Heartache over beta distribution...

trancheitup · April 5th, 2007, 1:17 pm

Given the beta distribution is defined over the interval [0,1] it is a logical choice for recovery rate modeling. But fitting to observed data via mean/standard deviation often leads to a u-shaped distribution (i.e. looks at Moody's CDOROM. The assumed mean/std deviation for US Senior Unsecured are 45%/35% respectively. A beta distribution matching these parameters is distinctly u-shaped). If one is focused on loss distribution, for example to quantify tail risk, seems like this recovery rate model might not be ideal. Any thoughts/opinions out there?

PKKoop · April 5th, 2007, 1:44 pm

Will not any distribution with 35% vol confined to [0,1] be multimodal? The std uniform vol is around 29%. And is multi-modality necessarily unrealistic in the tail? A realistic model would assign finite point mass at zero and unity; these guys argue that fitted beta distributions are bound to be biased for that reason:http://www.crest.fr/doctravail/document/2006-31.pdf.

trancheitup · April 5th, 2007, 2:39 pm

Good point. And thanks for the reference, this is exactly along the lines of what I was looking for. I've been primarily focused on Moody's research and haven't actually seen an emperical recovery distribution, only the stats reported in the studies. Certainly in the case of senior unsecured debt it seems reasonable there is a non-negligible likelihood of either 100% recovery or 0%, however, I'm not sure what emperical data suggests, relative to an average recovery rate around 45%. Thanks again for the reply!