Optimization for Algorithmic Trading

Background

Much of the literature for systematic trading focuses on testing different financial price forecasting models. What's wrong with forecasting financial time series?

1. Price forecasting doesn't align well with the objective of a trader. As a trader, I'm less interested in whether the price over the next n periods is going up, down, or sideways. What I'm truly interested in at any given point in time, is whether I should go long, short, or close out open positions.

2. Financial time series are highly random. A nonexhaustive list of issues associated with price forecasting financial series includes:

Issues:

• Leptokurtic characteristic of price changes.
• Apparent nonstationarity or unstable sample variances across periods.
• Discontinuities in prices e.g. jump discontinuities at market open or close.

Solutions:

• Fractional price changes. Price changes are random while fractional price changes can exhibit serial dependence.
• Use of "trading time". Although price changes are highly leptokurtic, price changes over transaction or volume based windows can be nearly gaussian over longer periods.

The goal of this project is to create a modeling framework that aligns with the objective of a trader. The included methodology and code can be used for optimizing trading systems.

Concept

$X$ = input matrix of covariates
$Y$ = matrix of target labels with elements $y_i \in {0,1,2}$
$F_k$ = model approximating conditional probability $P(Y_k|X)$

Assume we have some matrix $X$ of covariates that contain predictive information. The goal is to create a model that exploits this information to systematically place trades. Trading can be described using a three class sample space directly mapping to the three trading positions of "short", "long", and "closed". The labels $Y$, representing these three states, can be generated from fixed duration returns, which have no guarantee of optimality, or directly optimizing the labels as part of the modeling process. Optimizing the model and target labels while conditioning on the inputs can be done using a variant of Kadane's algorithm that accounts for trade frictions and "risk". Trade frictions should account for both expected transaction costs and slippage.

Given some risk constraint $r_k$ and the expected trade frictions, the algorithm maximizes returns. In this context, "risk" can be a measure of dispersion or some approximation of tail risk. The optimal labels $Y^{\ast}$ can change depending on this chosen risk constraint. For each possible solution $Y_k$ corresponding to a risk constraint $r_k$, a model $F_k$ can be fitted to approximate the conditional relationship between $X$ and $Y_k$. Then, the estimated probabilities $P(Y_k|X)$ can be used to evaluate the expected performance using time series cross validation. Among the candidate models $F_k(Y_k,X)$, there exists an optimal joint model and target label solution $F^{\ast}(Y^{\ast},X)$.

Code

• createEnv.sh - bash script for creating virtual python environment.
• backtest.py - class and methods used for FX trade label optimization and testing.
• backtest_futures.py - class and methods for trade label optimization and testing of futures contracts.
• main.ipynb - python notebook demonstrating usage and methodology.

Within the backtest.py module, the method target_optimal contains the algorithm for optimizing trade labels. This can be used to generate different potential solutions given some input target constraints. Then, the optimal model can be found using time series cross validation.

Setup Git Hooks

1. Within the project repo, run pre-commit install.
2. Then run pre-commit autoupdate.
3. To run pre-commit git hooks for flake8 and black run use pre-commit run --all-files.