The Difference Between a Prediction and a Probability

Where is the S&P 500 going to end the year?

This is one of the most popular questions in financial media. Why? Because viewers are said to love nothing more than a prediction involving a precise level on a specific date.

There are two ways to answer this kind of question…

1) The Prediction (based on feeling or opinion):

Bullish pundit: 3000. This is going to be another 1999.

Bearish pundit: 1000. This is going to be another 2008.

2) The Probability (based on evidence):

I don’t know. Predicting a precise level on a specific date is a fool’s game that’s not helpful to anyone. The best we can do is arrive at a range of possible outcomes…

The S&P ended last week at 2343.98. We are 57 trading days into the year with 194 trading days until year-end.

Since 1928, the average price return over 194 trading days is +5.74%. The standard deviation of 194-day returns is 17.06%.

If the market followed a normal distribution, we could arrive at the following confidence intervals for the ranges of S&P 500 levels at year end:

68.27% probability of the S&P 500 being within 2079 and 2878 (1 standard deviation).

95.45% probability of the S&P 500 being within 1679 and 3278 (2 standard deviations).

99.73% probability of the S&P 500 being within 1279 and 3678 (3 standard deviations).

You’ll notice that being 95.45% and 99.73% confident of something in the markets requires an extremely wide range of outcomes. These ranges, though, are likely not wide enough.


Because market returns are not normally distributed but instead fat tailed. In plain English that means extreme events (multi standard deviation) occur with higher frequency than one would expect. A normal distribution predicts that a move greater than 3 standard deviations should occur only 0.27% of the time while we have actually seen such moves occur 1.08% of the time when looking at 194-day returns.

Based on actual past returns, then, there is a 99.73% probability of the S&P 500 being within a much wider range of 890 and 3790.

The Difference Between a Prediction and a Probability

When it comes to year-end levels, no one wants to hear a wide range which is why you’ll never hear the probability-based answer on TV. Viewers are said to want action and they can’t act on a range of possible outcomes.

Tell them the market is going to 3000 and they can buy on margin. Tell them the market is going to 1000 and they can sell everything.

But are these types of extreme calls helpful to investors?

It would be hard to argue that they are, for even if they are correct it would require perfect execution on the part of the investor and perfect timing in terms of reversing the trade in the future.

But isn’t doing something better than doing nothing?

No, the opposite is true. The most important rule in investing is to do no harm. And acting based on feelings or opinions is going to do much more harm than good to the vast majority of investors.

The difference between a prediction and a probability is the difference between a pundit and a professional. One makes concentrated bets on the belief that they can predict the future and the other diversifies with the understanding that they cannot.

When you can admit to yourself and others that you cannot predict the future, you are ready to succeed in markets.

So where is the S&P 500 going to end the year?

Let’s say it together: I don’t know.


Related Posts:

The 3 Most Important Words in Investing

Pundit or Professional

First, Do No Harm

Fat Tails and Expecting the Unexpected

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This writing is for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation regarding any securities transaction, or as an offer to provide advisory or other services by Pension Partners, LLC in any jurisdiction in which such offer, solicitation, purchase or sale would be unlawful under the securities laws of such jurisdiction. The information contained in this writing should not be construed as financial or investment advice on any subject matter. Pension Partners, LLC expressly disclaims all liability in respect to actions taken based on any or all of the information on this writing.



Charlie Bilello is the Director of Research at Pension Partners, LLC, an investment advisor that manages mutual funds and separate accounts.  He is the co-author of four award-winning research papers on market anomalies and investing. Mr. Bilello is responsible for strategy development, investment research and communicating the firm’s investment themes and portfolio positioning to clients. Prior to joining Pension Partners, he was the Managing Member of Momentum Global Advisors and previously held positions as a Credit, Equity and Hedge Fund Analyst at billion dollar alternative investment firms.

Mr. Bilello holds a J.D. and M.B.A. in Finance and Accounting from Fordham University and a B.A. in Economics from Binghamton University. He is a Chartered Market Technician (CMT) and a Member of the Market Technicians Association. Mr. Bilello also holds the Certified Public Accountant (CPA) certificate.

You can follow Charlie on twitter here.

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