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...

There are three fundamental ways of testing the validity of an investment algorithm against historical evidence: a) the walk-forward method; b) the resampling method; and c) the Monte Carlo method. By far the most common approach followed among academics and practitioners is the walk-forward...

In this article, the authors present a conceptual framework named 'Adaptive Seriational Risk Parity' (ASRP) to extend Hierarchical Risk Parity (HRP) as an asset allocation heuristic. The first step of HRP (quasi-diagonalization) determining the hierarchy of assets is required for the actual...

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...

Convex optimization solutions tend to be unstable, to the point of entirely offsetting the benefits of optimization. For example, in the context of financial applications, it is known that portfolios optimized in sample often underperform the naïve (equal weights) allocation out of sample.This...

In this paper we present a novel and highly flexible method to simulate correlation matrices of financial markets. It produces realistic outcomes regarding stylized facts of empirical correlation matrices and requires no asset return input data. The matrix generation is based on a...

Successful investment strategies are specific implementations of general theories. An investment strategy that lacks a theoretical justification is likely to be false. Hence, an asset manager should concentrate her efforts on developing a theory, rather than on back-testing potential trading...

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

Economics (and by extension finance) is arguably one of the most mathematical fields of research. However, economists' choice of math may be inadequate to model the complexity of social institutions. In a constructive spirit, this note offers some advice on how students could increase their...