S&P 500 Historical Valuation

Dr. Robert Shiller is a leading authority on behavioral finance, a field that attempts to get at the heart of market economics. What’s at this heart? People, naturally. What’s the point? I argue that it behooves traders and investors alike to retain some degree of insulation from the general population’s view on value, and instead rely on a more rational definition of value. Schiller’s cyclically-adjusted Price-to-Earnings (CAPE) and Price-to-Earning-to-Growth (CAPEG) ratios are indeed very simple, rational, and hold a great degree of predictive power.

Behavioral finance straddles the academic disciplines of finance, economics, and cognitive psychology. In my view, it is one man’s best hopes at understanding asset valuation and bubbles. In comparison, the Capital Asset Pricing Model and other factor models (e.g., Fama-French, Carhart, BARRA, etc…), and the Arbitrage Pricing Theory admit more precision than the “nature of the subject admits” (Aristotle, Nicomachaen Ethics). While considered a post-Modern branch of economics, this central premise of Behavioral Finance builds on other neoclassical schools of economic thought, including one of my favorites, the Austrian School. In 1841, a Scotsman presaged Shiller with the book, “Extraordinary Popular Delusions and the Madness of Crowds“.

Schiller describes how our human condition leads to asset bubbles and also prevent us from learning from the past ones. In his book “Irrational Exuberance“, he looks specifically at how perception has changed the asset valuation over long stretches of history and from a macro-economic perspective. The eponymous website, http://www.irrationalexuberance.com/, has some great resources and links to historical data.

In the rational world, the actual value of a firm’s equity is equal to the present value of the sum of its future disbursements to its shareholders. In other words, profitability (i.e., “earnings”), the growth rate thereof (i.e., “earnings growth”), and expected future payouts (i.e., dividends, stock repurchases, capital gains) form the foundation of equity valuation.

In the worlds of “Irrational Exuberance” and “Extraordinary Popular Delusions and the Madness of Crowds“, the values placed on profitability and growth are in constant flux. The reason for this flux is that people are the drivers of markets, more so than natural laws governing supply and demand, and people are prone to oscillate between periods of mass euphoria and hysteria. And these periods can last a long time. A famous mis-attribution to John Maynard Keynes says it beautifully: “Markets can remain irrational longer than you can remain solvent”.

Reconciling these two seemingly opposed worlds is actually simple. Perceived value, rather than actual value, always determines price. And, in turn, price always determines actual value. Warren Buffet probably stated it more clearly when he wrote, “Price is what you pay. Value is what you get.”

I was up late one night (no surprise there), and wanted to get smart on equity valuation. I then stumbled upon some S&P 500 earnings data on Dr. Shiller’s site. After playing with his stupidsimple CAPE-10 model, I realized that it was actually really good! I then took a step further, asking, “What happen if I apply the ideas of inflation-adjustments and cyclical-adjustment to the PEG ratio?”. I stumbled upon the 10 Year Cyclically Adjusted Price-to-Dividends (CAPEG-10) ratio (where CAPEG10 uses the simple 10 year growth rate of real earnings). I humbly submit my findings below.

This chart show that, no matter how you slice it, perceived value on corporate profitability has varied significantly in the last 130 years. If you run the numbers, you will find the following relationships:

Correlation Matrix: S&P 500 Price

S&P 500 Price
CAPE 10 66.56%
PEG 10 47.67%

Correlation Matrix: Logarithmic Change of S&P 500 Price

1 Month Forward Log Change of S&P 500 Price 1 Quarter Forward Log Change of S&P 500 Price
Log Change of CAPE 10 27.77% 12.75%
Log Change of PEG 10 19.70% 6.43%

In other words, Shiller’s take on PE and PEG have a statistically significant ability to forecast equity returns for 1 to 3 months into the future.

Conventional value investing states that a PEG ratio under 1 constitutes a good value. However, this analysis suggests that PE ratios are more reliable than PEG ratios.  (which contradicts some schools of thought). Although growth is an important factor, we need something more robust than simply taking a ratio of a ratio (which causes PE to lose its value as a unit-less metric). Two popular methods, ‘discounted cash flows‘ and ‘sum of perpetuities‘, both can accommodate real and/or expected growth rates.

If you were to use the simpler of the two, the sum of perpetuities method, you would find that your fair value estimate does not correlate to the market price. The reality is that ‘Reality’ is very complex, and there are many variables and relationships between variables that can cause the actual and perceived value of the same thing to wax and wane (read more on the Theory of Value, Utility Theory of Value, and the Exponential Utility Function).

The beauty of Shiller’s work on historical P/E ratios is that it partially discounts complexity in favor of simplicity. It’s usually enough to accept the fact that perceived values of things varies over time, and depending on what’s being valued. If you’re buying a stock with a high P/E or P/E/G, it doesn’t necessarily mean that you’re paying too much or making a bad investment. What it does mean, however, is does mean that you’re paying more per unit of profitability than you could pay elsewhere (hopefully for a good reason).

As a next step, I would recommend taking a look at two analyses that examine earnings and price-to-earnings for different market sectors. Again, perceived value often depends on what’s being valued, and this information will arm you with tools that will help you decide how much you should pay. I highly recommend leveraging the following reports:

  1. FactSet’s Historical P/E Ratios by Sector (Dated 20130712) 
  2. Yardeni Research’s Earnings, Revenues, & Valuation: S&P 500 Sectors (Dated 20130718)