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Many vendor risk models have many hundreds, or even thousands of factors (many of which are highly correlated with each other). Underlying all these risk models is some sort of covariance matrix in which these factors are the features/dimensions generating this matrix, at least roughly speaking (all have some form of cleaning process or idiosyncratic deviation from the general process).

For fixed income, at least, the number of observations going into this covariance matrix tends to be on the order of a few hundred to a thousand, although many have some sort of an exponential weighting scheme to weight recent observations more strongly. This means that the effective number of observations can actually be quite small.

Even assuming ideal (normal) data the situation appears hopeless, because of the well known problems with estimating covariance matrices when the dimensionality is comparable to, let alone much larger than, the number of effective observations (see here and here, for classic takes). It’s seems a safe bet that the covariance matrices underlying most vendor risk models are therefore likely to be extremely inaccurate – not merely slightly wrong, but perhaps deeply wrong. Of course any risk model is necessarily backward looking and should be viewed with caution for this reason alone, but from a pure statistical perspective the problem is that even one’s look backward is likely to be wildly distorted.

Nonetheless, they are widely used and viewed as useful. Therefore I assume such a model has virtues that I must be unaware of. What are these virtues? What is the thoughtful, quantitative answer to my skeptical take? Have I overstated the case against these mega-factor models?

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  • $\begingroup$ I went to a talk by Andrew Ang where he said BlackRock had defined a large number of factors because of demand from various customer groups. Some are interested in Scandinavian mortgage securities, some are interested in US stocks, some in Emerging Markets stocks and they have to provide something for each. I do not think anyone would use all these factors simultaneously, rather they are part of separate models for different groups of securities/users. That might be part of the answer you are looking for (i.e. the multiplicity of countries, assets classes, etc. that they cover). $\endgroup$ – noob2 May 2 at 0:56
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    $\begingroup$ I agree with the sociological explanation for why there are so many factors, but I am fairly certain that in order to produce TEVs or other risk analytics the entire covariance matrix is used, which means all the factors. I think Aladdin and FactSet both do this unless I am quite mistaken. $\endgroup$ – quant_zero May 2 at 11:59

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