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Type	Master's Thesis
Scope	Discipline-based scholarship
Title	Portfolio Optimization and the criticality of the covariance matrix in FX Markets
Organization Unit	Financial Economics (Thorsten Hens)
Authors	Manuel Mondia
Supervisors	Thorsten Hens
Language	English
Institution	University of Zurich
Faculty	Faculty of Business, Economics and Informatics
Number of Pages	89
Date	2019
Zusammenfassung	Portfolio optimization has always been a sensitive topic within the asset management industry. Starting from the principles introduced by Markowitz (1952), many authors tried to construct more eﬃcient asset allocations, based on either improved estimators of the expected returns and the covariance matrix, which are the two input required to form the portfolio or a diﬀerent weighting scheme that considers new features not included in the original formulation. Existing literature tested portfolio optimization within the context of FX markets widely. The motivation behind this choice is the existence of a rather reliable proxy for the expected returns of the various currencies: interest rate diﬀerentials. Ilmanen (2011) and Lustig et al. (2011) studied the potential of such estimator and veriﬁed the proﬁtability of strategies based on such data. Also, Ackermann et al. (2016) introduced it into portfolio optimization, conﬁrming its power. Nonetheless, there is a major issue that needs to be taken care of: the estimation of the covariance matrix. As argued by Ledoit and Wolf (2003), the usage of the sample covariance matrix is not recommendable due to the high measurement error, especially when the number of variables is large relative to the number of observations. As a result, the utilization of such estimate may lead to extreme positions that aﬀect the reliability of the entire optimization process. To this end, the thesis aims at testing a set of more complex estimators that should limit the measurement error included in the covariance matrix. In particular, it focuses on the approaches built by Ledoit and Wolf (2003, 2004a,b), who combine the sample covariance matrix with another matrix implying additional information that can reduce the noise contained in the former one. Furthermore, we merge these techniques with the ﬁndings of Maurer et al. (2018) who claim to achieve better results than traditional Mean-Variance analysis thanks to market timing, meant as dynamical adjustment of leverage on the tangency portfolio (the portfolio invested in all the risky assets), which is not allowed in the formulation of Markowitz. Initially, a theoretical overview is provided. We begin by deriving the portfolio designed by Markowitz (1952) and then we comment on its limitations. Hence, we provide a detailed explanation of Maurer et al. (2018) ideal asset allocation, paying attention to those features that, according to the authors, characterize its superior performance. As far as the estimators of the covariance matrix are concerned, we ﬁrst introduce more common ones (Sample, EWMA and PCA-based covariance matrices) and then we explain some of the variants of shrinkage introduced so far, presenting the rationale behind these approaches, their structure and the derivation of the optimal combinations. To conclude the overview, we comment on the key characteristics at the basis of the traditional factors acknowledged in FX Markets: Dollar, High-Minus-Low, Carry and Momentum factor. These will be used as a benchmark for the strategies developed in this thesis. Once the theoretical background has been deﬁned, we implement the various Mean-Variance optimizers and we apply them in real markets, simulating their performance for the period included between the 2nd of January 1976 and the 29th of January 2016. Using appropriate measures, we assess which optimizer would have been the most efﬁcient in a realistic environment. Moreover, we regress the time-series of the excess returns of each portfolio on the traditional factors and a set of macroeconomic vari-ables. This should help us to understand whether the optimizers’ performance can be explained by such elements and if they generate signiﬁcant alpha. Finally, we build controlled datasets which allow us to verify what would happen if we ruled out the possible drivers of the performance of the optimizers. By doing so, we can also check if the strategies implemented may be subject to biases of various nature. The results obtained conﬁrm that the usage of more robust estimators of both expected returns and covariance matrix leads to more eﬃcient asset allocation. Afterward, market timing seems to bring beneﬁts to portfolios who are allowed to adjust their leverage depending on market prices of risk. From an empirical point of view, traditional factors explain only part of the excess returns of such strategies, which generate remarkable and signiﬁcant alphas. Moreover, macroeconomic variables have limited explanatory power, especially with optimizers not based on interest rate diﬀerentials, for which the conditions of the economy may not be relevant. In conclusion, we can conﬁrm that the non-random nature of the prices and the welldocumented violation of the ”Uncovered Interest Parity” (or UIP), could be the key sources of the positive performance of the optimizers tested in this research.
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