Estimated Correlation Matrices and Portfolio Optimization

Abstract

Financial correlations play a central role in financial theory and also in many practical applications. From theoretical point of view, the key interest is in a proper description of the structure and dynamics of correlations. From practical point of view, the emphasis is on the ability of the developed models to provide the adequate input for the numerous portfolio and risk management procedures used in the financial industry. This is crucial, since it has been long argued that correlation matrices determined from financial series contain a relatively large amount of noise and, in addition, most of the portfolio and risk management techniques used in practice can be quite sensitive to the inputs. In this paper we introduce a model (simulation)-based approach which can be used for a systematic investigation of the effect of the different sources of noise in financial correlations in the portfolio and risk management context. To illustrate the usefulness of this framework, we develop several toy models for the structure of correlations and, by considering the finiteness of the time series as the only source of noise, we compare the performance of several correlation matrix estimators introduced in the academic literature and which have since gained also a wide practical use. Based on this experience, we believe that our simulation-based approach can also be useful for the systematic investigation of several other problems of much interest in finance.