Trading Systems

In finance one has to deal with a series of prices that are of a random nature. The problem of the trader – or of the investor – is to extract the signal buried in noise – if it exists – that is, to identify the stochastic process that best identifies it.

Is it possible to infer, from a series of financial prices, something about the successive prices that will be observed? This has much to do with their independence.

Some more issues about independence of successive prices using the favorite algorithm of Thomas Bayes.

Another issue that has to occupy the trader – or the investor – is whether the characteristics of a process tend to repeat themselves or if every time one seats in front of the PC he has to confront himself with an entire new world.

It makes a lot of difference if the stochastic process that governs the time series of prices can be worked out in an analytical form or not.

There would be no hope to make consistently profitable trades if there were no such things as those called trends. But are they there indeed?

We are back again confronted with a major issue: can we really infer from the past prices something about the future prices? Is there some insurance policy we may subscribe on this subject?

In a sense the Ljung-Box test is the insurance policy we were looking for in the previous chapter

.

Trends are not everything

:

financial prices

do have periodic components

which, if properly

identified

,

allow one to take correctly positions

long/short

.

The time series of prices in itself provides a limited amount of information; there is therefore the need to elaborate on these sets of prices

.

The series of past prices can be used to forecast future prices or to filter the prices themselves to find their true values. However, the normal criteria used to shape the models are of very little use, and new criteria have to be relied upon.

The ideas underlying the method of least squares and of the ordinary regression can be generalized using any family of fitting functions chosen wisely.

The complete open-loop scheme includes a block that is never present in normal system theory: the decision on whether to buy or sell. The indicator plus the decision block forms a trading system of which it is given a first example. A unique concept of optimization is introduced.

Not all trading systems are physically realizable and of course the commercial ones that provide the best results are often not physically realizable. The problem is reminiscent of that of the noncausal filters of system theory.

The equity line is itself the realization of a stochastic process (not to be confused with the one that governs the prices) and the most important question is whether the different profit & loss that compose it are of a chaotic nature or not.

There is nothing metaphysical in the word prediction because in reality it is just a definition. What really matters is if the prediction is good enough, no matter how it is made. In particular, this applies to the equity line, which for us is the fundamental parameter.

The indicator AR(3) and

the corresponding trading system are formalized. The pros and cons are listed.

Often the input of a map (or indicator) is the output of another (or the same) indicator. This practice can significantly improve the performance of the system in two stages so constituted.

The introduction of the transfer function

,

well known

to the devotees of

systems theory

,

facilitates the operations and

broadens the horizons

of trading

.

The use of well-known electronic circuits as models, simplifies the definition of indicators and trading systems.

More simple lag filters in series approximate well the Gaussian filter, which proves very useful also in the practice of trading.

An indicator (and the trading system eventually derived from it) should be stable, that is, it should follow more or less faithfully the directions of the price series.

A new circuit model is used – the classic lag compensator – from which a trading system is designed that can have no operations at a loss.

Another classic filter of electronics is used to separate the signal from the noise superimposed to the prices.

Here is another classic electronic filter, used to separate signal from noise superimposed to prices, with good results. But also the principle of parsimony peeps out.

The students of technical analysis are accustomed to indicators

that lag on prices. It may be interesting to discover the form of

an indicator that anticipates

the price trend

.

A celebrated filter

,

yet that gives

good results only by arranging two of them in series

.

A filter that is recommended to make fast trading. It must then be used only with assets possessing low transaction costs (Forex first).

How to change a trading system that is suitable for swing trading into a system best suited for fast trading (intraday and scalping) – and vice versa.

The trading systems react to changes that are rare but conspicuous (fat tails) and that – so to speak – should not be there.

Feedback trading entails staying on the sidelines during periods (and there are always) in which the trading system does not work properly.

The application to finance of the classical closed-loop scheme starts quietly, but then builds up into a very good performance.

We introduce a legendary representation of systems and show that it is capable of providing excellent results also in trading activities.

As time elapses, which changes undergo the values of the parameters that have been found in an optimization? Is this a significant problem?

This is definitely the best indicator possible to interpret the market, not necessarily to build a trading system.

The frequency response is yet another representation of systems which can result in a more accurate use of filters in the world of trading.

In which market conditions is it possible that

our trading system

may not work

well? The

signal-to-noise ratio provides us with

an answer

.

The popular measure of the goodness of the equity line, that is, the maximum drawdown, is not the best possible measure. You can do better.

We end this book with the sumptuous performances of the trading systems based on the Meyer algorithm.