Stanislaus Maier-Paape

Automatic one two three

Abstract In this paper, we show how market-technical trends can be calculated automatically from underlying price processes using a stop and reverse process. The basic tool is a so called minmax process indicating all relevant minima and maxima. For the existence of the minmax process, we give a constructive proof. Several successful trend-following trading strategies can be implemented automatically based on this 1-2-3-trend indicator.

A General Framework for Portfolio Theory—Part I: Theory and Various Models

Utility and risk are two often competing measurements on the investment success. We show that efficient trade-off between these two measurements for investment portfolios happens, in general, on a convex curve in the two-dimensional space of utility and risk. This is a rather general pattern. The modern portfolio theory of Markowitz (1959) and the capital market pricing model Sharpe (1964), are special cases of our general framework when the risk measure is taken to be the standard deviation and the utility function is the identity mapping. Using our general framework, we also recover and extend the results in Rockafellar et al. (2006), which were already an extension of the capital market pricing model to allow for the use of more general deviation measures. This generalized capital asset pricing model also applies to e.g., when an approximation of the maximum drawdown is considered as a risk measure. Furthermore, the consideration of a general utility function allows for going beyond the “additive” performance measure to a “multiplicative” one of cumulative returns by using the log utility. As a result, the growth optimal portfolio theory Lintner (1965) and the leverage space portfolio theory Vince (2009) can also be understood and enhanced under our general framework. Thus, this general framework allows a unification of several important existing portfolio theories and goes far beyond. For simplicity of presentation, we phrase all for a finite underlying probability space and a one period market model, but generalizations to more complex structures are straightforward.

Correctness of Backtest Engines

In recent years several trading platforms appeared which provide a backtest engine to calculate historic performance of self designed trading strategies on underlying candle data. The construction of a correct working backtest engine is, however, a subtle task as shown by Maier-Paape and Platen (cf. arXiv:1412.5558 [q-fin.TR]). Several platforms are struggling on the correctness. In this work, we discuss the problem how the correctness of backtest engines can be verified. We provide models for candles and for intra-period prices which will be applied to conduct a proof of correctness for a given backtest engine if the here provided tests on specific model candles are successful. Furthermore, we hint to algorithmic considerations in order to allow for a fast implementation of these tests necessary for the proof of correctness.