The Encyclopedia of Economic Principals

Chapter 51

Banks, Monitoring, Lending, and Credit Creation

Why banks monitor, when owners stay safe, what relationships know and why deposits commit.

Four of the chapter's worked examples, made interactive: delegated monitoring with diversified or correlated loans, charter-value discipline, relationship lending, and deposits as a fragile commitment device. Change one value at a time and watch the figure, the numbers and the hand calculation respond.

Every example here is a constructed teaching example: it uses the hypothetical numbers of the chapter's worked examples, plus a few values added for comparison and labelled as such in each panel. Nothing here measures a real market, firm or household.

Demonstration 1 of 4

One monitor or a hundred

When does a bank that monitors once beat every saver checking every borrower?

The bank replaces 1,000 checks with 10, but depositors must then watch the bank. Diversification across independent loans makes bank default rare, which keeps that second layer cheap.

Equation, written in LaTeX: 100(10)=1{,}000

Equation, written in LaTeX: \Pr(F\geq3)=1-\sum_{j=0}^{2}\binom{10}{j}(0.1)^j(0.9)^{10-j}\approx0.0701908.

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100 savers fund 10 loans of 10 million dollars; one check costs 4,000 dollars. A loan pays 11.5 million or, on failure, 4 million. The bank promises depositors 100 million; F is the number of failed loans and a bank default costs D in enforcement.

Predict first. If all ten loans fail together with probability 0.1, does the bank still beat direct monitoring?

Your prediction

Choose an example

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Figure: One monitor or a hundred. Left: distribution of loan failures with failure probability 0.10, default region shaded. Right: direct cost $4,000,000 against delegated cost $2,847,633.
Loan failure probability: 0.1, Loan outcomes: Independent, Bank default cost: $40 million
Constructed example: the chapter's hypothetical bank (100 savers, 10 loans, 4,000 per check, failure probability 0.1, default cost 40 million, independent or perfectly correlated loans); failure probabilities 0.05 and 0.20 and a 20 million default cost are added for comparison.

Calculated values

Pr(bank default)
0.0701908
Expected enforcement
$2,807,633
Delegated total
$2,847,633
Direct monitoring
$4,000,000
Cheaper
Bank (delegated)

Direct finance needs 100 x 10 = 1,000 checks, 1,000 x 4,000 = $4,000,000. The pool pays 115 - 7.5F million, below 100 once F >= 3; with failure probability 0.10, Pr(F >= 3) = 0.0701908. Expected enforcement is 0.070190826 x 40,000,000 = $2,807,633, and adding 10 x 4,000 = 40,000 of monitoring gives $2,847,633, below the $4,000,000 direct cost, so the bank wins.

Worked steps

  1. Direct: 100 x 10 x 4,000 = 4,000,000
  2. Pr(default) = 0.0701908 (F >= 3 of 10)
  3. Enforcement = 0.070190826 x 40,000,000 = 2,807,633
  4. Delegated = 40,000 + 2,807,633 = 2,847,633

Use the idea

Judge an intermediary's cost advantage by how independent its assets are, not just by how many loan files it holds.

Where the conclusion applies

Identical loans, a single period, a fixed default cost, and either independence or perfect correlation; real portfolios sit in between.

Check your understanding: Under perfect correlation, what is the total delegated cost?
0.1 x 40,000,000 = 4,000,000 of enforcement plus 40,000 of monitoring = 4,040,000, above the 4,000,000 direct cost.

Chapter 51 source: section "Delegated monitoring".

Demonstration 2 of 4

Franchise value keeps banks safe

How much future rent does a bank need before its owners prefer safety?

Risk raises the payoff now but raises the chance of losing the franchise. A larger franchise makes that loss heavier, so owners with valuable charters choose safety.

Equation, written in LaTeX: 8+0.98V=11+0.80V.

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V is the charter value, the present value of future rents, lost if the bank fails. The safe portfolio pays 8 million now and survives with probability 0.98; the risky one pays 11 million and survives with the probability shown. Owner value is payoff now plus survival probability times V.

Predict first. If competition cuts V to 10, which portfolio do owners choose?

Your prediction

Choose an example

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Figure: Franchise value keeps banks safe. Owner value against charter value for the safe and risky portfolios; the lines cross at V* = 16.67. At V = 30 safe is 37.4 and risky 35.0.
Charter value ($ million): 30, Risky survival probability: 0.8
Constructed example: the chapter's hypothetical bank (8 at 0.98 against 11 at 0.80, charter value 30 or 10); charter values 20 and 40 and risky survival probabilities 0.70 and 0.90 are added for comparison.

Calculated values

Safe value
37.4
Risky value
35.0
Threshold V*
16.67
Owners choose
Safe portfolio

Safe: 8 + 0.98 x 30 = 8 + 29.4 = 37.4. Risky: 11 + 0.80 x 30 = 11 + 24.0 = 35.0. The safe portfolio is worth more, so owners choose it. Indifference is at V* = 3 / (0.98 - 0.80) = 3 / 0.18 = 16.67.

Worked steps

  1. Safe = 8 + 0.98 x 30 = 37.4
  2. Risky = 11 + 0.80 x 30 = 35.0
  3. V* = (11 - 8) / (0.98 - 0.80) = 3 / 0.18 = 16.67
  4. V = 30 is above V*, so safe portfolio wins

Use the idea

When competition erodes bank rents, expect risk taking to rise unless supervision or capital replaces the lost discipline.

Where the conclusion applies

Two portfolios, risk-neutral owners and a charter lost entirely on failure.

Check your understanding: With V = 10, what are the two values and which wins?
Safe 8 + 0.98 x 10 = 17.8; risky 11 + 0.80 x 10 = 19; the risky portfolio wins.

Chapter 51 source: section "Charter-value discipline".

Demonstration 3 of 4

What the relationship lender knows

How does private information about a borrower change the lending decision?

The incumbent's records raise its success estimate, which raises expected repayment above the principal. The same information lets it charge more than the break-even promise, because outsiders cannot compete.

Equation, written in LaTeX: 0.90P^*+0.10(40{,}000)=100{,}000.

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A bakery borrows 100,000 dollars and promises 110,000 if its project succeeds; collateral yields the recovery shown if it fails. p is the lender's assessed success probability: 0.75 for an outsider, 0.90 for the incumbent. P* is the promise that returns the principal in expectation.

Predict first. Does the outsider with p = 0.75 lend at a 110,000 promise?

Your prediction

Choose an example

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Figure: What the relationship lender knows. Left: expected repayment $103,000 against the 100,000 principal. Right: expected repayment rises with the promise and reaches the principal at P* = $106,666.67.
Lender's success probability: 0.9, Collateral recovery: $40,000
Constructed example: the chapter's hypothetical bakery loan (100,000 principal, 110,000 promise, 40,000 collateral, p = 0.75 or 0.90); a probability of 0.85 and collateral of 20,000 and 60,000 are added for comparison.

Calculated values

Expected repayment
$103,000
Break-even promise P*
$106,666.67
Break-even rate
6.67%
Decision at 110,000
Lend

Expected repayment is 0.90 x 110,000 + 0.10 x 40,000 = 99,000 + 4,000 = $103,000, at or above the 100,000 principal, so the lender lends. The break-even promise is (100,000 - 0.10 x 40,000) / 0.90 = $106,666.67, a success-state rate of 6.67 percent.

Worked steps

  1. E = 0.90 x 110,000 + 0.10 x 40,000 = 103,000
  2. 103,000 >= 100,000, so lend
  3. P* = (100,000 - 4,000) / 0.90 = 106,666.67
  4. r* = 106,666.67 / 100,000 - 1 = 6.67%

Use the idea

Compare a borrower's quoted rate with the break-even rate an informed lender would need; the gap is the price of being informationally captured.

Where the conclusion applies

Risk-neutral lenders, two outcomes, no other costs, and the collateral recovery shown.

Check your understanding: What promise gives the incumbent exactly 100,000 in expectation?
P* = (100,000 - 0.10 x 40,000) / 0.90 = 106,666.67, a 6.67 percent rate.

Chapter 51 source: section "Relationship lending".

Demonstration 4 of 4

Demand deposits as a commitment device

When is it worth funding a relationship loan with runnable deposits?

Demandable deposits raise pledgeable income from beta C to the full 90 because a banker who withholds collections faces a run. The same run can strike for unrelated reasons, destroying the collection value the banker's skill protects.

Equation, written in LaTeX: (1-s)(30)+s(-18)=30-48s.

Equation, written in LaTeX: s<\frac{30}{48}=0.625.

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The banker can collect C = 120 from a loan costing 90; an outside buyer recovers only the share beta. Deposits commit the banker to pay out 90 but expose the loan to a panic sale before collection, which happens with probability s.

Predict first. Does a higher outsider recovery share raise or lower the panic threshold s*?

Your prediction

Choose an example

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Figure: Demand deposits as a commitment device. Left: expected surplus falls linearly in the panic probability and crosses zero at s* = 0.625; at s = 0.300 it is 15.60. Right: completion nets 30 and a panic sale -18.
Panic probability: 0.3, Outsider recovery share: 0.6
Constructed example: the chapter's hypothetical loan (C = 120, beta = 0.60, cost 90, threshold 0.625); the book leaves s symbolic, so panic probabilities 0.1, 0.3 and 0.8 and recovery shares 0.5 and 0.7 are added.

Calculated values

Outsider value beta C
72
Pledgeable with deposits
90
Liquidation loss
48
Expected surplus
15.60
Panic threshold s*
0.625

An outsider recovers 0.6 x 120 = 72, so a panic sale nets 72 - 90 = -18 and destroys 120 - 72 = 48. Expected surplus is (1 - 0.300) x 30 + 0.300 x (-18) = 21.00 + (-5.40) = 15.60, which is positive. It stays positive while s < 30 / 48 = 0.625.

Worked steps

  1. beta C = 0.6 x 120 = 72
  2. Panic outcome = 72 - 90 = -18
  3. E = (1 - 0.300) x 30 + 0.300 x (-18) = 15.60
  4. s* = 30 / 48 = 0.625

Use the idea

Weigh funding capacity from runnable liabilities against the expected cost of a panic sale; assets that sell well to outsiders tolerate more run risk.

Where the conclusion applies

A stylized one-loan bank, no other costs, and a panic probability unrelated to the loan itself.

Check your understanding: At beta = 0.6 and s = 0.3, what is expected surplus?
0.7 x 30 + 0.3 x (-18) = 21 - 5.4 = 15.6 dollars, the same as 30 - 48 x 0.3.

Chapter 51 source: section "Diamond-Rajan liquidity-creation fragility".