S&P 500 Drawdown

Jul 24, 2018 · 776 words · 4 minutes read financeplotsstock market

Whenever an equity’s value is below it’s all time high it is drawn down. There are a lot of questions we can ask about an equity’s drawdown behavior as we try to understand it. How often does it draw down? For how long? How much?

Below is the S&P 500 from January 2010 through June 2018 with drawdown periods in red and all time highs in white. The all time high is also shown with a blue step line.

The S&P 500 is drawn down during the majority of this timeframe (it’s difficult to clearly see what is happening during the entire history). There are long periods when the S&P 500 is drawn down followed by periods of sporadic all time highs.

For the rest of this post I’ll use the daily returns since January 1950.

What’s the drawdown distribution?

Below is a plot of the distribution of drawdowns using the daily adjusted closing prices from Jan. 1950 through June 2018. The distribution is restricted to positive values because a new all time high is 0% below itself.

Drawdown values represent a decline from the all time high, e.g. a 10% drawdown represents a price that is 10% less than (or 90% the value of) the all time high. The distribution shows the frequency of different magnitudes of drawdowns - it’s strictly positive, approximately zero inflated, and long-tailed.

About 7.32% of days had an adjusted closing price that was an all time high (i.e. a drawdown of exactly 0%) and 19.8% of days had a drawdown of less than 1%. The largest daily drawdown was 56.8% on Mar. 12, 2009. Of all drawdowns, half are less than a 5.69% decline and 95% of drawdowns are less than a 31.3% decline.

In addition to the drawdown magnitude we might also be interested in the drawdown durations - how long between all time highs.

How long do drawdowns last?

This next plot shows the distribution of drawdown durations. In other words, the frequency of consecutive days the S&P 500 was in drawdown.

By definition a drawdown must be at least one day, so instead of zero inflated this distribution is one inflated. This means that most drawdowns are fairly short. Like the distribution of drawdowns, the durations is long-tailed. In this case I truncated the distribution at 60 days so it is easier to see most of the data.

About 29.9% of drawdowns lasted only 1 day and 81.3% drawdowns lasted fewer than 20 days. The longest drawdown lasted 1,897 days (Jan. 12, 1973 to Jul. 12, 1980).

A natural question might be to ask about the relationship between drawdown magnitude and duration: do larger drawdowns last longer?

Do larger drawdowns last longer?

This next plot shows the duration of the drawdown in years (y-axis) by the largest drawdown (x-axis) during that period. Each point represents a period of one or more days between all time highs. The top 1% of longest drawdowns and largest 1% of drawdowns are labeled with the start date of the drawdown period.

As we know from above most drawdown periods are short and are a small decline from the all time high. There is a positive relationship between drawdown durations and their largest decline - however some drawdowns are highly influential points in suggesting that relationship.

The most extreme drawdowns are the 2007, 2000, and 1973 recessions. These periods lasted much longer than the other labelled periods (which are the top 1% of drawdowns by either duration or magnitude).

To better understand the majority of drawdown periods we can focus on the highest density data (95.8% of drawdowns had a maximum decline less than 10%). These drawdowns have a Pearson correlation of 0.78 (which is a respectable linear correlation). However optical estimation shows increasing variance - the greater the drawdown the more variation in duration - and fitting any sort of predictive model wouldn’t be useful anyway because we can’t know the largest decline during a drawdown until we’re returned to an all time high.

Instead of the maximum drawdown during a period we can look at the drawdown on the first day. This addresses the question: can we tell how long the S&P 500 will be drawn down from the first day?

The short answer is, no we can’t easily tell how long the S&P 500 will be drawndown just from the first day.

Most of the time the market is only in drawdown for a short period - some of the longest drawdown periods have only a very mild initial decline from the all time high and some of the largest initial drawdowns lasted only a few weeks or days.