A procedure for loss-optimising the timing of loan recovery under uncertainty

Abstract

The point at which a loan is in default is posited to be a portfolio-specific, probabilistic, and risk-based "point of no return" beyond which loan collection becomes sub-optimal if pursued any further. A method is presented for finding a delinquency threshold at which the overall loss of a given portfolio is minimised, i.e., loans are forsaken neither too early nor too late. This method, called the Loss-based Recovery Optimisation across Delinquency (LROD) procedure, incorporates the time value of money, risk-adjusted costs, and the fundamental trade-off between accumulating arrears versus forsaking future interest. The procedure is demonstrated across a range of portfolio compositions and credit risk scenarios using a simulation-based testbed. The computational results show that threshold optima can exist across all reasonable values of both the payment probability (default risk) and the loss rate (loan collateral). Furthermore, the procedure reacts positively to portfolios afflicted by either systematic defaults (due to economic downturns) or episodic delinquency (cycles of curing and re-defaulting). For real-world loans, which are typically right-censored, a forecasting step is proposed during which the remaining cash flows of each censored account are first ‘completed’ before applying the LROD-procedure. This approach is illustrated using residential mortgage data from a large South African bank. The empirical results show that riskier scenario-based forecasts of credit risk yield smaller threshold optima. Furthermore, censored cash flows are iteratively forecast in an additional Monte Carlo-based step, thereby analysing the stability of threshold optima yielded by the procedure. In conclusion, this work can enhance relevant business strategies, improve related modelling, and help revise the policy design of most banks, especially in tweaking the quantitative aspects of collection policies.