Risk Filtering

A big misunderstanding originates from the gap between two domains of the quantitative finance: the descriptive statistics (to explain the risk) and the decision mathematics (to allocate the risk). The same words are sometimes used in both contexts, such as the important notion of robustness, but do not mean the same thing. As a consequence, risk models which are acknowledged as robust in a descriptive risk analysis framework will not be suitable in a decision making context, and vice versa.

For example, empirical estimations might be the best estimates of the covariance matrices in a statistical approach, but using them in a portfolio optimization context can be highly dangerous. Indeed, statistical analysis shows that empirical covariance matrix estimators cannot capture properly the small contributions to risk, especially when using noisy market data.

These small contributions to risk can be neglected when explaining the risk of a portfolio. Indeed, 95% or so of the information is sufficient to analyse/decompose the risk. Furthermore, such risk management approaches use large estimation windows (1 year or more) to compute the covariance matrix, which allows to reduce statistical errors.

But this is not the case in a decision making framework such as portfolio optimization. Indeed, to design a reactive (optimization-oriented) risk model and take the right allocation decision, we need to use shorter estimation windows, especially in times of highly volatile markets. The Random Matrix Theory tells us that the lesser data we use, the more underestimated the small contributions to risk.

When optimizing a portfolio, underestimating these contributions (i.e. the smallest eigenvalues) can be very dangerous. Indeed, it implies that there exists a theoretical portfolio with a volatility close to zero ! If this portfolio happens to have a positive expected return, then its Sharpe ratio will be +∞, and the optimizer will be lured by this aberrant portfolio. In the end, this means that the portfolio optimization process is essentially driven by noise… hence implying very large turnovers and operational risk at each reallocation.

RaisePartner risk models embed a filtering method that allows to control the conditioning of the matrix as well as the deformation applied to the sample covariance matrix.

To read the full article and learn more about matrix filtering issues, please download the PDF file below.


See also : Lorentz cone, SDP,