How Micro Risk Became Aggregate Risk

Chile's credit program produced a striking contrast: riskier firms were more likely to enter and accumulate guaranteed debt, yet the portfolio's estimated aggregate loss remained relatively contained. This chapter explains how that can happen. The key is to follow the interfaces between firm risk, loan size, guarantee coverage, bank exposure, and the denominators used to measure loss. A high default probability matters, but so does how many dollars are placed with that group and who must absorb the loss when repayment fails.

Portfolio loss depends on risk and the amount placed at risk

A firm-level selection result tells us how likely a type of borrower is to seek or receive credit. An aggregate loss calculation asks a different question: how much money was allocated to that type of borrower, and what fraction of that exposure was expected to default? In the study, expected loss is constructed by multiplying the amount of program loans in a risk group by its predicted default probability. The calculation uses the risk assessment formed from 2019 information, before the outcome of the pandemic was known.

By the end of 2020, guaranteed loans in the study's coverage totaled US$11.504 billion, equal to 4.6 percent of 2019 GDP. The distribution was not an equal slice across risk groups. High-risk formal firms received 7 percent of the guaranteed loans, while low- and medium-low-risk firms received 65 percent. Their predicted default probabilities moved in the opposite direction: 18.2 percent for the high-risk group and 2.1 percent for the low-risk group.

Those figures explain why micro-level risk and macro-level loss need not move together. The high-risk group has the greater chance of default per dollar, but it represents a smaller share of the dollars in the portfolio. The low-risk groups have a much lower predicted default rate, but their larger loan volume gives their outcomes greater weight in the total. The study therefore finds that aggregate loss is relatively contained partly because most loans went to larger, generally safer borrowers, even though riskier firms increased their debt more in proportional terms. This is a portfolio-weighting result, not evidence that the risky borrowers were unimportant.

The allocation broadly tracks firms' sales weights. That follows from the program's loan limit being tied to sales: a larger firm can receive a larger loan even when its proportional increase in debt is smaller. This creates a difference between leverage intensity and exposure volume. A small, risky firm may experience a large debt increase relative to its sales, while a large, safer firm can account for more of the total dollars. Aggregate risk follows the dollars, not the emotional salience of the most vulnerable borrower.

The study's baseline expected loss is 0.27 percent of GDP for formal firms. When the calculation includes natural persons who borrowed as firms under the program, it rises to 0.45 percent of GDP. The corresponding credit-weighted default probability for all guaranteed credit is 9.8 percent in the broader calculation. These are not interchangeable numbers.