QUESTIONS AND ANSWERS, 1996 THIRD QUARTER NEWSLETTER

Ulcer Index: I have seen the term "ulcer index" in MoniResearch and other publications. What is it, and what does it say about the Select Switching System? The ulcer index was developed as a measure of risk by Steve Shellans, the editor and publisher of the MoniResearch Newsletter (800/615-6664), which evaluates the performance of market timers and "dynamic asset allocators." I fit into the latter category, and I was included in a special issue covering new money managers last October. Starting with the most recent issue, the performance of my managed accounts is now included in the three issues per year devoted to asset allocators.

The basic concept in the computation of the ulcer index is that of drawdown. Simply stated, drawdown is the percentage at any time that a system, (managed) account, individual trade, or stock index is below the maximum value it had achieved previously. If the current value is a new high, then the drawdown is 0%. One measure of risk is the maximum amount of drawdown over some time period. This is a valid way of evaluating risk in that it quantifies what might be considered the worst case loss. However, the maximum drawdown has at least three deficiencies as a risk measure: a) drawdowns less than the largest one are ignored, b) the length of time the drawdowns last is not considered; and c) there is no comparison to the market environment in which the drawdowns occurred.

Shellans designed the ulcer index to remedy these problems and produce a single number that enabled a comparison of the risk of a system or money manager to the market. His basic idea is that a large drawdown has ulcer causing potential, and so does a shallower one that lasts a long time. His method starts by adding up the drawdowns at regular intervals over the period being evaluated, say at the end of each month. For example, suppose that starting from a new high, the system dropped by 8% in the first month, gained a little in the second month so that it was 5% below the high, recovered to make a new monthly high at the end of the third month, and fell by 2% from the third month new high in the fourth month. Then the total of the monthly drawdowns for the period is 8%+5%+0%+2% = 15%. This method emphasizes deep drawdowns and prolonged ones. To get the ulcer index for the system, do a similar computation for the measure of the market, say the S&P 500 index, and divide the sum of the drawdowns for the system by the sum of the drawdowns for the market. With this definition, the market has an ulcer index of 1. A system with a lower value is less likely than the market to cause ulcers, but a system with higher values is more likely than the market to produce abdominal pains.

So how does the Select Switching System I use to manage accounts rate? I did the calculations a bit differently from Shellans in two respects. First, I used the Vanguard Index 500 fund instead of the S&P 500 since that is my standard benchmark. In effect, the Index 500 fund is the S&P with dividends reinvested less Vanguard's small management fee, so there is little qualitative difference between the two. The second difference is that I did the drawdown calculations on a weekly rather than a monthly basis since that was more natural given the structure of my research database. I don't think that using weekly rather than monthly data should make much of a difference in the calculation of the ulcer index. Over the 1987-95 period, the Selects Switching System hypothetically invested in one fund at a time would have an ulcer index of 0.85. One way of interpreting this value is to say that the system was 15% less likely to be bothersome than buying and holding the Index 500 fund over the same period.

For the curious, the maximum drawdown for the same period, also on a weekly basis, was 23.6% for Selects Switching and 32.9% for the Index 500 fund. The system's was a prolonged process lasting from August 1987 to August 1988. The system would have avoided the October 1987 crash, but it would not have done well for the first eight months of 1988. By contrast, the buy and hold maximum drawdown took place in about three months starting in August 1987 due to the crash. The system would have recovered the maximum drawdown and made new highs several months earlier than the Index 500 fund. These behaviors are included in the ulcer index computation.


Added to the web site and not in the orginal newsletter:
Steve Shellans was not the first to use the term "ulcer index." That honor apparently goes to Peter Martin and Byron McCann in their 1989 book "The Investors Guide to Fidelity Funds" (John Wiley & Sons). To confuse matters, their method of calculation is significantly different than the one used in MoniResearch. For more information and for a free download of that book, which is no longer in print:
See Martin's web page

Number of Funds in Client Accounts: You have indicated that some client accounts are invested in just one fund at a time while others hold two or three funds. What are percentages of accounts of each type? Currently, about 16% hold one fund, 55% hold two, and 29% have three Select funds in their accounts. These values will change because of new clients or clients who withdraw from the program. In some cases, the number of funds held by a client will change, often according to plan. For example, I tend to phase new clients into three different Select funds over time, but then allow the account to transition to two or even one fund as the system calls for such consolidation. While it would be possible to own four or more Selects, it would be difficult to maintain these higher numbers without using the money market fund to a considerable extent, especially if owning correlated funds is to be avoided. Such a strategy would reduce returns significantly, although there would probably also be a considerable reduction in volatility.

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