The Ulcer Index - A Measure of Investor Stress

Want a tool to measure the stress of holding a stock? Then try the Ulcer Index, a technical indicator that describes the pain of continuously falling share prices.

To many people, the terror of falling share prices is often significant, often more so than the pleasure of gains. Accordingly, investors often want to minimize downside volatility as a part of their portfolio planning.

Investors already have several tools to measure downside volatility, including the lower partial moment and the maximum drawdown. The Sortino Ratio, for example, is a performance benchmark that uses the lower partial moment as a risk measure.

The lower partial moment, however, doesn’t entirely describe the panic of investors facing continuously falling stock prices, and the maximum drawdown only captures a single event. A different tool is needed.

Developed by Peter Martin in 1987, the Ulcer Index measures the human stress of holding a stock. It’s a volatility measure that only captures continuous downside movements in share price, and ignores upside volatility. The more continous and prolonged the drawdown, the higher the index.

The Ulcer Index is based on an N day rolling time window, and captures all of the drawdowns within that period. It’s defined by the following equations.

N is the size of the time window (measured in days)
price_i is the share price on day i
maxprice is the most recent running high
R_i is the drawdown from the previous high.

As you can see from the equations, the Ulcer Index is the square root of the average percentage squared loss. The squaring means that larger losses are penalized more heavily than smaller losses.

This means that investment strategies that are characterized by

a few large losses but many small gains have large values of the Ulcer Index (in this case, the large losses take a long time to recover from)
a few large gains and some small losses will have small values of the Ulcer Index (in this case, the upside volatility overwhelms the downside volatility

Although the Ulcer Index is an empirical measure and should only be used in tandem with other technical indicators, a value of

less than 5 is considered safe (investors can breathe easily)
greater than 5 is considered dangerous (at least for nervous investors, who should probably take sedatives, or sell up)

Some technical analysts also define the Martin Ratio or Ulcer Performance Index (UPI) as a risk-adjusted performance benchmark. The UPI is the excess return divided by the Ulcer Index.

UPI is similar to the Sortino Ratio, but it penalizes sustained losses more heavily. UPI is often used to rate the relative performance of several investments, with a higher UPI being better.

Calculate the Ulcer Index in Excel

This spreadsheet shows you how to calculate the Ulcer Index in Excel over a 14-day rolling window (although changing to longer or shorter windows is easy). The spreadsheet uses the BP share price from 10^th October 2009 to 10^th October 2012. A VBA function UlcerIndex() accepts a cell range of share prices, and outputs the UlcerIndex for that range.

The spreadsheet also plots the share price and Ulcer Index

As you can see, the Ulcer Index shot up to over 60 at the time of the Deepwater Horizon oil spill on April 20th 2010. A few months after the spill, once the share price started rising again, the index decreases to around 5.

Had I owned BP stock around the time of the spill, my blood pressure would have spiked.

Download Excel Spreadsheet to Calculate the Ulcer Index