A Monte Carlo Simulation For The 2016 Year-End S&P 500

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C-J estimates a 74% chance the S&P 500 will end the year above 2059.74.

The model estimates an 8.9% chance the market will end the year down by 10% or more.

C-J estimates a 7.6% chance the S&P 500 will end 2016 below its recent low of 1829.08.


In a previous article, I discussed the results of my Monte Carlo simulation for the second quarter of 2016 using the C-J model. For those readers who are unfamiliar with my work, C-J is a Monte Carlo simulation model used to assess risk and uncertainty in the S&P 500. While it may be tempting to use such a model to forecast the level of the S&P 500, I designed C-J to provide me with probabilities of future changes in the market based on mathematical and financial patterns in the stock market over the last 50 years. The advantage of C-J is that it corrects for a series of problems often ignored in traditional stock market models including leptokurtosis (fat tails), serial correlation, and volatility clustering. And unlike models used by some asset management firms, C-J uses not one, but a series of conditional statistical distributions to assess the likelihood of certain movements in the S&P 500 over time. The various conditional distributions reflect historical tendencies in the market, with the forecast likelihood of future movements coming from 2,000 simulations of the S&P 500.

Year End 2016

Over the last few weeks, and given that the first quarter just closed recently, I've seen numerous financial analysts on TV providing their analysis of where they believe the S&P 500 will be at the close of 2016. Generally these analysts provide a single point estimate, although in some cases, recognizing the uncertainty associated with the market, they provide a range they believe the S&P will be within when the year closes. Those discussions got me wondering what C-J's projections for the end of the year would look like at this time. To put things into perspective, at the end of March the S&P 500 stood at 2059.74. That is an increase of 0.8% since the December 2015 close of 2043.94. Furthermore, the S&P 500 has traded within a roughly 300-point range since April 2014. So with that as a backdrop, the charts below show the C-J simulation results for the period March 31 through end of the year.

S&P 500 changes through

December 31, 2016

N = 2000 simulations


% of simulations

-10% or worse


-5 to -9.9%


-3 to -4.9%


-1 to -2.9%


0 to -0.9%


0 to 0.9%


1 to 2.9%


3 to 4.9%


5 to 9.9%


10% or better


median % change in the S&P 500 through December 31 = +7.8%

Click to enlarge

*% of simulations may not equal 100% due to rounding.

A few things strike me as particularly noteworthy. First, the likelihood of a 10% or more decline from the March close of 2059.74 is estimated at 8.9%. A 10% decline from this level would take the S&P 500 down to 1853.77, a decline of 13% from its May 2015 high of 2130.82. To put this in perspective, in an unconditional context, the historical probability of the S&P 500 declining by 10% or more over a 9-month period is 11.7%. So the current estimate is slightly lower, although we must take care as the 11.7% figure makes no assumption about market patterns prior to the 9-month period.

Second, C-J estimates the probability of a 10% or more increase in the S&P 500 over the next 9 months to be 43.7%. That is compared to a 39.3% historical probability. Again, we must take care as the 39.3% historical figure takes no account of the market patterns prior to those periods. Furthermore, the median result from the C-J simulations calls for a 7.8% increase in the S&P 500 over the 9-month period.

Collectively, these results suggest an environment over the next 9 months that has slightly lower probabilities of extreme bad outcomes and slightly higher probabilities of good outcomes than would otherwise be suggested by a simple examination of historical returns. In essence, the 9-month horizon estimates have moved closer toward the extremes, particularly the positive one. C-J estimates only a 25.7% likelihood the market will end the year in the -4.9% to +4.9% range from where it ended March. Thus, given that the 6.6% increase in the S&P 500 in March was a positive fat tail event, I take the C-J simulation results through December 2016 with guarded optimism and am careful not to read the recent March 2016 increase as a preview of what I should expect for the remainder of the year.

Above 2130 or Below 1829?

In my last article, I noted that for the last 2 years the S&P 500 Index has moved within a roughly 300 point range. The reference to 2130 in the heading is that 2130.82 was the high over the last few years which occurred on May 21, 2015, while the low of 1829.08 occurred this past February. So in that article, I used C-J to assess the probabilities that the S&P 500 would be above or below those figures at the end of April as well as June. Given the context of this article, and the significant fluctuations we have witnessed in the markets the first 3 months of 2016, I again used C-J to assess the probability of being within that range, although in this case the simulations were with respect to the end of the year. The table below shows the results.

S&P 500 Above 2130.82

N = 2000 simulations


% of simulations

end 2016


S&P 500 Below 1829.08

N = 2000 simulations


% of


end 2016


Click to enlarge

Taken as a whole, the simulation results suggest that by the end of 2016, there is a 63.2% chance the S&P 500 will be above the May 2015 high and a 7.6% chance we will have fallen below the February 2016 low. That leaves a 29.2% chance the index will still be within the previously noted range at the end of 2016. My takeaways from these results again suggest guarded optimism. First, while the results are generally positive, there is a 1 in 13 chance that the year will end lower than the February 11 close. That would be an 11.2% decline from where we ended March 2016. Second, there is a roughly 3 in 10 chance the S&P 500 will end the year within the previously noted range. Given that as March concluded the S&P 500 was closer to the upper end of that range, and that we have just experienced a positive fat-tail month, I temper my enthusiasm over the March results with recognition of possible risks over the remainder of the year.

Disclaimer: This article contains model-based projections that are forward-looking and, as with any quantitative model, are subject to uncertainties and modeling assumptions. The C-J model is intended as a tool to assess risk in the S&P 500, and not as a forecast of the future value of the S&P 500 or any other market. The results of C-J are for informational purposes only. Nothing in this article should be construed as specific investment advice.

Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.