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.