Chief Investment Strategist
Summary: We show that macro variables on the US housing market, consumer confidence, change in money supply, the US 2-year yield, unemployment rate, hourly earnings, and lending standards are the most important macro variables for explaining the variance in the earnings yield on the S&P 500 in the period 1994-2022. Our earnings yield model also have long periods during the dot-com bubble and the Covid-19 pandemic where the predicted earnings yield is considerably above the actual earnings yield suggesting these two periods are driven by strong investor sentiment and optimism not explainable by the macro backdrop.
US housing market and consumer confidence are key for equity valuation
When we set out to build an earnings yield model on S&P 500 our aim was to find the factors that can explain the variation in the earnings yield. Our first model was using mostly aggregate company fundamentals on the S&P 500 such as EBIT margin, revenue growth, capex-to-sales etc., with the 12-month trailing earnings yield as the target in the model. This model was misspecified for several reasons including the 12-month trailing earnings yield being too volatile and lagging, but more importantly company fundamentals on the S&P 500 are economically related to earnings and thus not offering an interesting model driven by external variables from the companies themselves.
In the final model, we switched from aggregate fundamental data to time series on the US economy or financial markets other than the equity market. We also changed the earnings yield from 12-month trailing to 12-month forward because this variable is more stable, and the forward-looking nature of the variable is also more interesting and how the equity market operates. We started out with a simple linear regression, but since we are modelling the earnings yield and not changes in the earnings yield we could not get rid of the autocorrelation in the residuals, which is a key violation of the linear regression model assumptions. We therefore ended up with a random forest model which is a less strict model in terms of assumptions of residuals and the underlying distribution of the data. Our final model consists of 25 features describing different aspects of the US economy and financial markets.
From the random forest model we can compute the feature importance and based on the model output the features (ordered with the most important at the top) below are the ones that explain 50% of S&P 500 12-month forward earnings yield. The two most important features are the NAHB Index taking the temperature in the US housing market and consumer confidence. These two indicators remain currently above their historic average, but both are at risk with tighter financial conditions (and higher mortgage rates) and rising inflation putting pressure on consumers. The third most important feature in explaining the S&P 500 earnings yield is the yearly change in US home prices. In other words, the US housing market is very important for US equity valuations.
Is the S&P 500 earnings yield at fair value?
Based on the model fit we can see whether the current 12-month earnings yield on the S&P 500 makes sense given the US economic backdrop. The current 12-month forward earnings yield on the S&P 500 is 5.15% or 19.4 in P/E terms and the model says the earnings yield should be 5.31% or 18.8 in P/E, based on the historical relationship between the earnings yield and the features, which is a small mispricing of 3%. In other words, given the current macro indicators the S&P 500 is correctly priced as you would expect is an efficient market.
What happens if we make a new prediction given that we change the most important features to some new values that are mostly in a worse direction?
Based on the above changes holding the other variables constant, the model would predict an earnings yield of 18.2 or 6% below the current earnings yield.
Overreactions in the equity market
What is the most interesting about modelling the earnings yield on the S&P 500 with macro variables is that the earnings yield is consistently below the model’s earnings yield during the dot-com bubble period and the recent pandemic. The US equity market during these two periods is reflecting something else than the underlying macro indicators. Both periods were driven by excess investor sentiment and optimism leading to an overreaction relative to the economy. While the difference between the actual earnings yield and the model’s earnings yield is persistently negative over longer periods during sentiment-driven periods of optimism, the difference also exhibits short-lived spikes on the upside (the earnings yield being higher than the predicted value by the model).
There are four distinct periods where the equity market overreacts with a too high earnings yield relative to the macro backdrop and those are in late 2002 to early 2003 before the equity market bottoms out for good post the dot-com collapse, 2008-2009 during the financial crisis, late 2011 during the euro crisis, and again during in late 2018 during the Fed’s policy mistake on rates as the economy was deteriorating. In these periods the equity market is often driven by risk reductions and liquidity constraints accelerating selloffs more than what is warranted by economic data.
The important features are constantly changing
The final model is a random forest with its hyperparameters optimized using cross-validation. The model fit is based on the in-sample data using these optimized parameters. The idea is to explain the variance and not make predictions on future values of the earnings yield. In the cross-validation the model error is considerably larger (three times larger) than the errors seen in the in-sample fit (actual earnings yield vs the model’s earnings yield). What we see in the data is that the model’s ability to explain the variance in the earnings yield rapidly deteriorates after the model fit, which is not surprising.
The factors driving the earnings yield are time-varying and dynamic making the model inherently unstable. This means that the conclusions in this equity note are valid as of today but will begin changing over the next year. The US housing market has played a bigger role in the US economy since 1994 compared to the period before 1994, which likely explains its importance in explaining the earnings yield in the period 1994-2022. We expect other variables to grow in importance over time. Quarterly Outlook
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