Multi-period Robust Mean-Risk Portfolio Optimization

Abstract

Portfolio optimization, a fundamental area of study in financial engineering,
plays a crucial role in creating efficient portfolios. In this thesis, we consider
a robust multi-period Mean-Variance portfolio optimization framework and
apply it to real-world market data. The approach we look at incorporates a
time-consistent structure that considers the variance of each period, aiming
to minimize their sum, while ensuring that the expected return for each period
exceeds a predefined threshold. Additionally, we introduce proportional
transaction costs to simulate real-world market conditions. To account for uncertainties
and increase robustness, we employ a distribution uncertainty set
within a Wasserstein ball around the empirical distribution of historical data.
This enables us to select worst-case portfolio scenarios for deriving robust optimal
solutions. We aim to compare this method with other existing portfolio
optimization methods, which we describe in depth in our analysis, to assess
its effectiveness.
To achieve the aforementioned research objectives, we conducted an extensive
review of portfolio optimization literature, exploring both Mean-Variance
and Mean-CVaR portfolio optimization problems. Our research also included
robust approaches on portfolio optimization including different distribution
and parameter uncertainty sets. We proceeded to construct a comprehensive
set of numerical experiments, evaluating portfolio optimization methods performance
on real market data. Moreover, we included the S&P500 index to
compare them against market performance. In these experiments, we randomly
selected stock sets and evaluation period to work on, in order to ensure
an unbiased assessment of the methods.
To evaluate the performance of each method, we used the Sharpe ratio of
the realized portfolio returns. Our key findings indicate that, in most cases,
at least one of the portfolio optimization models outperformed S&P500, suggesting
that portfolio optimization problems perform relatively well in the
real world. Furthermore, single-period models demonstrated better performance
compared to multi-period having higher Sharpe ratio most of the times.
Notably, robust optimization models exhibited superior performance compared
to nominal models, underlying the significance of accounting for uncertainty.
The implications of our research are twofold. Firstly, portfolio optimization
problems, especially in the single-period context, demonstrated
promising performance and should be embraced by financial practitioners
seeking optimal risk-return investment strategies. Secondly, we recommend
the preference for robust approaches over traditional models, as they offer improved
flexibility to market uncertainties and potentially mitigate downside
risks.