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Forecast Optimization via Parameter Tuning: Performance Gain and Overfit

Most predictors used in systematic trading are designed as functions of available data streams. The functional form of these signals involves tuning a number of parameters such as the trading frequency, sample sizes, entry and exit thresholds, stop losses, and so on to improve the performance of the predictor. It is well known that such tuning leads to overfitting, meaning that the constructed signal fits historical returns well but may poorly predict their future behavior. One of the central questions that has not been previously addressed is how much each fitting parameter contributes to the overall performance improvement. In this article, this question is addressed both quantitatively and qualitatively. The author concentrates on a simple, but very common in practice, fitting technique consisting of smoothing the signal using the weighted moving average. It is shown that the improvement of the Sharpe ratio mainly depends on the signal autocorrelation and its alpha decay parameter. The findings are confirmed by numerical simulations. This result sheds more light on the overfitting phenomenon in the context of investment strategy construction and reveals the sources of performance improvement in forecast design. TOPICS: Big data/machine learning, portfolio construction, simulations, statistical methods Key Findings • Fitting the parameters of return predictors on historical data unavoidably leads to statistical overfitting, which may result in partial or total failure of the signal in the out-of-sample period. • This article introduces a novel framework capable of precisely estimating the level of overfitting or performance gain arising from optimization over every parameter. • An illustration of the power of the new methodology is provided using the ubiquitous example of exponential moving average smoothing of the forecast.