# Ockham's Razor and the Market Cycle - John Hussman

July 14, 2014

Ockham’s razor is a principle that states that among various hypotheses that might be used to explain a set of observations, the hypothesis – consistent with the evidence – that relies on the smallest number of assumptions is generally preferred. Essentially, the razor shaves away what is unnecessary and retains the most compact explanation that is consistent with the data. The same basic principle runs through the history of thought from Ptolemy (“We consider it a good principle to explain the phenomena by the simplest hypothesis possible”) to Einstein (“A theory should be made as simple as possible, but not so simple that it does not conform to reality”).

Suppose, for example, that one periodically sets hot cherry pies near the window to cool, and sometimes they disappear, with an empty pie tin usually later found in the kids’ treehouse, and cherry stains around their lips. When pies go missing, one would normally not assume that aliens had come down to earth, taken the pie, devoured it in mid-air, brushed by the kids’ lips leaving cherry stains in the process, erased the kids’ memory, discarded the tin in the treehouse, and then returned to Xenon.

When we observe the increasingly tortured arguments that “this time is different,” we see investors discarding straightforward explanations that are fully consistent with the evidence and opting instead for the aliens-from-Xenon theory.

Valuations

Let’s start with valuations and expected long-term returns. For well over a quarter of a century, I've used the same essential set of calculations to project long-term returns for the S&P 500, typically on horizons of 7-10 years. These models are not “back-fitted” to the data, but are instead straightforward arithmetic. Let’s do that arithmetic. If math makes your head hurt, just skim through what follows till the pain stops:

Price = Price

Price = Fundamental * Price/Fundamental

Price_future = Fundamental_future * Price_future/Fundamental_future

Price_today = Fundamental_today * Price_today/Fundamental_today

Price_future/Price_today =
Fundamental_future/Fundamental_today * (P/F_future / P/F_today)

Note that this holds regardless of what fundamental we use, but ideally, we would like to use some fundamental that is relatively smooth, so that the growth rate of that fundamental is not highly volatile over time. Notice also that what we have here is a mathematical identity, which can also be written in terms of annual returns and growth rates. Observe that:

Expected annual capital gain = {Price future / Price_today}^(1/T) – 1

where T is some number of years into the future. Similarly:

Annual growth of the fundamental = {Fundamental_future/Fundamental_today}^(1/T) – 1

Writing the expected annual growth rate of the smooth fundamental as “g”, we can combine all of this to:

Expected annual capital gain = (1+g) * [P/F_future / P/F_today]^(1/T) – 1

Now for total returns, one needs to include dividend income. A rough estimate of that is simply to add in the current dividend yield. But given that the price/fundamental ratio may change over time, and that dividends are likely to grow roughly alongside other smooth fundamentals, a better estimate of average dividend income over time is the average of the current dividend yield and the yield that is likely to prevail at the expected future price/fundamental ratio. I trust it’s easy enough to demonstrate that this works out to:

Expected dividend income = dividend yield * (1 + P/F_today / P/F_future)/2

So it’s a mathematical identity and an implication of basic arithmetic that one can estimate the T-year nominal total return of stocks as:

Expected annual total return =
(1+g)*[P/F_future / P/F_today]^(1/T) + dividend yield * (1 + P/F_today / P/F_future)/2 – 1

Again, it’s helpful to use smooth fundamentals that have relatively stable growth rates over time, and where the price/fundamental ratio tends to mean revert. As I demonstrated in my Wine Country Conference talk, VeryMean Reversion, the proper test of mean reversion is not whether the P/F ratio itself “looks” like it mean reverts. Rather, the proper test of mean reversion is actually whether the log(P/F) ratio is inversely correlated with the actual subsequent percentage change in price.

For practical purposes, the most accurate horizon for these estimates is about 1.5 market cycles (again, see the WCC talk to understand why), which works out to a 7-10 year horizon. The best choice for "P/F_future" on this horizon is the norm that is associated with reasonably normal market returns (using the pre-bubble average works well, but the overall calculation can be done repeatedly for various assumptions, as we typically do in practice. See my calculations in 2000 for example). As for g, growth in nominal GDP, corporate revenues, and corporate earnings in the U.S. is quite stable at about 6% annually from peak-to-peak across economic cycles - regardless of the rate of inflation (there are economic reasons for this relating to the exchange equation MV = PY, which implies %P = %M + %V - %Y and is reflected empirically in a tendency for real growth and inflation to be negatively correlated, but I'll leave more equations for another time).

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