chapter  11
20 Pages

Regularized Robust Portfolio Estimation

WithTheodoros Evgeniou, Massimiliano Pontil, Diomidis Spinellis, Nick Nassuphis

Diomidis Spinellis Department of Management Science and Technology, Athens University of Economics and Business

Nick Nassuphis 31 St. Martin’s Lane, London

11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 11.2 Finding Robust Autocorrelation Portfolios . . . . . . . . . . . . . . . . . . . . . . 239

11.2.1 Financial Time Series: Notation and Definitions . . . . . . . . 239 11.2.2 Regularization Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 11.2.3 Interpretation of the Case →∞ . . . . . . . . . . . . . . . . . . . . . . . 241 11.2.4 Connection to Slow Feature Analysis . . . . . . . . . . . . . . . . . . . 242

11.3 Optimization Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 11.4 Robust Canonical Correlation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 244 11.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

11.5.1 Synthetic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 11.5.2 S&P 500 Stock Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

11.6 Conclusion and Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 11.7 Appendix: Robust cca Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254

Vector

11.1 Introduction Given a vector-valued time series, we study the problem of learning the

weights of a linear combination of the series’ components (e.g., a portfolio), which has large autocorrelation, and discuss the extension to the problem of learning two combinations, which have large cross-correlation. Both problems have been studied from different perspectives in various areas, ranging from computational neuroscience [27], to computer vision [20, 14], to information retrieval [15], among others. In this chapter, we address these problems from the point of view of robust optimization (see, e.g., [5, 8] and references therein) and regularization, and highlight their application to the context of financial time series analysis; see, e.g., [25].