#08-12
Optimal Mortgage Loan Diversification
Kourosh M. Rasmussen and Stavros A. Zenios, November 2007
Abstract: Homebuyers in several countries may finance the purchase of their
properties using different variants of either adjustable fixed rate mortgages
(ARMs) or fixed rate mortgages (FRMs). The variety and complexity
of these loan products poses a risk management task for mortgage bank
advisors to recommend the right mortgage loan strategy for the individual
mortgagor; almost all mortgage banks advise their customers
to take a single loan product. This argument is often justified by the
fact that trade frictions make it unattractive to hold a portfolio of
loans as a private home owner. Even with transaction costs, however,
we show in this paper that most mortgagors with some degree of risk
aversion benefit from holding a mortgage portfolio. To do so we develop
a multi stage Mean-Conditional Value at Risk (MCVaR) model
to consider the risk of the mortgage payment frequency function explicitly
using a coherent risk measure. In addition to the diversification
benefits we also show that the multistage model produces superior results
as compared to single stage models and that the solutions are
robust with regards to changes in uncertainty parameters in particular
for risk averse mortgagors. Finally, we show how the model can be
used to calculate fair premia for adjustable rate mortgages with interest
rate guarantees (caps) which are becoming increasingly popular as
a hybrid product between the existing ARM and FRM mortgages.
Keywords: Mortgage loans products, CVaR modeling, stochastic
programming..
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