Outlier-Robust Dynamic Portfolio Optimization based on Bear-Bull-Regimes

Abstract: The work in this thesis is meant to improve an existing algorithm described in Nystrup (2017). As the original model uses a normal distribution to approximate the daily logarithmic returns, the authors of this thesis aim to improve the approximation by using Student’s t-distribution which may be a better approximation of financial data. The algorithm uses a two state hidden Markov model to estimate the current state (also known as regime) of the market, bull or bear. Based on the estimation, predictions of future returns are made. The algorithm will then use this information to trade a risky asset, in this case the S&P 500 stock index. A portion of the available capital will be placed in the asset and the rest will be held in cash at the risk free rate. The portion of the available capital the algorithm is to invest in the risky asset is decided using model predictive control. Using model predictive control one is able to maximize the return for the entire portfolio over a future time horizon. In the maximization one is as well able to include transaction costs and a general aversion against both risk and trading. The algorithm is able to obtain a greater return at a lower risk than just investing in a static portfolio of the stock index. This will yield a greater Sharpe ratio than the stock index. The resulting algorithm works the best if the portfolio is long-only, i.e. if the algorithm is not allowed to go short in the traded asset. Even though the long-short portfolio is able to yield a higher return to the investor, it will contain more risk and therefore have a lower Sharpe ratio. The final recommendation will therefore be for the investor to use the algorithm with a long-only portfolio restriction. The algorithm allows the use of Bayesian optimization for obtaining optimal model hyperparameters, for instance the risk- or trading aversion, to maximize performance on the in-sample data set. The usage will however lead to a huge risk of over-fitting the model to the in-sample data set and the desired properties are most probably lost going out-of-sample. The hyperparameters should therefore be chosen manually with great care and thorough testing. Changing one hyperparameter may also lead to undesired effects as the many of the hyperparameters are mutually dependent making in-sample training more difficult.