Blending Independent Components and Principal Components Analysis

4.4 Caveats

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4.4          Caveats

When carrying out blended PCA/ICA analyses of financial series date it may be worth bearing in mind that:

(a)    It is common, at least for equity-based risk models, for there to be far more series than there are datapoints in each series. This alters eigenvector dynamics and therefore we might presume the dynamics of the equivalent importance rated factors extracted using a blended PCA/ICA approach. For example, however many series there are, the number of eigenvectors it is possible to distinguish is limited by the number of points in the series (and is no larger than  if there are  datapoints in each series. Moreover, practical risk model design requires additional elements able to cater for incomplete data series (e.g. for stocks that have only recently listed or have recently demerged).

(b)   Any added robustness that we might appear to identify for a blended approach may merely be an artefact of look-back bias. See e.g. Kemp (2009) for an explanation of look-back bias and why it may apply here, even when any backtesting approach we might have used is ‘out of sample’.

(c)    In any case, past market dynamics may not turn out to be a good predictor of future market dynamics, even if weight of academic opinion seems to believe that volatility is ‘more predictable’ than, say, future return.

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