Unknown Unknowns: Predicting Stock Trends

NEW YORK (TheStreet) -- How significant to you is it that Wall Street strategists have lowered their equity market forecasts from mid-double-digit returns for 2013 to single-digit returns for 2014?

It turns out that those forecasts are worth a lot less than you might think.

Equity-return modeling generally incorporates estimating the average trend in economic factors, and then assigning a price multiple to that future trend. (The new price multiple is almost always anchored within 1 or 2 of the current multiple). To add some complexity, in the recent bull market leading up to the 2008 to 2009 financial crisis, Wall Street firms opened up this single-point price target. Some major firms now offer binomial path outcomes instead -- a bull case and a bear case scenario, with a probability assigned to each.

Most people -- including the strategists themselves -- focus on such important details. But these probabilities could be risk-adjusted so that the future price can be extrapolated using a risk-neutral investor approach, or the actual probabilities could stay in absolute terms and an appropriate risk rate could be used to determine the future price target.

Leaving this whole complication aside, the point here is that the major source of uncertainty among Wall Street forecasters remains on macro calls of what the price multiple would be on the future earnings trend. Are they generally optimistic or generally pessimistic? This can account for a large explanation of the generally double-digit difference in the higher year-end targets versus the lower year-end targets. If the current multiple is, for example 15, and a pessimist anticipate a 0.5 change and an optimist estimated a 2.0 change, then the 1.5 difference is 10% of the original 15. This is an important idea, as we uncover an additional 12%-or-so spread that risk mis-timing forces onto things.

The core middle-of-the-pack entered this year looking for a single-digit return in 2014. Of course, as any long-term strategist outside of Wall Street would note, the end of 2014 is quite an arbitrarily brief period of time. And these net returns just take into account a long-run average amount of risk within that period. Of course this masks an ugly truth about the nature of risk, which is that it doesn't occur in the same way and time frame as the economic return factors that monopolize the intellectual demands of Wall Street analysts.

Now let's assume that the major risks implicit in each calendar year are one 10% correction and two 5% corrections -- 20% annual total, 40% biennial.

But in reality, these corrections will happen when they choose. They are calendar agnostic and do not conform to the smooth parameters of economic growth extrapolations.

Looking at the probability of the risk convolutions for any one given year, we can suggest the other combinations that can play out in our hypothetical scenario of 40% biennial risk. Namely look at these other examples, which could occur in 2014 and 2015 (including in reverse order, so that either year could be Year A, and the other be Year B). Any event that shifted from Year A, to Year B, is italicized. The probabilistic weight is provided above each combination. The ordering of the risk events in any given year is irrelevant.

So if there is 40% biennial risk, then that could be distributed as follows.

1/4 weight
Year A --> -10%, -5%, -5%
Year B --> -10%, -5%, -5%

1/3 weight
Year A --> -10%, -5%
Year B --> -10%, -5%, -5%, -5%

1/4 weight
Year A --> -5%, -5%
Year B --> -10%, -5%, -5%, -10%

1/6 weight
Year A --> -10%
Year B --> -10%, -5%, -5%, -5%, -5%

What we see here is the finicky nature of how year-end targets can unravel based solely on the independent displacement of major risk events, relative to the end of the calendar year. A recent example of this is the suppression of a correction in the equity markets at the end of 2013, creating a gap in the actual 2013 stock market return vs. Wall Street forecasters who themselves were caught shooting in the dark as they erratically changed their full-year forecasts throughout 2013. And alas, the correction initiated precisely in January 2014. Of course these large forecasting gaps can equally go in either direction.

The weights and the distributions of the risk events shown above yield a 6% standard deviation (AA). Or an interquartile range (75th percentile to 25th percentile) that is usually mathematically higher than 12%.

So the timing of risk we just showed creates just as much independent uncertainty as does the inherent growth model uncertainty between the higher price target forecasters vs. the lower price target forecasters!

In the illustration below, we'll see a scaled version of what a 2014 forecast for a 5% rise in equity markets really looks like based just on risk timing.

A few forecasts are shown, and the along vertical axis we see the typical deviation we have on that annual forecast from just the timing of risk. Sure, something near a 5% return in 2014 can happen, though there is a very strong likelihood that you'll see nothing close to this. You may easily see a negative return. Conversely you could see a double-digit return.

Even if the return were in the single digits, we know it is within a one I range of other true return patterns, such as that for a 0% return or a 10% return. Or if we include the uncertainty beyond risk mis-timing, then this is only within a half I range, or within a one I range of either -5% and 15% returns.

So, not much is truly known about the equity returns when considering the multiple sources of error uncertainty. When Wall Street strategists start the year by providing a lower return forecast, they've added very little helpful information for long-term asset allocators.

This is due to the current lack of Wall Street discussion of risk modeling into calendar-year investment projections. But similar to the trend in providing a broader distribution of rankings and binomial paths, perhaps this knowledge will one day enter the mainstream.

For now, those that celebrate and subscribe to these quirky, full year targets for important long-term investment decision-making could heed the quote of the 19th century social reformer, Robert Owens:

All things I thought I knew; but now confess
The more I know, I know, I know the less.

At the time of publication, the author held no positions in any of the stocks mentioned.

This article represents the opinion of a contributor and not necessarily that of TheStreet or its editorial staff.

Salil Mehta is a statistician and risk strategist, who has developed an engaging method to teach quantitative techniques. 

Salil has 17 years of experience, of which a dozen years were on Wall Street, performing proprietary trading and economic research for firms such as Salomon/Citigroup, and Morgan Stanley.  He also served for two years in a leadership role, as the Director of Analytics, in the U.S. Department of the Treasury for the Administration's $700 billion TARP program.  Salil is also the former Director of the Policy, Research, and Analysis Department in the Pension Benefit Guaranty Corporation.  He completed a graduate degree in mathematical statistics from Harvard and also completed the Chartered Financial Analyst exams, as well as being a current dual candidate member of the Society of Actuaries.  In addition to having lectured on probability and economics at a number of leading universities, Salil has authored academic articles.  He currently provides advisory to the heads of several organizations, and he teaches graduate statistics at Rutgers on the weekends this year, in addition to current Georgetown teachings. 

Salil has also been acknowledged or on air interviewed and by a number of leading publications, such as the National Bureau of Economic Research, American Statistical Association, New York Times, CNBC, Wall Street Journal, Financial Times, Barron's, CFA Institute, Tom Keene, Bloomberg, and Businessweek.  He has also completed a statistics and analytics topics book, a working draft of which is available for Georgetown library users.  His blog, Statistical Ideas, provides an interesting discussion of various statistical applications, and the bottom of this link offers downloadable, refresher presentations on the basics of probability and statistics.  Also the site has been added to the syllabus of several leading universities. 

This site is also added to RePEc's selective blog aggregator.  You directly contact Salil and follow him on Facebook and Google+ and Skype (name: saliltreasury).  And you can subscribe to the site.

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