## An options strategy such as this can totally eliminate such terminal losses

If we were to determine the optimal f on this stream of trades, we would find its corresponding geometric mean, the growth factor on our stake per play, to be 1.12445.

Now we will take the exact same trades, only, using the Black-Scholes stock option pricing model from Chapter 5, we will convert the entry prices to theoretical option prices. The inputs into the pricing model are the historical volatility determined on a 20-day basis (the calculation for historical volatility is also given in Chapter 5), a risk-free rate of 6%, and a 260.8875-day year (this is the average number of weekdays in a year). Further, we will assume that we are buying options with exactly .5 of a year left till expiration (6 months) and that they are at-the-money. In other words, that there is a strike price corresponding to the exact entry price. Buying long a call when

 the system goes long the underlying, and buying long a put when the system goes short the underlying, using the parameters of the option pricing model mentioned, would have resulted in a trade stream as follows: Date Position Entry P&L Cumulative Underlying Action 870106 L 9.623 0 0 24107 LONG CALL 870414 F 35.47 25.846 25.846 27654 870414 L 15.428 0 25.846 27654 LONG PUT 870507 F 8.792 -6.637 19.21 29228 870507 L 17.116 0 19.21 29228 LONG CALL 870904 F 21.242 4.126 23.336 31347 870904 L 14.957 0 23.336 31347 LONG PUT 871001 F 10.844 -4.113 19.223 32067 871001 L 15.797 0 19.223 32067 LONG CALL 871012 F 9.374 -6.423 12.8 30281 871012 L 16.839 0 12.8 30281 LONG PUT 871221 F 61.013 44.173 56.974 24294 871221 L 23 0 56.974 24294 LONG CALL

If we were to determine the optimal f on this stream of trades, we would find its corresponding geometric mean, the growth factor on our stake per play, to be 1.2166, which compares to the geometric mean at the optimal f for the underlying of 1.12445. This is an enormous difference. Since there are a total of 6 trades, we can raise each geometric mean to the power of 6 to determine the TWR on our stake at the end of the 6 trades. This returns a TWR on the underlying of 2.02 versus a TVV'R on the options of 3.24. Subtracting 1 from each TVV'R translates these results to percentage gains on our starting stake, or a 102% gain trading the underlying and a 224% gain making the same trades in the options. The options are clearly superior in this case, as the fundamental equation of trading testifies.

Trading long the options outright as in this example may not always be superior to being long the underlying instrument. This example is an extreme case, yet it does illuminate the fact that trading strategies (as well as what option series to buy) should be looked at in light of the fundamental equation for trading in order to be judged properly.

As you can see, the fundamental trading equation can be utilized to dictate many changes in our trading. These changes may be in the way of tightening (or loosening) our stops, setting targets, and so on. These changes are the results of inefficiencies in the way we are carrying out our trading as well as inefficiencies in our trading program or methodology.

I hope you will now begin to see that the computer has been terribly misused by most traders. Optimizing and searching for the systems and parameter values that made the most money over past data is, by and large a futile process. You only need something that will be marginally profítable in the future. By correct money management you can get an awful lot out of a system that is only marginally profitable. In general, then, the degree of profítability is determined by the money management you apply to the system more than by the system itself

Therefore, you should build your systems (or trading tech-niques, for those opposed to mechanical systems) around how certain you can be that they will be proBtable (even if only marginally so) in the future. This is accomphshed primarily by not restricting a system or technique's degrees of freedom. The second thing you should do regarding building your system or technique is to bear the fundamental equation of trading in mind. It will guide you in the right direction regarding inefficiencies in your system or technique, and when it is used in conjunction with the principle of not restricting the degrees of freedom, you will have obtained a technique or system on which you can now employ the money-mmagement techniques. Using these money-management techniques, whether empirical as detailed in this chapter, or parametric (which we will delve into starting in Chapter 3), will determine the degree of profítability of your technique or system.

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