In seventh grade science class, we studied how things are classified – the systems used to organize various kinds of rocks, elements, species, different types of clouds. I’ve always liked the name “cumulonimbus” – the sort of big billowy heap of a cloud that has a dark grey underside – full of water, not yet transformed into rainfall. If you see those clouds and suddenly feel a cool breeze, that’s often the storm’s “gust front” racing ahead of the rain – and a good time to head for cover.
You wouldn’t look at the rainfall and think it has come from nowhere. Looking at the cloud, you know the rainfall was already there – just waiting for enough conditions to show itself. As warm, humid air rides up over the wedge of cooler air, the cloud builds – water vapor beading into droplets, gathering weight until they finally let go as rain.
We call rainfall a “conditioned” phenomenon because it depends on many other factors. When causes and conditions are sufficient, the rainfall manifests. When causes and conditions are no longer sufficient, the rainfall ceases to manifest.
We should be careful, when talking about rainfall, to consider the causes and conditions that produce rain. We might say the average amount of rainfall is this, or the average frequency is that, but if we don’t change our estimate even when there’s a cumulonimbus cloud over our head and a cool breeze in our hair, we may get soaked.
Likewise, suppose we look at historical stock market returns over any particular horizon, whether daily, weekly, or annual – regardless of valuations, market behavior, investor sentiment, monetary policy and other factors. We can collect all of those returns in a heap called an “unconditional” probability distribution. Historically, average annual market returns on the order of 10%, more or less, have been most common, so the heap is highest at that point, with progressively smaller “tails” for returns that are wildly positive or wildly negative. The overall profile looks roughly like a “bell curve.”
We might say the average market return is this, or the average frequency of a crash is that, but if we don’t change our estimate even when valuations are at the highest levels in history and market internals are ragged and divergent, we may get soaked.
It would be incorrect to say that the market plunges of 2000-2002 and 2007-2009 came from nowhere. Looking at a bubble, you know the crash is already there – just waiting for enough conditions to show itself.
Whatever market conditions may be, it can help to look at the probability distribution of returns, “conditional” on some important factor, or a combination of them. We can then ask questions like “What’s the profile of likely market returns and risk, given this or that set of conditions?” That’s what we call the “conditional” probability distribution. In nearly every case, the distribution includes both positive and negative outcomes. The average outcome may be higher or lower than the “unconditional” average, but even then, we typically can’t rule out outcomes on the opposite side. The best we can do is talk about the likely distribution of returns, rather than specific “point forecasts.” To interpret a distribution as a forecast is far too demanding about what’s possible.
That’s part of the reason we talk about the “return/risk profile” of the market, rather than relying on forecasts or scenarios. Nearly every market condition we identify is characterized by a distribution that includes both positive and negative returns, often quite large ones in both directions. To imagine that a probability distribution is a “forecast” is to be caught in a concept of reality. A classification or label – overvalued, undervalued, constructive, defensive – is only a tool that describes a distribution. It’s not something to take literally as a forecast.
The bell curves below show fitted probability distributions of actual weekly S&P 500 total returns since 1940. They’re not quite “lognormal” curves. The full distribution of S&P 500 returns has a slightly narrower peak, a bit of skew, and fatter tails than a classical bell curve. I’ve also included two “conditional” probability distributions – not because they’re great models, but simply to partition market conditions by a crude version of “valuation and market action” using commonly available indicators.
The blue curve is the “unconditional” probability distribution of weekly S&P 500 total returns. In contrast, the green and red curves are “conditional” – based on the “yield” implied by Shiller cyclically-adjusted P/E (CAPE) relative to 10-year bond yields, and the percentage of U.S. stocks “participating” in a market advance, as measured by their position relative to their own 200-day average. Geek’s note: each curve is defined by its own data subset, so the area under each is 1.0.
Notice that the conditional distributions include both positive and negative returns. For the red distribution, the average S&P 500 weekly total return is slightly positive, but lags T-bill returns by about 2% annually (that is, annualizing the cumulative S&P 500 returns that comprise the red distribution). In contrast, the average weekly return in the green distribution exceeds T-bill returns by close to 12% annually. The red distribution is the widest (has the highest “standard deviation”), while the green distribution is the narrowest. That means that unfavorable market conditions generally involve much greater volatility than favorable market conditions. Observe in particular how fat the tail of the red distribution is on the right side. When people say how much investors would lose by “missing the 10 best” days or weeks of market returns, keep in mind that these “rewarding” instances generally occur during periods when the market is crashing. ..........
The chart below shows the conditional distributions that we estimate based on our actual classification of market return/risk profiles – reflecting our adaptations in recent years – particularly in 2021 and 2024. I’ve condensed them into just two groups – bearish/hard-negative (which includes neutral positions) and leverage/constructive. There are more subtle variations in practice, but two “conditional distributions” are enough to illustrate the key idea.
While the overall profile of these distributions is similar to the previous ones that use crude gauges to classify market conditions, the average returns are profoundly different. In the red distribution, average S&P 500 total returns are negative, and lag T-bills by about -22% annualized. In the green distribution, average total returns exceed T-bills by about 28% annualized. There’s no assurance that future returns will be similar, but we see the same overall profile in subsets of the data across history, from the recent bubble all the way back to the Great Depression ...................

Every market return/risk profile we define maps into a probability distribution that includes both positive and negative outcomes. The average returns may be extremely different, but any individual outcome is largely unpredictable. It’s only by aligning our outlook with prevailing market conditions – again, and again, and again – that we have an expectation that our returns will capture some of those differences as investment returns.
Record extremes
Presently, the U.S. equity market stands at the most extreme valuations in history, on the measures we find best correlated with actual subsequent market returns across a century of market cycles. The chart below shows our most reliable gauge of market valuations in data since 1928:
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Our outlook will continue to change as measurable, observable market conditions change. In our view, the best way to take good care of the future is to take good care of the present moment – again, and again, and again. No forecasts or scenarios are required.
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