Welcome to the first issue of the ninth volume of The Journal of Investment Strategies.
In this issue, you will find three papers that cover a backtesting environment for trading strategies, optimal dynamic strategies for Gaussian returns and the design of eigenportfolios of US equities using an exponential correlation model.
In our first paper, “Is trading indicator performance robust? Evidence from scenario building”, Andreas Thomann provides quantitative developers with a backtesting environment in which they can test their trading strategies, so they might see how robust their strategies and parameterizations are. The scenario-building process can be used to simulate multiple assets from different asset classes. From a computational perspective, the parallel bootstrapping process implicitly handles the cross-dependencies among the data series. The simulation process therefore reduces the complexity of the task enormously, as the number of parameters and the time needed to execute the computation increase only linearly with the number of assets that are handled. This is different to approaches that model cross-dependencies based on estimates of the variance–covariance matrix, where the dimension of the problem increases quadratically with the number of assets.
In “Optimal dynamic strategies on Gaussian returns”, the issue’s second paper, Nick Firoozye and Adriano S. Koshiyama derive closed-form expressions for the first four moments of their strategy’s returns, in terms of correlations between the random signals and unknown future returns, and assuming Gaussian returns and Gaussian dynamic weights or signals. By allowing for randomness in the asset allocation and in modeling the interaction of strategy weights with returns, the authors demonstrate that positive skewness and excess kurtosis are essential components of all positive Sharpe dynamic strategies. They also show that total least squares or orthogonal least squares are more appropriate than ordinary least squares for maximizing the Sharpe ratio. Finally, they prove that their results are applicable asymptotically to a wide range of stationary time series.
In our third paper, “Eigenportfolios of US equities for the exponential correlation model”, Ali N. Akansu and Anqi Xiong model empirical correlations of asset returns in a basket with an exponential function. They use these correlations to design model- based eigenportfolios. The authors also design eigenportfolios using an empirical correlation matrix generated from market data and compare the performances of the two eigenportfolio sets. This paper demonstrates that exponential approximation to empirical correlations provides a good model for designing eigenportfolios and evaluating their performance. Akansu and Xiong also compare the performances of minimum variance, market and eigenportfolios for the end-of-day returns of US equities, along with index and sector exchange-traded funds. They conclude that of all the portfolios considered in their study, the first eigenportfolio (EP1) almost always provides the best performance.
On behalf of the editorial board, we hope you are keeping well during the Covid-19 pandemic. We would like to thank our readers for their continued support of and keen interest in our journal. We look forward to sharing with you our growing list of practical papers – that we continue to receive from academics and practitioners alike – on the broad variety of topics that constitutes modern investment strategies.
Arthur M. Berd
Founder and CEO, General Quantitative LLC
Managing Partner, Sauma Capital LLC & Professor, Columbia University
This paper challenges widely applied trading indicators with regard to their ability to generate a robust performance.
It is hoped that this paper will form a foundational approach to the study of dynamic strategies and how to optimize them. We make efforts to understand their properties without claiming to understand why they work (ie, why there are stable…
In this paper, the eigendecomposition of a Toeplitz matrix populated by an exponential function in order to model empirical correlations of US equity returns is investigated.