Money & Banking
Video 04—Interest Rates II
The Behavior of Interest Rates (Chapter 5)
Interest Rate Determination (Chapter 6)
Hal W. Snarr
8/20/2015
Chapter 5
The Behavior of Interest Rates
Bond Demand
The quantity of bonds demanded increases as p falls.
P
D
B
Bond Demand
The quantity of bonds demanded increases as p falls.
Bond demand increases in
• Expected return relative to other assets
• Liquidity relative to other assets
• Wealth
P
D
B
Bond Demand
For 1-year discount
bonds held for 1 year,
The quantity of bonds demanded increases as p falls.
R=i
Bond demand increases in
• Expected return relative to other assets
• Liquidity relative to other assets
• Wealth
P
D
Bond demand decreases in
•
•
•
Riskiness relative to other assets
Expected inflation
Expected interest rate
B
Bond Supply
The quantity of bonds supplied increases as p rises.
P
S
B
Bond Supply
The quantity of bonds supplied increases as p rises.
Bond supply increases in
•
•
•
Expected profitability of investment opportunities
Expected inflation
Government budget deficits
P
S
B
Supply and Demand
Excess supply: the price suppliers are asking for is too high
P
D
95
S
15
25
B
Supply and Demand
Excess supply: the price suppliers are asking for is too high
• For a zero-coupon $100 bond held for one year
P
i
D
95
5.3
S
15
25
B
100
F
i
1
P
95
Supply and Demand
Equilibrium: the quantities of bonds supplied and demanded equal
• For a zero-coupon $100 bond held for one year
P
i
D
95
5.3
92
S
15
20
25
B
Supply and Demand
Equilibrium: the quantities of bonds supplied and demanded equal
• For a zero-coupon $100 bond held for one year
P
i
D
95
5.3
92
8.7
S
20
B
i
100
F
1
P
92
Supply and Demand
Excess demand: the price suppliers are asking for is low
• For a zero-coupon $100 bond held for one year
P
i
D
95
5.3
92
8.7
90
S
15
25
B
Supply and Demand
Excess demand: the price suppliers are asking for is low
• For a zero-coupon $100 bond held for one year
P
i
D
95
5.3
92
8.7
90
11.1
S
15
25
B
i
100
F
1
P
90
Supply and Demand
Equilibrium: the quantities of bonds supplied and demanded equal
• For a zero-coupon $100 bond held for one year
P
i
D
95
5.3
92
8.7
90
11.1
S
15
20
25
B
The Fisher Effect
Suppose expected inflation rise by 6 percentage-points.
P
D
S
95
i
5.3
20
B
The Fisher Effect
Suppose expected inflation rise by 6 percentage-points.
D
P
S
95
i
5.3
D
92
8.7
15
20
B
The Fisher Effect
Suppose expected inflation rise by 6 percentage-points.
D
P
S
95
5.3
S
D
i
92
8.7
90
11.1
15
20
B
The nominal rate of interest rises by 5.8 pct. pts.
The Fisher Effect
Source: Mishkin (1981) “The Real Interest Rate: An Empirical Investigation” Carnegie-Rochester
Conference Series on Public Policy 15: 151–200. These procedures involve estimating expected inflation
as a function of past interest rates, inflation, and time trends.
The Fisher Effect
Source: FRED
The Fisher Effect
1978-2007
18
i = 1.1pe + 1.7
R² = 0.47
16
14
12
10
8
6
4
2
0
0
2
4
6
8
Source: FRED
10
12
The Business Cycle and Interest Rates
Suppose economic growth is accelerating.
P
D
S
i
95
5.3
18
B
The Business Cycle and Interest Rates
Suppose economic growth is accelerating.
P
D
S
i
S
95
5.3
92
8.7
18
23
B
The Business Cycle and Interest Rates
Suppose economic growth is accelerating.
P
D
D
S
i
S
95
93
92
5.3
7.5
8.7
18
23 23
B
The quantity and price of bonds both increase
The Business Cycle and Interest Rates
Source: Federal Reserve: www.federalreserve.gov/releases/H15/data.htm.
The quantity and price of bonds both increase
Keynes’ liquidity preference framework
•
•
holding money and buying bonds are the only stores of wealth
the quantity of loanable funds people and firms supply = the value of bonds purchased
Total Wealth = Bs + Ms = Bd + Md
Loanable
Bond Market
funds Market
LD i
P
Bs – Bd =Ms – Md
BD
92
8.7
BS
LS
L
15
B
ifloanable
bond
==0=0if0ifthe
market
in
funds
formarket
money
market
is in
in
equilibrium
Keynes’ liquidity preference framework
•
•
holding money and buying bonds are the only stores of wealth
the quantity of loanable funds people and firms supply = the value of bonds purchased
Loanable funds Market
LD i
i LD
8.7
8.7
LS
LS
L
15
15
L
Keynes’ liquidity preference framework
•
•
•
holding money and buying bonds are the only stores of wealth
the quantity of loanable funds people and firms supply = the value of bonds purchased
The interest rate in these markets are the same
Loanable funds Market
The market for money
i LD
i
MD
8.7
LS
15
L
M
The Liquidity Effect
•
Money supply shifts to the right (increases) if
o The Fed injects money into the banking system with OMP
o Banking lending increases
Loanable funds Market
The market for money
i LD
i
MD
8.7
7.5
LS
15
L
M
The Price-level Effect
•
A one time increase in MS permanently raises the price level by end of year: i = r + p
o bond demand falls because the return falls (the supply of loanable funds falls)
o bond supply rises because the cost of borrowing falls (demand for loanable funds rises)
o money demand increases
Bond Market
Loanable funds Market
P
BS
BD
95
i
i
8.7
8.7
5.3
5.3
92
LD
LS
L
15
B
The market for money
15
L
MD
M
The Expected-Inflation Effect
•
An increase in MS causes inflation expectations to rise, which may diminish over time.
o bond demand falls (the supply of loanable funds falls)
o bond supply rises (demand for loanable funds rises)
o money demand increases
Loanable funds Market
The market for money
i
i
8.7
8.7
5.3
5.3
LD
LS
15
L
MD
M
The Income Effect
•
An increase in MS is an expansionary influence on the economy.
o demand for loanable funds rises
o money demand increases
Loanable funds Market
The market for money
i
i
7.1
7.1
5.3
5.3
LD
LS
15
L
MD
M
The Total Effect
Figure 11
Response to an
Increase
in MS Growth
The Total Effect
Figure 11
Response to an
Increase
in MS Growth
The Total Effect
4
5
2
6
9
5
6
1
2
3
4
a
7 7
8
8
3
1
9
a
b
b
Sources: Federal Reserve: www.federalreserve.gov/releases/h6/hist/h6hist1.txt.
Figure 12 Annual M2 Growth and 3-month T-bill (1950–2011)
Chapter 6
Interest Rate Determination
Interest Rate Determination
Nominal Rate (i)
=
+
+
+
–
+
+
Real Rate (r)
Expected Inflation (p e)
Default Risk Premium (d)
Illiquidity Risk Premium (l)
Tax exemption discount (t)
Maturity Premium (int – it)
Liquidity Premium (lnt)
Interest Rate Determination
Nominal Rate (i)
Risk structure
=
+
+
+
–
Real Rate (r)
Expected Inflation (p e)
Default Risk Premium (d)
Illiquidity Risk Premium (l)
Tax exemption discount (t)
The Risk and Term Structures of Interest Rates
• Risk structure: Bonds with the same maturity (n)
have different interest rates because of
– default risk premium (d)
– illiquidity risk premium (l)
– income tax risk discount (t)
• Term structure: For bonds with identical
characteristics, the interest rate (i) increases as
maturity (n) increases
– maturity premium (int – it)
– liquidity premium (lnt)
– The yield curve is the relationship between i and n.
Risk Structure
Default risk premium
• Default risk is the probability that the issuer of the bond is unable
or unwilling to make interest payments or pay off the face value
o U.S. Treasury bonds are considered default free
o Default risk premium (d) is the spread between the interest rates on bonds
with default risk and the interest rates on Treasury bonds, holding l, t, n,
lnt, and int – it equal
Risk Structure
Default risk premium
TABLE 1
Risk Structure
Default risk premium
P
i
P
i
Sc
St
950
5
950
5
Dt
Dc
Q
Corporate Bond
Market
Q
U.S. Treasury Bond
Market
Risk Structure
Default risk premium
P
i
P
i
Sc
St
950
5
925
6
950
5
Dt
Dc
Dc
Q
Corporate Bond
Market
Q
U.S. Treasury Bond
Market
Risk Structure
Default risk premium
P
i
P
i
Sc
St
950
5
925
6
975
4
950
5
Dt
Dt
Dc
Dc
Q
Corporate Bond
Market
Q
U.S. Treasury Bond
Market
Risk Structure
Default risk premium
P
i
P
i
Sc
St
4
975
2
925
6
Dt
Dt
Dc
Dc
Q
Corporate Bond
Market
Q
U.S. Treasury Bond
Market
Risk Structure
Default risk premium
You own a $1000, 10% GM bond that matures next year. The
Obama Administration abrogated 100 years of bankruptcy law
when it stripped primary bond holders of their first claim rights
on corporate assets during the GM bailout. Explain why
corporate bond prices would be lower in the post bailout era,
holding all else equal. If the GM bond sold for $1068 before the
bailout but sells for $1023, compute the yields on the bonds
before and after the bailout.
Pre-bailout
Post-bailout
N=1
I% = A
PV = -1068
PMT = 100
FV = 1000
N=1
I% = A
PV = -1023
PMT = 100
FV = 1000
Risk Structure
Default risk premium
You own a $1000, 10% GM bond that matures next year. The
Obama Administration abrogated 100 years of bankruptcy law
when it stripped primary bond holders of their first claim rights
on corporate assets during the GM bailout. Explain why
corporate bond prices would be lower in the post bailout era,
holding all else equal. If the GM bond sold for $1068 before the
bailout but sells for $1023, compute the yields on the bonds
before and after the bailout.
Pre-bailout
Post-bailout
N=1
I% = 2.996
PV = -1068
PMT = 100
FV = 1000
N=1
I% = 7.527
PV = -1023
PMT = 100
FV = 1000
Risk Structure
Illiquidity risk premium
• Liquidity is the relative ease with which an asset can be converted
into cash
o Cost of selling a bond
o Number of buyers/sellers in a bond market
o Illiquidity risk premium (l) is the spread between the interest rate on a
bond that is illiquid and the interest rate on Treasury bonds, holding d, t, n,
lnt, and int – it equal.
o E.g., assume an investor is looking at buying two corporate bonds that have
the same coupon rates and maturities, but only one is traded on a public
exchange. The investor is not be willing to pay as much for the non-public
bond. The difference in yields the investor is willing to pay for each bond is
the liquidity premium.
Risk Structure
Illiquidity risk premium
P
i
P
i
Sc
St
950
5
950
5
Dt
Dc
Q
Corporate Bond
Market
Q
U.S. Treasury Bond
Market
Risk Structure
Illiquidity risk premium
P
i
P
i
Sc
St
950
5
925
6
950
5
Dt
Dc
Dc
Q
Corporate Bond
Market
Q
U.S. Treasury Bond
Market
Risk Structure
Illiquidity risk premium
P
i
P
i
Sc
St
950
5
925
6
975
4
950
5
Dt
Dt
Dc
Dc
Q
Corporate Bond
Market
Q
U.S. Treasury Bond
Market
Risk Structure
Illiquidity risk premium
P
i
P
i
Sc
St
4
975
2
925
6
Dt
Dt
Dc
Dc
Q
Corporate Bond
Market
Q
U.S. Treasury Bond
Market
Risk Structure
Illiquidity risk premium
You are considering owning two $1000 bonds that
mature next year. One is a corporate bond, the other
is a Treasury, and both have an 8% coupon rate.
Why is the price of Treasuries higher than corporate
bonds with the same attributes? If the price of
treasuries is $1058 and the price of a similar
corporate
bond with the same bond
Corporaterating is $1001,
Treasury
compute the yields on the two bonds.
N=1
I% = A
PV = -1058
PMT = 80
FV = 1000
N=1
I% = A
PV = 1001
PMT = 80
FV = 1000
Risk Structure
Illiquidity risk premium
You are considering owning two $1000 bonds that
mature next year. One is a corporate bond, the other
is a Treasury, and both have an 8% coupon rate.
Why is the price of Treasuries higher than corporate
bonds with the same attributes? If the price of
treasuries is $1058 and the price of a similar
corporate
bond with the same bond
Corporaterating is $1001,
Treasury
compute the yields on the two bonds.
N=1
I% = 2.079
PV = -1058
PMT = 80
FV = 1000
N=1
I% = 7.892
PV = 1001
PMT = 80
FV = 1000
Risk Structure
Tax exemption risk discount
• Income tax considerations
o Interest payments on municipal bonds are exempt from federal income
taxes.
o Tax exemption risk discount (t) is the spread between the interest rate on
a tax exempt municipal bond and the interest rate on Treasury bonds,
holding d, l, n, lnt, and int – it equal.
o The discount shrinks if
o federal income taxes are lowered or there is talk of doing so
o politicians seriously consider ending the exemption
o the exemption is repealed.
Risk Structure
Tax exemption risk discount
P
i
P
St
i
Sc
950
5
950
5
Dm
Dt
Q
Municipal Bond
Market
Q
U.S. Treasury Bond
Market
Risk Structure
Tax exemption risk discount
P
i
P
i
St
Sc
950
5
950
5
925
6
Dm
Dt
Dt
Q
Municipal Bond
Market
Q
U.S. Treasury Bond
Market
Risk Structure
Tax exemption risk discount
P
i
P
i
St
Sc
975
4
950
5
Dm
950
5
925
6
Dt
Dc
Dc
Q
Municipal Bond
Market
Q
U.S. Treasury Bond
Market
Risk Structure
Tax exemption risk discount
P
i
P
i
St
Sc
4
975
-2
925
Dt
6
Dt
Dt
Dt
Q
Municipal Bond
Market
Q
U.S. Treasury Bond
Market
Risk Structure
Tax exemption risk discount
You are considering owning two $1000 bonds that
mature next year. One is a corporate bond, the other
is a tax-free municipal, and both have an 8% coupon
rate. If the bonds have a current yield of 3.5%, and
you intend to hold them for their final year, compute
the price you would be willing to pay assuming a
federal income
tax rate of 50%.
Corporate
Tax-free municipal
N=1
I% = 3.5
PV = A
PMT = 80
FV = 1000
N=1
I% = 3.5
PV = A
PMT = 40
FV = 1000
Risk Structure
Tax exemption risk discount
You are considering owning two $1000 bonds that mature next year.
One is a corporate bond, the other is a tax-free municipal, and both
have an 8% coupon rate. If the bonds have a current yield of 3.5%,
and you intend to hold them for their final year, compute the price
you would be willing to pay assuming a federal income tax rate of
50%.
Tax-free municipal
Corporate
N=1
I% = 3.5
PV = -1043.48
PMT = 80
FV = 1000
N=1
I% = 3.5
PV = -1004.83
PMT = 40
FV = 1000
Risk Structure
Sources: Board of Governors of the Federal Reserve System, Banking and Monetary Statistics,
1941–1970; Federal Reserve; www.federalreserve.gov/releases/h15/data.htm.
Figure 1—Long-Term Bond Yields, 1919–2011
Interest Rate Determination
Nominal Rate (i)
=
+
+
+
–
+
+
Real Rate (r)
Expected Inflation (p e)
Default Risk Premium (d)
Illiquidity Risk Premium (l)
Tax exemption discount (t)
Maturity Premium (int – it)
Liquidity Premium (lnt)
Interest Rate Determination
Nominal Rate (i)
Risk structure
Term structure
=
+
+
+
–
+
+
Real Rate (r)
Expected Inflation (p e)
Default Risk Premium (d)
Illiquidity Risk Premium (l)
Tax exemption discount (t)
Maturity Premium (int – it)
Liquidity Premium (lnt)
Term Structure
• Time to maturity affects interest rates because
– Time increases exposure to risk, causing investors to
demand higher yields on securities with longer
maturities.
• The term structure of interest rates refers to
difference in the yields on instruments that are
identical except for term to maturity.
• Term structure is represented graphically by a
yield curve.
– Yield curves consider only the relationship between
maturity or term of a security and its yield at a
moment in time, otrs.
Term Structure
Facts that the theory must explain:
1.
Interest rates on bonds of different maturities move together over time
Term Structure
Sources: Federal Reserve; www.federalreserve.gov/releases/h15/data.htm.
Figure 4—Interest rate movements on Treasuries with different maturities
Term Structure
Facts that the theory must explain:
1.
Interest rates on bonds of different maturities move together over time
2.
When short-term interest rates are low, yield curves are more likely to have
an upward slope; when short-term rates are high, yield curves are more
likely to slope downward and be inverted
3.
Yield curves almost always slope upward
Term Structure
February 4, 2005
68
Term Structure
Figure 7 Yield Curves for U.S. Government Bonds
Term Structure
Figure 6
Term Structure
Facts that the theory must explain:
1.
Interest rates on bonds of different maturities move together over time
2.
When short-term interest rates are low, yield curves are more likely to have
an upward slope; when short-term rates are high, yield curves are more
likely to slope downward and be inverted
3.
Yield curves almost always slope upward
Three Theories that explain these facts
1.
Segmented markets theory explains fact three but not the
first two
2.
Expectations theory explains the first two facts but not the
third
3.
Liquidity premium theory combines the two theories to
explain all three facts
Term Structure
maturity premium
• Expectations theory says the yield on a long-term
bond equals the average of the short-term interest
rates people expect toe occur
over
its life
e
e
int 
it  it 1  it  2  ...  it  ( n 1)
n
– Maturity Premium is the spread between the interest
rates on bonds with n years and 1 year to maturity,
holding d, l, t, and lnt equal.
int – it
– Buyers of bonds
o do not prefer bonds of one maturity over another
o do not hold any quantity of a bond if its expected return is
less than that of another bond with a different maturity
o consider bonds with different maturities to be perfect
substitute
Term Structure
maturity premium
The table below shows current and expected future one-year interest rates,
as well as current interest rates on multiyear bonds. Use the table to
calculate the liquidity premium for each multiyear bond.
e
e
e
e
e
i

i

i

i

i

i
i nt  t t 1 t  2 t 3 t  4 t 5
n
Term Structure
maturity premium
The table below shows current and expected future one-year interest rates,
as well as current interest rates on multiyear bonds. Use the table to
calculate the liquidity premium for each multiyear bond.
e
e
e
e
e
i

i

i

i

i

i
i nt1t  t t 1 t  2 t 3 t  4 t 5
n
Term Structure
maturity premium
The table below shows current and expected future one-year interest rates,
as well as current interest rates on multiyear bonds. Use the table to
calculate the liquidity premium for each multiyear bond.
e
e
e
e
e
i

i

i

i

i

i
i2t  t t 1 t  2 t 3 t  4 t 5
n
Term Structure
maturity premium
The table below shows current and expected future one-year interest rates,
as well as current interest rates on multiyear bonds. Use the table to
calculate the liquidity premium for each multiyear bond.
e
e
e
e
e
i

i

i

i

i

i
i 3t  t t 1 t  2 t 3 t  4 t 5
n
Term Structure
maturity premium
The table below shows current and expected future one-year interest rates,
as well as current interest rates on multiyear bonds. Use the table to
calculate the liquidity premium for each multiyear bond.
e
e
e
e
e
i

i

i

i

i

i
i4t  t t 1 t  2 t 3 t  4 t 5
n
Term Structure
maturity premium
The table below shows current and expected future one-year interest rates,
as well as current interest rates on multiyear bonds. Use the table to
calculate the liquidity premium for each multiyear bond.
e
e
e
e
e
i

i

i

i

i

i
i 5t  t t 1 t  2 t 3 t  4 t 5
n
Term Structure
maturity premium
The table below shows current and expected future one-year interest rates,
as well as current interest rates on multiyear bonds. Use the table to
calculate the liquidity premium for each multiyear bond.
e
e
e
e
e
i

i

i

i

i

i
i 6t  t t 1 t  2 t 3 t  4 t 5
n
Term Structure
maturity premium
Graph the maturity adjusted yields over maturity
2.20
2.00
i
1.80
1.60
1.40
1.20
1.00
1
2
3
4
n
5
6
Term Structure
maturity premium
Graph the maturity adjusted yields over maturity
2.20
2.00
i
1.80
1.60
1.40
1.20
1.00
1
2
3
4
n
5
6
maturity
premium
for a 1-year
bond
0%
Term Structure
maturity premium
Graph the maturity adjusted yields over maturity
2.20
2.00
i
1.80
1.60
maturity
premium
for a 2-year
bond
0.325%
1.40
1.20
1.00
1
2
3
4
n
5
6
Term Structure
maturity premium
Graph the maturity adjusted yields over maturity
2.20
2.00
i
1.80
maturity
premium
for a 3-year
bond
0.57%
1.60
1.40
1.20
1.00
1
2
3
4
n
5
6
Term Structure
maturity premium
Graph the maturity adjusted yields over maturity
2.20
2.00
i
1.80
maturity
premium
for a 4-year
bond
0.7675%
1.60
1.40
1.20
1.00
1
2
3
4
n
5
6
Term Structure
maturity premium
Graph the maturity adjusted yields over maturity
2.20
2.00
i
maturity
premium
for a 5-year
bond
0.93%
1.80
1.60
1.40
1.20
1.00
1
2
3
4
n
5
6
Term Structure
maturity premium
Graph the maturity adjusted yields over maturity
2.20
2.00
i
maturity
premium
for a 6-year
bond
1.06%
1.80
1.60
1.40
1.20
1.00
1
2
3
4
n
5
6
Term Structure
Expectations Theory
Yield Curve
2.20
2.00
i
1.80
1.60
1.40
1.20
1.00
1
2
3
4
n
5
6
Term Structure
liquidity premium
• The interest rate on a long-term bond will equal an
average of short-term interest rates expected to
occur over the life of the long-term bond plus a
liquidity premium that responds to supply and
demand conditions for that bond
• Bonds of different maturities are partial (not
perfect) substitutes
– Liquidity premium is the spread between the interest
rates on bonds with n and one years to maturity, holding d,
l, t, and int – it equal
lnt
Term Structure
liquidity premium
Suppose the liquidity premium is linear in maturity:
lnt = 0.08n
Term Structure
Expectations Theory
Yield Curve
2.75
2.50
2.25
2.00
1.75
1.50
1.25
1.00
1
int 
2
3
4
5
it  ite1  ite 2  ...  ite ( n 1)
n
6
 lnt
Term Structure
Liquidity Premium Theory
Yield Curve
2.75
2.50
2.25
2.00
1.75
1.50
1.25
1.00
1
int 
2
3
4
5
it  ite1  ite 2  ...  ite ( n 1)
n
6
 lnt
Interest Rate Determination
Nominal Rate (i)
Risk structure
Term structure
=
+
+
+
–
+
+
Real Rate (r)
Expected Inflation (p e)
Default Risk Premium (d)
Illiquidity Risk Premium (l)
Tax exemption discount (t)
Maturity Premium (int – it)
Liquidity Premium (lnt)