We carry out several test cases to illustrate how the Probability of Backtest Overfitting (PBO) performs under different scenarios. We also assess the accuracy of PBO using two alternative approaches (Monte Carlo Methods and Extreme Value Theory).The paper "The Probability of Backtest...

Proofs to the propositions in "Stop-Outs Under Serial Correlation".The paper "Stop-Outs Under Serial Correlation and 'The Triple Penance Rule" to which these Appendices apply is available at the following URL: "http://ssrn.com/abstract=2201302" http://ssrn.com/abstract=2201302

The False Strategy theorem tells us that the optimal outcome of an unknown number of historical simulations is right-unbounded — with enough trials, there is no Sharpe ratio sufficiently enough to reject the hypothesis that a strategy is false. Given the ease with which one can use a computer...

When prices reflect all available information, they oscillate around an equilibrium level. This oscillation is the result of the temporary market impact caused by waves of buyers and sellers. This price behavior can be approximated through an Ornstein-Uhlenbeck (OU) process.Market makers provide...

We introduce Kinetic Component Analysis (KCA), a state-space application that extracts the signal from a series of noisy measurements by applying a Kalman Filter on a Taylor expansion of a stochastic process. We show that KCA presents several advantages compared to other popular noise-reduction...

We solve a multi-period portfolio optimization problem using D-Wave Systems' quantum annealer. We derive a formulation of the problem, discuss several possible integer encoding schemes, and present numerical examples that show high success rates. The formulation incorporates transaction costs...

For large portfolio managers, a sequence of single-period optimal positions is rarely multi-period optimal. In particular, transaction costs can prevent large portfolio managers from monetizing most of their forecasting power. The solution is to compute the trading trajectory that comes...

Empirical Finance is in crisis: Our most important "discovery" tool is historical simulation, and yet, most backtests published in leading Financial journals are flawed.The problem is well-known to professional organizations of Statisticians and Mathematicians, who have publicly criticized the...

In this paper, the authors construct a pipeline to benchmark Hierarchical Risk Parity (HRP) relative to Equal Risk Contribution (ERC) as examples of diversification strategies allocating to liquid multi-asset futures markets with dynamic leverage ("volatility target"). The authors use...

In the field of mathematical finance, a “backtest” is the usage of historical market data to assess the performance of a proposed trading strategy. It is a relatively simple matter for a present-day computer system to explore thousands, millions or even billions of variations of a proposed...