Intermarket Three S&P 500 Index - CME-Daily 04/21/82 - 12/19/96

450000

400000

350000

300000 - 250000 I 200000 150000

100000 50000 0

50000 - --------- ------ ----------- --------,----------

1 21 41 61 81 101 121 141 161 181

Number of Trades

Equity • Peaks

One reason is that many technical analysis indicators merely explain the same thing in different ways. Therefore, we are adding indicators that are so highly correlated with each other that they duplicate each other. Furthermore, additional filters may start to be contradictory to the existing filters. This would lead to fewer trades, but worse results.

This system averages about one trade per month. If more filters cut the number of trades down substantially, some practical problems may result. The most obvious one is that the historical data may not yield sufficient trades for the systems performance to be statistically valid.

In addition, we may be aiming toward the ultimate example of curve fitting. We can see that the S&P has gone up for the entire history at a relatively constant slope. Once we know this, a system that trades very little will be expected to do very well in backtesting, but may not hold up under different conditions.

In this example, we chose a very simple linear model of the data. Future efforts, designed toward improving upon these results, or toward investigating other intermarket relationships, can use a somewhat more complex approach. The tools of linear regression or multiple regression can be effectively used. The data can be better pre-processed by using, for example, ratios, logarithms, weighted or exponential averages, or myriad other approaches.

References

Box, George E. P., Hunter, William J., and Hunter, J. Stuart, Statistics for Experimenters-An Introduction to Design, Data Analysis and Model Building New York: John Wiley & Sons, 1978.

Deming, W. Edwards, Statistical Adjustment of Data, New York: Dover Publications, 1938, 1943.

Farnum, Nicholas R., and Stanton, La Verne W, Quantitative Forecasting Methods, Boston: PWS-Kent Publishing, 1989.

Jutik, Mark G., "Developing Indicators for Financial Trading," in Jess Lederman and Robert A. Klein

(Eds.), Virtual Trading, Chicago: Probus Publishing, 1995. Keeping, E. S., Introduction to Statistical Inference, New York: Dovet Publications, 1995. Mandel, John, The Statistical Analysis of Experimental Data, New York: Dover Publications, 1964. Vince, Ralph, The Mathematics of Money Management, New York: John Wiley & Sons, 1992.

Conclusion

We have shown by example the development of a simple system utilizing intermarket analysis. The concepts presented can easily be adapted to help traders develop trading systems that will improve their probability of success.

Complex Indicators: Nonlinear Pricing and Reflexivity

Christopher Thomas May

The purpose of this chapter is to give potential investors an overview of the need for using nonlinear pricing technology. In the financial market, especially, we see how well the components of this technology work in concert. Nonlinear pricing affects asset allocation, stock selection, option pricing, and risk management.

Background

Some of the best minds, both academician and practitioner, are heralding a fundamental change in economic thinking. The practical implications are far reaching and raise two important questions: How can we quickly improve our understanding of market behavior? How have we been misled in decades past? We will begin with the latter question.

A common approach to market analysis is to assume that large price changes are usually traceable to well-determined causes that should be eliminated before attempting a stochastic model of the remainder. Such preliminary censorship brings any distribution of price changes closer to resembling the popular and better understood Gaussian curve. The distinction between the causal and random areas is sharp in the normal (Gaussian) case and very diffuse in the stable (Paretian) case. The difference between these two distributions may allow for arbitrage opportunities as it changes a fundamental assumption in financial theory. More on that later (see Figure 15.1).

The very practice of fitting linear (e.g., regression) models, particularly those involving trended variables, acted to filter out low-frequency variance and outliers, thereby making real distributions appear "normal." But they are not normal at all. The appearance is just an artifact of a shotgun wedding of deterministic theory with "random shocks." Although the motivation is to have this filtered data fit current linear theory, it is not a scientific approach.

Why does this motivation for linear models exist? John Holland, father of the genetic algorithm said, "It is little known outside the world of mathematics that most