By analyzing a coin-tossing model used to justify theinvention and sale of constant proportion debt obligations (CPDOs), we 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 timespan is precisely the goal, described more than two thousand years ago in Zeno's Paradox of the Dichotomy, of achieving 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 purchaser who experienced a loss on the first, or any, coin toss was doomed, with high probability, to suffer losses for hundreds of successive tosses. We find, in light of these results, that our fears about the on-going worldwide financial crisis are heightened by the prospects that there may exist other arcane financial derivatives with structure even more bizarre that that of CPDOs.