Finance-Theory · Unit 6 · Video 1 · Interactive Practice

Credit, Not Cost: Why the Fed Held Rates, Rescued AIG and Let Lehman Fail

IKey Formulas

Formula	Name	What it says
$\dfrac{50\ \text{bp}}{200\ \text{bp}} = \dfrac{1}{4}$	Room left to cut	One basis point is $0.01$ percentage point, so a $2\%$ target sits $200$ bp above $0\%$ , the floor as it was seen in 2008; a $50$ bp cut would have used a quarter of that room
$1 + r_{\text{real}} = \dfrac{1 + r_{\text{nominal}}}{1 + \pi}$	Exact real rate	$\pi$ is the inflation rate; over short periods a nominal rate can sit below it, and then $r_{\text{real}} \lt 0$
$r_{\text{real}} = \dfrac{1.02}{1.05} - 1 \approx -2.86\%$	The video's illustration	A $2\%$ nominal rate with an illustrative $5\%$ inflation: $1 saved buys about $0.97 of today's goods a year later

Key Insight: A rate cut lowers the cost of funds; lending supplies the funds themselves, which addresses their availability. The Fed apparently judged September 2008 to be a crisis of availability, so it held its target at 2% and lent up to $85 billion to AIG.

IIHow Much Room a Cut Uses

With the target at 2%, every cut spends part of the 200 basis points of room above zero.

Cut (bp) 50

IIIWhat the Loan to AIG Was For

On the Fed's apparent reasoning, the ostensible reason Lo offered, which response stops the chain from an AIG failure to forced selling: a rate cut or a loan?

Fed response Step 6 / 6

💡 Lo was openly speculating here: the Fed's real reasons cannot be known from outside, so availability over cost is its apparent judgment.

IVA Rate Below Inflation

A nominal rate below inflation makes the real rate negative, and the saver ends the year poorer.

r nominal (%) 2 Inflation π (%) 5

VQuiz Questions

Problem 1 · A Quarter of the Room

Given: on Tuesday 16 September 2008 the fed funds target was $2\%$ , and $0\%$ was then seen as the floor. Find the fraction of the room above the floor that a cut of $50$ basis points would have used.

✅ Correct!

50

bp is

0.50

percentage point, and

0.50 / 2 = \tfrac{1}{4}

: the target would fall to

1.50\%

, leaving

150

bp of room.

❌ Half a point is not half the room.

50

bp is half of one percentage point. The room is

2

percentage points,

200

bp, so the cut uses

50/200 = \tfrac{1}{4}

of it.

❌ Check the unit.

\tfrac{1}{40}

treats

50

bp as

0.05

percentage point. One basis point is

0.01

point, so

50

bp is

0.50

point and

0.50/2 = \tfrac{1}{4}

❌ That is the room left over. After a

50

bp cut,

150

of the

200

bp remain, which is

\tfrac{3}{4}

. The cut itself uses the other

\tfrac{1}{4}

Show solution

One basis point is $0.01$ percentage point, so the room from a $2\%$ target down to $0\%$ is

2\% - 0\% = 2 \text{ percentage points} = 200 \text{ bp}

A $50$ bp cut uses

\frac{50}{200} = \frac{1}{4}

of it, taking the target to $1.50\%$ and leaving $150$ bp. This was Lo's first reason for the Fed's restraint: another fifty basis points would have left very little flexibility later.

Problem 2 · The Exact Real Rate

Given: $r_{\text{nominal}} = 2\%$ and, for illustration, $\pi = 5\%$ . Find the exact real rate $r_{\text{real}}$ .

✅ Correct!

\dfrac{1.02}{1.05} - 1 \approx 0.9714 - 1 = -0.0286

, a real rate of about

-2.86\%

❌ That is the subtraction shortcut.

2\% - 5\% = -3\%

is close, but the exact relation divides:

\dfrac{1.02}{1.05} - 1 \approx -2.86\%

❌ The ratio is upside down.

\dfrac{1.05}{1.02} - 1 \approx +2.94\%

puts inflation in the numerator. The nominal factor goes on top:

\dfrac{1.02}{1.05} - 1 \approx -2.86\%

❌ The ones are missing.

\dfrac{2}{5} - 1 = -0.60

divides the bare rates. The relation divides the growth factors

1 + r_{\text{nominal}} = 1.02

and

1 + \pi = 1.05

Show solution

Use the exact relation from earlier in the course:

1 + r_{\text{real}} = \frac{1 + r_{\text{nominal}}}{1 + \pi} = \frac{1.02}{1.05} \approx 0.9714

r_{\text{real}} \approx 0.9714 - 1 = -0.0286 = -2.86\%

The nominal rate sits below inflation, so the real rate is negative: $1 saved at 2% buys only about $0.97 of today's goods a year later. The shortcut $2\% - 5\% = -3\%$ is an approximation that drifts further from the exact value as the rates grow.

Problem 3 · A Saver's Real Loss

Given: a saver deposits $500 for one year at a nominal rate of $3\%$ , while inflation over the year is $6\%$ .

What is the real rate, to two decimals?

The year-end balance is worth how much in today's goods?

✅ Correct!

\dfrac{1.03}{1.06} - 1 \approx -2.83\%

, and the $515.00 balance buys about $485.85 of today's goods: a real loss of about $14.15.

❌ That is the subtraction shortcut.

3\% - 6\% = -3\%

approximates; the exact rate is

\dfrac{1.03}{1.06} - 1 \approx -2.83\%

❌ The ratio is upside down.

\dfrac{1.06}{1.03} - 1 \approx +2.91\%

puts inflation on top. A rate below inflation gives a negative real rate.

❌ Wrong denominator.

\dfrac{0.03 - 0.06}{1.03} \approx -2.91\%

divides by

1 + r_{\text{nominal}}

. The exact real rate is

\dfrac{r_{\text{nominal}} - \pi}{1 + \pi} = \dfrac{-0.03}{1.06} \approx -2.83\%

, the same as

\dfrac{1.03}{1.06} - 1

❌ The interest is missing. 500 / 1.06 ≈ 471.70 deflates the original deposit. The saver holds $515.00 at year end, and 515 / 1.06 ≈ 485.85.

❌ That uses the shortcut rate. 500 × 0.97 = 485.00 applies

-3\%

. With the exact

-2.83\%

: 500 × 0.9717 = 485.85.

❌ Deflate by dividing. 515 × 0.94 = 484.10 multiplies by

1 - \pi

. Prices rose by the factor 1.06, so today's-goods value is 515 / 1.06 ≈ 485.85.

Show solution

Step 1: the real rate.

1 + r_{\text{real}} = \frac{1.03}{1.06} \approx 0.9717, \qquad r_{\text{real}} \approx -0.0283 = -2.83\%

Step 2: the nominal balance. $500 at 3% grows to $515.00.

500 \times 1.03 = 515

Step 3: deflate by a year of 6% inflation.

\frac{515}{1.06} \approx 485.85

So the balance buys about $485.85 of today's goods. Check with the real rate: $500 \times 0.9717 = 485.85$ ✓. The saver ends the year $14.15 poorer in real terms, though the account shows $15.00 more.

Problem 4 · Availability, Not Cost

Given: a central bank judges that banks and firms cannot obtain funds at all, although the rates on offer are already low. Choose the response that fits the reading Lo attributed to the Fed in September 2008.

✅ Correct! Lending more at the discount window supplies the funds themselves and puts money into the system without moving the policy rate.

❌ That treats cost. A rate cut lowers the cost of funds, but the problem here is that funds are not available at all. It would also spend room the Fed had little of.

❌ Prices are not a crystal ball. Market prices contain information, but in September 2008 they priced a cut that never came. Waiting supplies no funds either.

❌ A failure supplies no funds. The Fed did let Lehman fail, but it lent to AIG because, in its apparent judgment, an AIG failure would set off forced selling across the credit markets.

Show solution

Lo's reading, which he said was speculative, was that the Fed saw a crisis of availability (a credit crisis, a crisis of liquidity), not of cost.

A rate cut lowers the cost of funds: it answers the wrong problem.
Supplying the funds addresses availability. The loan to AIG was one way; letting banks borrow more at the discount window, on easier terms, was another, and it leaves the policy rate unchanged. Other central banks were injecting money in the same way.

Waiting on futures prices and letting a firm fail supply no funds, so neither addresses availability.

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