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

Money & Banking

Video 04—Interest Rates II

The Behavior of Interest Rates (Chapter 5)Interest Rate Determination (Chapter 6)

Hal W. Snarr8/20/2015

Chapter 5

The Behavior of Interest Rates

Bond Demand

P D

The quantity of bonds demanded increases as p falls.

B

Bond Demand

D


Bond demand increases in• Expected return relative to other assets • Liquidity relative to other assets • Wealth

P

B


Bond demand increases in• Expected return relative to other assets • Liquidity relative to other assets • Wealth

Bond demand decreases in • Riskiness relative to other assets• Expected inflation• Expected interest rate

Bond Demand

DP

B

Expected return relative to other assets

For 1-year discount bonds held for 1 year,

R = i

S

Bond Supply

P

The quantity of bonds supplied increases as p rises.

B

The quantity of bonds supplied increases as p rises.

Bond supply increases in• Expected profitability of investment opportunities• Expected inflation• Government budget deficits

Bond Supply

S

P

B

Supply and Demand

DP

B

S

Excess supply: the price suppliers are asking for is too high

95

15 25

Supply and Demand

DP

B

S

Excess supply: the price suppliers are asking for is too high• For a zero-coupon $100 bond held for one year

95 1F

P i

i

100

955.3

15 25

Supply and Demand

DP

B

S

Equilibrium: the quantities of bonds supplied and demanded equal• For a zero-coupon $100 bond held for one year

95

15 25

92

20

i

5.3

Supply and Demand

DP

B

S


95

92

20

i

5.3

1F

P i

100

928.7

Supply and Demand

DP

B

S

Excess demand: the price suppliers are asking for is low• For a zero-coupon $100 bond held for one year

90

15 25

i

5.3

8.7

95

92

Supply and Demand

DP

B

S

Excess demand: the price suppliers are asking for is low• For a zero-coupon $100 bond held for one year

1F

P i

i

100

9011.190

15 25

5.3

8.7

95

92

Supply and Demand

DP

B

S


i

11.190

15 25

5.3

8.7

95

92

20

The Fisher Effect

DP

B

S

Suppose expected inflation rise by 6 percentage-points.

i

5.395

20

The Fisher Effect

DP

B

S


i

15

5.3

8.7

95

92

20

D

The Fisher Effect

DP

B

S


i

11.190

15

5.3

8.7

95

92

20

SD

The nominal rate of interest rises by 5.8 pct. pts.

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

http://research.stlouisfed.org/fredgraph.png?g=mhi

Source: FRED

The Fisher Effect

0 2 4 6 8 10 120

2

4

6

8

10

12

14

16

18

f(x) = 1.13529243123702 x + 1.67610504602249R² = 0.474925680118875

1978-2007

http://research.stlouisfed.org/fredgraph.png?g=mhi

The Business Cycle and Interest Rates

SPD

i

5.395

B18

Suppose economic growth is accelerating.


SP

B

Di

23

5.3

8.7

95

92

18

S




The quantity and price of bonds both increase

SP

B

Di

23

5.3

8.7

95

92

18

S

D

23

7.593


Source: Federal Reserve: www.federalreserve.gov/releases/H15/data.htm.

The quantity and price of bonds both increase

= 0 if bond market in

equilibrium

= 0 if loanable funds market in

equilibrium

Keynes’ liquidity preference framework

i

8.7

Bond Market

B

92

BD

BS

Loanable funds Market

LS

LDP

L 15

• 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

Bs – Bd =Ms – Md

= 0 if the market for money is in

equilibrium


• 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


15

8.7

LS

LD i

L 15

8.7

LS

LDi

L


.


15

8.7

LS

LDi

L

i

MD

M

• 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

The market for money

15

8.7

LS

LDi

L

.


i

MD

M

The market for money

7.5

• Money supply shifts to the right (increases) ifo The Fed injects money into the banking system with OMPo Banking lending increases

The Liquidity Effect

B

95

BD BS

P

L 15

15

5.3

LSLD

i

L

i

MD

M

Bond Market Loanable funds Market The market for money

92

8.7

5.3

8.7

• 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 o bond supply rises because the cost of borrowing fallso money demand increases

(the supply of loanable funds falls)(demand for loanable funds rises)

The Price-level 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

15

5.3

LSLD

i

L

i

MD

M

Loanable funds Market The market for money

The Expected-Inflation Effect

5.3

8.7 8.7

• An increase in MS is an expansionary influence on the economy.o demand for loanable funds riseso money demand increases

15

5.3

LSLD

i

L

i

MD

M

Loanable funds Market The market for money

The Income Effect

5.3

7.1 7.1

Figure 11 Response to an

Increase in MS Growth

The Total Effect

Figure 11 Response to an

Increase in MS Growth

The Total Effect

Figure 12 Annual M2 Growth and 3-month T-bill (1950–2011)

Sources: Federal Reserve: www.federalreserve.gov/releases/h6/hist/h6hist1.txt.

The Total Effect

2

2

3

34

4

5

5

6

6

88 9

9

a

a

1

1

bb

7 7

Chapter 6

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)



+ Default Risk Premium (d)+ Illiquidity Risk Premium (l)– Tax exemption discount (t)

Risk structure

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 valueo 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

TABLE 1


Corporate Bond Market

U.S. Treasury Bond Market

P Pi i

950 5

DcDt

Q Q


Sc St

950 5



P Pi iSc St

DcDc

Q Q


950 5 950 5

6925

Dt



P Pi iSc St

DcDcDt

Dt

Q Q


950 5 950 5

6

4975

925



P Pi iSc St

DcDcDt

Dt

Q Q


6

4975

925

2

Pre-bailout

N = 1I% = APV = -1068PMT = 100FV = 1000

Post-bailout

N = 1I% = APV = -1023PMT = 100FV = 1000

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

N = 1I% = 2.996PV = -1068PMT = 100FV = 1000

Post-bailout

N = 1I% = 7.527PV = -1023PMT = 100FV = 1000

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.


• Liquidity is the relative ease with which an asset can be converted into casho 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 Pi i

950 5

DcDt

Q Q

Sc St

950 5




P Pi iSc St

DcDc

Q Q

950 5 950 5

6925

Dt




P Pi iSc St

DcDcDt

Dt

Q Q

950 5 950 5

6

4975

925




P Pi iSc St

DcDcDt

Dt

Q Q

6

4975

925

2


Treasury

N = 1I% = APV = -1058PMT = 80FV = 1000

Corporate

N = 1I% = APV = 1001PMT = 80FV = 1000

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 rating is $1001, compute the yields on the two bonds.



Treasury

N = 1I% = 2.079PV = -1058PMT = 80FV = 1000

Corporate

N = 1I% = 7.892PV = 1001PMT = 80FV = 1000

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 rating is $1001, compute the yields on the two bonds.

• Income tax considerationso 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 ifo 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

Municipal Bond Market


PP ii

950 5

DtDm

QQ

ScSt

950 5



PP iiScSt

DtDt

QQ

950 5950 5

6925

Dm




PP iiScSt

DcDcDt

Dm

QQ

950 5950 5

6

4975

925




PP iiScSt

DtDtDt

Dt

QQ

6

4975

925

-2



Tax-free municipal

N = 1I% = 3.5PV = APMT = 80FV = 1000


Corporate

N = 1I% = 3.5PV = APMT = 40FV = 1000

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%.

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

N = 1I% = 3.5PV = -1043.48PMT = 80FV = 1000

Corporate

N = 1I% = 3.5PV = -1004.83PMT = 40FV = 1000

Figure 1—Long-Term Bond Yields, 1919–2011

Sources: Board of Governors of the Federal Reserve System, Banking and Monetary Statistics, 1941–1970; Federal Reserve; www.federalreserve.gov/releases/h15/data.htm.

Risk Structure







Risk structure

Term structure

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.

Facts that the theory must explain:1. Interest rates on bonds of different maturities move together over time

Term Structure

Figure 4—Interest rate movements on Treasuries with different maturities

Sources: Federal Reserve; www.federalreserve.gov/releases/h15/data.htm.

Term Structure


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

68February 4, 2005

Term Structure

Figure 7 Yield Curves for U.S. Government Bonds

Term Structure

Figure 6

Term Structure


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

Three Theories that explain these facts1. 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 Structurematurity premium

• Expectations theory says the yield on a long-term bond equals the average of the short-term interest rates people expect to occur over its life

– 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 anothero 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

1 2 ( 1)...e e et t t t n

nt

i i i ii

n

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.

i 1 2 3 4 5e e e e e

t t t t t ti i i i i i

n

nt


1 2 3 4 5e e e e e


n

nt


1ti



1 2 3 4 5e e e e e


n

2ti



1 2 3 4 5e e e e e


n

3ti


4t


1 2 3 4 5e e e e e


n

i


5t


1 2 3 4 5e e e e e


n

i


6t


1 2 3 4 5e e e e e


n

i


Graph the maturity adjusted yields over maturity


i

n

1.00

1.20

1.40

1.60

1.80

2.00

2.20

1 2 3 4 5 61.00

1.20

1.40

1.60

1.80

2.00

2.20

1 2 3 4 5 61.00

1.20

1.40

1.60

1.80

2.00

2.20

1 2 3 4 5 61.00

1.20

1.40

1.60

1.80

2.00

2.20

1 2 3 4 5 61.00

1.20

1.40

1.60

1.80

2.00

2.20

1 2 3 4 5 61.00

1.20

1.40

1.60

1.80

2.00

2.20

1 2 3 4 5 6



1.00

1.20

1.40

1.60

1.80

2.00

2.20

1 2 3 4 5 6

i

n

maturity premium for a 1-year bond0%


1.00

1.20

1.40

1.60

1.80

2.00

2.20

1 2 3 4 5 6


i

n

maturity premium for a 2-year bond0.325%


1.00

1.20

1.40

1.60

1.80

2.00

2.20

1 2 3 4 5 6


i

n



1.00

1.20

1.40

1.60

1.80

2.00

2.20

1 2 3 4 5 6


i

n



1.00

1.20

1.40

1.60

1.80

2.00

2.20

1 2 3 4 5 6


i

n



1.00

1.20

1.40

1.60

1.80

2.00

2.20

1 2 3 4 5 6


i

n


Term StructureExpectations Theory

1.00

1.20

1.40

1.60

1.80

2.00

2.20

1 2 3 4 5 6

i

n

Yield Curve

Term Structureliquidity 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

Suppose the liquidity premium is linear in maturity:

lnt = 0.08n

Term Structureliquidity premium

1 2 ( 1)...e e et t t t

n tt nni i i

nl

ii

Term StructureExpectations Theory

1.00

1.25

1.50

1.75

2.00

2.25

2.50

2.75

1 2 3 4 5 6

Yield Curve

Term StructureLiquidity Premium Theory

1.00

1.25

1.50

1.75

2.00

2.25

2.50

2.75

1 2 3 4 5 61.00

1.25

1.50

1.75

2.00

2.25

2.50

2.75

1 2 3 4 5 61.00

1.25

1.50

1.75

2.00

2.25

2.50

2.75

1 2 3 4 5 61.00

1.25

1.50

1.75

2.00

2.25

2.50

2.75

1 2 3 4 5 61.00

1.25

1.50

1.75

2.00

2.25

2.50

2.75

1 2 3 4 5 61.00

1.25

1.50

1.75

2.00

2.25

2.50

2.75

1 2 3 4 5 6

1 2 ( 1)...e e et t t t

n tt nni i i

nl

ii

Yield Curve




Risk structure

Term structure

Documents

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