Question 1: Does a rise in S&P 500 become more likely after a drop?
Answer:
Consider two situations,
Case 1: S&P 500 drops by -5% or more in a week
Case 2: S&P 500 rises by 5% or more in a week
Is the chance of say a 5% rise in S&P 500 over the subsequent month after Case 1 or Case 2 occurs much higher for one versus the other?
The answer is absolutely!
Turns out, chances of a 5% rise over the next month (20 trading days) is meaningfully more for Case 1, where the S&P has just suffered a big loss, versus Case 2.
Specifically, chances of a 5% rise in S&P 500 over the next month:
= 34% after Case 1, where S&P 500 drops by 5% in a week
versus,
= 26% after Case 2: where S&P 500 rises by 5% in a week
Question 2: What about the other way around, does a drop in S&P 500 become more likely after a rise?
Answer:
Consider, once again, two cases
Case 1: S&P 500 drops by 5% in a week
Case 2: S&P 500 rises by 5% in a week
Turns out the chances of a 5% drop after Case 1 or Case 2 has occurred, is actually quite similar, both pretty close to 15%.
Question 3: Does patience pay?
Answer:
According to data and Trefis machine learning engine's calculations, absolutely!
Given a drop of 5% in S&P 500 over a week (5 trading days), while there is only about 18% chance the S&P 500 will gain 5% over the subsequent week, there is more than 50% chance this will happen in 6 months, and 74% chance it’ll gain 5% over a year (about 250 trading days).
The table below shows the trend:
Given a change of: Then chances S&P 500 will change: Likelihood =
-5% over 5 days, +5% over 1 day 5%
-5% over 5 days, +5% over 5 days 18%
-5% over 5 days, +5% over 10 days 30%
-5% over 5 days, +5% over 20 days 34%
-5% over 5 days, +5% over 60 days 52%
-5% over 5 days, +5% over 250 days 74%
Worthy to note row 1 in the table above.
Question 4: What about the possibility of a drop after a rise if you wait for a while?
Answer:
Two interesting things we see.
First, after seeing a rise of 5% over 5 days, the chances of a 5% drop in S&P 500 are about 15% over the subsequent month of waiting (20 trading days). However, this chance drops slightly to about 13% when the waiting period is a quarter (60 trading days). Why is that?
We think it’s the result of two opposing forces: the positive bias for S&P 500 that increases the likelihood that S&P 500 will increase over long enough time periods, and the counter force, that a meaningful drop of -5% is just more likely over 60 days as opposed to 20 trading days.
This latter force is also evident when you compare the first two rows of the table below.
Given a change of: Then Chances S&P 500 will change: Likelihood =
+5% over 5 days, -5% over 1 day 1%
+5% over 5 days, -5% over 5 days 6%
+5% over 5 days, -5% over 10 days 8%
+5% over 5 days, -5% over 20 days 15%
+5% over 5 days, -5% over 60 days 13%
+5% over 5 days, -5% over 250 days 14%
