*Excerpt from the Hussman Funds' **Weekly Market Comment** (7/14/14):*

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.

...

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 holdsregardlessof 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 amathematical 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 theactual subsequentpercentage change in price.

...

The upshot is that given a reasonable projected growth rate g for some smooth fundamental, and a reasonable assumption about the future price/fundamental ratio, one can estimate the long-term expected return that is consistent with current price levels.Not with back-fitting, but with straightforward arithmetic. Notice that if the fundamental enjoys a surprising “error” by growing faster than expected over the T-year period, it’s also likely that the future price/fundamental ratio at the end of T years will be lower than one would have expected. The fact that these “errors” offset in a way that preserves overall accuracy should not be surprising.

For numerous smooth fundamentals, including the Shiller CAPE (S&P 500 / 10-year smoothed inflation-adjusted earnings), S&P price/revenue, and even market capitalization / nominal GDP, this relationship has provided clear guidance about expected market returns across a century of market history, andhas not failed at alleven in recent decades.

It’s certainly possible to turn this into a “real” model by introducing additional assumptions about future inflation, but one can easily show that inflation works its way through the arithmetic so that the expectedrealreturn is simply the expectednominalreturn as calculated above, minus whatever inflation figure one might have assumed. Whether one discounts nominal fundamentals with a nominal discount rate or real fundamentals with a real discount rate, one obtains the same price/fundamental ratio.

...

Ockham’s razor and the half-cycle since 2009

What then, is one to make of the challenges we’ve experienced in the half-cycle since 2009, after coming through so strongly in previouscompletemarket cycles? There are several possibilities. One is the explanation that is consistent with everything I’ve written and all that has occurred in real-time during this half-cycle: that I insisted on stress-testing our methods against Depression-era outcomes in a fiduciary decision that I made – in hindsight – at the worst possible time, that we missed a strong market rebound in the interim of addressing that “two-data sets problem,” that we did encounter a truly “different” element in the current cycle to the extent that severely overvalued, overbought, overbullish conditions have persisted much longer than has historically been the case – primarily because of Fed-induced yield seeking, that we believe the severe consequences of these extremes have merely been deferred rather than avoided, and that while we do remain defensive here because of how extreme and uncorrected conditions have become, I also strongly believe that we’ve adapted to the potential for these speculative, yield-seeking episodes without the likelihood of similar challenges in future cycles.

An alternative explanation for our challenges in this half-cycle is that I’m simply a permabear. But that’s harder to square with my being a fully-leveraged “lonely raging bull” in the early 1990’s, or with our strongly constructive shift (despite valuations that were still elevated relative to historical norms) in early 2003 as a new bull market was taking hold, and is also inconsistent with our similarly constructive shift after the market plunge in 2008. I’ve consistently observed that the strongest return/risk profiles are associated with at least a moderate retreat in valuations coupled with an early improvement in market action. Indeed, I observed the same thing in late-2008 (see Why Warren Buffett is Right and Why Nobody Cares). The challenge in the half-cycle since 2009 is that when we examined measures of “early improvement” that were quite effective in post-war data, they were much more vulnerable to whipsaws and large interim losses in Depression-era data, and coupled with economic and financial collapse that was “out of sample” from a post-war perspective, I felt a fiduciary duty to stress test our methods. We haveeveryexpectation of shifting our investment stance in response to evidence of a favorable shift in the market return/risk profile, and we have every reason to expect that the completion of the present market cycle will provide that opportunity at significantly lower levels than we presently observe.

It’s easier to assume that I have a permabearish outlook on the market, and until we demonstrate otherwise, it’s reasonable to wonder whether we’ll maintain our tendency of being early at market peaks (my expectation is yes, somewhat, but far less in coming cycles than one would infer from pre-crash bubbles in recent memory). Broadly speaking though, the permabear hypothesis is inconsistent with the evidence. As Einstein said, a theory should not be so simple that it does not conform to reality. We’ve extensively discussed why challenges emerged in this half-cycle. We’ve detailed what we’ve done to address them. I have greater confidence about our approach than at any time in the decades I’ve been in this profession. But people can believe what they wish. We don’t have any interest in drawing investors to our case, or in urging investors to sell the market, as someone else would have to hold stocks at these prices regardless. We’ve never had a marketing or advertising department. We’re content to articulate and adhere to our discipline for those who find or expect those efforts to be useful, without any expectation of changing anyone else’s mind. Maybe I’m the only guy left who isn’t willing to abandon the lessons of history to “get in on this.” Then again, maybe when a lopsided majority thinks the same thing about the market, it’s time to think for yourself.

...

On the circular relationship between valuation and expected return

For any given set of expected future cash flows, there is a circularity: you tell me the price, and I can tell you the long-term return you can expect over time. Conversely, you tell me the long-term return you want to achieve, and I can tell you the price that would be consistent with that expected return. In other words, there is a direct arithmetic mapping from price to expected return and vice versa.

A widespread misunderstanding comes in when people start using the phrase “fair value.” For any given set of expected future cash flows, if you tell me the price, I can tell you the long-term return, period. If you tell me the long-term return, I can tell you the price, period. Nothing changes this. If you want to say that lower interest rates “justify” a low expected return, and therefore justify a higher price, that’s fine. Just understand that the low expected return willstillfollow that higher price. If you want to say that in a zero interest rate world, stocksshouldbe priced for zero expected returns over the next 8 years, I have no problem with the conclusion that under that assumption, stocks are at “fair value” here. Just understand that under that conception of “fair value” stocks canstillbe expected to return nothing over the next 8 years. What is emphatically not true, and not mathematically consistent, is to say that low interest rates “justify” a low expected return, and therefore justify a higher price, but then to turn around and say that since stocks are “fairly valued” under that assumption, they can be expected to achieve normal returns in the future.

For that reason, we are much more comfortable estimating long-term total returns directly, rather than converting them to a price that we think is “fair.” The “fair” price always embeds some assumption about future returns, and investors may very well differ on what is fair. Frankly, if you think that an asset class that is quite capable of repeatedly losing half of its value should compensate for that risk with historically normal total returns of about 10% annually over time, I would tell you that “fair value” is about 950 on the S&P 500.