the total return oscillator (TR-Osc) and present it here.

Oscillatory gauge

Mean reversion is the underpinning of all valuations metrics. The basic concept of valuations relies on the notion that value oscillates between an upper bound (overvalued) and an lower bound (undervalued) around a median (fair-valued). How do you calibrate a gauge that has an unbounded output or with a drifing median that confuses mean reversion? A functioning valuations gauge should resemble a pseudo sine-wave oscillator with quasi-periodicity.

Although the cyclically adjusted price-to-earnings ratio (CAPE) oscillated around a stable geometric mean of 14 from 1880 to 1994, its mean has risen to 26.2 since 1995 (Figure 1A) – a telltale sign of mean reversion malfunction. By contrast, my TR-Osc has been bounded by well-defined upper and lower demarcations for over a century. The mean of TR-Osc measured from 1875 to 1994 is almost identical to the value computed over the last 20 years (Figure 1B). After reaching either extreme, TR-Osc always reverts toward its long-term historical mean.

From 1880 to 1950, TR-Osc and CAPE were almost in sync. After 1955, the two indicators began to diverge. Although both the CAPE and TR-Osc detected the dot-com bubble in 2000 (red squares), only the TR-Osc warned us about the 1987 Black Monday crash (red circle). After the 2000 peak, CAPE stayed elevated and came down only once in mid-2009 to touch its historical mean at 14. The TR-Osc, however, dropped to its lower bound in January 2003 (green arrow) getting ready for the six-year bull market from 2003 to 2008. The TR-Osc did it again after the housing bubble when it dipped below the lower bound of 0% in February 2009, just in time to reenter the market at the start of a seven-year bull market from 2009 to present.

In 2008, the TR-Osc reached a minor summit (red triangle) while CAPE exhibited no peak at all. Both TR-Osc and CAPE indicate that the meltdown in global financial markets did not stem from an overvalued equity market. I will expand on this later when I discuss the real estate sector.


Common deficiencies in all contrarian indicators

There are two common deficiencies shared by all contrarian indicators including all traditional valuations models. First, their signals are often premature because the market can stay overvalued or undervalued for years. Greenspan's 1996 irrational exuberance speech alluded to an overvalued market but it was four years too early. From 1996 to the dot-com peak in 2000, the S&P500 surged 87% and the NASDAQ 288%.

The second deficiency of all contrarian indicators is that the market can reverse direction without hitting either extreme at all. The CAPE, for example, was not undervalued in 2002 or 2009. Value investors would have missed out on huge gains of 90% and 180% from the two spectacular bull markets in the 2000s.

The dual gauges of the TR-Osc: scalar and vector

Before I explain how the TR-Osc overcomes these two deficiencies, let me first describe the TR-Osc. The TR-Osc captures what investors in the aggregate earn by investing in the S&P 500. That is the sum of two components – the first from price changes and the second from dividend yields. Price return is the trailing five-year compound annual growth rate (CAGR). Dividend yield is the annual return from the dividends investors received. The look-back period doesn't necessarily have to be five years. All rolling periods from 2 to 20 years can do the job. In addition, both real (inflation-adjusted) and nominal TR-Osc's work equally well because inflation usually does not change much over a five-year period.

The TR-Osc overcomes the two deficiencies by having two orthogonal triggers, a scalar marker and a vector sensor. The oscillatory and mean-reverting attributes of the TR-Osc allow overvaluation and undervaluation markers to be clearly defined (Figure 2). When the TR-Osc was near the upper bound (the 20% overvalued marker), the S&P 500 often peaked. When the TR-Osc was near the lower bound (the 0% undervalued marker), the market soon bottomed. But in 2008, the TR-Osc only reached 12% and the market was not overvalued. Investors had no warning from the valuation marker to avert the impending subprime meltdown. Valuation markers (scalar) alone are not enough. The TR-Osc needs a second trigger, a motion sensor (vector) that tracks the up or down direction of valuations.


Let me illustrate how the scalar and vector triggers work in concert and how buy/sell signals are executed. When the TR-Osc is rising (an up-vector) or drops below the lower bound at 0% (an undervalued marker), a bullish market stance is issued. When the TR-Osc is falling (a down vector) but stays above 0% (not undervalued), or when it exceeds the upper bound at 20% (an overvalued marker), a bearish alarm is sounded. The asymmetry in the buy/sell rules stems from prospect theory, which contends that losses have more emotional impact to people than an equivalent amount of gains.

When a bullish signal is issued, buy the S&P 500 (e.g. SPY). When a bearish alarm is sounded, sell the S&P 500. After exiting the stock market, park the proceeds in 10-year Treasury bonds. The return while holding the S&P 500 is the total return with dividends reinvested. The return while holding U.S. Treasury bonds is the geometric sum of both bond yields and bond price percentage changes caused by interest rate changes.

The performance data presented in this article assume that all buy and sell signals issued at the end of the month were executed at the close in the following month. When the TR-Osc signals were executed closer to the issuance dates, both return and risk performances were slightly better.

TR-Osc performance stats

Figure 3 shows two hypothetical cumulative returns from 1880 to 2015 – the TR-Osc with the buy/sell rules stated above and the S&P 500 total return. Over 135 years, the TR-Osc has a 190 basis point CAGR edge over the buy-and-hold benchmark with less than half of the drawdown risk.

The TR-Osc traded infrequently – less than one round trip a year on average. The TR-Osc is an insurance policy that protects investors against catastrophic market losses while preserving their long-term capital gain tax benefits.


Let's take a closer look at the TR-Osc signals in two more recent time windows. Since 1950, there have been 10 recessions. Figure 4A shows that the TR-Osc kept investors out of the market in all 10 of them. Figure 4B shows that the latest TR-Osc bearish call was issued in September 2015. The TR-Osc sidestepped the recent stock market turmoil and has kept investors' money safe in Treasury bonds.


Table 1 shows performance stats for various sets of bull and bear market cycles. TR-Osc beats the S&P500 total return in CAGR, maximum drawdown, and volatility. The consistency in outperforming the S&P500 in returns and in risk over different sets of full bull/bear cycles demonstrates the robustness of TR-Osc.


TR-Osc has universal applicability

Like the CAPE, the TR-Osc’s efficacy is not limited to the S&P 500. It can also measure valuations in overseas markets (developed and emerging), hard assets and currencies. For example, Figure 5 shows three alternative spaces – raw materials (Figure 5A), oil and gas (Figure 5B) and real estate (Figure 5C) (data source: Professor Kenneth French). This universal applicability of the TR-Osc also enables intermarket synergies. Recall in Figure 2 that the stock market was not overvalued in 2008 according to both the CAPE and the S&P 500 TR-Osc. Note that the real estate TR-Osc correctly detected the housing bubble (red square in Figure 5C). When the systemic risk spread to the stock market, the S&P 500 TR-Osc vector sensed the danger and turned bearish.


Figures 6A to 6C shows that the TR-Osc improves both the return and drawdown in two distinctively different spaces – precious metals (data source: Professor Kenneth French), the Canadian dollar and the Australian dollar (data source: FRED). Prices in precious metals fluctuate widely at rapid speeds while foreign currencies crawl in narrow ranges at a snaillike pace. It's remarkable that the TR-Osc works equally well across drastically different investment classes. How does the TR-Osc help a diverse group of characters with different personalities perform better?


The analytics of TR-Osc

You may say that TR-Osc is just a five-year rolling total return. But what breathes new life into an otherwise ordinary formula is the analytics behind the TR-Osc. The adaptability of buy and sell rules is the reason behind the TR-Osc's universal applicability. As indicated previously, the TR-Osc has two triggers: valuation markers (scalar) and valuation directional sensor (vector). How did I pick the values for these triggers? The vector is obvious – up is bullish and down is bearish – but how do I select the valuation markers?

In Figures 2, 5 and 6, the middle blue line is the mean. The upper blue lines are the overvaluation markers and the lower blue lines, undervaluation markers. The upper blue lines are M standard deviations above the mean and the lower blue lines, N standard deviations below the mean. Each time series has a unique personality. For example, the means of most currencies are near 0% while the mean of the S&P 500 is near 9%. More volatile investments like precious metals, oil and gas would have larger standard deviations than the serene currency space. The values of M and N are selected to match the personality of each underlying investment. The general range for both M and N is between 1 and 2.

A common flaw in the design of engineering or investments systems is over-fitting. I have developedfive criteria to minimize this bad practice. The five criteria are simplicity, sound rationale, rule-based clarity, sufficient sample size, and economic cycle stability. The TR-Osc not only meets all of these criteria but offers one additional merit – universal applicability. It works not only on the S&P 500, but on overseas markets and across a diverse set of alternative investments.

Theoretical support for TR-Osc

Traditional valuation metrics rely on fundamentals, which often experience paradigm shifts across secular cycles. Fundamental factors can be influenced by generational changes – technological advances, demographic waves, socioeconomic evolutions, structural shifts, political reforms or wars. Therefore the means in many of the traditional valuation metrics can drift when the prevailing fundamentals change.

The TR-Osc downplays the importance of the external fundamental factors and focuses primarily on the internal instinct of the investors. Investors' value perception has two behavioral anchors. The first anchor drives investors toward the greed/fear emotional extremes. For example, when the S&P 500 delivers a five-year compound annual return in excess of the 20%, euphoria tends to reach a steady state and investors become increasingly risk adverse. When their returns get stuck at 0% five years in a row, investors are in total despair and the market soon capitulates. Both greed and fear extremes can be quantified by the TR-Osc's over- and undervaluation markers.

The second behavioral anchor is the tendency of herding with the crowd. When neither greed nor fear is at extreme levels, investors have a behavioral bias toward crowd-herding. Once a trend is established in either up or down direction, more investors will jump onboard the momentum train and price momentum will solidify into sustainable trends. The collective movement of the masses is tracked by the TR-Osc's vector sensor.

Concluding remarks

Unlike fundamental factors which can be altered by paradigm shifts over long arcs of time, human behaviors which are hardwired into our brains have not changed for thousands of years. The efficient market hypothesis assumes that markets are made up of a large number of rational investors efficiently digesting all relevant information to maximize their wealth. Behavioral finance theory suggests that investors are often driven by the inherent cognitive psychology of people whose decisions are often irrational and their actions exhibit behavioral biases. Perhaps the aberration (the malfunctioned mean reversion) observed in many of the traditional valuations ratios suggests that investors are not 100% homo economicus beings after all. More often than not, investors behave irrationally when they are besieged by emotions.

The TR-Osc captures the essence of both traditional finance and behavioral economics by reading investors' value perception from both the rational and the emotional wirings of their brains. It elucidates many valuable but abstract concepts from both schools into quantitative, objective and actionable investment strategies. As long as humans continue to use their dual-process brains (see also Dr. Daniel Kahneman) in decision making, TR-Osc will likely endure as a calibrated valuation gauge until humans evolve into the next stage.

The TR-Osc asserts that the current stock market is not overvalued. Instead, since mid-2015, its vector has been reverting towards its stable historical mean.

Theodore Wong graduated from MIT with a BSEE and MSEE degree. He served as general manager in several Fortune-500 companies that produced infrared sensors for satellite and military applications. After selling the hi-tech company that he started with a private equity firm, he launched TTSW Advisory, a consulting firm offering clients investment research services. For over three decades, Ted has developed a true passion in the financial markets. He applies engineering statistical tools to achieve absolute investment returns by actively managing risk in both up and down markets. He can be reached at

Figure 1 The Shiller CAPE

Is the Market Overvalued or are the Measuring Gauges Broken?

Originally Published March 8, 2016 in Advisor Perspectives

It is remarkable that market-top calls have enticed many advisors and analysts to fully embrace the cyclically adjusted price-to-earnings ratio (CAPE) as their crystal ball to foretell the future of the stock market. Such faith, as I will demonstrate, is misguided.

For nearly three decades, the CAPE that professors John Campbell and Robert Shiller created in 1988and updated in 2015 has been adopted as the scale for measuring market valuations.

This is not surprising. As Figure 1 shows, CAPE has had great foresight for predicting major stock market calamities over the last century. It spiked above 27 only three times, in 1928, 1999 and 2007 (red circles), and all three spikes were followed by historic disasters. The CAPE also reached three minor summits in 1900, 1937 and 1966 (blue circles), which all led to prolonged bear markets. When CAPE hit 27 in 2015 (orange box), even perma-bulls lost confidence in prospective performance.


Figure 1 The Shiller CAPE

A hazy crystal ball at best

Despite the mirage of reliability on its surface, advisors need to exercise extreme caution as many CAPE-based research analyses have become unhinged from basic statistical principles. The apparent linkage between valuations levels and the posterior stock returns spurred much research on market forecasts. In performing a 10-year regression on CAPE, one starts with 144 years of Shiller's data. Ten years are used to smooth earnings and ten for forward-return calculations. This leaves 124 years of monthly data, which should be enough to do regression analyses, right?

But consider the fact that regressions are graded by R-squared. R-squared denotes how well the independent variables (e.g., CAPE) explain the dependent ones (e.g., 10-year forward returns). To show just how dubious many of these yardsticks are, Figure 2 is Vanguard's ranking of 15 valuations metrics by their predictive power R-squared. CAPE had the best R-squared, but half of the metrics ranked below simple rainfall as a predictor for stock market returns.

Figure 2 R-squared Ranking of 15 Valuation Metrics

Figure 3 shows that my study of CAPE has an R-squared of 33.7% – lower than Vanguard's 43%. It's probably due to difference in timeframes used (1880-2015 in my study, versus 1926-2011 in Vanguard's).

Let's illustrate what a 33.7% R-squared entails. Using a regression analysis, the CAPE, currently at 24.6, equates to a 5.4% total return over the next 10 years. But the same 5.4% return can also be attained using an undervalued CAPE of 7.0, as well as an overvalued CAPE of 36. These meaningless regression results are the consequences of the relatively low R-squared.

Figure 3 Market Forecast with Overlapped Data

Researchers commonly use this regression methodology, but it's statistically flawed. In a 10-year rolling regression, each sample period overlaps 90% of its data with the next sample point. Only 12 samples (124 years divided by 10 years) are truly independent. Figure 4 shows that if only 12 samples are used, R2 would be reduced to 21.3%, too low to be useful. Also 12 samples are too few to be statistically significant. Hence, both forecasting methodologies are problematic – with and without using overlapped intervals.

Figure 4 Market Forecast with Non-Overlapped Data

A widespread anomaly

Low predictive power and overlapping intervals are not the only issues of which analysts need to be aware. Another major challenge is calibrating the gauge used to actually measure valuations. Generally, calibration relies on a universal assumption of mean reversion, which has been the norm for over a century. Since the mid-1990s, however, readings from many valuations metrics have failed to revert toward the century-old mean. Looking deeper, one might ask whether the current market is overvalued, or the measuring gauges are off calibration due to a 20-year hiatus in the assumed mean reversion.

Consider Figure 5A, which shows a range-bound CAPE from 1880 to 1994 with a stable geometric mean of 14. Beginning in 1995, its mean climbed to 26.2 and has remained elevated since. At 26.2, the new mean exceeded all CAPE readings from 1880 to 1994 except one in 1929. Mean CAPE values have been completely out of character in the last two decades from what they were in the entire preceding century.

Figure 5A The Shiller CAPE

Mean instability is not limited to CAPE. Figure 5B shows the standard P/E ratio based on one year of earnings. Its mean almost doubled after 1995. Since earnings appear in the denominators in both the CAPE and P/E ratios, it's logical to speculate that the overshoots must be caused by under-reported earnings.

The case of the runaway CAPE has generated much interest. Professor Jeremy Siegel was the first to point out the negative earnings impact by the FAS 142 accounting rules issued in 2001. He used various profit proxies to capture real earnings, yet his adjustments did not remove the post-1995 elevation; rather, it only lowered the curves evenly over time (pg.13).

If earnings distortions inflated CAPE in the past two decades, then perhaps valuations metrics that are not based on earnings would have a stable mean. Let's look at two well-known valuations ratios – price-to-dividends (data source: Shiller) and price-to-book (data source: Goyal). Prices are set by the market. Book value comes from the balance sheets, not the income statements. Dividends come out of cash flow, not from earnings. Therefore, one would expect both ratios to be impervious to any earnings distortion and to have a stable mean.

To the contrary, Figures 6A and 6B show that these two ratios surged even more than the CAPE or P/E. Since 1995, the means of both ratios have jumped 2.5 times, so one can conclude that accounting and regulatory changes alone cannot explain the anomaly.

Figure 6A Price-Dividend Ratio Figure 6B Price-Book Value Ratio

Irregularities also appeared in two other popular valuation metrics. Tobin's Q is the ratio of the combined market value of all public companies to the total asset replacement value in those firms.Buffett defined his eponymous indicator as market cap-to-GNP. Since 1995, the Tobin's Q dipped below its 134-year mean only once. The Buffett indicator fell below its 63-year mean only twice.

The six metrics presented above are not the only ones that show elevated levels. Many less popular valuations ratios also exhibit similar aberrations in the past twenty years (see Chart 2 in this reference ). Is the stock market truly overvalued, or are the measuring gauges malfunctioned in their mean-reversion process?

A misguided faith in mean reversion?

The market can be considered overvalued if the 20-year lofty readings from many valuations ratios are all statistical outliers and will eventually revert back to their historical means. However, it's naive to think the last two decades were outliers. If the outliers are the results of randomness, they will regress to the mean. On the other hand, if they are caused by unidentified but nonrandom factors, then there may be no mean reversion. Indeed, Shiller proposed in 2014 that the elevated CAPE might be driven by behavioral factors. Such factors might be irrational, but they are certainly not random.

The misguided expectation faith in mean reversion has far-reaching impacts in the field of investments beyond market valuations. That will be the subject of a future article.

In my next article, I will present an original gauge I developed many years ago. It measures valuations not by the traditional ratios, but by the market dynamics forged by the aggregate investor behaviors. This gauge has been range-bound for over a century and continues to revert to an inherently stable mean today. Stay tuned!

Theodore Wong graduated from MIT with a BSEE and MSEE degree. He served as general manager in several Fortune-500 companies that produced infrared sensors for satellite and military applications. After selling the hi-tech company that he started with a private equity firm, he launched TTSW Advisory, a consulting firm offering clients investment research services. For over three decades, Ted has developed a true passion in the financial markets. He applies engineering statistical tools to achieve absolute investment returns by actively managing risk in both up and down markets. He can be reached at