#### The Rules, Part LVIII: Mathematical Models, Investing, And Reality by David Markel, CFA of the Aleph Blog

Can contingent claims theory for bond defaults be done on a cash flow/liquidity basis?  KMV-type models seem to fail on severely distressed bonds that have time to breathe and repair.

We’re getting close to the end of this series, and I am scraping the bottom of the barrel.  As with most aspects of life, the best things get done first.  After that diminishing marginal returns kick in.

Here’s the issue.  It’s possible to model credit risk as a put option that the bondholders have sold to the stockholders.  As such, equity implied volatility helps inform us as to how likely default will be.  But implied volatilities are only available for at most two years out, because they don’t commonly trade options longer than that.

Here’s the scenario that I posit: there is a company in lousy shape that looks like a certain bankruptcy candidate, except that there are no significant events requiring liquidity for 3-5 years.  In a case like this, the exercise date of the option to default is so far out, that the company can probably find ways to avoid bankruptcy, but the math may make it look unavoidable.  Remember, the equity has the option to default, but they also control the company until they do default.  Being the equity is valuable, because you control the assets.

Bankruptcy means choking on cash flows out that can’t be made.  Ordinarily, that happens because of interest payments that can’t be made, rather than repayment of principal.  If interest payments can be made, typically principal payments can be refinanced, unless credit gets tight.

The raw math of the contingent claims models do not take account of the clever distressed company manager who finds a way to avoid bankruptcy, driving deals to avoid it.  The more time he has, the more clever he can be.

This is a reason why I distrust simple mathematical models in investing.  The world is more complex than the math will admit.  So be careful applying math to markets.  Think through what the assumptions and models mean, because they may not reflect how people actually work.