Finance-Theory · Unit 8 · Video 1 · Interactive Practice

Yields Up, Banks Merged: How Regulators Tried to Stop the Run in September 2008

IKey Formulas

Formula	Name	What it says
$P = \dfrac{F}{(1+y)^{1/4}}$	Three-month bill price	$F$ is the face value and $y$ the annualized yield. At $y = 0.72\%$ , $P = \dfrac{100}{(1.0072)^{1/4}} \approx 99.82$ per $100 of face, against $99.99$ at 3 bp: a higher yield is a lower price
$4.40\% - 4.22\% = 0.18\ \text{pp} = 18\ \text{bp}$	Basis points	One basis point is $0.01$ percentage point. The 30-year Treasury yield fell 18 bp from 24 September to class on 29 September 2008
$\text{outcome} = P_{\text{sale}} - P_{\text{purchase}}$	Rescue or bailout	Positive: a savvy investment; negative: a bailout. A short sale is the same arithmetic: sell at $P_0$ , buy back at $P_1$ , gain $P_0 - P_1$
$\text{Citigroup} = \min(L, 42), \quad \text{FDIC} = \max(L - 42,\ 0)$	The 29 September Wachovia plan	$L$ is the loss, in billions of dollars, on a $312 billion pool of Wachovia loans; Citigroup would absorb the first $42 billion or so and the FDIC the rest

Key Insight: On 29 September 2008 a rising bill yield was good news: 71–72 bp, up from 30–40 bp the week before, meant fewer investors fleeing into safety. Selling into a panic supplies liquidity; the Treasury, which alone can issue bills, did exactly that at near-zero rates, and whether its rescue turns out to be a bailout depends only on the price it pays and the price it later sells for.

IIShort the Bill: Small Loss, Large Gain

Shorting a bill yielding 3 bp loses only $75 per $1 million of face if the yield falls to zero, but gains far more if yields rise.

Yield when the short is closed (bp) 72

💡 Shorting means borrowing the bill from an owner who will lend it, at a premium, and only the United States Treasury can issue new bills. The Treasury did: it sold new bills into the panic and borrowed at interest rates near zero.

IIIBailout or Savvy Investment

Whether a rescue is a bailout depends on two prices only: what the government pays and what it sells for.

Buy (month) 5 Sell (month) 20

IVWho Absorbs Wachovia's Loan Losses

Under the 29 September plan, Citigroup took the first $42 billion or so of losses; the FDIC covered the rest.

Losses on the pool ($ bn) 60

💡 This plan did not survive the week: on 3 October 2008 Wells Fargo agreed to buy all of Wachovia in an all-stock deal valued at about $15.1 billion, the deal that went through and was completed at the end of 2008.

VQuiz Questions

Problem 1 · The Long End in Basis Points

Given: the 30-year Treasury yield was $4.40\%$ on 24 September 2008 and $4.22\%$ during class on 29 September. Find the change.

✅ Correct!

4.40\% - 4.22\% = 0.18

percentage points, and each percentage point is 100 bp, so the yield fell

18

bp. The video read it as inflation concern easing somewhat.

❌ Check the direction. The yield went from

4.40\%

down to

4.22\%

: that is a fall, not a rise.

❌ Check the units. The difference

0.18

is in percentage points. One percentage point is

100

bp, so

0.18

pp is

18

bp.

❌ Not quite.

0.18 / 4.40 \approx 4.1\%

is the proportional change in the yield. Basis points measure the absolute difference in yields:

0.18

= 18

bp.

❌ Not quite. Subtract the yields, then convert percentage points to basis points.

Show solution

4.40\% - 4.22\% = 0.18\ \text{percentage points}

0.18\ \text{pp} \times 100\ \tfrac{\text{bp}}{\text{pp}} = 18\ \text{bp}

The yield fell by $18$ bp. Because the whole curve had moved with the panic, the video cautions that a move at the long end is no clean measure of inflation.

Problem 2 · Judge the Rescue by Two Prices

Given: during a panic a government buys securities at $70$ per $100 of face value. Their market price then falls to $55$ before calm returns, and the government sells them at $80$ . Was the purchase a bailout or a savvy investment?

✅ Correct!

\text{outcome} = P_{\text{sale}} - P_{\text{purchase}} = 80 - 70 = 10 > 0

. The price along the way never enters the verdict.

❌ Not quite.

55 - 70 = -15

is where the position stood at the bottom of the panic, but the government did not sell there. Only the sale price and the purchase price decide the outcome.

❌ Not quite.

80 - 55 = 25

measures the recovery from the low, but the government paid

70

, not

55

. Use the price it actually paid.

❌ Not quite.

100 - 80 = 20

compares the sale price with the face value. The government never paid

100

; it paid

70

❌ Not quite. Subtract the purchase price from the sale price.

Show solution

By the video's rule, the outcome depends on two prices only:

\text{outcome} = P_{\text{sale}} - P_{\text{purchase}} = 80 - 70 = +10 \text{ per 100 of face}

The sale price exceeds the purchase price, so the rescue turned out to be a savvy investment. Buying from frightened sellers supplied liquidity, and the provider did well once markets calmed; the interim low of $55$ is irrelevant to the result.

Problem 3 · The Lopsided Short

Given: on 17 September 2008 you short a three-month bill with $1,000,000 of face value at a yield of $3$ bp, a price of $\dfrac{1{,}000{,}000}{(1.0003)^{1/4}} \approx 999{,}925$ . You close the position right away, so the bill still has $T = \tfrac14$ year to run. Rounding each price to whole dollars, find your loss if the yield falls to $0$ , and your gain if it rises to $1\%$ .

Loss if the yield falls to 0?

Gain if the yield rises to 1%?

✅ Correct! The downside is only 75 dollars even if the yield falls all the way to zero, and yields cannot fall far below zero, while a move to

1\%

pays 2,409 dollars, about 32 times as much.

❌ Not quite.

\dfrac{1{,}000{,}000}{1.0003} \approx 999{,}700

discounts for a whole year. The bill has three months to run, so the exponent is

\tfrac14

❌ Check the units.

1{,}000{,}000 \times 0.000003 = 3

reads

3

bp as

0.000003

, but

3

bp is

0.03\% = 0.0003

. The loss is the rise in price from

999{,}925

to the face value.

❌ Not quite. A fall from

3

bp to

0

is still a fall in yield, so the price rises to the full face value and the short loses the difference.

❌ Not quite.

999{,}700 - 990{,}099 = 9{,}601

prices both bills with a full year to maturity. Use

T = \tfrac14

❌ Not quite.

1\%

of the face value is a year's interest, and it ignores the

3

bp you started from. Price the bill at each yield and subtract.

❌ Close, but…

1{,}000{,}000 - 997{,}516 = 2{,}484

measures the fall from face value. You sold at

999{,}925

, not at face.

❌ Check the loss. At a zero yield the bill is worth its face value; subtract the price you sold at.

❌ Check the gain. Price the bill at

1\%

with

T = \tfrac14

and subtract it from the price you sold at.

Show solution

A short sale gains $P_0 - P_1$ : the price you sold at minus the price you buy back at. You sold at $P_0 = 999{,}925$ .

Yield falls to 0: the bill is worth its face value.

P_1 = \frac{1{,}000{,}000}{(1.00)^{1/4}} = 1{,}000{,}000, \qquad P_0 - P_1 = 999{,}925 - 1{,}000{,}000 = -75

Yield rises to 1%:

P_1 = \frac{1{,}000{,}000}{(1.01)^{1/4}} = \frac{1{,}000{,}000}{1.0024907} \approx 997{,}516

P_0 - P_1 = 999{,}925 - 997{,}516 = 2{,}409

A 75-dollar worst case against a 2,409-dollar gain for a move back toward 1%: the downside looked tiny and the upside large. The obstacle is borrowing the bill to short it.

Problem 4 · The Deposit Insurance Ceiling

Given: a depositor holds $180,000 in a single account category at a bank that fails. The FDIC guarantee was $100,000 per depositor, per account category in 2008, raised temporarily to $250,000 on 3 October 2008. Find the insured amount if the bank failed on 29 September 2008, and the uninsured amount if it failed after 3 October 2008.

Insured amount, failure on 29 September 2008?

Uninsured amount, failure after 3 October 2008?

✅ Correct! Insured

= \min(\text{balance}, \text{ceiling})

\min(180{,}000,\ 100{,}000) = 100{,}000

before the change, and

\min(180{,}000,\ 250{,}000) = 180{,}000

after it, leaving nothing uninsured.

❌ Not quite. On 29 September the guarantee stopped at 100,000 dollars per depositor, per account category; the balance above that was not insured.

❌ Not quite. The 250,000-dollar ceiling came in on 3 October, and no ceiling pays out more than the balance: the depositor has only 180,000 dollars.

❌ Not quite.

180{,}000 - 100{,}000 = 80{,}000

is the part above the ceiling, which is uninsured. The insured part is the first 100,000 dollars.

❌ Not quite. 80,000 dollars was the uninsured part under the old 100,000-dollar ceiling. After 3 October the ceiling was 250,000 dollars.

❌ Not quite.

250{,}000 - 180{,}000 = 70{,}000

is unused room under the ceiling, not money at risk. The whole balance fits under it.

❌ Not quite. The raise was temporary, but it applied to failures while it was in force, and no deposit in this account falls outside it.

❌ Check the insured amount. Take the smaller of the balance and the ceiling in force on that date.

❌ Check the uninsured amount. Subtract the insured amount under the 250,000-dollar ceiling from the balance.

Show solution

Per depositor, per account category, the FDIC pays up to the ceiling in force:

\text{insured} = \min(\text{balance},\ \text{ceiling}), \qquad \text{uninsured} = \text{balance} - \text{insured}

29 September 2008 (ceiling 100,000):

\min(180{,}000,\ 100{,}000) = 100{,}000 \text{ insured}, \qquad 180{,}000 - 100{,}000 = 80{,}000 \text{ uninsured}

After 3 October 2008 (ceiling 250,000):

\min(180{,}000,\ 250{,}000) = 180{,}000 \text{ insured}, \qquad 180{,}000 - 180{,}000 = 0 \text{ uninsured}

Every insured dollar is one the FDIC must pay out if the bank fails, which is why the video calls a takeover that keeps the bank's good business going the cost-minimizing solution.

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