Transcript Document

Lecture 4
Interest Rates and Interest Rate Determination
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.
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.
LIBOR is the most widely used benchmark or
reference rate for short term interest rates. It is
compiled by the British Bankers Association
and 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.
3 month LIBOR vs. PRIME
Prime
LIBOR
Note:
- Not substitute libor for prime
- Must remember libor is variable rate prime is “fixed”
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 So What will drive bond prices up ?
10%
$91
1%
$99
•Pension funds want bonds
•Foreign investors want bonds
Another Way To See the Same Thing
Suppose you have a 4% bond with
Face Value
Coupon
$100
$4
If it sells for $100, its current return is 4% ($4/$100). Now
suppose 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
$4 coupon  $4 capital gain
$96
 (about ) 8%
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 “are
most 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 then
“got out” of 10 year bonds causing its price to fall and its
return to rise.
2. Discount vs. Yield
Some money market instruments are quoted on a
discount basis, (T-bills, commercial paper, bankers
acceptances), others on a yield basis (government
notes and bonds, corporate bonds, mortgage
securities, etc).
Here is the difference. Suppose you pay $90 for one
year T-bill that returns $100 face value in one year.
Interest $10
Yield (roughly)

 11%
Price $90
But the amount below face that the bill sold for (i.e. its
Discount price) is
Amt Below Face
$10
Discount 

 10%
Face Value
$100
Recent Treasury Bill Auction Results
Term
Issue
Date
Maturity Discount Investment
Date
Rate % Rate %
CUSIP
3.049
Price
Per
$100
99.766
28-day
7-7-05
8-4-05
3.000
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
912795VK4
Rates rise in Treasury bill auction
Tuesday, November 26, 2002
Associated Press
WASHINGTON —
Interest rates on short-term Treasury securities rose in Monday's
auction.
The Treasury Departme nt 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.
3.Nominal Returns vs. REAL
Returns
• Nominal interest rate = real
interest rate + expected inflation
where nominal rate is advertised
market rate;
real rate is extra purchasing power
lender demands of borrower.
Proof
a) In zero inflation world, if M&M’s cost $1.00 and you
lend $10.00, you’re lending 10 bags of M&M’s
b) If you want a real return of 10%, you need 11 bags so
you 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
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.
1  i (1  t )
E
1 P
Where PE is expected inflation
Therefore 1 + rat = 1  i (1  t )
1  PE
or,
rat  P E  rat P E
i
1 t
which implies
i 1  rat

1
E
1 t
P
INTEREST RATE “FACTS”
1. Until recently (January 2003) the Discount
Rate 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.
FED FUNDS-DISCOUNT SPREAD
1966-2003
20
18
Fed Funds and Discount Rates
16
14
12
10
8
6
4
2
0
-2
-4
1966
1968
1970
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
Year
Fed Funds Rate
Discount Rate
Difference
1994
1996
1998
2000
2002
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.
To raise rates, Fed sells Treasury Bills to government securities
dealers. Dealer writes check to Fed drawn on a bank. Dealer’s
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.
Key Concern
Retail sweep

decreased bank
reserves

OMO can make Fed
Funds volatile
New proposal to pay interest on reserves to
keep reserve levels higher.
3. Yield curve spread: the difference between the 10 year Treasury
Yield and 3 Month Treasury Discount.
Treasury Yield Curve
A.
B.
Typically low right before a recession
•
Boom raises short term real rates.
•
Inflation has raised short rates.
•
Higher short term rates kill consumer
demand.
Primary reason spread widens in
recession
•
Slowdown in economic activity depresses
short term rate.
•
Investors expect interest rates to go up
again when economy recovers so
longer
term rates are higher.
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.
2. But, we must note that the spread can fall either
because short rates rise, or long rates fall.
 If the former (i.e. short rates rise), then
falling spread reliably forecasts recession
because borrowing cost increase means less
borrowing, fewer car loans, fewer cars, etc.
 But, if the latter (i.e. falling long rates) it is
much 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.
The Yield Curve as a Predictor
of U.S. Recessions
Arturo Estrella and Frederic S. Mishkin
Estimated Recession Probabilities for Probit Model Using the Yield
Curve Spread
Four Quarters Ahead
Recession Probability
(Percent)
5
10
15
20
25
30
40
50
60
70
80
90
Value of Spread
(Percentage Points)
1.21
0.76
0.46
0.22
0.02
-0.17
-0.50
-0.82
-1.13
-1.46
-1.85
-2.40
Federal Reserve Bank of New York
Current Issues in Economics and Finance, June 1996, Vol. 2, No. 7
Long Rates Drop
Because
“inflation” is
Dead !
Long rates drop because of
Treasury refinancing and
increased demand for Longterm govt’s.
3.
Impact of Foreign Investors. Without them bidding for
our debt, interest rates would be higher.
 When will they bid more? When value of dollar is expected
to rise. So a strong dollar lowers interest rates, all else
fixed.
4.
Why would Fed fear inflation?
 inflation would raise interest rates and stall recovery.
 inflation would raise interest rates and hurt stock
market.
 inflation would raise interest rates and raise
government deficit.
50’s
60’s
70’s
80’s
90’s
5. Why would Fed fear deflation?
 Since i = r + expected inflation, with r = 2% or 3%,
deflation of 4% or more would cause normal rates to be
negative ! How would loan markets then work ?
 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 not
impossible.
 If deflation is persistent, people will all wait to buy things
(i.e. wait for the lowest price), which means economy will
stall.
6. Pegging "Real" Rates. The
Fed’s Current Policy?
 Idea is that higher real rates
slow the economy, lower real
rates bolster the economy. So to
slow it down, Fed raises real
rates.
In place of the money supply, … Greenspan
indicated he’s putting greater reliance on
“real” short term rates…”
“because
the ‘real’
federal
funds rate,
i.e. adjusted
for inflation
would still
be positive
and above
its typical
level.
Lower to stimulate
the economy
REAL RATE (1 YR TREAS - CPI INFLATION)
0.1
0.08
0.06
0.02
Real rate
-0.02
-0.04
-0.06
Negative Real Interest Rates !
Pay Borrowers to Borrow !
YEAR
02
20
00
20
98
19
96
19
94
19
92
19
90
19
88
19
86
19
84
19
82
19
80
19
78
19
76
19
74
19
72
19
70
19
68
19
66
19
64
19
62
19
60
19
58
0
19
PERCENT
0.04
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 lower
interest rates to get rid of it, or
3. To increase money, Fed buys Government
Securities by “printing” money. When
demand for Securities rises, price of
securities rise. When price of a security
rises, its return (interest rate) falls.
• Fisher Effect: creating to much money causes
more money chasing some amount of goods. So,
price of goods goes up. But if price increases
cause inflation, interest rates will rise! More on
this later…
So, Money   Inflation   Interest Rates 
This is why high money growth in the 60’s/70’s led to
higher, not lower, interest rates.
This also explains why Greenspan was reluctant to
create too much money in late 1990’s.
He felt it would just cause inflation and
higher (not lower) interest rates.
Fisher Equation : i = real rate + expected inflation
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 don’t 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.