The C-J Monte Carlo Simulation Model
As discussed in my previous article, C-J is a Monte Carlo simulation model used to assess risk in the S&P 500. C-J uses a series of conditional statistical distributions based on S&P 500 data going back to 1950 to correct for problems often ignored in traditional stock market models including leptokurtosis (fat tails), serial correlation and volatility clustering. The conditional distributions are linked in such a way that what happens to the S&P 500 in one month influences changes in future months. C-J then runs 2,000 simulations of the S&P 500 for periods as far as 18 months into the future, and uses the results to assess the probability of various market outcomes.
April 2016
The S&P 500 Index finished the month of March at 2059.74. That is an increase of 6.6% from its February close at 1932.23. It also marks the first month since November 2015 where the S&P 500 has increased. Putting the March result into perspective, a 6.6% increase ranks in the top 6% of monthly changes in the S&P 500 since 1950. Given such a significant increase in March, I used C-J to assess the S&P 500 for April. The chart below shows C-J's outlook.
S&P 500 1-month changes for April 2016 N = 2000 simulations | |
Range |
% of simulations |
-10% or worse |
0.2% |
-5 to -9.9% |
7.3% |
-3 to -4.9% |
4.0% |
-1 to -2.9% |
11.5% |
0 to -0.9% |
7.4% |
0 to 0.9% |
13.8% |
1 to 2.9% |
23.7% |
3 to 4.9% |
15.5% |
5 to 9.9% |
16.9% |
10% or better |
0.0% |
median percentage change in the S&P 500 for April = +1.6% |
*% of simulations may not equal 100% due to rounding.
A number of results stand out for the April simulation. First, the results are decidedly more positive than the March 2016 forecast from my previous article. In fact, in this case, C-J estimates a 69.9% chance that the April change in the S&P 500 index will be positive. That number is above the historical norm as the S&P 500 has increased on a one-month basis about 59% of the time since 1950. Such a result is not surprising however as history suggests that abnormally large increases in the S&P 500 in a given month are on average followed by increases the following month (about 70% of the time) and these increases tend to be above average in magnitude. Furthermore, the median estimate from C-J's projections is for a 1.6% increase, a rate that is more than twice the historical average monthly change. So given recent movements in the S&P 500, C-J's projections look similar to historical patterns we have seen since 1950.
Second, C-J estimates the risk of a fat-tail event to be significantly reduced compared to the March forecast. Prior to joining academia, I spent 14 years with the U.S. Department of the Treasury in Washington, D.C., where I often did work on estimating risk in financial markets. So with models like C-J, my natural inclination is to examine worst-case scenarios and ask myself whether I am comfortable taking that level of market risk given the possibility of such a negative outcome. You might think of it as a form of stress-testing my portfolio as well as my risk tolerance as an investor. So looking at C-J's negative results, you can see that the likelihood of a decline of 5% or more in the S&P 500 for April is estimated at only 7.5%, a number that is lower than the historical occurrence rate of 8.8%. This is not surprising as historically increases in the S&P 500 of 6% or more have only on 4 occasions resulted in declines of 5% or more the following month. The last time that happened was in August 2000 when the S&P 500 increased 6.1% but then declined by 5.3% in September. Furthermore, the C-J estimates suggest only a 0.2% chance that the S&P 500 will decline by 10% or more in April. This is a lower likelihood forecast of a negative fat-tail event than we would normally expect to see from C-J, but still above the historical rate. Taken as a whole, the results suggest a generally positive outlook for April with a greater likelihood of an increase and a lower likelihood of a significant negative change.
Looking Ahead To the Second Quarter
Given the results for April, I was curious as to C-J's estimates for the second quarter. The table below shows C-J's estimates as to the change in the S&P 500 through June 30, 2016.
S&P 500 3-month changes through June 2016 N = 2000 simulations | |
Range |
% of simulations |
-10% or worse |
3.8% |
-5 to -9.9% |
7.1% |
-3 to -4.9% |
5.6% |
-1 to -2.9% |
8.3% |
0 to -0.9% |
4.4% |
0 to 0.9% |
6.6% |
1 to 2.9% |
12.5% |
3 to 4.9% |
13.1% |
5 to 9.9% |
25.4% |
10% or better |
13.4% |
median percentage change in the 2 ^{nd} quarter = +3.3% |
*% of simulations may not equal 100% due to rounding.
Again the results are decidedly more positive than the 3-month forward results C-J made in my previous article. For the second quarter, C-J now forecasts the likelihood of a decrease in the S&P 500 at 29.2%, with the probability of a loss of 5% or more at 10.9%. A 5% loss would only take the S&P 500 down to 1956.75, a level still above where the market ended the month of February. Looking at the positive side, C-J now forecasts a more than 50% chance that the S&P 500 Index will increase by 3% or more in the second quarter. But it is noteworthy that even with more positive patterns potentially playing out in the market, C-J still estimates a 3.8% chance the market will fall by 10% or more during the quarter. Such a result, were it to occur, would take the S&P 500 down to 1853.77, a level similar to some of the relative lows experienced in the market since October 2014.
Above 2130 or Below 1829?
As I was writing this article, one more thought entered my mind. Since April 2014, the S&P 500 has fluctuated within the roughly 300-point range of 1829 and 2130. The high of 2130.82 was attained back on May 21, 2015, while the low of 1829.08 occurred on February 11th of this year. Being bound within this range for almost two years led me to the question of how likely is it that the S&P 500 will close out either the month of April or the second quarter of 2016 above 2130.82 or below 1829.08. Plugging these questions into C-J yielded the following results:
S&P 500 Above 2130.82 N = 2000 simulations | |
Month |
% of simulations |
end April |
30.5% |
end June |
48.8% |
S&P 500 Below 1829.08 N = 2000 simulations | |
Month |
% of simulations |
end April |
0.0% |
end June |
3.0% |
The results are interesting in that they suggest an almost one in three chance that the S&P 500 will close out April above its May 2015 high of 2130.82. And that probability rises to 48.8% by the end of June. On the opposite side, none of the 2000 simulations resulted in the S&P 500 closing out the month of April below its February 2016 low of 1829.08. Obviously, the true probability is not zero. Rather, this result is simply to say that none of the 2000 simulations C-J ran resulted in such an outcome. But if we look out to the June result, C-J now estimates a 3.0% chance the S&P will end the month of June below the 1829.08 level. That would represent an 11.2% drop from the end of March level.
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.