*John Hussman will be speaking at the Wine Country Conference held in Sonoma, CA on May 1 ^{st} and 2^{nd}, 2014. Net proceeds from the conference will go to the Autism Society of America for grant requests focusing on high-impact programming for individuals on the autism spectrum and their families. More information at www.winecountryconference.com.*

The equity market remains valued at nearly double its historical norms on *reliable* measures of valuation (though numerous *unreliable* alternatives can be sought if one seeks comfort rather than reliability). The same measures that indicated that the S&P 500 was priced in 2009 to achieve 10-14% annual total returns over the next decade presently indicate estimated 10-year nominal total returns of only about 2.7% annually. That’s up from about 2.3% annually last week, which is about the impact that a 4% market decline would be expected to have on 10-year expected returns. I should note that sentiment remains wildly bullish (55% bulls to 19% bears, record margin debt, heavy IPO issuance, record “covenant lite” debt issuance), and fear as measured by option volatilities is still quite contained, but “tail risk” as measured by option skew remains elevated. In all, the recent pullback is nowhere near the scale that should be considered material. What’s material is the *extent* of present market overvaluation, and the continuing breakdown in market internals we’re observing. Remember – most market tops are not a moment but a process. Plunges and spikes of several percent in either direction are typically forgettable and irrelevant in the context of the fluctuations that occur over the complete cycle.

The Iron Law of Valuation is that every security is a claim on an expected stream of future cash flows, and given that expected stream of future cash flows, the *current price* of the security moves opposite to the *expected future return* on that security. Particularly at market peaks, investors seem to believe that regardless of the extent of the preceding advance, future returns remain entirely unaffected. The repeated eagerness of investors to extrapolate returns and ignore the Iron Law of Valuation has been the source of the deepest losses in history.

A corollary to the Iron Law of Valuation is that one can only reliably use a “price/X” multiple to value stocks if “X” is a *sufficient statistic* for the very long-term stream of cash flows that stocks are likely to deliver into the hands of investors for decades to come. Not just next year, not just 10 years from now, but as long as the security is likely to exist. Now, X doesn’t have to be *equal* to those long-term cash flows – only *proportional* to them over time (every constant-growth rate valuation model relies on that quality). If X is a sufficient statistic for the stream of future cash flows, then the price/X ratio becomes *informative* about future returns. A good way to test a valuation measure is to check whether variations in the price/X multiple are closely related to *actual subsequent returns* in the security over a horizon of 7-10 years.

This is very easy to do for bonds, especially those that are default-free. Given the stream of cash flows that the bond will deliver over time, the future return can be calculated by observing the current price (the only variation from actual returns being the interest rate on reinvested coupon payments). Conversely, the current price can be explicitly calculated for every given yield-to-maturity. Because the stream of payments is fixed, par value (or any other arbitrary constant for that matter) is a sufficient statistic for that stream of cash flows. One can closely approximate *future* returns knowing nothing more than the following “valuation ratio:” price/100. The chart below illustrates this point.

[Geek's Note: the estimate above technically uses logarithms (as doubling the bond price and a halving it are “symmetrical” events). Doing so allows other relevant features of the bond such as the maturity and the coupon rate to be largely captured as a linear relationship between log(price/100) and yield-to-maturity].

Put simply, every security is a claim on some future expected stream of cash flows. For any given set of expected future cash flows, a higher price implies a lower future investment return, and vice versa. Given the price, one can estimate the expected future return that is consistent with that price. Given an expected future return, one can calculate the price that is consistent with that return. A valuation "multiple" like Price/X can be used as a shorthand for more careful and tedious valuation work, but *only* if X is a sufficient statistic for the long-term stream of future cash flows.

Margins and Multiples

The Iron Law of Valuation is equally important in the stock market, as is the need for *representative* measures of future cash flows when investors consider questions about valuation. It’s striking how eager Wall Street analysts become – particularly in already elevated markets – to use *current earnings* as a sufficient statistic for long-term cash flows. They fall all over themselves to ignore the level of profit margins (which have *always* reverted in a cyclical fashion over the course of *every* economic cycle, including the two cycles in the past decade). They fall all over themselves to focus on price/earnings multiples alone, without considering whether those earnings are representative. Yet they seem completely surprised when the market cycle is completed by a bear market that wipes out more than half of the preceding bull market gain (which is the standard, run-of-the-mill outcome).

The latest iteration of this effort is the argument that stock market returns are *not* closely correlated with profit margins, so concerns about margins can be safely ignored. As it happens, it’s *true* that margins aren’t closely correlated with market returns. But to use this as an argument to ignore profit margins is to demonstrate that one has not thought clearly about the problem of valuation. To see this, suppose that someone tells you that the length of a rectangle is only weakly correlated with the area of a rectangle. A moment’s thought should prompt you to respond, “of course not – you have to know the height as well.” The fact is that length is not a good sufficient statistic, nor is height, but the *product* of the two is identical to the area in every case.

Similarly, suppose someone tells you that the size of a tire is only weakly correlated with the number of molecules of air inside. A moment’s thought should make it clear that this statement is correct, but incomplete. Once you know both the size of the tire *and* the pressure, you know that the amount of air inside is proportional to the product of the two (Boyle’s Law, and yes, we need to assume constant temperature and an ideal gas).

The same principle holds remarkably well for equities. What matters is *both* the multiple and the margin.

Wall Street – You want the truth? *You can't handle the truth!* The truth is that in the valuation of broad equity market indices, and in the estimation of probable future returns from those indices, *revenues* are a better sufficient statistic than year-to-year earnings (whether trailing, forward, or cyclically-adjusted). Don’t misunderstand – what ultimately drives the value of stocks is the stream of cash that is actually delivered into the hands of investors over time, and that requires earnings. It’s just that profit margins are so variable over the economic cycle, and so mean-reverting over time, that year-to-year earnings, however defined, are flawed sufficient statistics of the *long-term* stream of cash flows that determine the value of the stock market at the *index* level.

As an example of the interesting combinations that capture this truth, it can be shown that the 10-year total return of the S&P 500 can be reliably estimated by the log-values of two variables: the S&P 500 price/book ratio and the equity turnover ratio (revenue/book value). Why should these unpopular measures be reliable? Simple. Those two variables – *together* – capture the valuation metric that's actually relevant: *price/revenue*. If you hate math, just glide over any equation you see in what follows – it’s helpful to show how things are derived, but it’s not required to understand the key points.

price/revenue = (price/book)/(revenue/book)

Taking logarithms and rearranging a bit,

log(price/revenue) = log(price/book) + log(book/revenue)

If price/revenue is the relevant explanatory variable, we should find that in an unconstrained regression of S&P 500 returns on log(price/book) and log(book/revenue), the two explanatory variables will be assigned nearly the *same* regression coefficients, *indicating that they can be joined without a loss of information*. That, in fact, is exactly what we observe.

Similarly, when we look at trailing 12-month (TTM) earnings, the TTM profit margin and P/E ratio of the S&P 500 are all over the map. When profit margins contract, P/E ratios often soar. When profit margins widen, P/E ratios are suppressed. All of this introduces a terrible amount of useless noise in these indicators. As a result, TTM margins and P/E ratios are notoriously unreliable *individually* in explaining subsequent market returns. But use them together, and the estimated S&P 500 return has a 90% correlation with actual 10-year returns. Moreover, the two variables – again – come in with nearly identical regression coefficients. Why? Because they can be *joined* without a loss of information, that is, the individual components contain no *additional* predictive information on their own. Just like the area of a rectangle and Boyle’s Law:

price/revenue = (earnings/revenue)*(price/earnings)

Again taking logarithms

log(price/revenue) = log(profit margin) + log(P/E ratio)

The chart below shows this general result across a variety of fundamentals. In each case, the fitted regression values have a greater than 90% correlation with actual subsequent 10-year S&P 500 total returns. Let’s be clear here – I’m not a great fan of this sort of regression, strongly preferring models that have structure and explicit calculations (see for example the models presented in It is Informed Optimism to Wait for the Rain). The point is that one can’t cry that “profit margins aren’t correlated with subsequent returns” without thinking about the nature of the problem being addressed. The question is whether P/E multiples, or the Shiller cyclically-adjusted P/E, or the forward operating P/E, or price/book value, or market capitalization/corporate earnings, or a host of other possibilities can be used as *sufficient statistics* for stock market valuation. The answer is no.

What we find is that both *margins and multiples matter*, and they matter with nearly the same regression coefficients – all of which imply that *revenue* is a better sufficient statistic of the long-term stream of future index-level cash flows than a host of widely-followed measures. Emphatically, one should not use unadjusted valuation multiples without examining the relationship between the underlying fundamental and revenues. That is why we care so much about record profit margins here.

Note that in each of these regressions, the coefficients *could* place a low weight on profit margins and other measures that are connected with revenues, if doing so would improve the fit. They *could* place significantly different coefficients on margins and multiples, if doing so would improve the fit. They just don’t, and like the area of a rectangle and Boyle’s Law, this tells you that it is the *product* of the two measures that drives the relationship with subsequent market returns.

[Geek’s Note: Gross value added (essentially revenue of U.S. corporations including domestic and foreign operations) is estimated as domestic financial and nonfinancial gross value added, plus foreign gross value added of U.S. corporations inferred by imputing a 10% profit margin to the difference between total U.S. corporate profits after tax and purely domestic profits. Varying the assumed foreign profit margin has *very* little impact on the overall results, but this exercise addresses the primary distinction (h/t Jesse Livermore) between normalizing CPATAX by GDP versus normalizing by estimated corporate revenues.]

To illustrate these relationships visually, the 3-D scatterplot below shows the TTM profit margin of the S&P 500 along one bottom axis, the TTM price/earnings ratio on the other bottom axis, and the actual subsequent 10-year annual total return of the S&P 500 on the vertical axis. This tornado of points is not distributed all over the map. Instead, you’ll notice that the worst market returns are associated with points having two simultaneous features: not only above-average profit margins, but elevated price/earnings multiples as well. This combination is wicked, because it means that investors are paying a premium price per dollar of earnings, where the earnings themselves are cyclically-elevated and unrepresentative of long-term cash flows. This is the situation we observe at present. It bears repeating that the S&P 500 price/revenue multiple, the ratio of market capitalization to GDP, and *margin-adjusted* forward P/E and cyclically-adjusted P/E ratios remain *more than double* their pre-bubble historical norms.

[Geek’s Note: On a 3-D chart where the Z variable is determined by the sum or product of X and Y, a quick way to visually identify the relationship is to view the scatter from either {min(X},max(Y)} or {max(X),min(Y)} as above].

The upshot is that regardless of the metrics used, S&P 500 nominal total returns in the coming decade are likely to be in the very low single digits – from current levels. But remember the Iron Law of Valuation – for a given stream of long-term expected cash flows, as valuations retreat, prospective returns increase. This should be a cause for *optimism* about future investment opportunities. Unfortunately, not present ones.