Ulcer index

The index is based on a given past period of days. Working from oldest to newest a highest price (highest closing price) seen so far is maintained, and any close below that is a retracement, expressed as a percentage: R_i = 100 \times \frac{\text{price}_i - \text{max price}}{\text{max price}} For example, if the high so far is $5.00 then a price of $4.50 is a retracement of −10%. The first R is always 0, there being no drawdown from a single price. The quadratic mean (or root mean square) of these values is taken, similar to a standard deviation calculation. \text{Ulcer} = \sqrt { R_1^2 + R_2^2 + \cdots R_N^2 \over N } Because the values are squared it is immaterial whether they are expressed as positives or negatives; both result in a positive Ulcer Index. The calculation is relatively immune to the sampling rate used. It gives similar results when calculated on weekly prices as it does on daily prices. Martin advises against sampling less often than weekly though, since for instance with quarterly prices a fall and recovery could take place entirely within a period and thereby not affect the index. == Usage ==

Martin recommends his index as a measure of risk in various contexts where usually the standard deviation (SD) is used for that purpose. For example, the Sharpe ratio, which rates an investment's excess return (return above a safe cash rate) against risk, is: \text{Sharpe ratio} = \frac{ \text{return} \ -\ \text{risk-free return}}{\text{SD}} The ulcer index can replace the SD to make an ulcer performance index (UPI) or Martin ratio: \text{UPI} = \frac{ \text{return} \ -\ \text{risk-free return}}{\text{ulcer index}} In both cases, annualized rates of return would be used (net of costs, inclusive of dividend reinvestment, etc.). The index can also be charted over time and used as a kind of technical analysis indicator, to show stocks going into ulcer-forming territory (for one's chosen time-frame), or to compare volatility in different stocks. As with the Sharpe Ratio, a higher value of UPI is better than a lower value (investors prefer more return for less risk). == References ==