Mean of Ratios or Ratio of Means: statistical uncertainty applied to estimate Multiperiod Probability of Defaul

TL;DR

This paper compares two estimators for multiyear default probability in mortgages, finding that the ratio of means estimator has lower statistical uncertainty and results in a slightly lower default probability estimate.

Contribution

It provides a statistical analysis of two estimators for multiyear default probability, highlighting the superior precision of the ratio of means estimator.

Findings

Ratio of means estimator has lower statistical uncertainty.

Application reduces estimated default probability by eleven basis points.

Supports using ratio of means for more accurate default estimation.

Abstract

The estimate of a Multiperiod probability of default applied to residential mortgages can be obtained using the mean of the observed default, so called the Mean of ratios estimator, or aggregating the default and the issued mortgages and computing the ratio of their sum, that is the Ratio of means. This work studies the statistical properties of the two estimators with the result that the Ratio of means has a lower statistical uncertainty. The application on a private residential mortgage portfolio leads to a lower probability of default on the overall portfolio by eleven basis points.