Hochschule Düsseldorf
University of Applied Sciences
Fachbereich Medien
Faculty of Media

ISSN: 2567-2347

editor-in-chief: Peter Vogel, peter.vogel@hs-duesseldorf.de

staff-member: Patrick Blättermann, patrick.blaettermann@hs-duesseldorf.de

The series TRADING, founded on July, 2017, covers scientific reports about algorithmic trading.
This includes, for example, the topics investing, order execution and evaluation of stock price data.
The series intends to bridge the gap between theory and practice, reporting scientific results without secretiveness and giving new insights.
Technical terms are kept to a minimum in order to reach a broader readership.

Trading 1: Investing under constraints - part 1: Investing as Random Trial

An investment algorithm is introduced for a market of individual securities by maximizing the amount of investment for each trading day.

This is done under constraints in order to limit the risk and trading costs and to take into account an individual investor.

Purchased securities are selected randomly among those who meet the buy condition, making trading a RANDOM TRIAL.
The expected return is evaluated for the investment algorithm with respect to the random selection for a holding period of one day, i.e. securities are sold after one trading day.

(short abstract)

Trading 2: Investing under constraints - part 2: Extension of the statistics for holding periods greater than one day

The second part of the series drives forward considerations about investing in the securities of a market, started in the first part.

It is addressed to experts of financial mathematics and may be of relevance for funds managers and private investors.

All considerations are based on constraints determining the amount of new investments, depending on investment parameters.

Another investment parameter is the holding period, defining how long a new investment is hold before finished.

The theory, developed further on in this second part, is marked as follows:

  • The theory is free of assumptions about the price development of the securities. Hence, no attempt is made to establish a realistic model fpr price movements.
  • A finite number of securities are traded, building a market.
  • Investing in a security requires to meet a buy condition. After expiry of the holding period, the investment is finished.
  • Trading is described by elementary recursive equations. Evaluation of the equations for the whole trading period yields the return of investment at the end of trading. The equations are excited by two exogenuous quantities:

    The number of securities for each trading day, which meet the buy condition and the gain, resulting from the sales of the securities after expiration of the holding period.

  • Investiting will be idealized in order to express the return in dependence from the exogenous quantities and investment parameters without evaluating the recursive equations. This is done by the so-called IDEAL TRADING SYSTEM.

The return of the ideal trading system extends the statistical description of part 1 towards holding periods greater than one day.

Since causality is violated by the idealizations, the ideal trading system cannot be implemented for security trading.

However, it can be simulated and is more easily quantifiable.

The effect of violating causality on the trading process and return is investigated experimentally and theoretically depending on investment parameters in detail.

(short abstract)