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I’ve been thinking about valuations a lot lately. If you’ve been following the stock market in recent months, then you will doubtlessly be aware that the past 6-months have witnessed a historic 44% rally across global markets. This rally has drawn particular attention because it has been dominated by tech stocks which deftly shrugged of lockdowns and the ensuing recession. The combination of stretched valuations and tech dominance has compelled some to compare this current era to that of the late 90’s Tech Bubble whose collapse ushered in the Lost Decade and culminated in the 2008 Financial Crisis.

Like any good investor I follow valuations closely and have been wondering what all of this means for asset allocation in the years to come. Is this time really different? The pervasiveness of technology in our daily lives certainly seems undeniable, legacy industries seem increasingly outmoded and the broad macro environment compels a preference for tech over just about anything else. Perhaps these factors do justify higher valuations.

To address these questions I have found inspiration in the work of Robert Shiller who in 1998 and 2001 released a series of highly provocative papers which concluded that the stock market was historically overvalued and that the ensuing 10 years would produce very poor returns indeed.

In the analysis to follow I offer an update on these prescient insights to investigate what current valuations imply about the prospect for future earnings and returns. Along the way I have included all of the R code I used to generate my results for you to replicate yourself.

### The Theory of Financial Ratios

Financial ratios like Price/Earnings (PE), Price/Book (PB), and Enterprise Value/EBITDA (EV/EBITDA) are commonly used by financial analysts to gauge the relative value of a stock. For example, a PE ratio of 15 tells us that we are required to pay $15 up front in order to access$1 of earnings. A high PE ratio might imply that a company is expected to grow aggressively while a low PE might tell us that a company is attractively valued.

Financial ratios can be expressed on either a trailing or forward-looking basis. The Forward PE is calculated by taking the current price divided by an estimate for earnings over the next 12-months. More commonly the PE is expressed on a trailing basis which takes the current price divided by earnings over the previous 12-months.

The PE for the S&P 500 has averaged about 16 over its 100+ year history but in any one year can deviate significantly. Take a look at the below graph of the PE ratio for 1926-2000. The average might be 16, but the ratio has rarely stayed there for very long and can be quite volatile year to year (or quarter to quarter).

I excluded the 2010’s in the previous graph for a reason. The ’08 Financial Crisis and Great Recession were so severe that for a period of time the trailing 12-month earnings for the S&P were negative which had the odd effect of making stocks look wildly expensive when they were actually very cheap. You can see this dynamic in the graph for the PE from 1926-2020. The long run dynamics of the PE are distorted during this period of time and confound our understanding of what relative valuations mean for stocks.

In order to smooth out the fluctuations in corporate profits that are part of the business cycle and reduce the volatility of valuations, Shiller developed the Cyclically Adjusted Price/Earnings (CAPE) ratio which takes as the denominator an average of the previous 10-year’s earnings adjusted for inflation.

You can see the effect this has in the below graph which depicts the CAPE ratio for 1926-2020. The volatility of the ratio is significantly reduced and the oddness of 2010’s is replaced by the behavior we would expect (i.e. cheap valuations coming out of recession). One feature about the CAPE chart that’s particularly useful is that it demonstrates that the ratio is stable.

#### Stability, Mean Reversion and Valuation Ratios

It’s imperative to understand what the stability of a valuation ratio implies about mean reversion. If we accept the premise that valuation ratios (like CAPE) are, in fact, stable and will continue to fluctuate within their historical range and not move permanently outside or “get stuck” at historically extreme levels, then we are claiming that valuations are mean reverting. It follows that when a valuation ratio is at an extreme level, then eventually something must happen to restore a long run equilibrium. In the case of a CAPE ratio that is historically high, either the numerator (i.e. Price) must decline or the denominator (i.e. Average 10-Year Earnings) must grow to bring the ratio back to a normal level.

If this is the case, then something must be forecastable based on the ratio; either the numerator or the denominator. If we are using the P/E ratio, then the P/E must be able to forecast either the future trajectory of the stock price or the future path of earnings.

The random walk hypothesis states that stock prices are essentially random and only drift up slowly over time. If this is true, then we should find that the CAPE has no ability to forecast future stock prices. On the other hand, analysts have a pretty good record of forecasting earnings based on traditional fundamental analysis which we might expect our analysis to corroborate.

This will be the focus of the study to follow: by using the CAPE ratio are we able to forecast stock prices or earnings?

All of the data used in this study can be obtained from Robert Shiller’s website here. I created a few of variables in Excel and you can download that spreadsheet here.

### CAPE Ratio and Earnings Forecasts

The time period we will examine spans 1980-2019. To evaluate the relative ability of using the CAPE to forecast earnings we will separately look at earnings growth over 1-year and the annualized earnings growth over 5 years. This is done using a simple linear regression model with the quarterly value of the CAPE serving as the independent variable and the subsequent 1-Year/5-Year earnings growth serving as the dependent variable.

We begin with the 1-year forecast. The below R Code shows the model and graphs it using ggplot2.

The preliminary results from the model indicate that the CAPE as little ability to forecast the earnings growth over the next year. The coefficient for the CAPE is not statistically significant and the Adjusted R-Squared is a paltry .003. However, examination of the graph shows some irregularities. While the majority of earnings growth rates are tightly grouped between -1 and 1, there are 3 observations that lie substantially outside of the main cluster which might be throwing off the results. Let’s hone in on them by labeling these points on the graph.

We see that these 3 points occurred during the first 3 quarters of 2009. As I remarked above, things were so bad during 2008 that for a time earnings for the S&P 500 were negative which was (and still is) unprecedented. As such, it makes sense that earnings would experience a significant rebound in the coming quarters primarily due to the resumption of economic activity and having very little to do with valuations.

To correct for this, we can winsorize the data. Winsorization is a technique to deal with outliers that replaces extreme values with less extreme ones rather than removing them entirely. In our case, we will replace the values from Q1-Q3 of 2009 with the 97.5% percentile of the rest of the data.  Doing so will still reflect strong earnings growth, but more “typical” growth that is in line with the majority of the data.

Rerunning the model, you can see that it actually does a little worse after the adjustment. The results from the regression indicate that the CAPE ratio remains insignificant and the Adjusted R-Squared has actually gone negative; indicating that including the CAPE ratio as an explanatory variable is worse than taking a simple mean. The graphical results depict this visually. The plot shows a cloud of points with earnings growth that can be low or high regardless of the CAPE therefore implying no systematic relationship between the CAPE and 1-Year Earnings Growth.

Perhaps we should not be surprised that the CAPE ratio is unable to forecast 1-Year earnings growth. As we have seen, earnings growth can be quite volatile. Moreover, the CAPE ratio smooths out the earnings over 10 years to reveal long term trends in valuation. Perhaps, the CAPE ratio will do better at forecasting over a horizon longer rather than 1 year. Let’s examine how well the CAPE ratio predicts the 5-year annualized earnings growth.

The results from the model show that the CAPE is a slightly better predictor for 5-Year earnings growth than 1-Year growth. The coefficient for CAPE is strongly statistically significant which implies that valuations do play some role in the future earnings growth. Nevertheless, it is a small role (like an extra or stagehand) as the Adjusted R-Squared remains a modest 7%. Graphically, again, we observe no obvious relationship between the two variables.

Up to this point we have investigated the relationship between the CAPE and earnings. In short, there appears to be no relationship with the CAPE able to meaningfully forecast earnings growth at both a 1-year and 5-year horizon. For myself, this result makes sense. If we consider a valuation ratio at a basic level it is essentially a Price that is determine by the market, divided by a fundamental variable which is controlled by the firm. A valuation ratio is something an investor uses to determine if a stock is a good investment or not. On the other hand, it’s unclear of what use a valuation ratio is to management; surely they would not set corporate priorities in order to bring valuations down.

With this in mind, let’s turn to price appreciation and see if we can use the CAPE ratio to forecast future returns.

### CAPE Ratio and Return Forecasts

Just as we did for earnings, we’ll separately explore if the CAPE is able to forecast returns over a 1-Year and 5-Year horizon.

Below are the results for the 1-Year forecast:

Unfortunately, the CAPE appears to be of little value for predicting the return over the next year. The coefficient for CAPE is negative which implies that high valuations are associated with lower price returns in the future which aligns with our expectations. The coefficient is highly significant, suggesting that the impact of valuations is meaningful, but with an R-Squared of 4% the ratio only accounts for a small proportion of the variation in returns.

We finally come to the 5-Year returns forecast. As I remarked in the introduction, if we accept the notion that valuations are more that just random noise, then they must be able to predict something. To this point we have determined that the CAPE cannot predict future earnings growth and is only very weakly able to explain the return observed in the next year. Can the CAPE ratio predict returns over a long horizon? Below are the results for the 5-Year forecast:

The regression output shows that the CAPE ratio is a very good predictor of the 5-year price return. The coefficient is negative as we would expect and highly significant. Moreover, over 40% of the variance in returns is explained by this single variable.

Graphically, we see a pronounced downward relationship between the CAPE and returns. A low value for the CAPE (i.e. stocks are cheap) is tightly associated with impressive returns in the next 5 years. Conversely, high valuations are associated with poor future returns. In fact, in 16 of the 19 times the CAPE has been above 30, returns over the next 5-years have actually been negative…

### So, What Does This Mean?

What is the takeaway from these findings?

The conclusions of this study are consistent with what Shiller demonstrated in the 90’s. Valuations imply nothing about future earnings growth in either the short or long term. While empirically important, valuations have only limited relevance for predicting short run returns. It is over the long run that valuations demonstrate their utility and become a major factor for predicting the future direction of markets.

What does this mean for our current moment and future returns?

As of market close on 10-23-20, the current reading for the Shiller CAPE was 31.69. Given the above discussion of returns when the CAPE has been over 30 this figure is more than a little disturbing and promises low and volatile returns over the next 5 years.

### Concluding Remarks

My hope is that this post has taught you a little more about stock valuations: what they tell us and what they do not. Now, use my R code and apply it to your own portfolio.

Until next time, thanks for reading!

-Aric Lux.

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