Optimal Dynamic Strategies on Gaussian Returns

32 Pages Posted: 2 Jun 2019

See all articles by Nick Firoozye

Nick Firoozye

UCL - Computer Science

Adriano Koshiyama

University College London, Financial Computing and Analytics Group, Department of Computer Science, Students

Date Written: May 9, 2019

Abstract

Dynamic trading strategies, in the spirit of trend-following or mean-reversion, represent an only partly understood but lucrative and pervasive area of modern finance. Assuming Gaussian returns and Gaussian dynamic weights or signals, (e.g., linear filters of past returns, such as simple moving averages, exponential weighted moving averages, forecasts from ARIMA models), we are able to derive closed-form expressions for the first four moments of the strategy's returns, in terms of correlations between the random signals and unknown future returns. By allowing for randomness in the asset-allocation and modelling the interaction of strategy weights with returns, we demonstrate that positive skewness and excess kurtosis are essential components of all positive Sharpe dynamic strategies, which is generally observed empirically; demonstrate that total least squares (TLS) or orthogonal least squares is more appropriate than OLS for maximizing the Sharpe ratio, while canonical correlation analysis (CCA) is similarly appropriate for the multi-asset case; derive standard errors on Sharpe ratios which are tighter than the commonly used standard errors from Lo; and derive standard errors on the skewness and kurtosis of strategies, apparently new results. We demonstrate these results are applicable asymptotically for a wide range of stationary time-series.

Keywords: Algorithmic Trading, Dynamic Strategies, Over-Fitting, Quantitative Finance, Signal Processing

Suggested Citation

Firoozye, Nick and Soares Koshiyama, Adriano, Optimal Dynamic Strategies on Gaussian Returns (May 9, 2019). Available at SSRN: https://ssrn.com/abstract=3385639 or http://dx.doi.org/10.2139/ssrn.3385639

Nick Firoozye

UCL - Computer Science ( email )

Gower Street
London, WC1E 6BT
United Kingdom

Adriano Soares Koshiyama (Contact Author)

University College London, Financial Computing and Analytics Group, Department of Computer Science, Students ( email )

Gower Street
London, London WC1E 6BT
United Kingdom

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