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131.00 207
,02.,8 278
208 121.14 234
212.12 134 301.82 82
TABLE
II-1
Dollar Volatilities (First Line) and Number of Contracts Equivalent to 10 New S&P 500s on 12/31/1998 (Second Line) Broken Down by Market and Year (Continued)
132.09 213 103.10 232 78.00 350
80.81 284 01.04 300 80.50 317
130.08 218 94.31 301 30.50 352 137.00 207
10602 170 03.50 2.38 70.00 370 102.50 175
1Y.40 21, 1oo.so 286 100.50 232 223.00 124 221.81 128
123.78 2 8 234.02 121 130.50 152 330.13 04 338.87 3.4
125.04 12657 225 224
150.08 180 ea.38 328 207.84 130 227.3, 125 115.58 24s 72.01 380 150.50 188 142.00 200
157.31 15 1.04 180 187
145.38 100 217.40 130 351.12 81 317.34 88
124.80 227 2c0.70 137 201.05 37
183.42 147
151.03 ,a2
130.01 203 180.78 140 0,022 40
,08.08 282 208.01 130 332.50 85
02.88 305 ,048, 172 201.30 141
130.33 204 210.04 ,20 332.05 0.5
200.74 251.10 104 113 254.05 351.75 11, 81 024.30 3,
338.40 1021.57. 84 28
ooo.,o 081.03 583.44 32 42 43
and the number of contracts that would have to be traded to equal the dollar volatility of 10 new S&P 500 contracts at the end of 1998. For the current studies, the average daily volatility is computed by taking a 200-day moving average of the absolute value of the difference between the current close and the previous one. The average daily volatility is then multiplied by the dollar value of a point, yielding the desired average daily dollar volatility. The dollar value of a point can be obtained by dividing the dollar value of a tick (a market s minimum move) by the size of a tick (as a decimal number). For the new S&P 500 contract, this works out to a value of $250 per point (tick value/tick size = $25/0.10). To obtain the number of contracts of a target market that would have to be traded to equal the dollar volatility of IO new S&P 500 contracts on 12/31/1998, the dollar volatility of the new S&P 500 is divided by the dollar volatility of the target market; the result is multiplied by 10 and rounded to the nearest positive integer. All the simulations reported in this book assume that trading always involves the same amount of dollar volatility. There is no compounding; trade size is not increased with growth in account equity. Equity curves, therefore, reflect returns from an almost constant investment in terms of risk exposure. A constant-investment model avoids the serious problems that arise when a compounded-investment approach is used in simulations with such margin-based instruments as futures. With margin-based securities, it is difficult to define return except in absolute dollar amounts or in relationship to margin requirements or risk, simple ratios cannot be used. In addition, system equity may occasionally dip below zero, creating problems with the computation of logarithms and further obscuring the meaning of ratios. However, given a constant investment (in terms of volatility exposure), monthly returns measured in dollars will have consistent significance over time, t-tests on average dollar return values will be valid (the annualized risk-to-reward ratio used to assess performance in the tests that follow is actually a resealed t-statistic), and it will be easy to see if a system is getting better or worse over time, even if there are periods of negative equity. The use of a fixed-investment model, although carried out more rigorously here by maintaining constant risk, rather than a constant number of contracts, is in accord with what has appeared in other books concerned with futures trading. This does not mean that a constant dollar volatility portfolio must always be traded. Optimal f and other reinvestment strategies can greatly improve overall returns; they just make simulations much more difficult to interpret. In any case, such strategies can readily and most appropriately be tested after the fact using equity and trade-by-trade data generated by a fixed-investment simulation. BASIC TEST PORTFOLIO AND PLATFORM
A standardportfolio of futures markets is employed for all tests of entry methods reported in this section. The reason for a standard portfolio is the same as that for a fixed-exit strategy or dollar volatility equalization: to ensure that test results will
be valid, comparable, and consistent in meaning. All price series were obtained from Pinnacle Data in the form of continuous contracts, linked and back-adjusted as suggested by Schwager (1992). The standard portfolio is composed of the following markets (also see Table II-l): the stock indices (S&P 500, NYFE), interest rate markets (T-Bonds, 90-day T-Bills, lo-Year Notes), currencies (British Pound, Deutschemark, Swiss Franc, Japanese Yen, Canadian Dollar, Eurodollars), energy or oil markets (Light Crude, #2 Heating Oil, Unleaded Gasoline), metals (Gold, Silver, Platinum, Palladium), livestock (Feeder Cattle, Live Cattle, Live Hogs, Pork Bellies), traditional agriculturals (Soybeans, Soybean Meal Soybean Oil, Corn, Oats, Wheat), and other miscellaneous commodities (Coffee, Cocoa, Sugar, Orange Juice, #2 Cotton, Random Lumber). Selection of markets was aimed at creating a high level of diversity and a good balance of market types. While the stock index bond, currency, metal, energy, livestock, and grain markets all have representation, several markets (e.g., the Nikkei Index and Natural Gas) would have improved the balance of the portfolio, but were not included due to the lack of a sufficient history. In the chapters that follow, entry models am tested both on the complete standard portfolio and on the individual markets that compose it. Since a good system should be able to trade a variety of markets with the same parameters, the systems were not optimized for individual markets, only for the entire portfolio. Given the number of data points available, optimizing on specific markets could lead to undesirable curve-fitting. Unless otherwise noted, quotes from August 1, 1985, through December 31, 1994, are treated as in-sample or optimization data, while those from January 1, 1995, through February 1,1999, are used for out-of-sample verification. The number of contracts traded is adjusted to achieve a constant effective dollar volatility across all markets and time periods; in this way, each market and time period is more comparable with other markets and periods, and contributes about equally to the complete portfolio in terms of potential risk and reward. All tests use the same standardized exit technique to allow meaningful performance comparisons between entry methods.
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