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March 14, 2005

Getting Un-Specific: Point Forecasts vs Probability Distributions

John P. Hussman, Ph.D.
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One of the important elements of our investment approach is the distinction between "point forecasts" and "probability distributions." A point forecast is a specific prediction about the future, such as "the S&P 500 will decline by 4% over the coming 6 months." In contrast, a probability distribution specifies an entire range of possible future outcomes. Typically, these distributions are shaped like a "bell curve:" if you draw a graph with the possible outcomes (negative to positive) along the bottom, with the height of the graph being the probability of each outcome, the graph starts with a low probability of extremely negative outcomes, rises to higher probabilities for outcomes near the average of the distribution, and then tails off with a low probability of extremely positive outcomes.

Clearly, making point forecasts (and trying to rely on them) is much more ambitious and demanding than identifying a probability distribution. To say "the market will rise by 8% in the coming 12 months" is definitely not the same thing as saying "the probability distribution for future 12-month returns has an average of 8% and a standard deviation of +/- 10%, so roughly speaking, if we draw from this distribution again and again and again, about two-thirds of the outcomes would be between -2% and +18%, and about one-third of the outcomes would be more extreme in one direction or another."

Notice the difference. A point forecast assumes that you can actually identify what the next "draw" from the probability distribution will be. In contrast, a probability distribution says something about the entire range of outcomes and their relative likelihood, without any presumption that the next specific outcome can be predicted.

As I frequently note, to identify a "Market Climate" does not imply a useful forecast of upcoming returns for the specific period ahead. Every Climate we identify includes both positive and negative returns, including large ones. Investors who believe that success lies in correctly "calling" short-term rallies and declines in the market invite endless frustration. It's probably true that the only way to consistently earn short-term profits is to consistently make correct short-term trades. But that's why consistent short-term profits are a pipe dream.

Fortunately, it's reasonably possible to identify different probability distributions in the market on the basis of valuations and the quality of market action. For instance, the combination of favorable valuation and favorable market action has historically been associated with high average returns and reasonably limited volatility. That Climate still includes some periods of decline, and even a few deep ones, but they're relatively few in number. In contrast, the combination of unfavorable valuations and unfavorable market action is a Climate that captures every major market crash on record. Even so, that Climate also includes some periods of very positive returns, despite the poor average return/risk profile. So while it's not possible (to my knowledge) to isolate conditions that have produced strictly positive or negative returns, there's a great deal of evidence that some distributions are much better than others in terms of their average risk/return profiles, and that taking more risk in those, and less risk in unfavorable distributions, is a useful way to approach long-term, risk-controlled investing.

Market timing versus "conditional investing"

Market timers like to think that it is possible to make accurate point forecasts about future market direction. Good investors usually reject this as fantasy, and believe instead that different market conditions (in our case, valuation and the quality of market action) result in different probability distributions. We invest based on the overall return/risk profile of the probability distribution that we think best describes likely market returns, based on existing market conditions.

For example, based on current valuations and market action, the probability distribution of likely stock market returns is generally positive but not very satisfactory from a return/risk standpoint. Though valuations are very rich, the quality of market action is still modestly resilient (though gradually deteriorating). Looking at short-term returns that this Climate has historically produced, the resulting probability distribution has an average annualized return of about 3%, but includes periods where stocks have achieved both more positive and negative returns. As one looks at longer-term returns produced from periods starting in this Climate, average returns become slightly negative. Not only does the entire curve shift lower, but the tail of positive returns becomes thinner and the tail of negative returns fattens.

Clearly, our reasonably defensive investment position here is not a forecast that the market will decline. Frankly, I have no idea whether the next "draw" from this distribution will be positive, negative, or flat. But on average, over a repeated number of draws, the tradeoff between prospective return and risk is not impressive. As a result, I've limited the exposure of the Strategic Growth Fund to overall market fluctuations. The principle is simple - take more risk in Climates where risk is well rewarded, on average, and less when it is not.

A look at good value managers shows the same general approach. As reporter John Waggoner points out, many of the best performing value managers are currently holding unusually large cash positions, including FPA Capital, Yacktman Fund, Longleaf Partners, Weitz Value, Royce Special Equities, and of course, Warren Buffett at Berkshire Hathaway. None of these investors see themselves as market timers. Rather, they understand that different conditions give rise to different outcomes, on average. They believe that on average, the probability distribution of returns is better when stocks are cheap than when they are expensive, and they believe in varying their exposure to risk based on that general principle, but none of them bother with point forecasts.

In his latest annual report ( ), Warren Buffett is clear in his understanding that the likely probability distribution of future market returns doesn't match the historical one, and that even the average return of a distribution isn't a very useful point forecast: "In one respect, 2004 was a remarkable year for the stock market, a fact buried in the maze of numbers on page 2. If you examine the 35 years since the 1960s ended, you will find that an investor's return, including dividends, from owning the S&P has averaged 11.2% annually (well above what we expect future returns to be). But if you look for years with returns anywhere close to that 11.2% - say, between 8% and 14% - you will find only one before 2004. In other words, last year's "normal" return is anything but."

Call it what it is

In my view, there's a distinction between "investing" and "speculation." To invest means to purchase a stream of future cash flows at a reasonable price. Successful investing, then, is making that purchase at a low enough price that the future cash flows will represent a satisfactory long-term return on the investment. Warren Buffett is clearly an investor in the classic, strict value sense of the term.

Speculation, on the other hand, is to risk money in anticipation of a profit, on average. Notice that speculation does not require "value" in the sense of long-term cash flows being appropriately priced. It only requires that the transactions are profitable, on average, over repeated and generally short-term holding periods. If an individual has some basis to expect that profitability, and can routinely speculate in a way that produces value without excessive risk, then it's rational speculation. But it's a decidedly short-term activity that shouldn't be confused with investing. When investors confuse speculative gains with "investment returns" (as they seem to be doing at present) they leave themselves vulnerable to major losses when valuations normalize.

Finally, there's a general term for risking money in expectation of a profit in a specific instance - it's called gambling. Notice that while rational speculation is based on repeated transactions that are expected to be profitable on average, gambling is distinguished by the expectation of a profit in a single instance, even if the odds are against the gambler on average. It amazes me how much of the activity in the financial markets (particularly trades that chase short-term market movements or investment performance) is little more than this sort of gambling.

In my view, the foundation of long-term returns is careful value-based investing. But there are enough speculative periods in the market where valuations depart from the norm (sometimes for very long periods of time) that the quality of market action and the speculative mood of investors cannot be overlooked. Historically, major market plunges have required not only high valuations, but also a measurable skittishness toward risk that can be inferred from the quality of market action. It's important, however, to understand that "speculative merit" can vanish quickly, and it is bad risk management to assume that overvaluation can ever be ignored.

At best, investors can rely only on probability distributions, not on point forecasts. Our job isn't to eliminate or ignore uncertainty, but to allow for it, to become comfortable with it, and to manage it well.

Market Climate

As of last week, the Market Climate in stocks remained characterized by unusually unfavorable valuations and still modestly favorable market action. That said, market action has taken on an increasingly tenuous quality in recent weeks, with breadth, leadership and interest rates acting poorly, along with generally deteriorating action in bank and financial stocks (which currently represent the largest segment of market capitalization). Against that, the market has retreated substantially in recent sessions and is now modestly oversold on a number of measures, which creates the possibility of a typical "fast, furious, prone to failure" advance to clear that condition.

Needless to say, it's not an environment in which point forecasts are likely to be very accurate - stocks being on one hand close to a dangerously negative shift in the Market Climate, yet at the same time being in a position that allows for a leaping rally. For our part, the Strategic Growth Fund remains about 70% hedged against the impact of market fluctuations with matched long put / short call positions (which behave as interest-bearing short sales on the S&P 100 and Russell 2000 indices), with the remaining 30% of our stock exposure hedged with put options only, leaving some amount of upside potential in the event that the market advances here. In addition, I purchased a moderate number of inexpensive call options in the Fund near Friday's close to provide for the potential for the market to recover and maintain a constructive Climate, without substantially expanding our risk in the event of a further market deterioration.

In bonds, we have a similar situation, with the Market Climate characterized by unfavorable valuations and moderately unfavorable market action, but with several measures suggesting a short-term oversold condition in the Treasury market. We continue to carry a limited duration of about 2.8 years in the Strategic Total Return Fund (meaning that a 100 basis point change in interest rates would be expected to impact the Fund by about 2.8% on the basis of bond price fluctuations). A substantial change in our duration profile would require an improvement in either valuations (through an increase in yields or a moderation in economic growth or inflation pressures) or an improvement in market action. A substantial widening of credit spreads or other indicators of default risk would also tend to support higher Treasury bond durations. For now, however, we continue to hold a limited exposure to interest rate risk. The Fund continues to carry an allocation of about 20% of assets to precious metals shares, which remain in a generally positive Market Climate on our measures.


The foregoing comments represent the general investment analysis and economic views of the Advisor, and are provided solely for the purpose of information, instruction and discourse.

Prospectuses for the Hussman Strategic Growth Fund, the Hussman Strategic Total Return Fund, the Hussman Strategic International Fund, and the Hussman Strategic Dividend Value Fund, as well as Fund reports and other information, are available by clicking "The Funds" menu button from any page of this website.

Estimates of prospective return and risk for equities, bonds, and other financial markets are forward-looking statements based the analysis and reasonable beliefs of Hussman Strategic Advisors. They are not a guarantee of future performance, and are not indicative of the prospective returns of any of the Hussman Funds. Actual returns may differ substantially from the estimates provided. Estimates of prospective long-term returns for the S&P 500 reflect our standard valuation methodology, focusing on the relationship between current market prices and earnings, dividends and other fundamentals, adjusted for variability over the economic cycle (see for example Investment, Speculation, Valuation, and Tinker Bell, The Likely Range of Market Returns in the Coming Decade and Valuing the S&P 500 Using Forward Operating Earnings ).

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