Buy the Dip: The Draw and Dangers of Contrarian Investing!

     When markets are in free fall, there is a great deal of  advice that is meted out to investors, and one is to just buy the dip, i.e., buy beaten down stocks, in the hope that they will recover, or the entire market, if it is down.  "Buying the dip" falls into a broad group of investment strategies that can be classified as "contrarian", where investors act in contrast to what the rest of the market is doing at the time, buying (selling) when the vast majority are selling (buying) , and it has been around through all of market history. There are strands of research in both behavioral finance and empirical studies that back up contrarian strategies, but as with everything to do with investing, it comes with caveats and constraints. In this post, I will posit that contrarian investing can take different forms, each based on different assumptions about market behavior, and present the evidence that we have on the successes and failures of each one. I will argue that even if you are swayed intellectually by the arguments for going against the crowd, it may not work for you, if you are not psychologically attuned to the stresses and demands that contrarian strategies bring with them.

Contrarianism - The Different Strands

    All contrarian investing is built around a common theme of buying an investment, when its price goes down significantly, but there are wide variations in how it is practiced. In the first, knee-jerk contrarianism, you use a bludgeon, buying either individual companies or the entire market when they are down, on the expectation that you will benefit from an inevitable recovery in prices. In the second, technical contrarianism, you buy beaten-up stocks or the entire market, but only if charting or technical indicators support the decision.  In the third, constrained contrarianism, you buy the stocks that are down, but only if they pass your screens for qualify and safety. In the fourth, opportunistic contrarianism, you use a price markdown as an opportunity to buy companies that you have always wanted to hold, but had not been able to buy because they were priced too high.

1. Knee-jerk Contrarianism

    The simplest and most direct version of contrarian investing is to buy any traded asset where the price is down substantially from its highs, with the asset sometimes being an individual company, sometimes a sector and sometimes the entire market. Implicit in this strategy is an absolute belief in mean reversion, i.e.,  that what goes down will almost always go back up, and that buying at the beaten down price and being willing to wait will therefore pay off.

    The evidence for this strategy comes from many sources. For the market, it is often built on papers (or books) that look at the historical data on what equity markets have delivered as returns over long periods, relative to what you would have made investing elsewhere. Using data for the United States, a  market with the longest and most reliable historical records, you can see the substantial payoff to investing in equities:

Download historical data

No matter what time period you use for your time horizon, stocks deliver the highest returns, of all asset classes, and there some who look at this record and conclude that "stocks always win in the long term", with the implication that you should stay fully invested in stocks, even through the worst downturns, if you have a reasonably long time horizon. These returns to buying stocks become greater, when you buy them when they are cheaper, measured either through pricing metrics (low PE ratios) or after corrections. There are two problems with the conclusion. The first is that there is selection bias, where using historical data from the United States, one of the most successful equity markets of the last century, to draw general conclusions about the risk and returns of investing in equities will lead you to underestimate equity risk and overestimate equity returns. The second is that, even with US equities, an investor who bought stocks just before a major downturn would have to wait a long time before being made whole again. Thus, investors who put their money in stocks in 1929, just ahead of the Great Depression, would not have recovered until 1954. 

    With individual stocks, the strongest backing for buying the dip comes from studies of "loser" stocks, i.e., stocks that have gone down the most over a prior period. In a widely cited paper from 1985, DeBondt and Thaler classified stocks based upon stock price performance in the prior three years into winner and loser portfolios, with the top fifty performers going into the "winner" portfolio, and the bottom fifty into the "losers portfolio", and estimated the returns you could have made on each group in the following thirty six months:

DeBondt and Thaler (1985)

As you can see, the loser portfolio dramatically outperforms the winner portfolio, delivering about 30% more on a cumulative basis than the winner portfolio in the thirty six months after the portfolios are created, which DeBondt and Thaler argued was evidence that markets overreact. About a decade later, Jegadeesh and Titman revisited the study, with more granular data on time horizons, and found that the results were reversed, if you shorten the holding period, with winner stocks continuing to win over the first year after portfolio creation. 

Jegadeesh and Titman (1993)

The reversal eventually kicks in after a year, but over the entire time period, the winner portfolio still outperforms the loser portfolio, on a cumulative basis. Jegadeesh and Titman also noted a skew in the loser portfolio towards smaller market cap and lower-priced stocks, with higher transactions costs (from bid-ask spreads and price impact). As other studies have added to the mix, the consensus on winner versus loser stocks is that there is no consensus, with evidence for both momentum, with winner stocks continuing to win, and for reversal, with loser stocks outperforming, depending on time horizon, and questions about whether these excess returns are large enough to cover the transactions costs involved.

    Setting aside the mixed evidence for the moment, the biggest danger in knee-jerk contrarian investing at the market level is that buying the dip in the market is akin to catching a falling knife, since that initial market drop can be a prelude to a much larger sell off, and to the extent that there was an economic or fundamental reason for the sell off (a banking crisis, a severe recession), there may be no near term bounceback. With individual stocks, that danger gets multiplied, with investors buying stocks that are being sold off to for legitimate reasons (a broken business model, dysfunctional management, financial distress) and waiting for a market correction that never comes. 

    To examine the kinds of companies that you would invest in, with a knee-jerk contrarian investing strategy , I looked at all US stocks with a market capitalization exceeding a billion dollars on December 31, 2024, and found the companies that were the biggest losers, on a percent basis, between March 28 and April 18 of 2025:

You will note that technology and biotechnology firms are disproportionately represented on the list, but that is the by-product of a bludgeon approach.

2. Technical Contrarianism

    In technical contrarianism, you start with the same basis as knee-jerk contrarianism, by  looking at stocks and markets that have dropped significantly, but with an added requirement that the price has to meet a charting or technical indicator constraint before becoming a buy. While there are many who consign technical analysis to voodoo investing, I believe that charting patterns and technical indicators can provide signals of shifts in mood and momentum that drive price movements, at least in the near term. Thus, you can view technical contrarianism as buying stocks or markets when they are down, but only if the charts and technical indicators point to a shift in market mood.

    One of the problems with testing technical contrarianism, to see if it works, is that even among technical analysts, there seems to be no consensus as to the best indicator to use, but broadly speaking, these indicators can be based on either price and/or volume movements. They range in sophistication from simple measures like relative strength (where you look at percentage price changes over a period) and moving averages to complex ones that combine price and volume. In recent decades, investors have added pricing in other markets to the mix, with the VIX (a traded volatility index) as well as the relative pricing of puts and calls in the options market being used in market timing. In sum, all of these indicators are directed at measuring fear in the market, with a "market capitulation" viewed as a sign that the market has bottomed out. 

    With market timing indicators, there is research backing up the use of VIX and trading volume as predictors of market movements, though with substantial error.

Source: S&P

As the VIX rises, the expected return on stocks in future periods goes up, albeit with much higher volatility around these expected returns. It is ironic that some of the best defenses of technical analysis have been offered by academics, especially in their studies of price momentum and reversal. Lo, Wang, and Mamaysky present a fairly convincing defense of technical analysis from the perspective of financial economists. They use daily returns of stocks on the New York Stock Exchange and NASDAQ from 1962 and 1996 and employ sophisticated computational techniques (rather than human visualization) to look for pricing patterns. They find that the most common patterns in stocks are double tops and bottoms, followed by the widely used head and shoulders pattern. In other words, they find evidence that some of the most common patterns used by technical analysts exist in prices. Lest this be cause for too much celebration among chartists, they also point out that these patterns offer only marginal incremental returns (an academic code word for really small) and offer the caveat that these returns may not survive transaction costs.

3. Constrained Contrarianism

    If you are in the old-time value investing camp, your approach to contrarian investing will reflect that worldview, where you will buy stocks that have dropped in value, but only if they meet the other criteria that you have for good companies. In short, you will start with a list of beaten up stocks, and then screen them for high profitability, strong moats and low risk, hoping to separate companies that are cheap from those that deserve to be cheap.

    As a constrained contrarian, you are hoping to avoid value traps, every value investor's nightmare , where a company looks cheap on a pricing basis (low PE, low price to book) and proceeds to become even cheaper after you buy it. The evidence on whether screening helps avoid value traps comes largely from studies of the interplay between proxies of value (such as low price to book ratios) and proxies for quality, including measures for both operating/capital efficiency (margins and returns on capital) and low risk (low debt ratios and volatility). Proponents of quality screens note that while value proxies alone no longer seem to deliver excess returns, incorporating quality screens seems to preserve these excess returns.  Research Affiliates, an investment advisory service, looked at returns to pure value screens versus value plus quality screens and presents the following evidence on how screening for quality improves returns:

Research Affiliates Study

The evidence is supportive of the hypothesis that adding quality screens improves returns, and does so more for stocks that look cheap (low price to book) than for expensive stocks. That said, the evidence is underwhelming in terms of payoff, at least on an annual return basis, though the payoff is greater, if you factor in volatility and estimate Sharpe ratios (scaling annual return to volatility).

    While much of the research on quality has been built around value and small cap investing, the findings can be extrapolated to contrarian investing, with the lesson being that rather than buy the biggest losers, you should be buying the losers that pass screening tests for high profitability (high returns on equity or capital) and low risk (low debt ratios and volatility). That may provide a modicum of protection, but the problem with these screens is that they are based upon historical data and do not capture structural changes in the economy or disruption in the industry, both of which have not yet found their way into the fundamentals that are in your screens.

    To provide just an illustration of constrained contrarianism, I again returned to the universe of about 6,000 publicly traded US stocks on April 18, 2025, and after removing firms with market capitalizations less than $100 million (with the rationale that these companies will have more liquidity risk and transactions costs), I screened first for stocks that lost more than 20% of their market capitalization between March 28 and April 18, and then added three value screens:

1. A PE ratio less than 15, putting the stock in the bottom quintile of US stocks as of December 31, 2024
2. A dividend yield that exceeded 1%, a paltry number by historical norms, but ensuring that the company was dividend-paying in 2024, a year in which 60% of US stocks paid no dividends
3. A net debt/EBITDA ratio of less than two, dropping it into the bottom quintile of US companies in terms of debt load

The six companies that made it through the screens are below:

I am sure that if you are a value investor, you will disagree about both the screens that I used as well as my cut offs, but you are welcome to experiment with your own screens to find bargains.

4. Opportunistic Contrarianism

    In a fourth variant of contrarian investing, you use a market meltdown as an opportunity to buy companies that you have always wanted to own but could not because they were over priced before the price drop, but look under priced after.  The best place to start an assessment of opportunistic investing is with my post on why good companies are not always good investments, with the first being determined by all of the considerations that go into separating great businesses from bad businesses, including growth and profitability, and the second by the price you have to pay to buy them. In that post, I had a picture drawing the contrast between good companies and good investments:

Put simply, most great companies are neutral or even bad investments, because the market prices them to be great. A year ago, when I valued the Mag Seven stocks, I argued that these were, for the most part, great businesses, with a combination of growth at scale, high profitability and deep moats, but that at the prices that they were trading  they were not great investments. 

I also argued that even great companies have their market travails, where for periods of time, investors lose faith in them and drive their prices down not just to value, but below. It happened to Microsoft in 2014, Apple in 2017, Nvidia in 2018, Tesla at multiple times in the last decade, and to Facebook, at the height of the Metaverse fiasco. While those corrections were caused by company-specific news stories and issues, the same process can play out, when you have significant market markdowns, as we have had over the last few weeks. 

    The process of opportunistic contrarianism starts well before a market correction, with the identification of companies that you believe are good or great businesses:

At the time that you first value them, you are likely to find them to be over valued, which will undoubtedly be frustration. You may be tempted to play with the numbers to make these companies look undervalued, but a better path is to put them  on your list of companies you would like to own, and leave them there. During a market crisis, and especially when investors are marking down the prices of everything, without discriminating between good and bad companies, you should revisit that list, with a caveat that you cannot compare the post-correction price to your pre-crisis valuation of your company. Instead, you will have to revalue the company, with adjustments to expected cash flows and risk premiums, given the crisis, and if that value exceeds the price, you should buy the stock. 

Contrarian Investing: The Psychological Tests!

    In the abstract, it is easy to understand the appeal of contrarian investing. Both behavioral and empirical research identify the existence of herd behavior in crowds, and point to tipping points where crowd wisdom becomes crowd madness. A rational decision-maker in the midst of animal spirits may feel that he or she has an advantage in this setting, and rightly so. That said, buying when the rest of the market is selling takes a mindset, a time horizon and a stronger stomach than most of us do not have.

1. The Mindset: Investing against the market will not come easily to those who are easily swayed by peer pressure, since they will have to buy, just as other investors (the peer group) will be selling, and often in companies that the market has turned against. There are  some who march to their own drummers, willing to take a path that is different from the rest, and these are better suited to being contrarians.
2. The Time Horizon: To be a contrarian, you don't always need a long time horizon, since corrections can sometimes happen quickly, but you have to be willing to wait for a long period, if that is what is necessary for the correction. Relatively few investors have this capacity, since it is determined as much by your circumstances (age, health and cash needs) as it is by your personality.
3. The Stomach: Even if your buy decision is based on the best thought-through contrarian investing strategies, it is likely that in the aftermath of that decision, momentum will continue to push prices down, testing your faith. Without a strong stomach, you will capitulate, and while your decision may have been right in the long term, your investment will not reflect that success.

As you can see, the decision on whether to be a contrarian is not just one that you can make based upon the evidence and theory, but will depend on who you are as a person, and your makeup. 

    I have the luxury of a long time horizon and the luck of a strong stomach, for both food and market surprises. I am not easily swayed by peer pressure, but I am not immune from it either. I know that buying stocks in the face of market selling will not come easily, and that is the reason that I initiated limit buys on three companies that I have wanted to have in my portfolio, BYD, the Chinese electric car maker, Mercado Libre, the Latin American online retail/fintech firm, and Palantir, a company that I believe is closest to delivering on thee promise of AI products and services. The limit buy kicked in on BYD on April 7, when it briefly dipped below $80,  my limit price, and while Palantir and Mercado Libre have a way to go before they hit my price limits, the crisis is young and the order is good until canceled!

YouTube Video

The Price of Risk: With Equity Risk Premiums, Caveat Emptor!

    If you have been reading my posts, you know that I have an obsession with equity risk premiums, which I believe lie at the center of almost every substantive debate in markets and investing. As part of that obsession, since September 2008, I have estimated an equity risk premium for the S&P 500 at the start of each month, and not only used that premium, when valuing companies during that month, but shared my estimate on my webpage and on social media. In my last post, on country risk premiums, I used the equity risk premium of 5.00% that I estimated for the US at the start of July 2023, for the S&P 500. That said, I don't blame you, if are confused not only about how I estimate this premium, but what it measures. In fact, an article in MarketWatch earlier this year referred to the equity risk premium as an esoteric concept, a phrasing that suggested that it had little relevance to the average investor. Adding to the confusion  are the proliferation of very different numbers that you may have seen attached to the current equity risk premium, each usually quoting an expert in the field, but providing little context. Just in the last few weeks, I have seen a Wall Street Journal article put the equity risk premium at 1.1%, a Reuters report put it at 2.2%, and a bearish (and widely followed) money manager estimate the equity risk premium to be negative. How, you may ask, can equity risk premiums be that divergent, and does that imply that anything goes? In this post, I will not try to argue that my estimate is better than others, since that would be hubris, but instead focus on explaining why these ERP differences exist, and let you make your own judgment on which one you should use in your investing decisions.

ERP: Definition and Determinants

    The place to start this discussion is with an explanation of what an equity risk premium is, the determinants of that number and why it matters for investors. I will try to steer away from models and economic jargon in this section, simply because they do little to advance understanding and much to muddy the waters.

What is it?

    Investors are risk averse, at least in the aggregate, and while that risk aversion can wax and wane, they need at least the expectation of a higher return to be induced to invest in riskier investments. In short, the expected return on a risky investment can be constructed as the sum of the returns you can expect on a guaranteed investment, i.e.,  a riskfree rate, and a risk premium, which will scale up as risk increases. 

Expected Return = Risk free Rate + Risk Premium

Note that this proposition holds even if you believe that there is nothing out there that is truly risk free, which is the case when you worry about governments defaulting, though it does imply that you have cleaning up to do to get to a riskfree rate. Note also that expectations do not always pan out, and the actual returns on a risky investment can be much lower than the risk free rate, and sometimes sharply negative.

    The risk premium that you demand has different names in different markets. In the corporate bond market, it is a default spread, an augmentation to the interest rate that you demand on a bond with more default risk. In the real estate market, it is embedded in a capitalization rate, an expected return used by real estate investors to convert the income on a real estate property into a value for that property. In the equity market, it is the equity risk premium, the price of risk for investing in equities as a class.

As you can see, every asset class has a risk premium, and while those risk premiums are set by investors within each asset class, these premiums tend to move together much of the time.

Determinants

    Since the equity risk premium is a price for risk, set by demand and supply, it stands to reason that it is driven not only by economic fundamentals, but also by market mood. Equities represent the residual claim on the businesses in an economy, and it should come as no surprise that the fundamentals that determine it span the spectrum:

My equity risk premium paper

Even a cursory examination of these fundamentals should lead you to conclude that not only will equity risk premiums vary across markets, providing an underpinning for the divergence in country risk premiums in my last post, but should also vary across time, since the fundamentals themselves change over time. 

    Market prices are also driven by mood and momentum, and not surprisingly, equity risk premiums can change, as these moods shift. In particular, equity risk premiums can become too low (too high) if investors are excessively upbeat (depressed) about the future, and thus become the ultimate receptacles for market hope and fear. In fact, one symptom of a market bubble is an equity risk premium that becomes so low that it is disconnected from fundamentals, setting up for an inevitable collision with reality and a market correction.

Why it matters

    If you are a trader, an investor or a market-timer, and you are wondering why you should care about this discussion, it is worth recognizing that the equity risk premium is a central component of what you do, even if you have never explicitly estimated or used it.

1. Market Timing: When you time markets, you are making a judgment on how an entire asset class (equities, bonds, real estate) is priced, and reallocating your money accordingly. In particular, if you believe that stocks are over priced, you will either have less of your portfolio invested in equities or, if you are aggressive, sell short on equities. Any statement about market pricing can be rephrased as a statement about equity risk premiums; if you believe that the equity risk premium, as priced in by the market, has become too low (relative to what you believe is justified, given history and fundamentals), you are arguing that stocks are over priced (and due for a correction). Conversely, if you believe that the equity risk premium has become too high, relative again to what you think is a reasonable value, you are contending that stocks are cheap, in the aggregate.  
2. Stock Picker: When you invest in an individual stock, you are doing so because you believe that stock is trading at a price that is lower than your estimate of its value. However, to make this judgment, you have to assess value in the first place, and while we can debate growth potential and profitability, the equity risk premium becomes an input into the process, determining what you should earn as an expected return on a stock. Put simply, if you are using an equity risk premium in your company valuation that is much lower (higher) than the market-set equity risk premium, you are biasing yourself to find the company to be under (over) valued. A market-neutral valuation of a company, i.e., a valuation of the company given where the market is today, requires you to at least to try to estimate a premium that is close to what the market is pricing into equities.
3. Corporate Finance: The role of the equity risk premium in determining the expected return on a stock makes it a key input in corporate finance, as well, because that expected return becomes the company's cost of equity. That cost of equity is then embedded in a cost of capital, and as equity risk premiums rise, all companies will see their costs of capital rise. In a post from the start of this year, I noted how the surge in equity risk premiums in 2022, combined with rising treasury bond rates, caused the cost of capital to increase dramatically during the course of the year.

Put simply, the equity risk premiums that we estimate for markets have consequences for investors and businesses, and in the next section, I will look at ways of estimating it.

Measurement

    If the equity risk premium is a market-set number for the price of risk in equity markets, how do we go about estimating it? Unlike the bond market, where interest rates on bonds can be used to back out default spreads, equity investors are not explicit about what they are demanding as expected returns when they buy stocks. As a consequence, a range of approaches have been used to estimate the equity risk premium, and in this section, I will look at the pluses and minuses of each approach.

1. Historical Risk Premium

    While we cannot explicitly observe what investors are demanding as equity risk premiums, we can observe what they have earned historically, investing in stocks instead of something risk free (or close). In the US, that data is available for long periods, with the most widely used datasets going back to the 1920s, and that data has been sliced and diced to the point of diminishing returns. At the start of every year, I update the data to bring in the most recent year's returns on stocks, treasury bonds and treasury bills, and the start of 2023 included one of the most jarring updates in my memory:

Spreadsheet with historical data

It was an unusual year, not just because stocks were down significantly, but also because the ten-year treasury bond, a much touted safe investment, lost 18% of its value. Relative to treasury bills, stocks delivered a negative risk premium in 2022 (-20%), but it would be nonsensical to extrapolate from a single year of data. In fact, even if you stretch the time periods out to ten, fifty or close to hundred years, you will notice that your estimates of expected returns come with significant error (as can be seen in the standard errors). 

    In much of valuation, especially in the appraisal community, historical risk premiums remain the prevalent standard  for measuring equity risk premiums, and there are a few reasons. 

• Perhaps, the fact that you can compute averages precisely gets translated into the delusion that these averages are facts, when, in fact, they are not just estimates, but very noisy ones. For instance, even if you use the entire 94-year time period (from 1928-2022), your estimate for the equity risk premium for stocks over ten-year treasury bonds is that it falls somewhere between 2.34% to 10.94%, with 95% confidence (6.64% ± 2* 2.15%). 
• It is also true that the menu of choices that you have for historical equity risk premiums, from a low of 4.12% to a high of 13.08%, depending on then time period you look at, and what you use as a riskfree rate, gives analysts a chance to let their biases play out. After all, if your job is to come up with a low value, all you have to do is latch on to a high number in this table, claim that it is a historical risk premium and deliver on your promise. 

   When using historical equity risk premiums, you are assuming mean reversion, i.e., that returns revert  to historic norms over time, though, as you can see, those norms can be different, using different time periods. You are also assuming that the economic and market structure has not changed significantly over the estimation period, i.e., that the fundamentals that determine the risk premium have remained stable. For much of the twentieth century, historical equity risk premiums worked well as risk premium predictors in the United States, precisely because these assumptions held up. With China's rise, increased globalization and the crisis of 2008 as precipitating factors, I would argue that the case for using historical risk premiums has become much weaker.

2. Historical Returns-Based Forecasts

    The second approach to using historical returns to estimate equity risk premiums starts with the same data as the first approach, but rather than just use the averages to make the estimates, it looks for time series patterns in historical returns that can be used to forecast expected returns. Put simply, this approach brings into the estimate the correlation across time in returns:

If the correlations across time in stock returns were zero, this approach would yield results similar to just using the averages (historical risk premiums), but it they are not, it will lead to different predictions. Looking at historical returns, the correlations start off close to zero for one-year returns but they do become slightly more negative as you lengthen your time periods; the correlation in returns over 5-year time periods is -0.15, but it is not statistically significant. However, with 10-year time horizon, even that mild correlation disappears. In short, while it may be possible to coax a predictive model using only historical stock returns, that model is unlikely to yield much in actionable predictions. There are sub-periods where the correlation is higher, but I remain skeptical of any ERP prediction model built around just the time series of stock returns.

    In an extension of this approach, you could bring in a measure of the cheapness of stocks (PE ratios or earnings yields are the most common ones) into the historical return data and exploit the relationship (if any) between the two. If there is a relationship, positive or negative, between PE ratios and subsequent returns, a regression of returns against PE (or EP) ratios can be used to generate predictions of expected annual returns in the next year, next 5 years or the next decade. The figure below is the scatter plot of earnings to price ratios against stock returns in the subsequent ten years, using data from 1960 to 2022:

A regression using this data yields some of the lowest estimates of the ERP, especially for longer time horizons, because of the elevated levels of PE ratios today. In fact, at the current EP ratio of about 4%, and using the historical statistical link with long-term returns, the estimated expected annual return on stocks, over the next 10 years and based on this regression is:

• Expected Return on Stocks, conditional on EP = .00254 + 1.4543 (.04) = .0607 or 6.07%
• ERP based on EP-based Expected Return = 6.07% - 3.97% = 2.10%

It is worth remembering that the expected return predictions come with error, and the more appropriate use of this regression is to get a range for the expected annual return, which yields predictions ranging from 4% to 8%. Extending the regression back to 1928 increases the R-squared and results in some regressions that yield predicted stock returns that are lower than the treasury-bond rate, i.e., a negative equity risk premium, given the EP ratio today. 

    Note that the results from this regression just reinforce rules of thumb for market timing, based upon PE ratios, where investors are directed to sell (buy) stocks if PE ratios move above (below) a “fair value” band. Since those rules of thumb have yielded questionable results, it pays to be skeptical about these regressions as well, and there are three limitations that those who use it have to keep in mind. 

• First, with the longer time-period predictions, where the predictive power is strongest, the same data is counted multiple times in the regression. Thus, with 5-year returns, you match the EP ratio at the end of 1960 with returns from 1961 to 1965, and then the EP ratio at the end of 1961 with returns from 1962 to 1966, and so on. While this does not imply that you cannot run these regression, it does indicate that the statistical significance (R squared and t statistics) are overstated for the longer time horizons. In addition, the longer your time horizon, the more data you lose. With a 10-year time horizon, for instance, the last year that you can use for predictions is 2012, with the EP ratio in that year matched up to the returns from 2013-2022. 
• Second, as is the case with the first approach (historical risk premiums), you are assuming  that the structural model is stable and that there will be mean reversion. In fact, within this time period (1928 - 2022), the predictive power is far greater between 1928 and 1960 than it is betweeen 196 and 2022.
• Third, while these models tout high R-squared, the number that matters is the standard error of the predictions. Predicting that your annual return will be 6.07% for the next decade with a standard error of 2% yields a range that leaves you, as an investor, in suspended animation, since you face daunting questions about follow through: Does a low expected return on stocks over the next decade mean that you should pull all of your money out of equities? If yes, where should you invest that cash? And when would you get back into equities again?

Proponents of this approach are among the most bearish investors in the market today, but it is worth noting that this approach would have yielded “low return” predictions and kept you out of stocks for much of the last decade. 

3. The Fed Model: Earnings Yield and ERP

    The problem with historical returns approaches is that they are backward-looking, when equity risk premiums should be about what investors expect to earn in the future. To the extent that value is driven by expected future cash flows, you can back out an equity risk premium from current stock prices, if you are willing to make assumptions about earnings growth and cash flows in the future. In the simplest version of this approach, you start with a stable-growth dividend discount model, where the value of equity can be written as the present value of dividends, growing at a constant rate forever:

If you assume that earnings will stagnate at current levels, i.e., no earnings growth, and that companies pay out their entire earnings as dividends (payout ratio = 100%), the cost of equity can be approximated by the earnings to price ratio:

Alternatively, you can assume that there is earnings growth and that companies earn returns on equity equal to their costs of equity, you arrive at the same result:

In short, the earnings to price ratio becomes a rough proxy for what you can expect to earn as a return on stocks, if you are willing to assume no earnings growth or that firms generate no excess returns.

    This is the basis for the widely used Fed model, where the earnings yield is compared to the treasury bond rate, and the equity risk premium is the difference between the two. In the figure below, you can see the equity risk premiums over time that emerge from this comparison, on a quarterly basis, from 1988 to 2023:

Download quarterly data

As you can see, this approach yields some "strange" numbers, with negative equity risk premiums for much of the 1990s, one of the best decades for investing in stocks over the last century. It is true that the equity risk premiums have been much more positive in this century, but that is largely because the treasury bond rate dropped to historic lows, after 2008. As interest rates have risen over the last year and a half,  with stock prices surging over the same period, the equity risk premium based on this approach has dropped, standing at 0.41% at the start of August 2023. Since this is the approach used in the Wall Street Journal article, it explains the ERP being at a two-decade low, but I do find it odd that there is no mention that this approach yielded negative premiums in the 1980s and 1990s. In a variant, the Wall Street Journal article also looks at the difference between the earnings yield and the inflation-protected treasury rate, which yields a higher value for the ERP, of about 3%, but suffers from many of the same issues as the standard approach.

    My problem with the earnings yield approach to estimating equity risk premiums is that the assumptions that you need to make to justify its use are are at war with the data. First, while earnings growth for US stocks has been negative in some years, it has been positive every decade for the last century, and there are no analysts (that I am aware of) expecting it be zero (in nominal terms) in the future. Second, assuming that the return on equity is equal to the cost of equity may be easy on paper, but the actual return on equity for companies in the S&P 500 was 19.73% in 2022, 17.04% over the last decade and has been higher than the cost of equity even in the worst year in this century (9.35% in 2008). If you allow for growth in earnings and excess returns, it is clear that earnings yield will yield too low a value for the ERP, because of these omissions, and will yield negative values in many periods, making it useless as an ERP estimator for valuation.

4. Implied ERP

    I start with the same general model for value that the earnings yield approach does, which is the dividend discount model but change three components

1. Augmented Dividends: It is undeniable that companies around the world, but especially in the US, have shifted from returning cash in the form of dividends to stock buybacks. Since two-thirds of the cash returned in 2022 was in the form of buybacks, ignoring them will lead to understating expected returns and equity risk premiums. Consequently, I add buybacks to dividends to arrive at an augmented measure of cash returned and use that as the base for my forecasts.
2. Allow for near-term growth in Earnings: Since the objective is to estimate what investors are demanding as an expected return, given their expectations of growth, I use analyst estimates of growth in earnings for the index. To get these growth rates, I focus on analysts who estimate aggregated earnings growth the index, rather than aggregating the growth rates estimated by analysts for individual companies, where you risk double counting buybacks (since analyst estimates are often in earnings per share) and bias (since company analysts tend to over estimated growth).
3. Excess Returns and Cashflows: I start my forecasts by assuming that companies will return the same percentage of earnings in cash flows, was they did in the most recent year, but I allow for the option of adjusting that cash return percentage over time, as a function of growth and return on equity (Sustainable cash payout = Growth rate/ Return on Equity). 

The resulting model in its generic form is below:

In August 2023, this model would have yielded an equity risk premium of 4.44% for the S&P 500, using trailing cash flows from the last twelve months as a starting point, estimating aggregate earnings for the companies from analyst estimates, for the next three years, and then scaling that growth down to the risk free rate, as a proxy for nominal growth in the economy, after year 5:

Download implied ERP spreadsheet

To reconcile my estimate of the equity risk premium with the earnings yield approach, you can set the earnings growth rate to zero and the cash payout to 100%, in this model, and you will find that the equity risk premium you get converges on the 0.41% that you get with the earnings yield approach. Adding growth and excess returns to the equation is what brings it up to 4.44%, and I believe that the data is on my side, in this debate. To the critique that my approach requires estimates of earnings growth and excess returns that may be wrong, I agree, but I am willing to wager that whatever mistakes I make on either input will be smaller than the input mistakes made by assuming no growth and no excess returns, as is the case with the earnings yield approach.

Picking an Approach

   I prefer the implied equity risk premium approach that I just described, as the best estimate of ERP,  but that may just reflect my comfort with it, developed over time. Ultimately, the test of which approach is the best one for estimating equity risk premium is not theoretical, but pragmatic, since your estimate of the equity risk premium is used to obtain predictions of returns in subsequent periods. In the figure below, I highlight  three estimates of equity risk premiums - the historical risk premium through the start of that year and the EP-based ERP (EP Ratio minus the T.Bond Rate) and the implied equity risk premiums, at the start of the year:

The historical risk premium is stable, but that stability is a reflection of a having a long tail of historical data that keeps it from changing, even after the worst of years. The implied and EP-based ERP approaches move in the same direction much of the time (as evidenced in the positive correlation between the two estimates), but the latter yields negative values for the equity risk premium in a large number of periods. 

    Ultimately, the test of whether an equity risk premium measure works lies in how well it predicts future returns on stocks, and in the table below, I try to capture that in a correlation matrix, where I look at the correlation of each ERP measure with returns in the next year, in the next 5 years and in the next 10 years:

Download data

None of the approaches yield correlations that are statistically significant, for stock returns in the next year, but the implied ERP and historical ERP are strongly correlated with returns over longer time periods, with a key difference; the former moves with stock returns in the next ten years, while the latter moves inversely. 

    While that correlation lies at the heart of why I use implied ERP in my valuations as my estimate of the price of risk in equity markets, I am averse to using it as a basis for market timing, for the same reasons that I cautioned you on using the EP ratio regression: the predictions are noisy and there is no clear pathway to converting them into investment actions. To see why, I have summarized the results of a regression of stock returns over the next decade against the implied ERP at the start of the period, using data from 1960 to 2022:

Download data

You can see, from the scatter plot, that implied ERPs move with stock returns over the subsequent decades, but that movement is accompanied by significant noise, and that noise translates into a wide range around the predicted returns for stocks. If you are a market timer, you are probably disappointed, but this type of noise and prediction errors is what you should expect to see with almost any fundamental, including EP ratios. 

Conclusion

   I hope that this post has helped to convince you that the equity risk premium is central to investing, and that even if you have never used the term, your investing actions have been driven by its gyrations. I also hope that it has given you perspective on why you see the differences in equity risk premium numbers from different sources. With that said, here are some thoughts for the road that can help you in future encounters with the ERP:

1. There is a true, albeit unobservable, ERP: The fact that the the true equity risk premium is unobservable does not mean that it does not exist. In other words, the notion that you can get away using any equity risk premium you want, as long as you have a justification and are consistent, is absurd. So, whatever qualms you may have about the estimation approaches that I have described in this post, please keep working on your own variant to get a better estimate of the ERP, since giving up is no an option.
2. Not all estimation approaches are created equal: While there are many approaches to estimating the equity risk premium, and they yield very different numbers, some of these approaches have more heft, because they offer better predictive power. Picking an approach, such as the historical risk premium, because its stability over time gives you a sense of control, or because everyone else uses it, makes little sense to me.
3. Your end game matters: As I noted at the start of this post, the equity risk premium can be used in a multitude of investment settings, and you have to decide, for yourself, how you will use the ERP, and then pick an approach that  works for you. I am not a market timer and estimate an equity risk premium primarily because I need it as an input in valuation and corporate finance. That requires an approach that yields positive values (ruling out the EP-based ERP) and moves with with stock returns in subsequent periods (eliminating historical ERP). 
4. Market timers face a more acid test: If you are using equity risk premiums or even earnings yield for market timing, recognize that having a high R-squared or correlation in past returns will not easily translate into market-timing profits, for two reasons. First, the past is not always prologue, and market and economic structures can shift, undercutting a key basis for using historical data to make predictions. Second, even if the correlations and regressions hold, you may still find it hard to profit from them, since you (and your clients, if you are a portfolio manager) may be bankrupt, before your predictions play out. Statistical noise (the standard errors on your regression predictions) can create havoc in your portfolios, even if it eventually gets averaged out.

YouTube Video

Data Links

1. Historical returns on Stocks, Bonds and Real Estate: 1928 - 2022
2. Earnings to Price Ratios and Dividend Yields, by Quarter: 1988 Q4- 2023 Q2
3. Implied ERP from 1960 to 2022: Annual Data
4. ERP and Stock Returns: 1960 to 2022

Spreadsheet

1. Implied ERP Spreadsheet for August 2023

Papers

1. Equity Risk Premiums (ERP): Determinants, Estimation and Implications- The 2023 Edition

Mean Reversion: Gravitational Super Force or Dangerous Delusion?

In my last post on the danger of using  single market metrics to time markets, I made the case that though the Shiller CAPE was high, relative to history, it was not a sufficient condition to conclude that US equities were over valued. In the comments that followed, many disagreed. While some took issue with measurement questions, noting that I should have looked at ten-year correlations, not five and one-year numbers, others argued that this metric was never meant for market timing and that the real message was that the expected returns on stocks over the next decade are likely to be low. I was surprised at how few brought up what I think is the central question, which is the assumption that the CAPE or any other market metric will move back to historic norms. This unstated belief that things revert back to the way they used to be is both deeply set, and at the heart of much of value investing, especially of the contrarian stripe. Thus, when you buy low PE stocks and or sell a stock because it has a high PE, you are implicitly assuming that the PE ratios for both will converge on an industry or market average. I am just as prone to this practice as anyone else, when I do intrinsic valuation, when I assume that operating margins and costs of capital for companies tend to converge on industry norms. That said, I continue to worry about how many of my valuation mistakes occur because I don’t question my assumptions about mean reversion enough. So, you should view this post as an attempt to be honest with myself, though I will use CAPE data as an illustrative example of both the allure and the dangers of assuming mean reversion.

Mean Reversion: Basis and Push Back

The notion of mean reversion is widely held and deeply adhered to not just in many disciplines but in every day life. In sports, whether it be baseball, basketball, football or soccer, we use mean reversion to explain why hot (and cold) streaks end. In investments, it is an even stronger force explaining why funds and investors that fly high come back to earth and why strategies that deliver above-average returns are  unable to sustain that momentum.

In statistics, mean reversion is the term used to describe the phenomenon that if you get an extreme value (relative to the average) in a draw of a variable, the second draw from the same distribution is likely to be closer to the average. It was a British statistician, Francis Galton, who first made official note of this process when studying the height of children, noted that extreme characteristics on the part of parent (a really tall or short parent) were not passed on. Instead, he found that the heights reverted back to what he called a mediocre point, a value-laden word that he used to describe the average. In the process, he laid the foundations for linear regressions in statistics.

In markets and in investing, mean reversion has not only taken on a much bigger role but has arguably had a greater impact than in any other discipline. Thus, Jeremy Siegel's argument for why "stocks win in the long term" is based upon his observation that over a very long time period (more than 200 years), stocks have earned higher returns than other asset classes and that there is no 20-year time period in his history where stocks have not outperformed the competition. Before we embark on on examination of the big questions in mean reversion, let's start by laying out two different versions of mean reversion that co-exist in markets.

• In time series mean reversion, you assume that the value of a variable reverts back to a historical average. This, in a sense, is what you are using when looking at the CAPE today at 27.27 (in August 2016) and argue that stocks are over priced because the average CAPE between 1871 and 2016 is closer to 16.
• In cross sectional mean reversion, you assume that the value of a variable reverts back to a cross sectional average. This is the basis for concluding that an oil stock with a  PE ratio of 30 is over priced, because the average PE across oil stocks is closer to 15. 

At the risk of over generalization, much of market timing is built on time series mean reversion, whereas the bulk of stock selection is on the basis of cross sectional mean reversion. While both may draw their inspiration from the same intuition, they do make different underlying assumptions and may pose different dangers for investors.

The nature of markets, though, is that every point of view has a counter, and it should come as no surprise that just as there are a plethora of strategies built around mean reversion, there are almost as many built on the presumption that it will not happen, at least during a specified time horizon. Many momentum-based strategies, such as buying stocks with high relative strength (that have gone up the most over a recent time period) or have had the highest earnings growth in the last few years, are effectively strategies that are betting against mean reversion in the near term. While it is easy to be an absolutist on this issue, the irony is that not only can both sides be right, even though their beliefs seem fundamentally opposed, but worse, both sides can be and often are wrong.

Mean Reversion: The Questions

You can critique mean reversion at two levels. At the level at which it is usually done, it is more about measurement than about process, with arguments centered around both how to compute the mean and the timing and form of the reversion process. There is a fundamental and perhaps more significant critique of the very basis of mean reversion, which is based on structural changes in the process being analyzed.

The Measurement Critique

Let’s say that both you and I both believe in mean reversion. Will we respond to data in the same way and behave the same way? I don't think so and that is because there are layers of judgments that lie under the words “mean” and “reversion”, where we can disagree. 

• On the mean, the numbers that you arrive at can be different, depending upon the time period you look at (if it time series mean reversion) or the cross sectional sample (if it is a cross sectional mean reversion), and you can get very different values with the arithmetic average as opposed to the median. With cross sectional data, for instance, the oil company analysis may be altered depending on whether your sample is of all oil companies, just larger integrated oil companies or smaller, emerging market oil companies. For time series variations, consider the historical time series of CAPE and how different the "mean" looks depending on the time period used and how it was computed.
  
• On the reversion part, there can be differences in judgment as well. First, even if we both agree that there is mean reversion, we can disagree on how quickly it will happen. That has profound consequences for investing, because there may be a time horizon threshold at which we may not be to devise an investment strategy to take advantage of the reversion. Second, we can disagree over how the metric in question will adjust. To illustrate, assume that the mean reversion metric is CAPE and that we both agree that  the CAPE of 27 should drop to the historic norm of 16 over the next decade. This can be accomplished by a drop in stock prices (a market crash) or by a surge in earnings (if you can make an argument that earnings are depressed and are due for recovery). The implications for investing can be very different.

In summary, there is a lot more nuance to mean reversion than its strongest proponents let on. One reason that they try to make their case look stronger than it is may be because they are selling others on their investment thesis and hoping that if they can convince enough people to make it self fulfilling. The other, and perhaps more dangerous reason, is to convince themselves that they are right, as a precursor to action. 

The Fundamental Critique

The process of mean reversion is built on the presumption that the underlying distribution (whether it be a time series or cross sectional) is stationary and that while there may be big swings from year to year (or from company to company), the numbers revert back to a norm. That is the elephant in the room, the really big assumption, that drives all mean reversion and it is its weakest link. If there are structural changes that alter the underlying distribution, there is no quicker way to ruin that trusting in mean reversion. The types of structural changes that can cause distribution to go awry range the spectrum, and the following is a list, albeit not comprehensive, of why these changes in the context of mean reversion over time.

• The first is aging, with the argument easiest to make with individual companies and more difficult with entire markets. As companies move through the life cycle, you will generally see the numbers for the company reflect that aging, rather moving to historic norms. That is especially true for growth rates, with growth rates decreasing as a company scales up and becomes more mature, but it is also true of both other operating numbers (margins, costs of capital) as well as pricing metrics (price earnings ratios and EV multiples). While markets, composed of portfolios of companies, are less susceptible to aging, you could argue that aging equity markets (the US, Japan and Europe) will exhibit different characteristics than they did when were younger and more vibrant. 
• The second is technology and industry structure, shaking up both the product market structure and creating challenges for accountants. This is true clearly at the company level, as is the case with retailing, where Amazon's entry and subsequent growth has laid waste to historic norms for this sector, bringing down operating margins and changing reinvestment patterns. It is also true at the market level, where an increasing proportion of the equity market (say, the S&P 500) are service and technology stocks and the accounting for expenses in these sectors (with many capital expenses being treated as operating expenses) creating questions about whether the E in the PE for the S&P 500 is even comparable over time.
• The third is changes in consumer and investor preferences, with the first affecting the numbers in product markets and the latter in financial markets. For instance, there is an argument to be made that the surge in index funds has altered how stocks are priced today, as opposed to two or three decades ago.

In the context of CAPE, again, and using Shiller's entire database, which goes back to 1871, let's take a quick look at how much both the US economy has grown and changed since 1871 and how those changes have affected the composition of US stocks.

In 1871, coming out of the civil war, the US was more emerging than developed market, with the growth and risk that goes with that characterization. In 1900, the US equity market had become the largest in the world, but 63% of its value came from railroad stocks, reflecting both their importance to the US economy then and their need for equity capital. For most of the next few decades, the US continued on its path as a growth market and economy, though the growth trend was brought to a stop by the great depression.  The Second World War firmly established the US as the center of the global economy and the period between 1945 and 2000 represents the golden age of mean reversion, a period where at least in the US, mean reversion worked like a charm not just across stocks but across time. It is worth noting that many of the now-accepted standard practices in both corporate finance and valuation, from using historical risk premiums for stocks to attaching premiums for expected returns to small-cap stocks to believing that value stocks beat growth stocks (with low PBV or low PE as a proxy for value) came from researchers poring over this abnormally mean-reverting financial history. I trace my awakening to the dangers of mean reversion to the 2008 crisis but I believe that the signs of structural change were around me for at least a decade prior. After all, the shift from a US-centric global economy to one that was more broadly based started occurring in the 1970s and continued, with fits and bounds, in the decades after. Similarly, the US dollar's reign as the global currency was challenged by the introduction of the Euro in 1999 and put under further strain by the growth in emerging market currencies.

So, how did 2008 change my thinking about markets, investing and valuation? First, globalization is here to stay and while it has brought pluses, it has already brought some minuses. As I noted in my post on country risk, no investor or company can afford to stay localized any more, since not only do market crisis in one country quickly become global epidemics, but a company that depends on just its domestic market for operations (revenues and production) is now more the exception than the rule. Second, the fact that financial service firms were at the center of the crisis, has had long term consequences. Not only has it led to a loss of faith in banks as well-regulated entities, run by sensible (and risk averse) people, but it has increased the role of central bankers in economies, with perverse consequences. In their zeal to be saviors of the economy, central bankers (in my view) have contributed to an environment of low economic growth and higher risk premiums. Third, the low economic growth and low inflation has resulted in interest rates lower than they have been historically in most currencies and negative interest rates in some. I know that there are many who believe that I am over reacting and that it only a question of time before we revert back to more normal interest rates, higher economic growth and typical inflation but I am not convinced. 

From Statistical Significance to Investment Return Payoff

The standard approach to showing mean reversion is start with historical data and establish mean reversion with statistics. I will start with that basis, again using CAPE as my illustrative example, but will then build on it to show why, even if you believe in mean reversion and you base it on sound statistics, it is so difficult to convert statistical significance into market-beating returns.

The statistics

If you were looking at a data series, how would you go about showing mean reversion? There are three simple statistical devices that you can draw. The first is graphical, a scatter plot of the data that shows the mean reversion over time. In the context of CAPE, for instance, this is the graph that you saw in my last post:

Historical data on Shiller CAPE

The problem with this plot is that it is weak evidence for investing, since you don't make money from buying or selling PE but from buying and selling stocks. In fact, even in this plot, you can see that the CAPE case that stocks are over priced is weakened because I have used a 25-year median for comparison. A stronger graphical backing for mean reversion would then graph stock returns in subsequent time periods as  a function of the CAPE today, with a higher CAPE (relative to history) translating into lower returns in a future period. 

Looking at this data, at least, the evidence seems strong that a high CAPE today goes with lower stock returns in future periods, with the mean reversion becoming stronger for longer time periods.

The relationship between the market timing metric and returns can be quantified in one of two ways. You could compute the correlation between the metric and returns, with a more negative correlation indicating stronger mean reversion. Updating my CAPE/ returns correlation metric, with 10-year returns added to the mix, you can see again the basis for the market timing argument:

You an build on these correlations and run regressions (linear or otherwise) where you regress returns in future periods against the value of the metric today. The results of those regressions, with CAPE as the market metric, are summarized below:

What does this mean? If you buy into mean reversion and can live with the noise or error in your estimate (captured in the R-squared), these regressions back up the correlation findings, insofar as your CAPE-based predictions get more precise for longer time period returns. In fact, if you are one of those who lives and dies by statistics, using today's CAPE of 27.27 in this regression will yield a predicted annualized return of 4.30% on stocks for the next 10 years:

Expected annualized return in next 10 years = 16.24% - 0.0044 (27.27) = 4.30%

Scary, right? But before you over react, first recognize that this prediction comes with a standard error and range and second, please read on.

The Investment Action

If you have sat through a statistics class, you have probably heard the oft-repeated caution that "correlation is not causation", a good warning if you are a researcher trying to explain a phenomenon but not particularly relevant, if you are an investor. After all, if you can consistently make a lot of money from a strategy, do you really need to know why? The biggest challenge in investing is whether you can convert statistical significance ( a high correlation or a regression with impressive predictive power) into investment strategy. It is at this level that market timing metrics run into trouble, and using CAPE again, here are the two ways in which you can use the results from the data to change the way you invest.

If you are willing to buy into the notion that the structural changes in the economy and markets have not changed the historical mean reversion tendencies in the CAPE, the most benign and defensible use of the data is to reset expectations. In other words, if you are an investor in stocks today, you should expect to make lower returns for the next 10 years than you have historically. This has consequences for how much investors should save for future retirement or how much states should set aside to cover future contractual obligations, with both set asides increasing because your expected returns are lower. 

It is when you decide to use the CAPE findings to do market timing that the tests become more arduous and difficult to meet. To understand what this means, let's go back to the basic asset allocation decision that all investment begins with. Given your risk aversion (a function of both your psychological make-up and the environment you are in) and liquidity needs (a function of your age, wealth and dependents), there is a certain mix of stocks, bonds and cash that is right for you. With market timing, you will alter this mix to reflect your views on desirable (or under priced) markets and undesirable ones. Thus, your natural mix is 60% stocks, 30% bonds and 10% cash, and you believe (using whatever market timing metric you choose) that stocks are over priced, you would lower your allocation to stocks and increase your allocation to either bonds or cash. You could further refine this market timing algorithm for domestic stocks versus foreign stocks or bring in other asset classes such as collectibles and real estate. The test of a market timing strategy therefore requires more structure than the statistical analysis of checking for correlation or regression:

1. Timing threshold: If you decide that you will time markets using a metric, you have to follow through with specifics. For instance, with CAPE as your market metric, and a high (low) CAPE being used as an indicator of an over valued (under valued) market, you have to indicate the trigger  that will initiate action. In other words, does the CAPE have to be 10% higher, 25% higher or 50% higher than the historic average for you to start moving money out of stocks?
2. Asset class alternatives: If you decide to move money out of stocks, you have to also specify where the money will go and you have four choices. 
3. Holding period: You will have to specify how long you plan to stay with the "market timed" allocation mix, with the answers ranging from a pre-specified time horizon (1 year, 2 years or 5 years) to until the market timing metric returns to safe territory. 
4. Allocation Constraints (if any): The allocation that you have for an asset class can be floored at zero, if you are a long only investor, but can be negative, if you are willing to go short. The cap on what you can allocate to an asset class is 100%, if you cannot or choose not to borrow money, but can be greater than 100%, if you can. 

Put simply, the lower your threshold, the more alternatives you have to investing in stocks, the shorter your holding period and the fewer your constraints, the more active you are as a market timer. It is in this context that I tried out different market timing strategies built around CAPE. The table below lists out the returns from a buy and hold strategy with a fixed mix of stocks, bonds and bills (60%, 30% and 10%) and contrasts it with returns over the same period from using a CAPE timing strategy of reducing the equity allocation to 40% if the CAPE is 25% higher than a 50-year median value and increasing the equity allocation to 80% if the CAPE is 25% lower than a 50-year median value. I report the numbers for the entire time period 1917-2016 and break it down into two fifty-year time periods (1917-1966, 1967-2016):

Download market timing spreadsheet

With this mix of timing choices (50-year median, 25% threshold and the given changes to equity allocation), the Shiller CAPE outperforms the buy and hold strategy for the 1917-2016 time period  but  under performs in the last fifty year time period. I know that your timing choices can be very different from mine and I have created options in this spreadsheet to let you change the choices to reflect your preferences to see if you can deliver better market timing results using CAPE. I did try a few variants and here is what I found.

1. Time Period: With every variation of timing that I tried, the CAPE delivers a positive market timing payoff in the first half of the entire time period (from 1917 to 1966) and a negative one in the second half (1967-2016). In fact, I could not find a combination of timing devices that delivered positive payoff in the second time period.
2. Choice of median: Using the lifetime median delivers better results during the "good" period (1917-1966) but worse results during the "bad" period (1967-2016). Using a shorter time periods for the median reduces the outperformance in the first half of the analysis period but improves it in the second half.
3. Buy and Sell: The CAPE's timing payoff is greater when it is used as a buying metric than as a selling metric. In fact, you make a positive payoff from using a low CAPE as a buying indicator over the entire period but using it is a signal of over priced markets costs you money in both time period. 
4. Market Timing magnitude: Increasing the degree to which you tilt towards or away from stocks, in reaction to the CAPE, just magnifies the return difference, positive or negative. Thus, in the first half of the century (1917-1966), changing your equity exposure more increases the payoff to market timing. In the second half, it makes the negative payoff worse.

In many ways, this testing is tilted in favor of finding that the Shiller CAPE works. First, while I have been careful not to use ex-post data, I have acted as if I know what the earnings for the year will be, at the end of each year, when my market timing decision is made. In reality, on December 31, 2012, I would know only the earnings for the first three quarters of 2012 and not quite the full year. Second, I am ignoring the transactions costs and taxes due from shifting large amounts in and out of stocks in my timing years. Those will represent a significant drain on my returns as an investor. Finally, I am assuming that there have been no structural shifts large enough to cause the mean reversion to break down. In spite of all of this, I am hard pressed to explain why we are so swayed by arguments based on this metric.

Conclusion

These are dangerous times for those who believe in mean reversion, for two reasons. The first is that our access to historical data is getting broader and deeper, with mixed consequences. Having more data allows us to find out more about the underlying fundamentals but since that data goes back so far, much of what we find no longer has relevance. The second is that doing statistical analysis no longer requires either homework or effort, with tools at our fingertips and statistical results are only a click away. Both in academia and in practice, I see more and more use of statistical significance as proof that you can beat markets and my reason devising and testing out market timing strategies with CAPE were not meant to be an assault on CAPE but more a cautionary note that statistical correlation is not cash in the bank. This may also explain why there are so many ways to beat the market, on paper, and so few seem to be able to deliver those magical excess returns, in practice. 

YouTube Video

Datasets

1. CAPE: 1881-2016 (Shiller Data)
2. Stock, Bond and Bill Returns (1881-2016)
3. Market Timing Spreadsheet