Why Information Matters in Lending
A borrower usually knows more than a prospective lender about the borrower’s own circumstances, plans, and willingness to take risks. This unequal access to relevant information is called asymmetric information. It can make it difficult to distinguish a sound financing opportunity from a poor one, even when the lender and borrower would both benefit from a successful project.
Information problems can occur at different stages. Before a contract is agreed, a lender may not know the borrower’s type or project quality. After funding, the lender may be unable to observe the borrower’s choices. These are different problems, and they call for different responses. Screening helps assess applicants before funding; monitoring helps observe or influence conduct afterward. Repeated dealings can also build information that makes later decisions more accurate.
In lending, a borrower’s underlying probability of repaying is an example of a characteristic that may be private before a loan. The borrower’s choice of how much risk to take after receiving the funds is an example of a potentially hidden action. These labels describe the source and timing of the information gap; they do not mean that borrowers necessarily behave dishonestly.
Adverse Selection and Pooled Lending
Suppose a lender cannot tell which applicants are relatively safe and which are relatively risky. If the lender offers one contract to everyone, the expected repayment depends on the mix of applicants and on each group’s probability of repayment. A contract that looks acceptable for safer borrowers individually may be unattractive when assessed using the pooled average.
This calculation assumes that default produces no repayment and that the stated probabilities describe the applicant population. It is a calculation of expected nominal receipts, not a complete measure of profitability: funding costs, administrative expenses, timing, and risk can also matter.
Worked Example: When the Pooled Expected Repayment Is Too Low
A hypothetical lender advances $200 to an applicant. The applicant is a safer type with probability 0.3 and, if so, repays $230 with probability 0.9. The applicant is a riskier type with probability 0.7 and, if so, repays $230 with probability 0.6. Otherwise, repayment is zero. The lender cannot observe the type. Ignoring interest, costs, and timing, calculate expected repayment and compare it with the advance.
Method. Weight each type’s repayment probability by the probability of that type, then multiply the resulting overall repayment probability by $230.
The overall probability of repayment is \(0.3(0.9)+0.7(0.6)=0.27+0.42=0.69\). Thus expected repayment is \(230(0.69)=\$158.70\).
The expected shortfall relative to the $200 advance is \(\$200-\$158.70=\$41.30\). For comparison, if the lender knew the applicant was the safer type, expected repayment would be \(230(0.9)=\$207\), which is $7 more than the advance. If the lender knew the applicant was the riskier type, expected repayment would be \(230(0.6)=\$138\), which is $62 less than the advance.
Check. The pooled result also equals the type-weighted expected receipts: \(0.3(230)(0.9)+0.7(230)(0.6)=\$62.10+\$96.60=\$158.70\). Even though lending to a known safer type has positive expected receipts over the advance, pooled lending does not under these assumptions. The calculation avoids the common mistake of reporting $161: the two weighted terms sum to \(0.27+0.42=0.69\), so the product is $158.70.
How Screening Can Improve Selection
Screening means gathering and evaluating information before deciding whether, and on what terms, to fund an applicant. Possible methods include reviewing financial records, asking for evidence about the project, requiring an appraisal, or using a structured application assessment. A screen need not identify every applicant’s type correctly. Its value depends on whether it improves the decision enough to justify its cost and any applicants it wrongly excludes.
An imperfect test can still be useful if it changes the mix of applicants who are accepted. The lender should calculate the probability of each test outcome, the composition of that group, and the expected receipts from lending to it. A positive result does not itself mean an applicant is safe; its meaning depends on the accuracy of the test and the underlying shares of each type.
Worked Example: Assessing an Imperfect Screening Test
Among hypothetical applicants, 40% are safer and 60% are riskier. A screening test is positive for 80% of safer applicants and for 25% of riskier applicants. The lender offers a $200 advance only to applicants with a positive result. A positive applicant repays $250 with probability 0.95 if safer and 0.55 if riskier; otherwise repayment is zero. The test costs $1 per applicant assessed. Ignoring all other costs and timing, compare screening with lending to everyone.
Method. First calculate the shares of all applicants who are positive and who are both positive and repay. This avoids treating the test’s sensitivity as the probability that a positive applicant is safe.
The fraction of all applicants who are positive and safer is \(0.40(0.80)=0.32\). The fraction who are positive and riskier is \(0.60(0.25)=0.15\). Therefore, the positive-test share is \(0.32+0.15=0.47\), and the probability that a positive applicant is safer is \(0.32/0.47\), about 0.6809.
For a randomly selected applicant, the share who are positive and repay is \(0.32(0.95)+0.15(0.55)=0.304+0.0825=0.3865\). Expected receipts per positive loan are therefore \(\$250(0.3865/0.47)\), about \(\$205.59\). The expected margin per positive loan, before screening costs, is about \(\$205.59-\$200=\$5.59\).
Per applicant assessed, expected receipts from positive loans are \(\$250(0.3865)=\$96.625\), and expected advances are \(\$200(0.47)=\$94\). Thus the expected margin before the test cost is \(\$96.625-\$94=\$2.625\). After subtracting the $1 screening cost, the expected margin is \(\$1.625\) per applicant assessed.
Without screening, lending to everyone gives repayment probability \(0.40(0.95)+0.60(0.55)=0.38+0.33=0.71\). Expected receipts per $200 advance are \(\$250(0.71)=\$177.50\), a shortfall of \(\$22.50\) before other costs. Under the stated assumptions, screening improves the expected result. It does not guarantee a profit in every case, and the conclusion depends on the test accuracy, loan terms, and costs. The final check is that the screened margin is calculated per applicant assessed, not per positive applicant.
Moral Hazard and Monitoring
A contract may be agreed on the basis of information available before funding, yet the borrower’s later decisions can change the probability of repayment. If the borrower receives some of the gains from taking additional risk while the lender bears much of the resulting loss, the borrower may have an incentive to choose more risk than the lender would prefer. This is a moral-hazard problem when the relevant action is difficult to observe or enforce.
Monitoring is the collection of information or oversight after funding. For example, a lender might review progress reports, inspect a project, or require that funds be used for an agreed purpose. Monitoring can be costly and cannot always prevent risky conduct. Its economic value depends on whether it changes behavior or reduces losses enough to outweigh its cost.
Worked Example: When Monitoring Changes the Borrower’s Choice
A hypothetical project requires a $200 advance and produces $300 if successful, zero if unsuccessful. The contract requires the borrower to repay $240 from successful-project proceeds. Under prudent conduct, success has probability 0.90. Under risky conduct, success has probability 0.65, and the borrower also receives a private benefit of $35. Assume the borrower’s payoff is the project proceeds after repayment, plus any private benefit. Without monitoring, the borrower chooses whichever conduct gives the higher expected payoff. A monitoring program costs the lender $10 per loan, detects risky conduct with probability 0.50, and imposes a collectible $100 penalty if risky conduct is detected. Calculate the choices and lender’s expected outcomes.
Method. Compare the borrower’s expected payoffs first. Then calculate the lender’s expected receipts under the conduct the borrower chooses. The calculation assumes the penalty is collectible and that prudent conduct does not trigger it.
With prudent conduct, the borrower receives \(\$300-\$240=\$60\) if successful and zero otherwise. Expected payoff is \(0.90(\$60)=\$54\). With risky conduct, the borrower’s expected project residual is \(0.65(\$60)=\$39\); adding the $35 private benefit gives \(\$39+\$35=\$74\). Without monitoring, the borrower therefore chooses risky conduct.
Under monitoring, the risky borrower’s expected penalty is \(0.50(\$100)=\$50\). The risky payoff falls to \(\$74-\$50=\$24\), below the prudent payoff of $54. The borrower now chooses prudent conduct. The lender then expects repayment of \(0.90(\$240)=\$216\). After the $200 advance and $10 monitoring cost, the expected net amount is \(\$216-\$200-\$10=\$6\).
Without monitoring, the borrower chooses risky conduct and the lender expects repayment of \(0.65(\$240)=\$156\). The lender’s expected net amount is \(\$156-\$200=-\$44\). Thus, in this model, monitoring changes incentives and improves the lender’s expected result from a $44 shortfall to a $6 surplus. The common mistake is to subtract the expected penalty only from the lender’s receipts: here, its stated role is to change the borrower’s choice. Because the borrower chooses prudent conduct under monitoring, no penalty is collected in the resulting outcome.
Why Ongoing Relationships Can Help
Repeated dealings can give an intermediary information that is difficult to obtain from a single application. A record of past repayments, project updates, and responses to agreed requirements can help assess a later request. This information may make screening more accurate or reduce the cost of evaluating a repeat borrower. A continuing relationship can also make monitoring more effective if the borrower expects future access to funding to depend on current conduct.
Relationship information is not a guarantee of repayment. A borrower’s circumstances can change, and past performance does not reveal every future risk. A relationship also has costs, including the time spent gathering records and the possibility that a lender becomes too reliant on an outdated assessment. The relevant comparison is whether the information’s expected benefit exceeds the cost of acquiring and maintaining it.
Worked Example: Is Gathering Relationship Information Worthwhile?
A lender is considering three future loans to the same hypothetical business. Without additional relationship information, each loan has an expected loss of $30. A review of the business’s payment history and operating records costs $20 once and, if completed, reduces the expected loss on each of the three loans to $18. Assume the review does not change the loan amounts or any other costs. Should the lender conduct the review?
Method. Compare total expected losses with and without the review, then subtract the review cost.
Without the review, total expected loss is \(3(\$30)=\$90\). With the review, expected loss on the loans is \(3(\$18)=\$54\). The reduction in expected loan losses is \(\$90-\$54=\$36\). After the $20 review cost, the net expected benefit is \(\$36-\$20=\$16\). Under these assumptions, conducting the review is worthwhile. The check is that the one-time cost is subtracted once, while the reduced expected loss applies to all three loans.
Deriving the Pooling Result
The central arithmetic behind pooled lending follows from the law of total probability. Let type \(j\) occur with probability \(p_j\), where the type probabilities sum to 1. Let \(q_j\) be the probability of repayment for type \(j\), and let \(R\) be the repayment amount if repayment occurs. If default yields zero, expected receipts are the sum of each type’s probability times its repayment probability times the repayment amount:
The first equality partitions outcomes by borrower type; within each type, repayment occurs with probability \(q_j\) and default with probability \(1-q_j\). The second equality uses the fact that multiplying by zero contributes nothing. If the lender cannot distinguish types and advances \(L\), expected receipts below \(L\) mean an expected shortfall before other costs. If safer applicants withdraw when the pooled terms are unattractive, the applicant mix may become less favorable still. This is one way adverse selection can obstruct funding even when some individual projects have positive expected returns.
The result is conditional on its assumptions. It does not account for recoveries after default, different repayment amounts, interest or funding costs, or the possibility that the applicant mix changes when the contract changes. Those features must be included when they matter.
Common Mistakes and Practical Meaning
- Confusing timing. Hidden borrower type before the contract is an adverse-selection issue; hidden borrower action after funding is a moral-hazard issue.
- Using a test’s sensitivity as a posterior probability. The fraction of safer applicants who test positive is not generally the fraction of positive applicants who are safer. Calculate the shares of the whole applicant pool first.
- Ignoring costs or the unit of comparison. A margin per approved loan is not the same as a margin per applicant assessed. Include screening and monitoring costs on the appropriate basis.
- Assuming monitoring always pays. Monitoring is useful only when its expected improvement in outcomes is sufficient to cover its cost.
- Treating relationships as certainty. Past information can improve assessment, but it does not eliminate changed circumstances or future uncertainty.
These mechanisms help explain why intermediaries can do more than match a source of funds with a potential user of funds. Their information-gathering and oversight activities can make some exchanges feasible that would otherwise be too uncertain or costly. This tutorial is aligned with the SOA VEE Economics (Validation by Educational Experience) syllabus.
Check Your Understanding
For each problem, state the key calculation or comparison and check that the result uses the correct population and time of the information problem.
- A lender advances $180 and receives $220 if the borrower repays; default yields zero. Applicants are 25% safer, with repayment probability 0.96, and 75% riskier, with repayment probability 0.50. Find pooled expected repayment and compare it with expected repayment if the lender knows an applicant is safer. (Answer: pooled repayment $135.30, a $44.70 shortfall; known-safer expected repayment $211.20, $31.20 above the advance.)
- Half of applicants are safer and half riskier. A test is positive for 90% of safer applicants and 20% of riskier applicants. Find the probability an applicant is safer given a positive result. (Answer: \(0.45/(0.45+0.10)=0.8182\), or 81.82%.)
- A lender advances $150 and receives $180 on repayment, with zero on default. Borrowers are 40% safer, repaying with probability 0.90, and 60% riskier, repaying with probability 0.50. Find the pooled expected repayment and its difference from the advance. (Answer: repayment probability \(0.40(0.90)+0.60(0.50)=0.66\); expected repayment $118.80, a $31.20 shortfall.)
- A business earns a borrower $50 after repayment if successful. Success probability is 0.90 with prudent conduct and 0.60 with risky conduct; risky conduct also gives a private benefit of $30. Monitoring reduces the borrower’s expected risky payoff by a $40 penalty, while prudent conduct is not penalized. Which conduct is chosen with and without monitoring? (Answer: prudent payoff \(0.90(50)=\$45\); risky payoff without monitoring \(0.60(50)+\$30=\$60\), so risky is chosen. With monitoring, risky payoff is \(\$60-\$40=\$20\), so prudent is chosen.)
- A lender expects losses of $24 on each of four future loans without a review. A one-time review costs $25 and reduces expected loss to $17 on each loan. Find the net expected benefit of the review. (Answer: loss reduction \(4(24-17)=\$28\); net expected benefit \(\$28-\$25=\$3\).)