Tài liệu Chương 3: Cơ cấu lãi suất pptx

Chapter Outline Characteristics of debt securities that cause their yields to vary  Explaining actual yield differentials  Estimating the appropriate yield  A closer look at the ter

Chapter 3

Structure of Interest Rates

Chapter Outline

 Characteristics of debt securities that

cause their yields to vary

 Explaining actual yield differentials

 Estimating the appropriate yield

 A closer look at the term structure

 International structure of interest rates

Characteristics of Debt Securities

 Credit (default) risk

higher yields to be chosen

securities

security issuer

 Can use bond ratings of rating agencies

 The higher the rating, the lower the perceived credit risk

 Ratings can change over time as economic conditions change

 Ratings for different bond issues by the same issuer can vary

Characteristics of Debt Securities (cont’d)

 Credit (default) risk (cont’d)

 Financial institutions may be required to invest only in

investment-grade bonds rated Baa or better by Moody’s

and BBB or better by Standard and Poor’s

Characteristics of Debt Securities (cont’d)

Description of Security Moody’s Standard and Poor’s

Characteristics of Debt Securities (cont’d)

 Credit (default) risk (cont’d)

 The risk premium corresponding to a particular bond rating can chance over time

 In general, credit ratings have served as reasonable indicators of the likelihood of default

 Credit rating agencies do not always detect financial problems of firms

Characteristics of Debt Securities (cont’d)

 Liquidity

Liquid securities can be easily converted to

cash without a loss in value

 Short-maturity securities with an active secondary market are liquid

higher yield to be preferred

Characteristics of Debt Securities (cont’d)

Y

Y at  bt 

Characteristics of Debt Securities (cont’d)

 Computing the equivalent before-tax yield

 The before-tax yield necessary to match the after-tax yield

on a tax-exempt security is:

 State taxes should be considered along with federal taxes

) 1

Computing the Equivalent

Before-Tax Yield

Assume a firm in the 30 percent tax bracket is

aware of a tax-exempt security that pays a

yield of 9 percent To match this after-tax yield,

taxable securities (with similar maturity and

risk) must offer a before-tax yield of

:

% 86

12 )

3 1 (

%

9 )

Characteristics of Debt Securities (cont’d)

 Term to maturity

 The term structure of interest rates defines the relationship

between maturity and annualized yield

 Special provisions

 A call feature allows the issuer of bonds to buy the bonds

back before maturity

 The yield on callable bonds should be higher than on noncallable bonds

 A convertibility clause allows investors to convert the bond

into a specified number of common stock shares

 The yield on convertible bonds is lower than on nonconvertible bonds

Explaining Actual Yield Differentials

points

 100 basis points equal 1 percent

 Commercial paper rates are higher than T-bill rates

 Eurodollar deposit rates are higher than yields on

other money market securities

 Market forces cause the yields of all securities to

move in the same direction

Explaining Actual Yield Differentials (cont’d)

 Municipal bonds have the lowest before-tax yield

 After-tax yield is higher than that of Treasury bonds

 Treasury bonds have the lowest yield

 No default risk

 Very liquid

 Investors prefer municipal or corporate bonds over

Treasury bonds only if the after-tax yield

compensates for default risk and lower liquidity

Estimating the Appropriate Yield

risk-free rate with adjustments to capture

various characteristics:

maturity of the risk-free security to that of the

security of concern

COND CALLP

TA LP

DP R

Yn  f,n     

Computing the Appropriate Yield

A company wants to issue 180-day commercial paper month T-bills currently have a yield of 7 percent

Six-Assume that a default risk premium of 0.8 percent, a

liquidity premium of 0.1 percent, and a 0.2 percent tax

adjustment are necessary to sell the commercial paper

to investors What is the appropriate yield the company

should offer on its commercial paper

?

% 2

% 1

% 8

% 7

A Closer Look at the Term

Structure

 Pure expectations theory

Pure expectations theory suggests that the

shape of the yield curve is determined solely

by expectations of future interest rates

 The yield curve will become upward sloping if interest rates are expected to rise

 The yield curve will become downward sloping if interest rates are expected to decline

Sudden Expectation of Higher

Sudden Expectation of Higher

Interest Rates (cont’d)

Yield Curve

YC1

YC2

Sudden Expectation of Lower

Sudden Expectation of Lower

Interest Rates (cont’d)

Yield Curve

YC1

YC2

A Closer Look at the Term

 The one-year interest rate in one year (the forward

rate) can then be estimated:

) 1

)(

1 ( )

1 ( t i2 2  t i1 t1r1

1 )

1 (

) 1

Computing the Forward Rate

Assume that the annualized two-year interest rate today is

8 percent Furthermore, one-year securities currently

offer an interest rate of 5 percent What is an estimate

of the forward rate

?

%09.11

105

.1

08.1

1)

1(

)1

(

2 1

2 2 1

t t t

A Closer Look at the Term

Structure (cont’d)

 Algebraic presentation (cont’d)

 The one-year interest rate in two years (the forward

rate) can also be estimated:

1 )

1 )(

1 (

) 1

(

1 1 1

3 3 1

i r

t t

t t

Computing the One-Year Interest Rate Two Years from Now

Continuing with the previous example, assume that year securities currently offer an interest rate of 10

three-percent What is an estimate of the one-year interest

rate that will prevail two years from now

?

1 ) 1109

1 )(

05 1 (

10 1

1 ) 1

)(

1 (

) 1

(

3

1 1 1

3 3 1

i r

t t

t t

A Closer Look at the Term

Structure (cont’d)

 Algebraic presentation (cont’d)

 Future annualized interest rates for periods other than one year can also be computed using the yield curve

 A one-year investment followed by a two-year investment should offer the same yield as a three-year security:

) 1

(

) 1

( 1

1

3 3

2 2 1

i

i r

t

t t







Computing the Two-Year Interest Rate One Year from Now

Continuing with the previous example, what is an

estimate of the two-year interest rate that will prevail

in one year

?

% 59 12

1 27

1

27 1

) 05 1 (

) 10 1

( 1

2 1

3 2

2 1

A Closer Look at the Term

Structure (cont’d)

 The theory assumes that forward rates are

unbiased estimators of future interest rates

 If forward rates are biased, investors should

attempt to capitalize on the discrepancy

A Closer Look at the Term

Structure (cont’d)

 According to the liquidity premium theory, the

yield curve changes as the liquidity premium

changes over time due to investor preferences

 Investors who prefer short-term securities will hold term securities only if compensated with a premium

long- Short-term securities are typically more liquid than term securities

long- The preference for short-term securities places

upward pressure on the slope of the yield curve

A Closer Look at the Term

Structure (cont’d)

 Estimation of the forward rate based on a liquidity

premium

 The yield on a security will not necessarily be equal to the yield from consecutive investments in shorter-term securities:

 The relationship between the liquidity premium and the term to maturity is:

2 1

1 1

2

2 ) ( 1 )( 1 ) 1

A Closer Look at the Term

Structure (cont’d)

 Liquidity premium theory (cont’d)

 Estimation of the forward rate based on a liquidity premium

(cont’d)

 The one-year forward rate can be derived as:

 A positive liquidity premium means that the forward rate overestimates the market’s expectations of the future interest rate

 A flat yield curve means the market is expecting a slight decrease in interest rates

 A slight upward slope means no expected change in interest rates

 /( 1 )

1 )

1 (

) 1

(

1 2

1

2 2 1

Computing the Forward Rate

With A Liquidity Premium

Assume that one-year interest rates are currently 10

percent Further assume that two year interest rates

are equal to 8 percent The liquidity premium on a

two-year security is 0.7 percent What is an estimate of the

one-year forward rate

?

 007 / 1 10

1 10

1

08 1

) 1

/(

1 )

1 (

) 1

(

2

1

2 1

2 2 1

A Closer Look at the Term

Structure (cont’d)

 According to segmented markets theory,

investors and borrowers choose securities with

maturities that satisfy their forecasted cash needs

 Pension funds and life insurance companies prefer term investments

long- Commercial banks prefer short-term investments

 Shifting by investors or borrowers between

maturity markets only occurs if the timing of their

cash needs change

Impact of Different Scenarios –

Segmented Markets Theory

Investors Have Mostly Short-Term Funds Available; Borrowers Want Long-Term Funds

Investors Have Mostly Long-Term Funds Available; Borrowers Want Short-Term Funds

Supply of short-term funds

provided by investors

Upward pressure Downward pressure

Demand for short-term funds by

borrowers Downward pressure Upward pressureYield on new short-term

securities

Downward pressure Upward pressure

Supply of long-term funds

A Closer Look at the Term

Structure (cont’d)

 Limitations of the theory

 Some borrowers and savers have the flexibility to choose among various maturity markets

 e.g., Corporations may initially obtain short term funds if they expect long-term interest rates to decline

 If markets were segmented, an adjustment in the interest rate in one market would have no impact on other markets, but evidence shows this is not true

A Closer Look at the Term

 The preferred habitat theory is a more flexible

perspective

 Investors and borrowers may wander from their markets given certain events

A Closer Look at the Term

Structure (cont’d)

 Research on term structure theories

 Interest rate expectations have a strong influence on the

term structure

 The forward rate from the yield curve does not accurately

predict future interest rates

 Variation in the yield-maturity relationship cannot be

explained by interest rate expectations or liquidity

 General research implications

 Some evidence for pure expectations, liquidity premium, and segmented markets theory

A Closer Look at the Term

Structure (cont’d)

 Forecast interest rates

 Pure expectations and liquidity premium theories can be used

 Forecast recessions

 A flat or inverted yield curve may indicate a recession in the near future since lower interest rates are expected

A Closer Look at the Term

 Financing decisions

 Assessing prevailing rates on securities for various maturities allows firms to estimate the rates to be paid on bonds with different maturities

A Closer Look at the Term

Structure (cont’d)

 If the Treasury uses a relatively large proportion of long-term

debt, this places upward pressure on long-term yields

 If the Treasury uses short-term debt, long-term interest rates

may be relatively low

 Early 1980s: downward sloping yield curve

 1982 to 2001: an upward sloping yield curve generally

persisted

 September 11, 2001: investors shifted funds into short-term

securities and the Fed provided funds to the banking system,

causing the yield curve to become steeper

International Structure of Interest

Rates

 Yield curves vary among countries

 Interest rate movements across countries tend to be positively correlated

 Interest rates may vary across countries at any particular point in time

countries cause differences