The Number Under the Rate | HL Hunt
The Number Under the Rate
Two lending books carry an identical 9% lifetime loss. One is flat and one is growing. Depending only on the denominator chosen, they report loss rates anywhere from 7.0% to 16.6%, and the growing book looks better on every measure. Every figure is correct. None of them is the loss. A rate is a property of the loans and of the number someone decided to put underneath them.
What you'll learn
Same loans, different loss rates
Take two lending books with identical credit quality. Every loan in both has the same 9% lifetime loss: nine cents of every dollar lent is eventually charged off, a few months after origination. The only difference is that one book is flat and the other is growing about 60% a year.
Now report a loss rate for each, using three denominators that are all in common use.
| Charge-offs over the last 12 months divided by | Flat book | Growing book |
|---|---|---|
| Average outstanding balance | 16.6% | 14.8% |
| Ending outstanding balance | 16.6% | 12.0% |
| Originations in the same 12 months | 9.0% | 7.0% |
Every figure in that table is arithmetically correct. None of them is the lifetime loss, and two of them would look like a credit improvement to anyone comparing the growing book against the flat one. The rate is not a property of the loans. It is a property of the loans and the number underneath them.
Why growth flatters every ratio
Losses arrive some months after a loan is made. A growing book always has more recent loans than old ones, so its denominator contains a large share of loans that have not yet had time to go bad.
- The numerator is set by last year's lending. Charge-offs today come from loans made months ago, when the book was smaller.
- The denominator is set by this year's lending. Balances and originations reflect the larger book.
- So the ratio falls while growth continues and rises when growth stops, with no change in credit quality at all.
That second consequence is the one that does damage. A lender that slows down sees its loss rate rise and reads it as deterioration, which is exactly when it is least able to afford a misreading. Per our growth analysis, the same lag that makes growth expensive in cash makes it flattering in ratios, and per our loss forecasting analysis, vintage curves exist because no single ratio taken on a moving book can separate quality from timing.
The same choice everywhere else
Lending is the clearest case, not the only one. Every operational rate has a denominator someone chose.
| Rate | Denominator A | Denominator B |
|---|---|---|
| Fraud | 12 of 10,000 transactions = 0.12% | $5,400 of $1.2m = 0.45% |
| Collections recovery on $486,000 | Of $6.0m placed = 8.1% | Of $1.9m contacted = 25.6% |
| Approval rate | Of all applications | Of applications that completed verification |
| Cure rate | Of accounts entering delinquency | Of accounts that were contacted |
The fraud row shows count against value. Fraud concentrates in larger transactions, so the same fraud is almost four times larger measured in dollars than in transactions. Per our fraud rate analysis, which one matters depends on whether the cost is per event or per dollar, and a report that gives only one hides the other.
The collections row shows how a denominator can exclude the hard cases. Measured on contacted balance, recovery is more than three times the rate on placed balance, because the accounts nobody reached have been removed. Per our benchmarking analysis, comparing an agency quoting one against an agency quoting the other compares nothing.
Who chooses, and why it is rarely cynical
It is tempting to treat this as manipulation. Mostly it is not.
Each denominator answers a different legitimate question. Loss on average balance is the right figure for pricing, because balance is what earns the yield. Loss on originations is the right figure for underwriting, because it is what the decision committed. Recovery on contacted balance is the right figure for evaluating agents, because uncontacted accounts were not theirs to work. Per our definition analysis, categories persist because each serves someone with a real purpose.
The problem arises when a figure built for one question is used to answer another, and the most common route is a single headline number that moves from an operating report into a board pack, a funding discussion or a published comparison without its denominator travelling with it. Per our target analysis, once that number becomes the thing people are measured on, the choice of denominator stops being neutral, because it is the cheapest lever available.
The case for a single standard definition
One response is to mandate a single definition, so every lender reports the same ratio. That has real value for comparison and is the reason standardized regulatory reporting exists. Its cost is that any single denominator is wrong for most of the questions people actually ask, and a standard definition can become the only number anyone computes. Per our reference point analysis, a published benchmark tends to become the target. The better standard is not one ratio but disclosure: every rate stated with its numerator, its denominator and its time window, so that a reader can see what was divided by what.
How to read a rate
- Ask what is underneath it. Count or dollars, average or ending, originated or outstanding, all or worked.
- Ask about the time window. A 12-month rate on a book with a 9-month loss lag is measuring last year's lending.
- Ask whether the book is growing. Growth flatters every ratio built on current balances or current originations.
- Prefer cohort measures for credit. Lifetime loss by origination month is the only measure that separates quality from timing.
- Check what the denominator excludes. Rates on worked, contacted or completed populations remove the cases that went worst.
- Insist on both count and value for fraud, disputes and losses.
- Look for the interval. Per our small numbers analysis, a rate on a small denominator is a range, whatever it says.
Item four is the one with the most consequence. A lender that tracks lifetime loss by vintage can see in the first months whether a new cohort is worse than the last one at the same age, independent of how fast the book is growing. Per our point-in-time analysis, the same discipline of fixing the date of measurement is what keeps model performance honest.
Item five is the one most often missed in comparisons. Per our cost to collect analysis and our collections metrics analysis, a rate that has quietly dropped the hardest accounts from its denominator will always look better than one that kept them, and the difference is the population, not the performance.
Testable implications
- Lenders reporting loss on current balances should show rising loss rates when growth slows, even where cohort-level loss is unchanged.
- Firms whose reported rates use worked or contacted denominators should show larger gaps from independently measured outcomes than firms using placed or originated denominators.
- Where a rate becomes a performance target, the share of reports using the most favourable available denominator should rise over time.
The first implication is the easiest to check and the most practically useful. Per our alert analysis, an indicator that moves for reasons unrelated to what it is meant to track generates exactly the false alarms that teach people to ignore it, and a loss rate that rises whenever growth slows is such an indicator.
Frequently asked questions
Because the denominator is a choice. Identical 9% lifetime loss shows up as anything from 7.0% to 16.6% depending on denominator and growth.
Losses lag lending, so a growing book divides old losses by a new, larger base. When growth stops the rate rises with no change in credit.
Usually not: each answers a real question. The problem is a number travelling without its denominator, especially once it becomes a target.
Ask what was divided by what, over what window, on a growing or flat base. Prefer cohort loss for credit and both count and value elsewhere.
Key takeaways
- Books with an identical 9% lifetime loss report loss rates from 7.0% to 16.6% depending on denominator and growth.
- Growth flatters every ratio built on current balances or originations, because losses lag lending.
- When growth stops, the reported rate rises with no change in credit quality, which invites a misreading.
- The same fraud is 0.12% by transaction count and 0.45% by dollars.
- Recovery on $486,000 is 8.1% of placed balance and 25.6% of contacted balance.
- Each denominator answers a legitimate question; the problem is a number travelling without its denominator.
- Lifetime loss by origination cohort is the only credit measure that separates quality from timing.
- The better standard is disclosure of numerator, denominator and window, not a single mandated ratio.
This analysis is educational and does not constitute financial, accounting, or investment advice. All figures are stylized illustrations using an assumed amortization schedule, loss timing, lifetime loss rate, growth rate, and transaction and recovery figures, and do not describe any particular lender or portfolio. Regulatory and accounting definitions of charge-off, loss and delinquency rates vary by institution type and jurisdiction. Consult a qualified adviser before relying on any reported rate.