Over the last month I have examined (what I think is) some of the most interesting data about the S&P 500. First up was the level volatility, which demonstrates that the market is not more efficient now than in decades past. Then I covered the history of the volume of the S&P 500; where we learned that almost 90% of the volume of this storied index has taken place in the last 20 years. More recently, I discussed the history of sigma events. Today I want to cover the history of the S&P 500 and its equity risk premium.

### Equity Risk Premium Defined

One of my favorite measures of equity market valuation is the equity risk premium (ERP). For those of you not in the know, the ERP is:

The difference in return available by investing in equities rather than a “risk-free rate.”

Setting aside the idea that I do not believe in a so-called “risk-free rate” [see: Rethinking the Risk-Free Rate, Exploding a Fundamental Assumption], my definition is ever so-slightly different than the standard definition. Specifically, my definition states that the ERP is *the difference in return* rather than the more traditional *excess return* language. Why?

### The Equity Risk Premium Can be Negative

First, and most importantly, there are periods in financial market history where fixed income, including government debts, outperform equities. How does the ERP defined as *excess return* explain these periods? It cannot.

Second, our understanding of the ERP comes from the Capital Asset Pricing Model (CAPM). Here, by definition, all increases in return over the “risk-free rate” is earned only by taking on additional risk. Consequently, the ERP has to be positive because it is assumed that the “risk free rate” is the starting/base rate for all other rates of return. Because equities are not “risk free” they have to offer an excess return relative to riskless assets. Otherwise, why invest in them? Parenthetically, in a world of constrained-by-style-box/asset-class investment management most investors at the security selection level do not have permission to compare and contrast expected returns in different asset classes. In other words, markets can defy theory. Said another way, theory ought to describe markets, and they don’t. In fact, they contribute to the very outcomes that defy themselves. But I digress.

Third, my preferred mathematical description of the ERP can and does go negative at times. And, it turns out, those are very interesting moments in financial market history. Further, those moments are predictive of future outcomes.

### My Mathematical Definition of the ERP

There are many different mathematical definitions of the ERP. However, my favorite ERP mathematical definition, and shared by other investors, though not all, is:

ERP = (1 ÷ Shiller Cyclically Adjusted Price to Earnings (CAPE) Ratio) – current yield on 10-year US Treasury bonds

For those in the know the first part of this equation can also be described as the “earnings yield.” It is simply the inversion of the P/E ratio. I prefer CAPE because of its adjustment for monkey business in financial statements, and its longer term focus on earnings. The academic ideal is to have a CAPE and Treasury whose time horizon matches your own.

### Advantages of This CAPE Version

- Easy to gather the data.
- Adjusts for monkey business in financial statements.
- Long time horizon.
- It makes sense.
- Predictive of future returns/good buying opportunities.

I talk about number 5 in my relating of the ERP data below. But, regarding “it makes sense” there are several points to make.

Earnings over time (as in the denominator of a P/E) are the yield on me owning the equity of a business. Furthermore, those earnings are purchased in a market for a price (P/E numerator). That said, if the prospects for future returns on equities are bad, to highlight the difference, I want an uncorrelated asset for comparison. In this case, the performance of Treasury securities tend not to correlate well with the equity risk premium. In fact, since January 1881 the correlation between these two measures is -47.3%.

Also, I reject the CAPM as predictive of future securities prices. In fact, it has been so beyond debunked for the past 50 years that it is a miracle it is still given credence. I also reject the idea of a risk free rate. In a universe of preferences and actions, there is always the chance that your preferred outcome after taking an action does not occur. Risk exists in a universe of action…period. I also reject the idea that financial markets are always rational. Instead investors are irrational (see my first Fact File article in this series), and the way assets are allocated in the aggregate is completely irrational and it leads to nonsensical investment choices, like pretending the style box is a valid way to invest. Thus, we ought to expect negative ERPs over time, and ding-ding-ding that is exactly what we see in the data. From a sheer intellectual, logical point of view, equities are always riskier than the safest Treasury, but in practice their pricing does not always reflect that logic.

Contact me so that I can help your investment firm. I make my living as a consultant, not as a writer. My job is to help you and your investment team get better.

Related: S&P 500 Level Volatility … Is the Market Efficient?