Chapter 6

Determining Market Interest Rates

Bond Market Today

During 2002, bonds reached very high prices and were paying very low yields. Bond markets were concerned with global deflation.

Bond markets predict economic recovery in the USA and high government budget deficits in the same country.

Objectives Construct Supply and Demand model of

bond markets. Evaluate the effects of different events on

bond yields/prices & quantities. Connect long-term & short-term interest

rates using expectations theory of the term structure.

Use uncovered interest parity to connect the interest rates paid on bonds in different currencies.

Bond Market

Economists use supply and demand to analyze markets for non-differentiated goods like flour or corn.

In real world financial markets, there is a wide variety of bonds with different qualities and different prices/yields at any given time.

In theory, we will abstract from these differences to analyze the price/yield of a generic, representative bond.

Savers & Borrowers

The bond market is made up of two types of traders. Savers have excess funds today and are trying to exchange them for bonds (savers). Borrowers are trying to exchange bonds for funds today (borrowers).

We can think of this market from two inverse perspectives.

1. Bond Market Perspective2. Loan Market Perspective

Bond Market Perspective Borrowers are sellers of bonds

represented by a supply curve relating the quantity of bonds they sell at a given bond price, P.

Savers are buyers of bonds represented by a demand curve relating the quantity of bonds they buy at a given bond price, P.

Quantity: Dollar value of bonds Price: Dollar price of bonds.

Loanable Funds Market Perspective

Savers are providers of funds to the bond market represented by a supply curve relating the quantity of funds they provide at a given bond interest yield, i.

Borrowers are takers of funds represented by a demand curve relating the quantity of funds they take at a given interest yield, i.

Quantity: Dollar value of funds Price: Bond yields

Q: Why does the Supply Curve for Loanable Funds Slope Up?

A: Holding expected inflation constant, a high interest rate on bonds increases the attractiveness of bonds and attracts more funds.

Q: Why does the Demand Curve for Bonds Slope Down. A high price for a given future face value reduces the attractiveness of bonds and attracts fewer funds.

Views of Savers: Loanable Funds

i

L

Quantity of Loanable Funds

LS

Views of Savers: Bond Market Perspective

PB

B

Quantity of Bonds

Bond Price

DB

Q: Why does the Demand Curve for Loanable Funds Slope Down?

A: If bond issuers must offer a high interest payment to borrow, the attractiveness of borrowing or financing borrowing in the bond market will drop.

Q: Why does the Supply Curve for Bonds Slope Up.

A: If bond issuers receive a high price for a given future face value, the attractiveness of borrowing or financing in the bond market rises.

View of Borrowers:Bond/Loan Market Perspective

i

L

LD

PB

B

BS

Equilibrium:Bond/Loan Market Perspective

i

L

LD

PB

B

BSLS

i*

BD

P*

L* B*

Q: What causes the the Supply Curve for Loanable Funds (Demand Curve for Bonds ) to shift?

A: The elements of portfolio allocation.

1. An increase in wealth shifts supply of loanable funds and demand for bonds to the right as investors increase the size of their portfolio.

2. An increase in expected inflation reduces the real returns from bonds. This shifts the supply of loanable funds in bond markets and demand for bonds to the left .

3. An increase in the expected returns on other assets besides bonds will shift the supply of loanable funds and demand for bonds to the left as portfolio holders shift to other assets.

4. An increase in the risk of bonds (relative to other assets) or an increase in the cost of acquiring information (relative to other assets) will shifts the supply of loanable funds and demand for bonds to the left as portfolio holders shift to other assets.

5. An increase in the liquidity of bonds (relative to other assets) will shift the supply of loanable funds and demand for bonds to the right as portfolio holders shift to other assets.

Bond Price vs. Stock Price

.950

.955

.960

.965

.970

.975

.980

7000

8000

9000

10000

11000

01:01 01:07 02:01 02:07 03:01 03:07 04:01 04:07

BOND_PRICE STOCK_PRICE

USA Financial Markets

Shift Chart: Attractiveness of Bonds

Event Shifts LS Shifts BD

Wealth E Alternative Asset Returns

Relative Bond Risk

Relative Bond Liquidity

Relative Bond Information Costs

Increase in Bonds’ Attractiveness Decrease in Bonds’ Attractiveness

i

L

LD

PB

B

BSLS

i*

BD

P*

L* B*

Event Quantity of Loanable Funds/Bonds

Bond Prices Bond Yields

Wealth

E wait wait wait

Alternative Asset Returns

Relative Bond Risk

Relative Bond Liquidity

Relative Bond Information Costs

Q: What causes the supply of bonds or the demand for loanable funds to shift?

New issuers of bonds will be firms financing capital investment or governments financing deficits.

Firms will issue new bonds if expected real interest rates fall or after tax profits from capital rise.

1. If expected inflation rises, expected real interest rates fall and bond supply/loanable funds demand shifts right .

2. If productivity of capital equipment rises, profits from capital investment rises and bond supply/loanable funds demand shifts right .

3. If business taxation rises, profits from capital investment falls and bond supply/loanable funds demand shifts left.

Government will issue new bonds if government deficits increase.

1. If deficits increase, bond supply/loanable funds shifts right .

Event Demand for Loanable Funds

Supply of Bonds

E

Capital Productivity

Business Taxes

Deficits

Shift Chart: Changes in Borrowing

Decrease in Borrowing Increase in Borrowing

i

L

LD

PB

B

BSLS

i*

BD

P*

L* B*

Event Quantity of Loanable Funds/Bonds

Bond Prices Bond Yields

E ambiguous

Capital Productivity

Business Taxes

Deficits

Equilibrium Response: Changes in Borrowing

Default Risk: Bonds by Rating

A bond is in default if the issuer misses a payment of interest or principal.

Though all bonds involve some risk, for all practical purposes, are default-free. In the $US bond market, U.S. Treasury bonds are the benchmark default free bond. In HK, Exchange Fund bonds play this role. (Be careful, not all government debt is risk-free).

Bond rating agencies (Moody’s and Standard & Poor’s assess default risk for bonds).

A bond with a significant probability of default must pay a higher return to compensate purchasers for the risk.

Term Structure of Interest Rates Bonds of different maturities typically

have different interest rates. Typically, bonds of longer maturity pay

higher yields over their lifetime. Segmented Market Theory: Long-term

bonds have greater interest rate risk and less liquidity. This explains why long-term bonds have greater yields on average.

Yield Curve

HK Exchange Fund Bill Yield Curve

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

1 year 2 year 3 year 5 year 7 year 10 year

YT

M %

Expectations Theory

Portfolio holders are indifferent between long and short-term bonds.

Yield to maturity over the life of a long-term bond must be equal to average yields on repeated rollovers of short-term bond holdings during the same period.

Consider two strategies which should have the same expected pay-off. Starting with $1.

1. Buy a two year discount bond and hold it for two years. Payoff:

2. Buy a 1 year bond. After 1 year, invest pay-off in another 1 year bond. Payoff:

2222

22 21)21()1( iiii

eeee iiiiiiii 1,111,111,111,11 1)(1)1()1(

Two Strategies

Arbitrage between markets implies equal returns on equal assets.

Equal pay-offs imply that yield on a two year bond is equal to the expected average yield of 1 year bonds over the next two years.

21,11

2

eiii

2

1 1, 1 2(1 ) (1 ) (1 )ei i i

• In general, if the pay-off for investing in an n period bond should be the same as the pay-off from rolling over 1 year bonds for n periods:

• Then a n period bond yield is (approximately) equal to the average expected yield on 1 period bonds between today and date n.

)1(...)1()1()1()1( 1,12,11,11en

eenn iiiii

n

iiiii

en

ee

n1,12,11,11 ...

Preferred Habitat Theory

Bonds have some differences in risk and liquidity characteristics. Regardless, they are close substitutes and the expectation theory well describes the connection between bonds of different yields.

Yields of bonds of period T are represented as the

The maturity premium hn tends to increase in n.

n

en

ee

n hn

iiiii

1,12,11,11 ...

Forecasting with the Term Structure

If the expectations theory holds, long-term interest rates can be used to infer market expectations of future interest rates.

Steep yield curve indicates low short-term rates and high future interest rates.

Inverted yield curve indicates high short-term rates and low future interest rates.

Inverted Yield Curve

9.6

10.0

10.4

10.8

11.2

11.6

12.0

1998:08

EX01EX02EX03

EX05EX10

August 1998 - Yield Curve

Steep Yield Curve

3.0

3.5

4.0

4.5

5.0

5.5

6.0

2001:08

EX01EX02EX03

EX05EX10

August 2001 - Yield Curve

Exchange Rate: EX - # of foreign currency units purchased for 1 domestic currency unit.

An increase in EX is an appreciation and a decrease in EX is a depreciation.

Define the expected growth rate of the exchange rate as

EX

EX

EX

EXEX eee

1

Exchange Rate Depreciation

Foreign Currency vs. Domestic Currency Bonds

Consider the decision to buy a HK bond with a yield of 1+i denominated in HK dollars or a Japanese bond denominated in Yen with a yield of 1+if. (Assume both bonds have equivalent risk, liquidity, and information characteristics).

With HK$1 you could buy a bond and receive HK$1+i after 1 period. With HK$1 dollar you could buy ¥EX, and buy a bond that would pay-off ¥(1+if)·EX. This could then be exchanged for 1

1

(1 ) (1 )f f

EXEX

EX i i

EX

Uncovered Interest Parity

If bond investors are indifferent between foreign and domestic bonds, these should have the same returns.

Approximately

1

(1 )1

fEX ii

EX

,

ef

f d

EXi i h

EX

Premium

Define hf,d as the premium paid by issuers of domestic bonds over foreign bonds.

hf,d can be either positive or negative. 1. If domestic bonds have more attractive risk or

liquidity properties, hf,d > 0.

2. If domestic bonds have less attractive risk or liquidity properties, hf,d < 0.

df

ef h

EX

EXii ,

International Interest Rates

0

2

4

6

8

10

12

14

Apr

-92

Apr

-93

Apr

-94

Apr

-95

Apr

-96

Apr

-97

Apr

-98

Apr

-99

Apr

-00

Apr

-01

Apr

-02

Apr

-03

Apr

-04

India

Hong Kong

Exchange Rate Appreciation

Rupees per HK$

0

1

2

3

4

5

6

7

Apr-9

2

Apr-9

3

Apr-9

4

Apr-9

5

Apr-9

6

Apr-9

7

Apr-9

8

Apr-9

9

Apr-0

0

Apr-0

1

Apr-0

2

Apr-0

3

Apr-0

4

Hong Kong Dollar Bond Market

Hong Kong Dollar Linked to US dollar. Supposing the representative Hong Kong Dollar

bond was about as risky as the representative US dollar bond, the interest rate should be the same.

If there are any differentials, the supply curve for HK loanable funds (the demand curve for HK bonds) shifts until the two interest rates are equal.

The HK dollar bond market adjusts to the US dollar market because the US dollar market is so much larger.

If the equilibrium HK dollar interest rate is higher than the equilibrium US dollar rate, the supply of loanable funds in Hong Kong will rise as investors shift their portfolios toward HK$ bonds. (If the equilibrium HK dollar bond price is lower than the equilibrium US dollar bond, demand for HK$ bonds will increase).

If the equilibrium HK dollar interest rate is lower than the equilibrium US dollar rate, the supply of loanable funds in Hong Kong will fall as investors shift their portfolios toward US$ bonds. (If the equilibrium HK dollar bond price is higher than the equilibrium US dollar bond, demand for HK$ bonds will increase).

Intuition

US$ Loanable Funds HK$ Loanable Funds

iUS iHK

iDiD

iS

iS

Yields

-2

0

2

4

6

8

10

12

14

Jun-

91

Jun-

92

Jun-

93

Jun-

94

Jun-

95

Jun-

96

Jun-

97

Jun-

98

Jun-

99

Jun-

00

Jun-

01

Jun-

02

Jun-

03

Jun-

04

USA Hong Kong

Speculation on the HK Dollar

-1

0

1

2

3

4

5

6

7

Dec-00

Mar

-01

Jun-

01

Sep-0

1

Dec-01

Mar

-02

Jun-

02

Sep-0

2

Dec-02

Mar

-03

Jun-

03

Sep-0

3

Dec-03

Mar

-04

Jun-

04

US

HK