Finance-Theory · Unit 7 · Video 1 · Interactive Practice

Ninety-Seven Cents a Share: How a Money-Fund Run Moved Treasury Bill Yields

IKey Formulas

Formula	Name	What it says
$P_{0,T} = \dfrac{F}{(1+y)^T}$	Bill price from its yield	$F$ is the face value and $T$ the years to maturity; a three-month bill has $T = \tfrac14$ , so at $y = 0.49\%$ the price is $\dfrac{100}{(1.0049)^{1/4}} \approx 99.88$ per $100 of face value
$(1+y)^{1/4} - 1$	Return over one quarter	Quoted yields are annualized: $(1.04)^{1/4} - 1 \approx 0.985\%$ , just under $1\%$ a quarter, and $(1.0049)^{1/4} - 1 \approx 0.122\%$ , about 12 cents on $100
$\dfrac{1}{(1+\pi)^{30}}$	Purchasing power in 30 years	$\pi$ is the inflation rate; at an illustrative $\pi = 2.5\%$ , $\dfrac{1}{(1.025)^{30}} \approx 0.48$ , so $1 paid in 30 years buys what about $0.48 buys today
$1.00 - 0.97 = 0.03 = 3\%$	Breaking the buck	A share priced at $0.97 returns 3 cents less on every dollar: $1,000 comes back as $970

Key Insight: A Treasury carries no nominal default risk, so its yield does not measure default. The bill yield recorded a panic: a run from prime money funds bid bill prices up and the yield down to 3 basis points. What a Treasury holder does risk is inflation and changes in interest rates.

IIPrice and Yield of a Three-Month Bill

A bill's price falls as its annualized yield rises: the move from 3 to 49 basis points cost about 11 cents per $100.

Yield (bp) 49 Date

IIIThe Whole Curve Rose

From 17 to 24 September 2008 every maturity rose, and the 30-year rose least.

Maturity

💡 Part of the 30-year's 32 basis points can plausibly be read as an added inflation premium after the $700 billion asset-purchase plan, but since every shorter maturity rose more, the rise is no clean measure of expected inflation.

IVWhy Everyone Redeems at Once

When holdings are worth $0.97 a share, each share paid out at $1.00 leaves less for those still in.

Shares redeemed 50 / 100

💡 The $0.97 is the Reserve Primary Fund's share value once its $785 million of Lehman commercial paper was valued at zero; the redemption path is an illustration, and the real fund soon froze withdrawals.

VQuiz Questions

Problem 1 · The 18 September Bill

Given: on 18 September 2008 the three-month bill yielded $23$ basis points, annualized. Find the price of a bill with $100 of face value, using $P_{0,T} = \dfrac{F}{(1+y)^T}$ with $T = \tfrac14$ .

✅ Correct!

\dfrac{100}{(1.0023)^{1/4}} \approx 99.94

: at a quarter-year to maturity the bill costs 6 cents less than its face value.

❌ Not quite.

\dfrac{100}{1.0023} \approx 99.77

discounts for a full year. The bill matures in three months, so the exponent is

T = \tfrac14

❌ Check the units. One basis point is

0.01\%

, so

23

bp is

0.23\% = 0.0023

, not

0.00023

❌ Not quite. A price above the $100 face value would mean a negative yield. Divide by

(1+y)^T

; don't multiply.

❌ Not quite. Use

y = 0.0023

and

T = \tfrac14

P = \dfrac{100}{(1+y)^{T}}

Show solution

$23$ basis points is $0.23\%$ , so $y = 0.0023$ , and three months is $T = \tfrac14$ year:

P_{0,1/4} = \frac{100}{(1.0023)^{1/4}} = \frac{100}{1.0005745} \approx 99.94

The bill costs about $99.94 per $100 of face value, 6 cents below face.

Problem 2 · Annualized, Not Quarterly

Given: from 1962 to 2002 the three-month bill yielded about $6\%$ on average, quoted as an annualized yield with annual compounding. Find what a bill yielding exactly $6\%$ earns over its three months.

✅ Correct!

(1.06)^{1/4} - 1 \approx 1.467\%

over the quarter; four such quarters compound back to exactly

6\%

❌ Not quite.

6\%

is the annualized quote. A three-month bill earns only a quarter-year's worth of it.

❌ Close, but…

6\% / 4 = 1.5\%

ignores compounding: four quarters at

1.5\%

give

(1.015)^4 - 1 \approx 6.14\%

, more than

6\%

. Take the fourth root instead.

❌ Not quite.

(1.06)^4 - 1 \approx 26.25\%

compounds

6\%

over four years. For one quarter the exponent is

\tfrac14

❌ Not quite. Convert with

(1+y)^{1/4} - 1

Show solution

A quoted yield is annualized: one year at $y$ grows $1 to $1+y$ . One quarter is a quarter of the year, so

(1.06)^{1/4} - 1 \approx 1.014674 - 1 \approx 1.467\%

Check: $(1.014674)^4 \approx 1.06$ . By the same step the video's $4\%$ is about $0.985\%$ a quarter, just under $1\%$ .

Problem 3 · The Day of the Guarantee

Given: on Thursday 18 September 2008 the three-month bill yielded $23$ basis points; on Friday 19 September, the day the Treasury announced its guarantee for money funds, it yielded $99$ basis points. Per $100 of face value, find the 19 September price and how far the price fell over the day.

Price on 19 September?

Fall in price from 18 to 19 September?

✅ Correct! The yield rose

76

bp and the price fell 19 cents per $100, about a quarter of

0.76

, because the bill has only a quarter-year left to run.

❌ Not quite.

\dfrac{100}{1.0099} \approx 99.02

discounts for a whole year; use

T = \tfrac14

❌ Not quite.

100 - 0.99

treats the annualized yield as dollars taken off the price. The price is

\dfrac{100}{(1.0099)^{1/4}}

❌ Not quite.

99.94

is the 18 September price at

23

bp. The yield rose, so the price fell below it.

❌ Check the price.

P = \dfrac{100}{(1.0099)^{1/4}}

❌ Not quite.

99 - 23 = 76

bp is the change in the annualized yield, not in the price. Subtract the two prices.

❌ Not quite. That is one day's gap between price and the $100 face value (what the bill earns to maturity). The fall is the 18 September price minus the 19 September price.

❌ Check the difference. Subtract the 19 September price from the 18 September price.

Show solution

18 September ( $y = 0.0023$ ): $\dfrac{100}{(1.0023)^{1/4}} \approx 99.94$ .

19 September ( $y = 0.0099$ ):

\frac{100}{(1.0099)^{1/4}} = \frac{100}{1.0024659} \approx 99.75

Fall in price: $99.94 - 99.75 = 0.19$ per $100 of face value.

The video warns that the asset-purchase plan and the short-selling ban came the same day, so this jump cannot be credited to the guarantee alone.

Problem 4 · What a Long Treasury Risks

Given: a 30-year Treasury bond pays $1,000 at maturity. For illustration, suppose prices rise $3\%$ a year for all 30 years.

In today's goods, the $1,000 buys about

Which risk does the holder bear?

✅ Correct! The $1,000 is certain in nominal terms, but at

3\%

inflation it buys only about $412 of today's goods; that erosion is the risk, and why a rising 30-year yield reads as an inflation premium.

❌ Not quite. $1,000 is the nominal payment, which is certain. The question asks what it will buy after 30 years of

3\%

inflation.

❌ Not quite.

1000(1 - 30 \times 0.03) = 100

subtracts

3\%

of the original value each year. Inflation compounds: divide by

(1.03)^{30}

❌ Close, but…

1000 \times (0.97)^{30} \approx 401

uses

1 - \pi

as if it were

\dfrac{1}{1+\pi}

. The exact factor is

\dfrac{1}{(1.03)^{30}}

❌ Check the purchasing power. Compute

\dfrac{1000}{(1.03)^{30}}

❌ Not quite. The United States issues the dollar and can always create dollars to pay; in nominal terms, as far as anyone knows, there is no default risk.

❌ Not quite. No default risk is not no risk: the bond pays dollars, and what those dollars buy is uncertain.

❌ Not quite. That was the risk inside prime money funds. A Treasury is an IOU from the government that issues the dollar, not company paper; its risk is what its dollars will buy.

❌ Check the risk. A nominal bond promises dollars, not goods.

Show solution

Prices rise by the factor $(1.03)^{30}$ over 30 years, so the $1,000 buys what

\frac{1000}{(1.03)^{30}} = \frac{1000}{2.4273} \approx 411.99

dollars buy today, about $412. The payment itself carries no nominal default risk; the risk is inflation, and, if the bond is sold before maturity, changes in interest rates.

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