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The ulcer index is a stock market risk measure or technical analysis indicator devised by Peter Martin in 1987, and published by him and Byron McCann in their 1989 book The Investors Guide to Fidelity Funds. It is a measure of downwards volatility, the amount of drawdown or retracement over a period.
Other volatility measures like standard deviation treat up and down movement equally, but most market traders are long and so welcome upward movement in prices, it is the downside that causes stress and the stomach ulcers that the index's name suggests. (The name pre-dates the discovery that most gastric ulcers are caused by a bacterium rather than stress.)
The term ulcer index has also been used (later) by Steve Shellans, editor and publisher of MoniResearch Newsletter for a different calculation, also based on the ulcer-causing potential of drawdowns. Shellans' index is not described in this article.