# Minimum Tests to Detect High Volatility Risk, from James Sogi

September 10, 2007 |

The problem that a short lookback period does not account for potential volatility regime change is well understood. This is really two questions First, what is the lookback period? Second, how does one accommodate quantitatively for volatility change?  This might be addressed in different ways. First, look for volatility similar to high volatility regimes such as big moves. Second, in Iceberg Risk, Kent Osband suggests taking two distributions, a normal for current everyday entry/exit, and one for outliers and tail risks, and combining the two. Risk control, money management principles and use of leverage could be combined with the trading signals and by using eight-sigma for the risk factor but a normal curve for entries. Phase in could be graduated as survival odds of low volatility drop, and reduce leverage rather than increase it.

Another approach is from Strange Curves, Counting Rabbits, & Other Mathematical Explorations by Keith Ball from the field of information theory. The question in his example would be how to compute the minimum number of tests to give a robust reading on the number of children with a certain blood condition. The analysis is similar to the finding the one different coin out of nine with the minimum number of weighing problem, which is solved by dividing the 9 into 3 groups. Rather than equal probabilities as with coins, Ball poses the problem of testing children for a rare blood condition. This is similar to testing for a tail event in the market using a binary protocol — is, or is not, a tail. The number of tests is m and the test is computed as 2^m to be greater than n. For n=3200, then m=12, or 4096, which is greater than 3200. This provides a simple rule of thumb, that might be applied to divide the period into 12 samples, or a lookback of 266 days. The results is derived from principles of entropy as the minimum number of tests to detect the condition. Applied to markets, the lower number detects the cycle changes better. The number of tests might be the divisor of the sample to compute the lookback period. The rare condition to try to detect is the risk of a large excursion. The empirical occurrence of a four-sigma event has a probability of 1/400 or .0025. Another rule of thumb would be 1+2mnp, or 1+2*3200*12*.0025=196. Still some additional risk parameters are needed for the eight-sigma events we're seeing again per the Osband approach for protection in the turns.

Another method would be to change trade parameters to fit expanded volatility, and read the newspaper to follow fundamental changes. And there is truly no substitute for experience and good judgment and a good attitude.

## Eric Ross writes:

Models are based on backtesting. Models are based on prior market moves that have happened. Thus, quants are nothing more than historians trying to predict future events from past performance. So, why is Wall Street looking to go black-box and and substitute historians for human traders? Isn't the human element of guts and feeling a powerful tool to trade by, when combined with charting and experience?

## Rod Fitzsimmons Frey explains:

The heart of the scientific method is, say something testable, then try to disprove it by testing. If you cannot disprove a hypothesis, you may use it as though it were true (it is now a 'model'); however, continue trying to disprove it, and as soon as you do, cease using it.

Counters try to apply this method to markets. The only way to apply the scientific method to markets is to form a hypothesis (the market goes up every Monday after a down Friday) and test it against historical data. There are well-established statistical tests to take a certain number of outcomes (X number of up Mondays after Y down Fridays) and say something about the odds that such an outcome happened by chance. If the odds are long that something has occurred by chance, you may be wise to place a bet the next time the conditions occur.

Insofar as human beings have invented the scientific method and its servant, statistics, nothing could be more human than applying these tools to the market, as we have to medicine, evolution, physics, chemistry, physiology, agriculture, biology and botany.

Aristotle teaches us that we should apply only the level of precision to an inquiry that its nature allows: seeking more or less precision is a fool's path. The debate is about how much the markets will yield to scientific inquiry. The view of the Palindrome is that the markets are more akin to psychology and sociology than physics; the truth of the markets is determined by time and place and one must not trust the past. In other words, do not attempt to apply the tools of physics.Intuition, common sense, and experience taught many things that were eventually shown to be wrong when the scientific method was applied — the Earth's being flat and heavy objects' falling faster are obvious examples. I wouldn't trust intuition, but maybe I have no guts.

Fortunately, unlike psychologists, priests, or economists, we in the markets have an excellent scorekeeping mechanism.

## Denis Vako remarks:

The "little birdy" model in the paper Mutual Information as a Tool for Identifying Phase Transitions in Complex Systems by Robert Wicks, Sandra Chapman and Richard Dendy covers regime change, clustering, entropy and velocity — all in one place!

## Russ Sears extends:

This is similar to the "credibility problem" actuaries face with Property and Casualty insurance.

Sometimes volatility changes due to a jump in the frequency of claims, but usually a regime shift occurs by when the size of the average claim jumps. New rulings or litigation or creative lawyers, besides more ordinary causes like inflation or new treatment cost.

The individual large jump should be looked at closely. Is it a new cause, or just an extreme example of current events? In other words, does this set precedent? Has the target changed, under new rules, or has the shooter changed, fighting more aggressively?

The volatility changes are important. Likewise it takes time and many more claims to establish a new norm.

Property and Casualty companies react to high-cost hurricanes poorly at first, due to the unknown of who got stuck with what claims. Then they rebound due to a softer regulatory environment and a mistaken assumption that because it happened once its more likely to happen again.

## Gary Rogan writes:

Unlike regime changes in the physical world that are usually tied to the invariant physical laws, regime changes in the markets have no reason to have any specific characteristics because human beings are actively trying to outsmart the system while at the same time other human beings as well as random, from the financial markets point of view, physical reality changes inject error signals into the markets. It is also unknowable when the change phase is over and the new regime begins. It is futile to hope that any amount of backtesting will result in a reliable model. While the regime is constant, backtesting works, but when the regime unpredictably changes it stops working.

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