2. . If the +DI crosses above the -DI, buy on the open of the next day. b. If the -DI crosses below the +DI, sell on the open of the next day.

In both cases the sjstem is alwajs in the maifcet.

Before seeing the actual results, it is possible to generalize the expected performance.

1. Case 2 must have more trades than case I as a result of alwajs tafcing a position when a crossing occurs.

2. Because there is no commitment to the trade (i.e., no channel), there could be frequent whipsaws in case 2.

3. Because case I uses the high and low of the prior day, its entrjprices will alwajs be equalto or worse than case 2.

4. If the Directional Indicator gives a highly reliable signal, it would be better to enter immediately, as in case 2. Parameters Defined

The piwpose of the optimization was to see if changes in the time intervals caused improvements in results Hochheimer chose the following parameters to test:

1. The +DM was calculated from 7 to 20 dajs.

2. The -DM varied from 5 above to 5 below the +DM value.

3. Two true ranges (TR) were calculated, the first using the weight of the +DM, the other using the weight of the -DM.

The test data covered all information available from 1970 to I98I. Results

Selected results are shown in Table 23-5. The patterns of the two cases are as espected. Case 2 has more trades, with a higher percentage of losses and higher rid;. The profit/loss shown in case I is generally higher than case 2, indicating that, even under ideal conditions, the RSI generates many false signals using these rules.

It can also be seen that those marfcets with a small amount of available data, T-bills, T-bonds, currencies, and gold had the shorter intervals selected for calculation. By observing the tendency for the products with more data to use longer intervals, a standard set of dajs should have been chosen rather than allowing an apparent overfitting of the data.

The philosophy of these tests, however, should be questioned. Although the independent varjing of the number of dajs in the +DM, -DM, and TR accounts for all combinations, it seems illogical. The Directional Movement Indicator is intended to be ameasurement of relative strength over a fixed time period; it produces a percentage from 0 to 100. In this study, the TR (the denominator) may have a time interval smaller than one of the +DM or -DM, generating a value greater than 100.

The independent varjing of the up and down segments of the indicator also allowed a long-term directional bias to appear. This can be seen in the optimum selection of those commodities with the shortest amount of data: the financials marfcets and the currencies. In case 2, almost all of the products with 11 years of data produced interval selections that were nearly identical, in the area of either 14 or 20 dajs.

TABLE 23-5 Comparative Performance of Directional Movement Sjstems

Kaufinans Sjstem Selection Indicator

A markets personality is in its price pattems. Some maricets, such as the stock index, are very volatile with gradual sustained upward moves and fast, sharp drops. In contrast. Eurodollars are very steadj, often trading high volume at the same price. Qualifjing martlets by noise allows you to decide which trading sU-ategj is most likely to be successful-Lower noise favors trending sjstems and high noise makes countertrend techniques more appropriate.

The concMnoise has been AsniEsed in nuniefUE sections flir«idioutttuEb(* and it is agaiu • great value when clioosiue olucli system to .ply to ama.ket, and ieiilftiue olien a maiket ts best trbd as treu»Lue essence, noise is market movement tiiat has no Arectlon or one in idiicli the amount . is ovendielmed by volatile eiratic up and dmi movement It is an un4*™rreut "f unrredirtiiile movement caused by a tToadrauee participants actme for tiieir ..wuindivi.bial objectives

The calculation for noise can be found with exanples in Chapter 17 (Adaptive Techniques"). As a simple reminder, it is defined as the efficiency ratio, ER:

Net price change

Sum of price changes as positive values

Time Frame

There alwajs appears to be more noise over short time periods. That is because noise remains at about the same level, but price trends are not clear until they have persevered for at least a few days, and often for weeks. For a trend comparison we should avoid very short-term trends; therefore, a 16day exponential smoothing will he used in the following comparison. To be certain that the efficiency ratio is stable, it will be calculated over a 65-day period.

Results of Efficiency Ratio Selection

Figure 23-10 shows that, when returns are compared using the efficiency ratio, profits are clearly greater when the ER is high; losses are laiger when the ER is low. Based on a broad sampling of maikets, this is a very useful pattern for classifjing maikets. The greatest profits are in the upper right part of the diagram where there is less noise; the greatest losses are in the lower left comer where there is the most noise. We can conclude that

FIGURE23-I0 Efficiency ratio and trend performance. A clear pattem can be seen when a long-term efficiency ratio (maiket noise) is plotted against the trend performance of a broad sampling of maikets using a 16-day exponential smoothing.

(65-Day Eff Ratio and 16-Day Tfend)

3 300 a

:S 200 I

% ™ - 0

-100

0.08 0.1 0.12 0.14 0.16 0.18 0-2 0 22 0 24 65-Dav Efficiency Ratio

Wlien the efficiency ratio is high, then a trend sjstem is a better strategj. When the efficiency ratio is low, then a countertrend sjstem is best.

in the second case, a countertrend approach does not mean that you must set a short position when the market is moving up. It can also mean taking profits on a long position when there is a countertrend sell signal, or building a long position when a countertrend buy signal occurs on a price drop. While the efficiency ratio is not apecifically a directional indicator, it does seem to classify markets as trending or nontrending.

PROBABILITY OF SUCCESS AND RUIN

The relative size of trading profits and losses, the fi-equency of the losses, and the sequence in which they occur comprise the equity profile of traders and sjstems. This profile can be used to determine the capitalization necessary to maintain trading during the losing periods and allow the sjstem to retum to its full potential. In investment terminologj-and probability theory, the level at which you no longer have enough money to continue trading is called the point of ruin, and the chance of getting there is the rid; of ruin. The probability of the risk of ruin is normally expressed as

where 0 < < 1,0 mdicares no risk, and 1 cenain ruin

A-P - i \ -P),P isthe proportion nf winning trades, also considered the traders

advantage = the beginning units of trading capital

A sjstem of trading that has 60° profitable trades and trading capital in $ 10, units will have arid; of ruin calculated as follows:

A = 0.60 - (1 - .oco) - 0.20 "W+0.20j U.20j ]

When 1 ($10,000), R= 0.33, and when 2 ($20,000), R= O.II. Therefore, the greater the traders advantage or the greater the capital, the smaller the rid; of ruin (Figure 23-11).

When using profit goals, the chance of ruin should decrease as the goal becomes smaller. The relatlonsh can be expressed as.