How Skewed are Simultaneously Long-Short Trading Gains?

Technical trading is often based on the idea of predicting trends in prices. However, these predictions are problematic for several reasons, e.g., regime breaks over time. In control theory, there is another approach that treats markets as machines and regulates them. The presumably best understood one of these feedback-based trading rules is the so-called Simultaneously Long Short (SLS) strategy. This strategy invests equally long and short at the beginning and shifts more and more investment to the better performing side according to affine linear feedback schemes. Due to this feedback loop, it is possible that the SLS rule adapts to regime breaks. Under specific assumptions, in theory as well as in backtests, notable results could be achieved for the SLS strategy. For implementations it is important that questions concerning the choice of the parameters and—highly interlinked—the risk associated with the SLS rule are considered. In this paper we derive for relatively general market models, which are based on semimartingales with time-varying parameters, a closed-form formula for the skewness of the distribution of the gain of the SLS strategy as a function of market and control parameters. Since the skewness can be seen as both a risk indicator (but not as a risk measure) and a property some traders might prefer, this formula can be used to choose the feedback parameters according to mean-variance-skewness considerations, thus, helping traders to meet their idiosyncratic risk aversions or preferences.