Lesson 16 of 25 · 7 min

Credit rationing: when price stops clearing the market

Beyond a certain rate a lender expects less back rather than more, so it shortens the queue instead of raising the charge.

In most markets a shortage is resolved by price. Credit is the standing exception, and the reason is that in credit the price changes the thing being priced.

Raising a rate does two things at once. It raises the payment if the loan performs, and it lowers the chance that it performs — partly because a larger payment is harder to make, and partly because the borrowers who accept the higher rate are systematically those with fewer alternatives. The lender's expected return is therefore not increasing in the rate all the way up. It rises, peaks, and falls.

expected return = p x (1 + r) + (1 - p) x R - 1

p: The probability the loan is repaid in full. It falls as the rate rises, for both of the reasons above.
r: The interest rate charged, as a decimal.
R: What the lender recovers per dollar lent when the loan does not perform.
expected return: The probability-weighted return per dollar lent. The quantity the lender is actually setting the rate to maximise.

With an illustrative recovery of 62 cents, a rate of 6 percent with a 98.5 percent repayment probability returns 5.34 percent; 8 percent with 96.8 returns 6.53; 10 percent with 94.0 returns 7.12; 12 percent with 89.5 returns 6.75; and 14 percent with 83.0 returns 5.16. The lender stops at 10 percent. Demand above that is not met at any price, which is what rationing means — not a refusal to lend, a refusal to lend more.

On a secured line this shows up somewhere other than the rate, because the rate was never the binding constraint. It shows up in advance rates, in eligibility, and in the size of an increase granted. The practical consequence is specific: there is generally no rate a borrower can offer to have a revised advance rate reversed, because the lender's problem is not that it is underpaid. Price is simply not the variable being adjusted.

Key terms

Credit rationing: Limiting how much is lent rather than raising the price until supply and demand meet. The normal way a credit market clears in a tightening.
Adverse selection: The tendency for a higher offered rate to attract the borrowers least able to pay it, so raising the rate degrades the pool being lent to.
Expected return to the lender: What a lender expects to collect per dollar lent, after the chance of not being repaid. It peaks at a finite rate and falls beyond it.

Worked example

Where the lender stops

Illustrative figures. Recovery of 62 cents per dollar on a loan that does not perform, and a repayment probability that falls as the rate rises.

6 percent, repayment probability 0.985: 5.34%
8 percent, probability 0.968: 6.53%
10 percent, probability 0.940: 7.12%
12 percent, probability 0.895: 6.75%
14 percent, probability 0.830: 5.16%

Charging 14 percent instead of 10 loses the lender almost two points of expected return, so the unmet demand is turned away rather than priced.

Check yourself

A lender recovers 55 cents per dollar on loans that fail. At an 11 percent rate the repayment probability is 0.930; at 15 percent it is 0.845. Which rate does the lender prefer, and what does that imply for a borrower offering to pay more?

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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.