DoI: 10.1145/1941487.1941510

technical Perspective
Complex financial Products:
Caveat Emptor

By David C. Parkes

 

the fLo W of capital in the financial industry relies on the packaging of assets into products that can be reliably valued and then sold to global investors. For example, many home mortgages were packaged into products known as Collateralized Debt Obligations (CDOs) in the run-up to the sub-prime mortgage crisis of 2007. An investor in a CDO buys the rights to a share of the principal and interest payments collected from homeowners. By pooling assets and promising to pass along payments before making payments to other investors, new financial products offering lower risk than the underlying assets can be constructed. CDOs are examples of financial derivatives, with a value that depends on the underlying assets—mortgages in this case—with which they are linked.

These kinds of complex financial products are the cause célèbre of the financial crisis, and many have called for their regulation or even elimination. In the following paper, Arora, Barak, Brunnermeier, and Ge provide new insight into the problem: a complexity-theoretic explanation for how sellers can hide bad assets in these derivatives. Even when buyers are fully informed, with correct beliefs about the probability with which underlying mortgages are likely to default, sellers can package a disproportionate number of bad assets into some products, and do so without detection. The reason is the intractability of checking whether or not this manipulation has occurred. By focusing on this missing angle of computational complexity, this paper starts to bridge the gap between the common view that derivatives can be rigged and a viewpoint from economics that this is impossible when buyers are fully informed. Computationally bounded buyers may end up significantly overpaying, and a trustworthy seller cannot even prove that financial products have not been rigged.

To understand the reason to sell
derivatives in the first place, we can
consider Akerlof’s famous “lemons
problem.” Suppose that 80% of second-
hand cars are good, and worth $1,000
to buyers, while the rest are lemons
and worth $0. Without the ability for a
seller to credibly signal the quality of a
car, buyers will only pay $800 and trades
of good cars by sellers with values in
the range [$800, $1,000] are forfeited.
If all sellers of good cars want close to
$1,000 then the effect of information
asymmetry between buyers and sellers
is much worse—only lemons remain
in the market and there is complete
market collapse! Still, a seller with 100
cars, each correctly known by a buyer
to be a lemon with probability 0.2, can
make a new deal: the right to use up to
80 of the cars. Because it is highly likely
that at least this many cars will be good,
this deal can be priced at about $80,000,
around the price at which it would trade
without information asymmetry. The
same thing happens in a simple model
of CDOs, in which a seller packages as-
sets into a single derivative that can be
accurately priced and sold.

David C. Parkes ( [e-mail]) is Gordon
McKay Professor of Computer Science in the School of
engineering and applied Sciences at Harvard university,
where he founded the econCS research group.
© 2011 aCM 0001-0782/11/05 $10.00