What is risk, and how is it measured? Risk is commonly defined in terms of the volatility of an investment's total return or the volatility of the price. The standard deviation is a good measure of volatility, since it measures the amount of variation around the average and is probably the most widely used measure of financial risk. But the standard deviation has two weaknesses for financial instruments. First, it measures the variation from the average in both the up (good) direction as well as the down (bad) direction. Second, the standard deviation does not distinguish between short or long sequences of losses. Investors are only concerned about downside risk (or the potential for losses), whereas upside changes or rapid increases in value create profits.
The Ulcer Index
by Gary H. Elsner, Ph.D.
A good risk index can be useful in the selection of stocks, funds, and trading systems. Here, then, is the ulcer index, why it is superior to the standard deviation statistic, and how it can be used in a variety of personal investing or professional money management applications.
The standard deviation may still be the most widely used because it has been around longer than other risk indices and most computer programs have the capability of calculating it. However, there is another measure of risk, superior to the standard deviation: the ulcer index.FIGURE 1: FIDELITY EMERGING MARKET. The ulcer index uses only the retracements from the price peaks (the shaded areas) in the calculation.
Peter G. Martin and Byron B. McCann are credited with the creation of the ulcer index. They describe it in their 1989 book, The Investor's Guide To Fidelity Funds. (To see the calculation for the ulcer index, see the sidebar "The ulcer index.") In contrast to the standard deviation, the ulcer index has none of the aforementioned weaknesses since it calculates retracement, which is the tendency for values to fall from previous highs, by measuring the depth of the drop and the time that it takes the performance measure to recover to the original level.
Another advantage is that the ulcer index doesn't measure downside changes from the average but from the previous high. For example, in Figure 1, all of the shaded areas are included in the calculation of the ulcer index. The measurement includes every drop in performance in the period being studied. Funds or trading systems with high ulcer index readings should be avoided unless they have such exceptionally high returns that the risks are justified. In addition, dividing returns by the ulcer index produces a useful risk-adjusted return measurement.
Excerpted from an article originally published in the April 1999 issue of Technical Analysis of STOCKS & COMMODITIES magazine. All rights reserved. © Copyright 1999, Technical Analysis, Inc.