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