Review of Quantitative Finance and Accounting, 12:3 (1999): 303–317
© 1999 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands.
Using Markov Chains to Estimate Losses from a
Portfolio of Mortgages
Assistant Professor of Accounting, Department of Accounting, Kogod College of Business Administration,
American University, 4400 Massachusettes Avenue, NW, Washington, D.C., 20016, E-mail:
Abstract. Under Statement of Financial Accounting Standards Number Five, Accounting for Contingencies
(SFAS 5), ﬁnancial institutions record a provision for loan losses and establish loan loss reserves when impair-
ment of a loan is probable and the loss can be reasonably estimated. Increasingly, Markov chain models are being
used to estimate these losses. This paper develops and test the suitability and forecast accuracy of alternate
Markov chain models of mortgage payment behavior using transition data from the Federal Home Loan Mort-
gage Corporation (Freddie Mac). In developing the models, the Freddie Mac transition data is examined to see
if it satisﬁes the Markovian assumptions of stationary transition probabilities and homogenous payment behav-
ior. The data examined in this paper did not satisfy these assumptions. With respect to accuracy in forecasting
loan losses, the Markov chain approach, when incorporating recent information on transition probabilities,
performed better than a random-walk model of loan losses.
Key words: Author please supply
Accurate estimation of loan losses is receiving increased attention from the investors,
managers, auditors, and regulators of ﬁnancial institutions. Two factors contribute to this
heightened interest: 1.) The elimination of tax considerations as the driving force in
setting loan loss reserves;
and 2.) Regulators concern with the methodology used to
estimate problem loans.
The removal of tax considerations and the increased pressure for
more sophisticated approaches to the estimation of loan losses has resulted in a number of
ﬁnancial institutions adopting Markov chain models of credit behavior for estimating loan
losses. This paper investigates the suitability
and forecast accuracy of three Markov chain
models of loan losses using data from the Federal Home Loan Corporation (Freddie
As a result, the paper contributes to the existing research on Markov chain models
of credit behavior by (1) developing a Markov chain model of mortgage payment behavior
and (2) providing the ﬁrst evidence on the suitability and effectiveness of Markov chain
models of credit behavior in estimating loan losses for a portfolio of mortgages.
Federal banking regulations require bank ﬁnancial statements to contain a balance sheet
account titled the allowance for loan and lease losses (also known as loan loss reserves).
This account represents a bank’s estimate of expected losses on existing loans as a result
of events that have already occurred. As losses are realized they are charged against loan
loss reserves. At the end of each accounting period the bank develops a new estimate of
@ats-ss11/data11/kluwer/journals/requ/v12n3art5 COMPOSED: 03/12/99 12:23 am. PG.POS. 1 SESSION: 9