In the second half of the nineties markets were trending sharply and consistently. In such an environment technical analysis was powerful; computer based models did extremely well: they are inherently trend-following. The Day Trading INDU Model also did very well (annual profits between 120% and 300%), although our model had incorporated defensive strategies against unforeseen "side-trends". These strategies pay a price in trending markets, and especially in mildly trending markets. Thus, when markets do trend (gently), the Daily INDU model tends to under-perform pure trend-chasing models, whereas in other times (especially during side-trends, when most models lose money) it over-performs them. After 2000, the performance of computer based models declined steadily: many models produced losses. The Day Trading INDU Model was also affected, albeit less than most other technical models: it has managed to stay in the black. The INDU model has been tested for decades backwards: it produces few years of slightly negative profits, a respectful number of years with slightly positive profits, and a respectful number of years with high or very high profits. Trending markets follow side markets: our Day Trading model is well equipped to take advantage of the next trending market.

Past and future performance

The Day Trading INDU Model has been tested in recent years to determine its (average, or expected) riskyness and profitability. The larger is the capital, the lower is the risk of being wiped out, but also the lower is the profit ratio. We have tested the model using a working capital of 3,2 times the (estimated) margins requirements - at the beginning of each year - of a standard broker in 2000. For example, to allow clients to trade a DJIA future overnight, in the year 2000 a broker might have required a "Minimum Deposit" of $6,250: no overnight positions would be allowed with less. The "Working Capital" required is thus everything more than $6,250: we used $20,000, which is = $6,250 * 3,2. And Total Capital = Minimum Deposit + Working Capital = $26,250.

In sample, the model - using the capital above - has been estimated to generate a 2,6% risk ...

Risk is defined here as the probability that during the (first) year of trading, a negative sequence will begin and will generate losses greater than the working capital, forcing an end of the trading activity. The negative sequence has to begin during the year considered

... and expected annual profits fluctuating around 120%.

These "in-sample" indicators, which are commonly used in financial circles to describe and publicize the performances of a forecasting financial model, would suggest that the Day Trading INDU Model is one of the best performing forecasting models of the US stock exchange. Out-of-sample testing, however, provides a much more reliable description of the true predictive powers of a forecasting model.

Although not entirely misleading, “in-sample” estimated performances clearly overstate the models' predictive power: after all, anyone is able to gain on the stock market if he knew in advance how it would have behaved. Traders should be well aware that most models publicized the Web are described through only “in-sample” estimated performance indicators (usually very good results are shown); but when they are used in the real world, i.e. out of sample, they often yield a poor performance at best .

Out of sample estimates have led us to the conclusion that the actual annual risk of the Day Trading INDU Model (with the parameters given above) is around 3,4% and the expected (or average) net pre-tax annual profit is around 75%, or somewhere between 50% and 105%. The profitability estimates are rather robust and reliable when the time period considered is long; and become increasingly unstable - as expected - when the trading period considered is reduced.

The Day Trading INDU Model exhibits a mild serial negative correlation of trading gains & losses, particularly on horizons of one-two month and of five years), but we were unable to improve the model's performance using this information, due mainly to its instability. To put it simply, what that means is, after one negative (couple of) month(s) (or five years) the model's predictive ability tends to rise slightly above its normal levels, and vice versa.

Finally, traders should be aware that the theoretical net (after trading commissions have been subtracted) performance may differ widely from actual performance, due mainly to:

• Slippage : this is a fairly minor element when the number of traded contracts is low, but it does tend to play slightly against the model (about 250$ to 400$ per year when trading one DJIA future).

• The model is defenceless against dramatic events occurring while markets are closed (unless the investor covers himself with a put option). However, it is also true that the Day Trading INDU Model is a better performer when the market's volatility is high (as after dramatic events & market moves).

For example, on Sept. 10, 2001 , the Model issued a BUY signal, and suffered a loss of about $6.000 when, after the terrorist attacks, the markets reopened on Sept. 16: obviously it had been unable to curtail the losses with the use of stop-loss orders while markets were closed. However, total September losses were limited to $650, while the Model Gained $2,200, 4,200, and 4,400 respectively in the last three months of 2001. The stress to the model caused by the dramatic September events is best seen through an analysis of the sequence of gains and losses of that whole period. From its historical peak of July 9, 2001, the sequence of accumulated profits reached a minimum on Sept.18, at $16,300 lower than its July peak. Therefore, suppose a very unlucky investor had started using the model right on July 9: he would have seen his working capital decline from $20,000 to $3,700 (total capital from $25,000 to $8,700); and would not have seen a recovery to above its initial levels until Dec.4, 2001.

• Accounting & Communication costs.
  
  
• Mistakes on placing the orders.
  
  
• Psychological inability of traders to actually follow the trading rule they have chosen. This is actually the greatest of all risks: it is recommended that traders form a team, with the specific aim of developing reciprocal control procedures to increase each members' discipline.
  
  
• On the positive side, one should consider any income derived from assets deposited to fulfill margin requirements.
  
  

More information on theoretical past performance

The Graph above shows how, notwithstanding the leverage of futures contracts, the Day Trading INDU Model struggled to recover the initial losses during the first seven months of 2003, but ultimately posted a nice profit (about 45%) at the end of the reported period (Dec.22, 2003). The 2003 performance was below the 1990's average due to the initial weakness of the upward trend that started on March 12, combined with the "side-trend" strategies that drove the model too often and at the wrong time. 2004 was one of the most difficult years for technical computer models, as the market

drifted trendless for most part of the year. In this environment the performance of the D.T.I.M (profits insignificant but positive, shown in the graph above) was outstanding, by far better than the (negative) performances of most computer-based technical models, and in the black once again.

The table below summarizes the performance of the Day trading INDU model in 1998 - 2003.

Assumptions of the Table "INDU MODEL - Theoretical Results"

• Each year a new, independent trading experiment is initiated.