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November 21, 2008

Interesting article but bad statistics

Daniel Gross has a piece in Slate (The Subprime Good Guys) where he blasts those trying to pin some (or most) of the blame for the financial crisis on subprime and other low-quality lending. I'm still unconvinced by his argument that since the CRA only applied to banks and non-banks did much of the bad lending that the CRA had nothing to do with this. We don't know what the sensitivity of the price of real estate was to marginal lending. If the CRA was pumping money into marginal borrower (those who otherwise would have rented) then it would have continued to drive up real estate prices in the US. That continued price appreciation held the default rate down to an artificially low level. Lenders it seems treated it instead as a regime change to lower credit risk and therefore lent out money at too low a rate. I'm not sure if that is what happened, but you cannot infer from the widespread origination of bad loans that the CRA had nothing to do with our current crisis.

But the article has another problem. In search of the ethical subprime-lending industry, he finds three nice companies that had low default rates on their loan portfolios and yet managed behave overall in a manner that he approved of, including lending to high risk borrowers. Maybe there was a better business model that all lenders could have followed, and he's found 3 firms that were doing it.

My problem with this analysis is that the three firms are small. Yes, even a couple billion in loans is small. The average mortgage size nationally was $191,917, so call that $200k. A firm with $2 billion in mortgages is just 10,000 mortgages and not all were issued in the boom years, many of the older ones were made when real estate prices were more reasonable and so the older and more established who borrowed from them are now more well established and there homes haven't lost as much relative to the loan value.

Default rates are ratios. The numerator is the value of the defaults and the denominator is the value of the total loans. Ratios behave oddly when there is great variation in the size of the entities for which we are calculating ratio. For the sake of argument, let's say that these firms don't have a superior business model. They all have the same probability of a lender defaulting, and call that probability 2% on any loan, although, among the high risk lenders the the delinquency rate has been about 7%. The fewer loans that a lender makes, the higher the probability of seeing the 2% delinquency rate because of the central limit theorem. As the number of loans increases, the standard deviation of that sample mean shrinks to zero around that mean of 7%. The analog in coins is as follows. When you flip a fair coin 20 times, the probability of getting 1/4 or fewer heads is close to 2%. Scale by to 200 flips and the probability is 4.19651E-13 of getting 50 or fewer heads. So if we had two large classrooms of kids recording the number of coin flipping successes, the first from 20 flips and the second from 200 flips, we'd expect to see a couple with 5 or fewer in the first room and non in the second getting fewer than 50.

The take away here is that when consuming ratio statistics, watch out for unequal (what we call unbalanced) samples. The likelihood of an event a fixed percentage away from the expected value varies greatly based on the size the ratio is sampled from.

This isn't my insight by any means. In Edward Tufte's The Visual Display of Quantitative Information, on pages 17-19 he has maps on cancer rates by US county, and the highest rates are observed in the counties with the smallest populations. My undergraduate professor Greg D. Adams pointed this phenomena out to me in the butterfly ballot situation in Florida in 2000. Yes it was highly unusual that Buchanan got such a high vote share in Miami-Dade county. But when you consider that there are small counties with unusual vote shares because of this ratio phenomena, it was much less unusual (although still odd).

Posted by OneEyedMan at November 21, 2008 9:29 AM

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