Applied Mathematics Seminar: Constant Proportion Debt Obligations, Zeno's Paradox, and the Spectacular Financial Crisis of 2008

We analyze a coin-tossing model used to justify the sale of constant proportion debt obligations (CPDOs) and prove that it was impossible for CPDOs to achieve the Cash-In Event. In the best-case scenario in which the coin is two-headed, we show that the goal of attaining the Cash-In Event in a finite lifetime is precisely the goal, described more than two thousand years ago in Zeno's Paradox of the Dichotomy, of evaluating the sum of an infinite geometric series with only a finite number of terms. In the case of a fair coin, we show that a CPDO player operating on 9X margin (and hence subject to margin calls) has, approximately, an 89% chance of bankruptcy; moreover, even if the margin broker is infinitely wealthy and infinitely patient, his CPDO customers who lose on the first or any given toss are doomed, with high probability, to suffer losses for hundreds of successive tosses. In light of these results, we are dismayed by many of the mathematical models propagated over the past decade by financial ``engineers'' and ``experts'' in structured finance, and it heightens our fears about the durability of the on-going worldwide financial crisis.