This document discusses why there are different interest rates in the economy. It explains that interest rates vary based on the risk, liquidity, and tax attributes of different financial instruments. Bonds have different interest rates depending on their default risk, with riskier corporate bonds paying higher rates than safer Treasury bonds. Liquidity also impacts rates, with less liquid bonds paying more than more liquid ones. Tax attributes matter as well, as tax-exempt municipal bonds pay lower rates than taxable bonds. The document provides examples of how risk premiums, liquidity premiums, and tax premiums contribute to the different interest rates observed in the market.

1. Learning Unit #12
Risk Structure of Interest Rates

2. Why There Are So Many Different Interest
Rates?
In the previous Learning Unit, you learned how a
market interest rate is determined in the bond
market framework. The market interest rate
determined on this framework is considered as
the base rate in the economy such as U.S.
Treasury bill rate. In reality there are many
different interest rates in the U.S. economy. This
Learning Unit and next will explain why there are
so many market interest rates and how they are
determined in markets.

3. Characteristics of Bonds and Interest
Rates
• Heterogeneous financial instruments: Each financial
instrument has different characteristics such as risk,
liquidity, and maturity.
− It depends on characteristics of issuers
(spender/borrowers) and specific characteristics
attached on a particular financial instrument.
• Heterogeneous preference: Saver/lenders have different
preferences on characteristics of financial instruments.
− Saver/lenders prefer a particular characteristic over
another.
• These heterogeneities lead to different demand and
supply among financial instruments.
− They result in different market interest rates.

4. Objectives of Learning Unit
■ Three Important Characteristics of Financial
Instruments
• Liquidity
• Default Risk
• Tax Attribute
■ Risk Premium and Demand

5. Variations in Long-term Interest Rates in
U.S.
Although all interest rates tend to move together,
• Some (Corporate Baa Bonds) almost always provide
higher interest rates than others (U.S. Government
Long-Term Bonds).
• Spreads (differences in interest rates) change over time
(e.g. a large difference in early 1930s).

6. Risk Premium
• Risk premium: An additional interest rate, that
an issuer of financial instruments pay to
buyers, over the risk-free instrument due to
riskiness of the financial instruments.
• If issuers want buyers to purchase financial
instruments with less favorable
characteristics, they must give some
incentive – additional return or interest rate.
• i = if
+ RP
i : interest rate on risky instrument
if
: interest rate on risk-free instrument
RP : risk premium

7. Default Risk
• Default risk: Uncertainty that a borrower may not
pay back the principal or interest.
− Some instruments are very risky, while others are
less risky.
− Risk of financial instruments depends on riskiness of
business investment opportunities for which funds are
used to finance (how likely they fail) and conditions
(under which borrowers pay back) attached on the
instruments.
• In general, buyers of financial instruments prefer
low risk instruments over high risk instruments.
− Higher the risk, the lower the demand.

8. Default Risk and Interest Rate
• Bonds with high risk have low demand, while
bonds with low risk have high demand.
• Price of high risk bonds (P2
c
) < Price of low risk bonds (P2
T
)
• Interest rate on high risk bonds (i2
c
) > Interest rate of low risk bonds (i2
T
)
• Risk premium = i2
c
– i2
T
High Risk Bonds Low Risk Bonds

9. Default Risk and Risk Premium
• Default-free instrument: U.S. Treasury
securities are considered as free of default.
− How could they be default-risk free?
• All other financial instruments have more or
less default risk.
− Why are they risky, even GM bonds?
• An additional interest rate paid by risky
instruments over the interest rate on U.S.
Treasury securities is a default-risk premium.
− There are many types of risk each of which
requires own risk premium (i.e. purchasing power
risk premium).

10. Example of Default Risk and Risk
Premium
• An interest rate on 30-year U.S. Treasury
bond is 6% (if
), while an interest rate on 30-
year corporate bond is 14% (i).
i = if
+ RP ⇒ 14% = 6% + RP
• A risk premium on the corporate bond is 8%
(RP). There is a possibility that the
corporation which issued the corporate bonds
may go out of business and default
payments.

11. Changes in Default Risk and Risk
Premium
• Default risk of financial instruments may change from
time to time, so as their risk premium.
• The spread (default-risk premium) between risk-free
bonds (U.S. Government Long-term bonds) and risky
bonds (Corporate Baa bonds) changes over time.
− A large default-risk premium in early 1930s, while small default-
risk premium in 1940s.

12. Causes of Changes in Default Risk
• During a recession, some corporations,
especially with high debt, are more likely to
default their obligations and go bankruptcy.
− Default risk increases during a recession.
• A default risk of bonds depends on perception
of buyers of financial assets.
− Even if some bonds are actually risky, buyers may
not perceive as risky bonds if they have not
defaulted for a long time.
− When some bonds default, buyers may perceive
that all other bonds are more likely to default than
before (even though default risk itself did not
change).

13. Changes in Default Risk during Recession
• During a recession risky bonds become
even riskier than usual.
• Buyers of bonds prefer less of risky
bonds and more of risk-free bonds.
• Demand for risky bonds decreases
(from D0
C
to D1
C
), while demand for risk-
free bonds increases (from D0
T
to D1
T
).

14. Effects of Changes in Default Risk during
Recession
• Price of risky bonds ↓ (from P0
C
to P1
C
) and price of risk-free bonds ↑
(from P0
T
to P1
T
)
• Interest rate of risky bonds ↑ (from i0
C
to i1
C
) and interest rate on risk-free
bonds ↓ (from i0
T
to i1
T
)
• Spread between risky bonds and risk-free bonds ↑ from RP0 to RP1
• A default risk premium increases.
P Pi i
i0
T
i1
T
i0
C
i1
C
P0
T
P0
C
P1
C
P1
T
D0
T
D1
T
D0
CD1
C
E0
T
E1
T
ST
SC
E0
C
E1
C
RP0
RP1
Bonds with Default Risk Default Risk-Free Bonds

15. Application: The Subprime Collapse and the
Baa-Treasury Spread
As the U.S. financial system moved into crisis since 2007, the spread
between corporate bonds and U.S. Treasury bonds increased, because the
financial crisis made more difficult firms to obtain necessary funds to
continue business and more likely firms to fail.
Corporate Bond Risk Premium and Flight to
Quality
0
2
4
6
8
10
Jan-07
M
ar-07
M
ay-07
Jul-07
S
ep-07
N
ov-07
Jan-08
M
ar-08
M
ay-08
Jul-08
S
ep-08
N
ov-08
Jan-09
Corporate bonds, monthly data Aaa-Rate
Corporate bonds, monthly data Baa-Rate
10-year maturity Treasury bonds, monthly data

16. Default Risk and Bond Rating
• Credit-rating agencies: investment advisory
firms that rate the quality of corporate and
municipal bonds in terms of the probability of
default.
− Ex. Moody’s and Standard & Poor’s
• Investment-grade securities: bonds with
relatively low risk of default (ratings of Baa/BBB
and above).
• Junk bonds (high-yield bonds): bonds with high
default risk (ratings below Baa/BBB).
− With high default risk junk bonds have high interest
rates.
− Due to high default risk some financial organizations
are not allowed to purchase junk bonds.

17. Bond Ratings by Moody’s and S&P’s
Why does United Airlines and Northwest Airlines have low ratings?

18. Liquidity
• Liquidity: How quickly a financial
instrument can be sold.
− Some instruments are liquid, while others
are not so liquid.
− Liquidity of financial instruments depends
on how many units of the instruments are
traded every day and how many buyers
participate in market.
• In general, buyers of financial
instruments prefer liquid instruments
over less liquid instruments.
− Higher the liquidity, the higher the demand.

19. Liquidity and Interest Rates
• Bonds with low liquidity have low demand, while
bonds with high liquidity have high demand.
• Price of low liquid bonds (P2
C
) < Price of high liquid bonds (P2
T
)
• Interest rate on low liquid bonds (i2
C
) > Interest rate of high liquid
bonds (i2
T
)
• Liquidity premium = i2
c
– i2
T
Liquidity
Premium
Bonds with Low Liquidity Bonds with High Liquidity

20. Tax and Return
• Saver/lenders are concerned with after-tax
return rather than before-tax return.
• Returns from financial instruments are taxed
at different rates.
• Saver/lenders prefer instruments with lower
tax rate even if the before-tax return is low.
• Example
− A before-tax returns on taxable bonds is 8% and a
before-tax return on tax-free bonds is 6%.
− At 50% tax rate, the after-tax return on the taxable
bonds is 4% (= 8% x 0.5) and the after-tax return
on the tax-free bonds is still 6%.

21. Tax Attribute
• Income tax exempt on municipal bonds
− Incomes earned from financial instruments are
subject to the federal and state income taxes
except for municipal bonds (tax exempt bonds).
• Income tax vs. Capital gain tax
− Incomes from financial instruments are divided
into interest incomes and capital gains.
− Interest (coupon) incomes are subject to the
income taxes, while capital gains are subject to
the capital gain tax.
− Income tax rates and capital gain tax rates are
different.

22. Tax-Free Bonds and Taxable Bonds
• Price of tax-free bonds (P2
m
) > Price of taxable bonds (P2
T
)
• Interest rate on tax-free bonds (i2
m
) < Interest rate of taxable bonds
(i2
T
)
• Tax premium = i2
T
- i2
m
• Tax-free (municipal) bonds have high demand, while
taxable Bonds have low demand, .

23. Changes in Tax Rates
• Any changes in tax rates on returns on financial
instruments will affect the after-tax returns on
instruments and their demands.
• When tax rates increase, after-tax return on
taxable bonds decreases.
• Demand for taxable bonds decreases (from D0
T
to D1
T
), while demand for tax-free bonds
increases (from D0
M
to D1
M
).

24. Effects of Increase in Tax Rates
P Pi i
i0
M
i1
M
i0
T
i1
T
P0
M
P0
T
P1
T
P1
M
D0
M
D1
M
D0
TD1
T
E0
M
E1
M
SM
ST
E0
T
E1
T
TP0
TP1
Taxable Bonds Tax-Free Bonds
• Price of taxable bonds ↓ (from P0
T
to P1
T
) and price of tax-free bonds ↑
(from P0
M
to P1
M
)
• Interest rate of taxable bonds ↑ (from i0T to i1T) and interest rate on tax-
free bonds ↓ (from i0
M
to i1
M
)
• Spread between taxable bonds and tax-free bonds ↑ from TP0 to TP1
• A Tax premium increases.

25. Capital Gain Tax Rates and Income Tax
Rates
• Some financial instruments pay most of
return in form of interest incomes such as
coupon payments from bonds. Other
instruments pay most of return in form of
capital gains such as stocks.
• If the tax rate of one type changes relative to
the tax rate of the other type, saver/lenders
may prefer to purchase one type over
another.

26. Example of Changes in Capital Gain Tax
Rates
• The federal government cut capital gain tax rates in
early 2000s.
• After-tax return on stocks (which mainly pay return in
form of capital gains) increases, while an after-tax
return on bonds (which mainly pay return in form of
interest income) decrease relative to stocks.
• Demand for stocks increases, while demand for
bonds decreases.
• Prices of stocks increase, while prices of bonds
decrease.
• Market interest rate (determined in a bond market)
increases.

27. Disclaimer
Please do not copy, modify, or distribute this presentation
without author’s consent.
This presentation was created and owned by
Dr. Ryoichi Sakano
North Carolina A&T State University