Finance-Theory · Unit 3 · Video 2 · Interactive Practice

Where Should the Bailouts Stop? Moral Hazard, Contagion, and Separating the Questions

IKey Relations

Relation	Name	What it says
$B + H \;\lt\; p\,L \;\Longrightarrow\; \text{rescue}$	Where the line falls	The bail-out's own cost $B$ plus the present value $H$ of the moral hazard it creates, set against the chance $p$ that the failure spreads and the loss $L$ if it does
$p^{*} = \dfrac{B + H}{L}$	Break-even chance of a panic	Above $p^{*}$ the rescue is the cheaper side of the balance; below it, letting the firm fail is
$\sum_{i \in F} e_{ij} \;\gt\; K_j \;\Longrightarrow\; j \text{ fails}$	How a failure travels	Firm $j$ takes losses $e_{ij}$ on the paper of the firms $F$ that have already failed; when those add past its capital $K_j$ , $j$ joins them
$\text{rescue} \Rightarrow \text{promise} \Rightarrow \text{less care over risk}$	The moral-hazard term $H$	Each rescue is an implicit promise to the future equity holders of institutions that large that a firm this size will not be allowed to collapse, and a firm that cannot fail loses the discipline the threat of failure provides

Key Insight: Over a forest fire you can put up a helicopter and see the whole blaze, which is what makes a ring of controlled burn around it work. In September 2008 there was no helicopter: nobody could see which firms were already failing, which would fail next, or where the hidden exposures lay, so neither $p$ nor $L$ could be measured and the line had to be drawn with real danger on both sides of it.

IIWhere the Rescues Stop

The rescues you can afford, drawn on the exposures you can see: does the failure still find a path around them?

Map Round 0

💡 Every rescue in this diagram is free. Its price is the promise it makes to the next firm's creditors, whose present value is the $H$ term above, and which falls due at the next crisis on a map nobody has drawn yet.

IIIWho Is Left Holding the Loss

The shareholders take the first loss either way; what a rescue changes is everything past their stake.

Loss on the assets $30bn

IVOne Question, Two Sets of Tools

Each issue can be settled only by the tools built for it, and one of them by neither.

Issue

💡 The same question was put twice before: in the Southeast Asian crisis of 1997 the international institutions decided to rescue and those countries survived, and in a later Latin American crisis they decided, led by the United States, not to, and the crisis ran its course. Neither outcome settles the next case.

VQuiz Questions

Problem 1 · Does the Failure Reach It?

Given: firm $j$ takes losses on the paper of two firms that have just failed, $45bn on one and $30bn on the other, against capital of $60bn, and nobody rescues it. Which statement is correct?

✅ Correct!

45 + 30 = 75

against

K_j = 60

, in $bn, so the failure travels one step further and

j

becomes the next firm whose obligations go bad.

❌ The losses do not queue up. Both holdings are worthless at the same moment, so what meets the capital is their sum,

45 + 30 = 75

❌ Too strong. A firm holding a failed firm's paper takes the loss, but it fails only when that loss is past its capital. Capital is exactly what stops the spread at some firms and not at others.

❌ Capital is not a reserve standing outside the loss. It is the cushion between the assets that fell and the obligations the firm still owes, so a $75bn fall in assets eats it first.

Show solution

Apply the condition for how a failure travels, with all figures in $bn:

\sum_{i \in F} e_{ij} = 45 + 30 = 75 \;\gt\; K_j = 60

Firm $j$ fails. The sum matters because both firms in $F$ have already failed: their paper is bad now, not one holding at a time.

Note what the condition also says. Had $j$ held $45bn and $10bn instead, the total of $55bn would sit inside its $60bn of capital and the chain would stop there. That is the whole reason a network of exposures does not always burn to the ground, and the reason you cannot tell in advance where it will stop without knowing every $e_{ij}$ and every $K_j$ .

Problem 2 · What the Takeover Promised

Given: when Fannie Mae and Freddie Mac were taken over on 7 September 2008, the shareholders lost their stake while the institutions and their paper were kept alive. A classmate concludes that no moral hazard was created, since the equity was wiped out. Where does that argument go wrong?

✅ Correct! What survived was the institutions and their paper, and what the market takes from that is that a firm this size will not be allowed to collapse. An institution that cannot be allowed to fail loses the discipline the threat of failure provides.

❌ One claim was wiped out; the other was not. Everybody who had lent to these institutions was made good, and that is the outcome the next lender will price on.

❌ The shareholders did lose. That is exactly what makes the argument tempting. The moral hazard sits in what was kept alive, not in what was lost.

❌ Moral hazard is created by the expectation, not by the cheque. The implicit promise is made to future equity holders of institutions like these, and it changes how much care investors take over risk from that day on.

Show solution

Separate the two claims on the institution. The equity was destroyed, so the rescue was no gift to the shareholders of the day. The paper was kept alive, so every creditor was made good.

\text{rescue} \Rightarrow \text{promise} \Rightarrow \text{less care over risk}

The promise runs forward, not backward: it tells the future equity holders and creditors of institutions of that size what to expect when the next one gets into trouble. Investors who expect the promise to hold take less care over risk, and that expectation is the cost $H$ , charged not to this rescue but to the next crisis.

This is why the rescues could not simply continue. Each one is cheap on the day and dear afterwards, and by September 2008 the concern was that the Fed could not be seen to rescue every institution in trouble.

Problem 3 · Drawing the Line by Arithmetic

Given: rescuing a failing bank costs $20bn now, and the extra risk-taking that the implicit promise invites is worth $30bn today, discounted back from the next crisis. Letting it fail risks a system-wide panic that would cost $400bn.

Above what chance of panic is the rescue the cheaper side?

The exposure map puts the chance of panic at $8\%$ . Which side is cheaper?

✅ Correct!

p^{*} = (20 + 30)/400 = 0.125

, and at a chance of

0.08

the expected cost of letting it fail is

0.08 \times 400 = 32

, below the

50

the rescue costs. Every number here is in $bn.

❌ That is $20/400$ . It counts the cheque written today and leaves out the moral hazard, which is the other half of what a rescue costs.

❌ $50bn is a cost, not a probability.

B + H = 50

is what the rescue comes to; the break-even chance is that total divided by what the panic would cost.

❌ That is $30/400$ . It counts the moral hazard and leaves out the cheque written today; the balance needs both.

❌ The $400bn only arrives if the panic does. Weigh it by the chance of that happening:

0.08 \times 400 = 32

❌ The right side, on the wrong ground. Nothing about a rescue makes it always the dearer option: above a

12.5\%

chance of panic this same arithmetic favours the rescue. It is the estimate of

8\%

that decides it here.

❌ Compare $50$ with $0.08 \times 400 = 32$ , in $bn. The two sides balance at

12.5\%

, not at

8\%

, and below that threshold the expected cost of letting the bank fail is the smaller number.

Show solution

Put both sides in $bn. Rescuing costs what is paid now plus the moral hazard the promise creates:

B + H = 20 + 30 = 50

Letting it fail costs the panic only when the panic happens:

p\,L = p \times 400

The two sides balance where

p^{*} = \frac{B + H}{L} = \frac{50}{400} = 0.125

so above a $12.5\%$ chance of panic the rescue is the cheaper side, and below it letting the bank fail is. At the estimated $8\%$ :

0.08 \times 400 = 32 \;\lt\; 50

and the bank is left to fail on these numbers.

The arithmetic is the easy part. In September 2008 neither $p$ nor $L$ could be read off anything: both depend on exposures between firms that nobody could see, which is why a calculation this simple settled nothing at the time.

Problem 4 · Two Answers, Opposite Directions

Given: a country is heading for default. Judged as an economic question the answer is never to bail it out, because each rescue adds to the moral hazard and raises the cost of borrowing for future generations in other countries. Judged as a political and social question the answer is to help a country in real need. Which course follows the method of the lecture?

✅ Correct! Split the question into its separate issues, use each set of tools on the questions it was designed for, answer each in isolation, and only then decide how to weigh the answers against each other. That final weighing is a decision for politicians and voters.

❌ Measurability is not what decides which tool applies. Economics cannot settle the political question and politics cannot settle the economic one, so neither answer outranks the other.

❌ The two answers are expected to point opposite ways. That is why the method ends in a weighing rather than in agreement, and why the weighing belongs to politicians and voters.

❌ The same question was answered both ways before. Southeast Asia in 1997 was rescued and survived; a later Latin American crisis was left to run its course. Neither case settles the next one.

Show solution

The method is to split the question instead of hunting for a single answer.

The economic issue is moral hazard. Judged by that alone the answer is never to bail out a failing country, because each rescue adds to the moral hazard and raises the cost of borrowing for future generations in other countries.

The political and social issue argues the opposite way. Refusing to help a country in real need risks social unrest, and where nobody offers a solution people follow whoever does, whether that solution is true or false.

Economics has no tool that prices unrest and politics has none that prices future borrowing costs, so each question is answered in isolation with the tools built for it. What remains is how heavily to weigh one answer against the other, and that is not a calculation either field performs: it is a decision for politicians and voters.

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