## Too Much Sensitivity To The Biggest Loss

A recurring criticism with the entire approach of optima] f is that it is too dependent on the biggest losing trade. This seems to be rather disturbing to many traders. They argue that the amount of contracts you put on today should not be so much a function of a single bad trade in the past.

Numerous different algorithms have been worked up by people to alleviate this apparent oversensitivity to the largest loss. Many of these algorithms work by adjusting the largest loss upward or downward to make the largest loss be a function of the current volatility in the market. The relationship seems to be a quadratic one. That is, the absolute value of the largest loss seems to get bigger at a faster rate than the volatility. (Volatility is usually defined by these practitioners as the average daily range of the last few weeks, or average absolute value of the daily net change of the last few weeks, or any of the other conventional measures of volatility.) However, this is not a deterministic relationship. That is, just because the volatility is X today does not mean that our largest loss will beX A Y. It simply means that it usually is somewhere near X A Y.

If we could determine in advance what the largest possible loss would be going into today, we could then have a much better handle on our money management.* Here again is a case where we must consider the worst-case scenario and build from there. The problem is that we do not know exactly what our largest loss can be going into today. An algorithm that can predict this is really not very useful to us because of the one time that it fails.

Consider for instance the possibility of an exogenous shock occurring in a market overnight. Suppose the volatility were quite low prior to this overnight shock, and the market then went locked-limit against you for the next few days. Or suppose that there were no price limits, and the market just opened an enormous amount against you the next day. These types of events are as old as commodity and stock trading itself. They can and do happen, and they are not always telegraphed in advance by increased volatility.

Generally then you are better off not to "shrink" your largest historical

"This is where using options in a trading strategy is so useful. Either buying a put or call outright in opposition to the underlying position to limit the loss to the strike price of the options, or simply buying options outright in lieu of the underlying, gives you a floor, an absolute maximum loss. Knowing this is extremely handy from a money-management, particularly an optimal f, standpoint. Further, you know what your maximum possible loss is in advance (e.g., a day trade), then you can always determine what the f is in dollars perfectly for any trade by the relation dollars at risk per unit/optimal f, For example, suppose a day trader knew her optimal f was .4. Her stop today, on a l-unit basis, is going to be $900. She will therefore optimally trade 1 unit for every $2,250 ($900/.4) in account equity.

fek loss to reflect a current low-volatility marketplace. Furthermore, there is the concrete possibility of experiencing a loss larger in the future than what WOS the historically largest loss. There is no mandate that the largest loss seen in the past is the largest loss you can experience today.3 This is true regardless of the current volatility coming into today.

The problem is that, empirically, the f that has been optimal in the past is a function of the largest loss of the past. There's no getting around this. However, as you shall see when we get into the parametric techniques, you can budget for a greater loss in the future. In so doing, you will be prepared if the ahnost inevitable larger loss comes along. Rather than trying to adjust the largest loss to the current climate of a given market so that your empirical optimal f reflects the current climate, you will be much better off learning the parametric techniques.

The technique that follows is a possible solution to this problem, and it can be applied whether we are deriving our optimal f empirically or, as we shall learn later, parametrically.

## Optimum Options

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