Probability distributions and leveraged trading strategies: an application of Gaussian mixture models to the Morgan Stanley Technology Index Tracking Fund

The purpose of this paper is twofold. Firstly, to assess the merit of estimating probability density functions rather than level or direction forecasts for one-day-ahead forecasts of the Morgan Stanley Technology Index Tracking Fund (MTK). This is implemented using a Gaussian mixture model neural network, benchmarking the results against standard forecasting models, namely a naïve model, a moving average convergence divergence technical model (MACD), an autoregressive moving average model (ARMA), a logistic regression model (LOGIT) and a multi-layer perceptron network (MLP). Secondly, we examine the possibilities of improving the trading performance of those models with confirmation filters and leverage. While the two network models outperform all of the benchmark models, the Gaussian mixture model does best: it is worth noting that it does well on a time series where the training period is showing a strong uptrend while the out-of-sample period is characterized by a downtrend.