Macro Course 2005 Lecture 4

8/8/2019 Macro Course 2005 Lecture 4

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Lecture 4

Interest Rates and Interest Rate Determination


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Key Interest Rates

1. Federal Fund Rate The rate at which banks lend reserves to one

another on an overnight basis.

Important Points

1) Key Federal Reserve Policy Variable

2) Market Rate, not fixed

3) Little Federal about it !

4) Will disappear as policy variable as

LIBOR proliferates.


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Key Interest Rates

2. Discount Rate The rate at which the Fed lends reserves

to banks and other financial institutions.

3. 10 Year Treasury

Imputed Rate on 10 yr. Treasury notes or

bonds (assumes reinvestment of coupons

at this rate).

4. 3 mo Treasury

Discount rate on 91 day T-bills.


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LIBOR is the most widely used benchmark or

reference rate for short term interest rates. It is

compiled by the British Bankers Associationand released to the market at about 11:00 each

day. LIBOR stands for the London Interbank

Offered Rate and is the interest rate at which

the banks borrow funds (US Dollars) from

other banks in the London interbank market.

LIBOR is typically pretty close to the Fed Funds

Rate but is well below the Prime Rate.


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3 month LIBOR vs. PRIME

Note:

- Not substitute libor for prime

- Must remember libor is variable rate prime is fixed

LIBOR

Prime


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INTEREST RATE MECHANICS

1. Bond prices and interest rates move in

opposite directions If bond prices rise, interest rates on those bonds fall.

If bond prices fall, interest rates on those bonds rise.

Q. If interest rates equal 10%, what would you pay for a zero coupon

bond that pays $100 one year from now?

A. About $91 (because your interest income would be $9 and $9/91 as

about 10%).

Q. If interest rates equal 1%, what would you pay for the same bond?

A. About $99

So, Interest Rate Price

10% $91

1% $99

So What will drive bond prices up ?

Pension funds want bonds

Foreign investors want bonds


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Another Way To See the Same Thing

Suppose you have a 4% bond with

Face Value $100

Coupon $4

If it sells for $100, its current return is 4% ($4/$100). Nowsuppose interest rates in the economy go up to 8%! Would

someone pay you $100 for this bond? No, because if Price =

$100 and coupon = $4, the return is 4%, not 8%.

What would someone pay? About $96.00 because

%8)about(96$

gaincapital4$coupon4$!


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Where Do We See This in the Real World?

The yield on the 10-year Treasury note, a benchmark for

corporate borrowing and home loans, soared to the highest in

a year after Fed Chairmen Alan Greenspan in July testified

before the House finance committee. Greenspan said

conditions compelling the Fed to buy longer-term government

debt in order to curb disinflation or buoy the economy aremost unlikely to arise. (Wall Street Journal)

This quote says that when the Fed announced it would not buy

long-term bonds, the market said Demand for the bond will

not be there in the future so its price will fall. Everyone thengot out of 10 year bonds causing its price to fall and its

return to rise.


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2. Discount vs. Yield

Some money market instruments are quoted on a

discount basis, (T-bills, commercial paper, bankersacceptances), others on a yield basis (governmentnotes and bonds, corporate bonds, mortgagesecurities, etc).

Here is the difference. Suppose you pay $90 for one

year T-bill that returns $100 face value in one year.

But the amount below face that the bill sold for (i.e. itsDiscount price) is

$

$

alueace

aceBelowmtDiscount 10

100

10!!!

%1190$

10$

Price

Interest(roughly)Yield !!!


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Recent Treasury Bill Auction Results

Term Issue Maturity Discount Investment Price CUSIPDate Date Rate % Rate % Per

$100

28-day 7-7-05 8-4-05 3.000 3.049 99.766 912795VK4

91-day 7/7/05 10/6/05 3.145 3.214 99.205 912795VU2

182-day 7/7/05 1/5/06 3.429 3.429 98.319 912705WH0

14-day 7/1/05 7/15/05 3.165 3.213 99.876 912795TN1

28-day 6/30/05 7/28/05 2.925 2.972 99.772 912795VJ7

91-day 6/30/05 9/29/05 3.080 3.147 99.221 912795VT5


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Rates rise in Treasury bill auctionTuesday, November 26, 2002

Associated Press

WASHINGTON Interest rates on short-term Treasury securities rose in Monday's

auction.

The Treasury Department sold $15 billion in three-month bills at a discount rate of

1.210 percent, up from 1.205 percent last week. An additional $15 billion was sold in

six-month bills at a rate of 1.265 percent, up from 1.245 percent.

Both the three-month and six-month rates were the highest since Nov. 4 when the

bills sold for 1.410 percent and 1.395 percent, respectively.

The new discount rates understate the actual return to investors 1.228 percent

for three-month bills with a $10,000 bill selling for $9,969.80 and 1.291 percent for a

six-month bill selling for $9,936.40.

In a separate report, the Federal Reserve said Monday the average yield for one-

year constant maturity Treasury bills, the most popular index for making changes

in adjustable rate mortgages, rose to 1.51 percent last week from 1.46 percent.


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3.Nominal Returns vs. REAL

Returns

Nominal interest rate = real

interest rate + expected inflationwhere nominal rate is advertisedmarket rate;

real rate is extra purchasing powerlender demands of borrower.


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Proof

a) In zero inflation world, if M&Ms cost $1.00 and you

lend $10.00, youre lending 10 bags of M&Ms

b) If you want a real return of 10%, you need 11 bags soyou charge 10% interest and get $11.00 back

c) If inflation is 20%, then you need $1.20 x 11 = $13.20

back to buy 11 bags and get your 10% real return.

This means you must charge a nominal rate of 32%d) 32% = 10% + 20% + 2%

Nominal real expected

Rate = rate + inflation + real rate inflation

Conclusion

Two fundamental determinants of interest rates are

strength of economy

expected (not past) inflation


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The Fisher Effect with Taxes

The real after tax purchasing power of a $1 investment

(1 + rat)

equals, by definition, my investment return after taxes divided by the

new price of goods I purchase.

Where PE is expected inflation

E

ti

P1

)1(1


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Therefore 1 + rat =

or,

E

ti

P1

)1(1

11

r1

Pimplieshich

1

PP

"

!

(

(

!

t

i

t

rri

at

atat


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INTEREST RATE FACTS

1. Until recently (January 2003) the DiscountRate was usually below Fed Funds about

100 basis points or so.

Was always the best rate in town.

Now it is a penalty rate just like in

European Banks.

Sometimes referred to as a Lombard

facility.


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FED FUNDS-DISCOUNT SPREAD

1966-2003

-4

-2

0

2

4

6

8

10

12

14

16

18

20

1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

Year

FedFundsandD

iscountRates

Fed Funds Rate Discount Rate Difference


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2. Using Open Market Operations to change Fed

Funds Rate

Benchmark interest rate monitored by Federal

Reserve

Everyday Board of Governors informs New

York Fed what Fed Funds should trade at.

At about 9:30 each day, New York Fed

intervenes to set rates at the target level.To raise Fed Funds rate, Fed must reduce

amount of reserves in banking system so that

banks have to pay more to borrow.


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To raise rates, Fed sells Treasury Bills to government securities

dealers. Dealer writes check to Fed drawn on a bank. Dealers

bank now owes Fed $. Fed just takes it out of the banks reserves.

To lower the Fed Funds rate, Fed buys Bills from Securities

dealers. It writes a check on itself which gets deposited in a bank.Bank sends check back to Fed to get $. Bank reserves rise,

interbank borrowing is easier and rates fall.


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Key Concern

Retail sweep decreased bank

reserves

OMO can make FedFunds volatile

New proposal to pay interest on reserves to

keep reserve levels higher.


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3. Yield curve spread: the difference between the 10 year Treasury

Yield and 3 Month Treasury Discount.

Treasury Yield Curve


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A. Typically low right before a recession

Boom raises short term real rates.

Inflation has raised short rates. Higher short term rates kill consumer

demand.

B. Primary reason spread widens inrecession

Slowdown in economic activity depresses

short term rate.

Investors expect interest rates to go upagain when economy recovers so

longer term rates are higher.


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TWO POINTS ON YIELD CURVE

SPREAD

1. You can use (somewhat reliably) the

spread to forecast recessions.

NOTE: Spread low before recession

1) Short term rates high as Fed slows

economy.

2) Long term rates low because

markets see recession.


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2. But, we must note that the spread can fall either

because short rates rise, or long rates fall.

yIf the former (i.e. short rates rise), thenfalling spread reliably forecasts recession

because borrowing cost increase means less

borrowing, fewer car loans, fewer cars, etc.

y But, if the latter (i.e. falling long rates) it ismuch less clear.

NOTE: Longer term rates can fall (thus narrowing

the spread) because of good things- inflation has been reduced permanently.

- government is borrowing less to finance

deficits.


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The Yield Curve as a Predictor

of U.S. Recessions

Arturo Estrella and Frederic S. Mishkin

Estimated Recession Probabilities for Probit Model Using the YieldCurve Spread

Four Quarters Ahead

Recession Probability Value of Spread

(Percent) (Percentage Points)

5 1.21

10 0.76

15 0.46

20 0.22

25 0.02

30 -0.17

40 -0.50

50 -0.8260 -1.13

70 -1.46

80 -1.85

90 -2.40Federal Reserve Bank of New York

Current Issues in Economics and Finance, June 1996, Vol. 2, No. 7


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Long Rates Drop

Because

inflation is

Dead !

Long rates drop because of

Treasury refinancing and

increased demand for Long-

term govts.


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3. Impact of Foreign Investors. Without them bidding for

our debt, interest rates would be higher.

y When will they bid more? When value of dollar is expected

to rise. So a strong dollar lowers interest rates, all elsefixed.


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4. Why would Fed fear inflation?

y inflation would raise interest rates and stall recovery.

y inflation would raise interest rates and hurt stock

market.y inflation would raise interest rates and raise

government deficit.

50s 60s 70s 80s 90s


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5. Why would Fed fear deflation?

y Since i = r + expected inflation, with r = 2% or 3%,

deflation of 4% or more would cause normal rates to benegative ! How would loan markets then work ?

y If you have deflation, debtors are in big trouble. They

have to work harder to pay off loans.

Suppose you owe me $100 and you sell

computers for $100 each. You only have to make 1

computer to pay me back. But if computers sell

for $1 each, you now have to make 100 computers

to pay me back ! Much more difficult, if notimpossible.

y If deflation is persistent, people will all wait to buy things

(i.e. wait for the lowest price), which means economy will

stall.


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In place of the money supply, Greenspan

indicated hes putting greater reliance on

real short term rates


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Lower to stimulate

the economy


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REAL RATE (1 YR TREAS - CPI INFLATION)

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

1958

1960

1962

1964

1966

1968

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

YEAR

PERCEN

T

Real rate

Negative Real Interest Rates !Pay Borrowers to Borrow !


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7. Money and Interest Rates

Liquidity effect: think of it one of these ways.

1. If something is plentiful, its price drops. So,

the more money is around, the lower is the

interest rate, or

2. When bank find money plentiful, they lowerinterest rates to get rid of it, or

3. To increase money, Fed buys Government

Securities by printing money. Whendemand for Securities rises, price of

securities rise. When price of a security

rises, its return (interest rate) falls.


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LEARNED

1. Nominal rates = real rates + expected inflation.

2. That interest rates, especially the Real Fed Funds Rate, has become

the focus of monetary policy.

3. That the Fed is now running countercyclical policy, i.e. if the

Economy heats up, they raise real rates.

4. That this countercyclical policy is why old relationships between

unemployment + Cap Util + inflation dont work as well today.

5. That the focus is so much on rates, that some economists just use

yield curve spreads to forecast economic activity, but this can be

wrong.

6. That when money grows to fast all you get is higher inflation +

higher rates since I = real + exp.infl.

7. Higher interest rates raise cost of financing government deficits and

decrease stock/bond prices.

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Macro Course 2005 Lecture 4

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