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?