One of the most common pieces of advice heard in the world of investing and the stock market is the phrase “buy low, sell high”, and many people believe that buying the dips in the market trends is how you can complete step one: buying low.

I recently came across this post by the Instagram page ChartRDaily which shows how well the market has done on days after drops of 2% or greater.

We can see from the chart that the stock market tends to have a higher probability of a positive return at 53.8%. I wanted to look deeper into this notion of “buying the dip”, and see if there were any other patterns that I could find rather than just looking at days after a drop of 2% or greater.

First, I had to gather the data. According to the chart, the data was collected from the S&P 500 since 1969. Yahoo Finance has daily returns of the S&P 500 going back to 1928 so I was able to download this data and load it into a pandas data frame.

Here is what the distribution of daily returns looks like:

*Note: The return is calculated as (Close – Open) / Open, so only movements during market hours are counted and any movements pre-market or during after market hours are not included.

The mean return of all days turns out to be .03%. This graph is zoomed in to get a better idea of the shape of the distribution, but the true distribution ranges from a -20.5% return on October 19, 1987, also known as Black Monday, and goes as high as 10.8% on October 28, 2008 during the global financial crisis.

When I tried to replicate the results shown in the chart, I got some slightly different results. My results showed that on days after a drop of 2% or greater, there were 172 positive days and 144 days, which means that 54.4% were positive. I reached out to ChartR to try to figure out why our data differed, but have not heard back as of yet.

It would be helpful to compare these percentages to the overall percent of market returns that are positive, which turns out to be 52.6%.

Now what about drops of different sizes than 2%? This graph shows the proportion of positive days that follow returns less than given amounts.

It looks like there tend to be positive returns on days after large drops (such as returns less than -4%). Something interesting to notice is that the return actually becomes more likely to be negative at a certain point (when the previous day had a return less than ~ -1.6%).

But what about the returns on days after a big gain? Is there an opposite effect?

It looks like days after extreme gains seem to be less likely to be positive on the next day. However, looking at the days after gains larger than 2%, we can see that about 56.3% of days were positive, which is even larger than we saw after a drop of the same size.

Proportions don’t give us all of the information that we need, so it would be nice to look at the averages as well. Remember we said the overall average return was .03%. After days with a return less than -2%, the average return turned out to be .19%, and after days with a return greater than 2%, the average return was .12%, which are both significantly higher than the overall average.

There was one last pattern I wanted to look for in this daily S&P 500 data. We have seen how events such as the spin of a roulette roll are independent, where the odds of a certain number or color appearing are just as likely no matter which results came before. I wanted to know if this was the same for the stock market.

I looked at the proportion of positive days after x negative days in a row and here’s what I found.

It looks like days after 0 negative days in a row seem to be more likely to be a positive day at 53.8%, while days after 1 or 2 negative days in a row seem to stick with the trend and and also seem to be more likely than usual to be a negative day.

Here’s what the average returns look like for the same situation.

Once again we can see that the average seems to be higher after 0 negative days in a row, and actually has been negative after 1 and 2 negative days in a row. After 5 negative days in a row, the average return has been 0.2%, but also has the overall average return within its 95% confidence interval.

Now let’s look at streaks of positive days.

It looks like we’re seeing the opposite patterns as the streaks of negative days. After 0 positive days in a row, there seems to be a lower chance of seeing a positive day, and a higher chance after 1 and 2 positive days in a row.

These patterns seem to stay consistent when looking at the averages as well. The average return is right around 0% after 0 positive days in a row, but shoots up to .07% and .08% after 1 and 2 positive days in a row.

If you’d like to look into some other patterns in these daily returns, I’ve made a GitHub repo of the code and data that you can check out here: https://github.com/MindingTheData/BuyTheDip

Thanks for reading and be sure to check out some of my other posts!