Tài liệu Chương 3: Cơ cấu lãi suất pptx

1
Chapter 3
Structure of Interest Rates
Financial Markets and Institutions, 7e, Jeff Madura
Copyright ©2006 by South-Western, a division of Thomson Learning. All rights reserved.
2
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
3
Characteristics of Debt Securities

Credit (default) risk

Securities with a higher degree of risk have to offer
higher yields to be chosen

Credit risk is especially relevant for longer-term
securities

Investors must consider the creditworthiness of the

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
4
Characteristics of Debt Securities
(cont’d)

Credit (default) risk (cont’d)

Rating agencies

Moody’s Investor Service and Standard and Poor’s
Corporation are the most popular

Agencies use different methods to assess the
creditworthiness of firms and state governments

A particular bond issue could have different ratings from each
agency, but differences are usually small

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

5
Characteristics of Debt Securities
(cont’d)

Ratings Assigned by:
Description of Security Moody’s Standard and Poor’s
Highest quality Aaa AAA
High quality Aa AA
High-medium quality A A
Medium quality Baa BBB
Medium-low quality Ba BB
Low quality (speculative) B B
Poor quality Caa CCC
Very poor quality Ca CC
Lowest quality (in default) C DDD, D
6
Characteristics of Debt Securities
(cont’d)

Credit (default) risk (cont’d)

Shifts in credit risk premiums

The risk premium corresponding to a particular
bond rating can chance over time

Accuracy of credit ratings

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
7
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

Securities with lower liquidity have to offer a
higher yield to be preferred
8
Characteristics of Debt Securities
(cont’d)

Tax status

Investors are more concerned with after-tax income
than before-tax income

Taxable securities have to offer a higher before-tax yield
to be preferred

The after-tax yield is equal to:

)1( TYY
btat
−=
9
Characteristics of Debt Securities
(cont’d)

Tax status

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( T
Y
Y
at
bt
−
=
10
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
)1(
=
−
=
−
=
T
Y
Y
at
bt
11
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
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Explaining Actual Yield Differentials

Yield differentials are often measured in basis
points

100 basis points equal 1 percent

Yield differentials of money market securities

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
13
Explaining Actual Yield Differentials
(cont’d)

Yield differentials of capital market securities

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
14
Estimating the Appropriate Yield

The yield on a debt security is based on the
risk-free rate with adjustments to capture
various characteristics:

Maturity is controlled for by matching the
maturity of the risk-free security to that of the
security of concern
CONDCALLPTALPDPRY
nfn
+++++=
,
15
Computing the Appropriate Yield
A company wants to issue 180-day commercial paper. Six-
month T-bills currently have a yield of 7 percent.

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?
%1.8
%2.%1.%8.%7
,
=
+++=
+++++= CONDCALLPTALPDPRY
nfn
16
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

Assuming an initially flat yield curve:

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
17

Sudden Expectation of Higher
Interest Rates
S
1
D
1
i
1
D
2
i
2
S
2
Market for short-term risk-free debt
S
2
D
2
i
2
D
1
i
1
S
1
Market for long-term risk-free debt
18
Sudden Expectation of Higher

Interest Rates (cont’d)
Yield Curve
YC
1
YC
2
19
Sudden Expectation of Lower
Interest Rates
S
1
D
1
i
1
D
2
i
2
S
2
Market for long-term risk-free debt
S
2
D
2
i
2
D
1

i
1
S
1
Market for short-term risk-free debt
20
Sudden Expectation of Lower
Interest Rates (cont’d)
Yield Curve
YC
1
YC
2
21
A Closer Look at the Term
Structure (cont’d)

Pure expectations theory (cont’d)

Algebraic presentation

The relationship between interest rates on two-year and
one-year securities is:

The one-year interest rate in one year (the forward
rate) can then be estimated:
)1)(1()1(
111
2
2

rii
ttt +
++=+
1
)1(
)1(
1
2
2
11
−
+
+
=
+
i
i
r
t
t
t
22
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
1
05.1

08.1
1
)1(
)1(
2
1
2
2
11
=
−=
−
+
+
=
+
i
i
r
t
t
t
23
A Closer Look at the Term
Structure (cont’d)

Pure expectations theory (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(
111
3
3
12
−
++
+
=
+
+
ri
i
r
tt
t
t
24
Computing the One-Year Interest
Rate Two Years from Now
Continuing with the previous example, assume that three-
year securities currently offer an interest rate of 10
percent. What is an estimate of the one-year interest
rate that will prevail two years from now?
%11.14
1

)1109.1)(05.1(
10.1
1
)1)(1(
)1(
3
111
3
3
12
=
−=
−
++
+
=
+
+
ri
i
r
tt
t
t
25
A Closer Look at the Term
Structure (cont’d)

Pure expectations theory (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
21
i
i
r
t
t
t
+
+
=+
+