Statistical Sampling to Measure Portfolio-At-Risk in Microfinance

This paper describes a statistical sample design to measure portfolio-at-risk in microfinance. It applies the design to the microfinance portfolio of Banco do Nordeste in Brazil. Statistical audit sampling requires no special knowledge of statistics and is useful for due-diligence inspections by possible creditors, possible owners, or in preparation for the possible securitization of a portfolio. The sample design here stratifies by branch and by loan officer because errors in the record of arrears in the management-information system are likely to vary along these dimensions. Because errors may also vary by loan size and are more costly for large loans than for small loans, loans are sampled with probability proportional to size. This implicitly stratifies the sample by amount outstanding. Furthermore, the design samples all of the largest loans and all rescheduled loans. Given these strata, given a definition of portfolio-at risk (for example, the outstanding balance of all loans with at least one payment at least one day overdue), given a desired upper bound on the accuracy of the estimated proportion of the portfolio-at-risk (for example, 2 percentage points), and given a desired precision for the confidence interval (for example, 90%), the paper tells (a) how many cases to draw; (b) how to estimate the proportion of the portfolio-at-risk; and (c) how to estimate the dollar amount of the portfolio-at-risk.