We started with a simple question that everyone is asking about the markets and S&P 500: given a certain drop or rise, say a 5% drop in a week, what should we expect for the next week? Is it very likely that the S&P 500 will recover the next week? What about the next month or a quarter?

In fact, we found that if the S&P 500 drops 5% in a week (5 trading days), there is only a ~12% chance that it will rise by 10% over the subsequent month (20 trading days). Want to try other combinations? You can test a variety of scenarios on the Trefis **Machine Learning Engine to calculate if S&P 500 dropped, what’s the chance it’ll rise**.

For example, after a 5% drop over a week (5 trading days), the Trefis machine learning engine says chances of an additional 5% drop over say the next month, are about 15%. Quite significant, and helpful to know for someone trying to recover from a loss. Knowing what to expect for almost any scenario is powerful. It can help you avoid rash moves. Given the recent volatility in the market, the mix of macroeconomic events, including the trade war with China, and the US Federal Reserve’s moves, we think investors can prepare better.

For clarity, in an earlier analysis in this series, we assessed what are the chances of S&P 500’s drop or rise in the first place. Here we focus on evaluating, given a certain drop or rise, what move can investors expect over the coming day, a week, or months.

Below, we also discuss a few scenarios and answer common investor questions.

__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% in a week

Case 2: S&P 500

*by 5% in a week*

**rises**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

*by 5% in a week*

**rises**Turns out the chances of a * 5% drop* over the next month 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:

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,
- 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.

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The views and opinions expressed herein are the views and opinions of the author and do not necessarily reflect those of Nasdaq, Inc.