# Examining Drawdowns and the Pain Index with R

Drawdowns and the Maximum Drawdown:

Drawdowns may be an unfamiliar concept to most investors out there. The good news is, they are extremely simple. Essentially a drawdown is a peak to trough decline expressed as a percentage of an asset or portfolio of assets. Examining a simple stock chart, we can find many drawdowns. The good news is, the PerformanceAnalytics package within R makes finding and graphing drawdowns super easy.

We can start the process by importing data using quantmod. We will then calculate the cumulative returns on the asset.

Next, we can utilize a plethora of functions within the PerformanceAnalytics package to visualize and examine the drawdowns for the stock over a given time frame. Please note, the Pain Index, Maximum Drawdown, and drawdowns are incredibly time specific. Let’s start by identifying some drawdowns in our time series we can do this with one simple line of code.

Next, we can start to look at some statistics on the drawdowns of the time series.

Let’s examine drawdown graphically with ggplot2. Note we can compare this with cumulative returns or the closing price of the asset as well. The depth, frequency, and duration of losses are displayed in the bottom portion of the plot representing the drawdowns.

Let’s examine drawdowns graphically over time with respect to the price of the asset. The red shaded rectangle represents the maximum drawdown for the time series.

The Pain Index:

Note the following risk measure are typically used to evaluate fund managers (used with mutual funds) and to evaluate a portfolio of assets. For the sake of simplicity, we can continue to examine a single asset.

The pain index is an essential measure of risk for an asset or fund. The pain index is the average of all of the drawdowns for a particular asset or portfolio over a given time frame. This may be a bit difficult to think of numerically but refer to the last chart highlighting the drawdown period to get a better picture. The Pain Index captures the depth, duration, and frequency of losses while also addressing the shortcomings of only calculating the maximum drawdown of a stock.

Let’s calculate the Pain Index and Pain Ratio.

Interpretation of the Pain Index:

So what does the pain index numerical value tell us as investors anyways? Nobody likes to lose money during any time frame. The pain index essentially is a numerical measurement of all losses during a time frame. Here, we are not just looking at the maximum drawdown for an asset or portfolio, rather all the drawdowns instead. Now you are probably wondering, what is a good value or bad value pertaining to the pain index? Essentially, the lower the better as we are looking at overall losses here. Ideally, we would like a value of 0. There are obviously a few caveats to this metric also.

Interpretation of the Pain Ratio:

The Pain Ratio is quite similar to the Sharpe Ratio, only a different measure of risk is defined. The Pain Ratio defines the Pain Index as the measure of risk within the calculation. Some believe the Pain Index takes into account risk more accurately than a simple volatility calculation. Like the Sharpe Ratio, the higher the number the better.

Flaws in the Pain Index:

Firstly, the pain index only examines the downside, while failing to examine the upside. Note we could have a very high number for the pain index signaling a large number of losses. During the time frame, the stock could have experienced a large number of gains also.