Algorithmic arbitrage of open-end funds using variational Bayes

Abstract

The open-end fund industry controls significant assets. At the same time, the US centric mutual funds scandal of 2003 highlighted some of the short comings of the structure of these securities. In this paper, we revisit some issues relating to this scandal and provide a quantitative framework to inspect for arbitrage opportunities in open-end funds. The framework presented is a hierarchical graphical model which allows parameter posteriors to be inferred by a variational Bayesian approach. This enables prior knowledge about the funds to be incorporated into the model at the same time as being computationally cheap to run. This class of models falls under the heading of Bayesian pattern recognition. Using linear Gaussian basis functions, a regression model is used to generate a predictive distribution for the high-frequency fair price of an open-end fund. This fair price can be used to estimate a latent pricing time for the fund. Using this information, and conditional on the cut-off time for purchase of the fund, a trading signal for arbitraging the open-end fund can be designed. This framework is applied to a sample of the 1,296 most highly capitalized open-end funds from Western Europe and simulations carried out. The trading strategy has a post-cost mean Sharpe ratio of over 1.6 when considered across the sample. The results suggest that the open-end fund industry in Europe still has lessons to learn from the scandal in the US a decade earlier.