Chapter 6. Risk and Term Structure of Interest Rates

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# Chapter 6. Risk and Term Structure of Interest Rates - PowerPoint PPT Presentation

Chapter 6. Risk and Term Structure of Interest Rates. Risk Structure Term Structure. Not all interest rates are created equal!. many interest rates at one time interest rates move together over time. January 2004. 3 mo Tbill 2.33% 3 mo Commerical Paper 2.52% prime rate 5.25%

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Not all interest rates are created equal!
• many interest rates at one time
• interest rates move together over time
January 2004
• 3 mo Tbill 2.33%
• 3 mo Commerical Paper 2.52%
• prime rate 5.25%
• 10 yr. Tnote 4.23%
• 10 yr. AAA corporate 5.46%
• 10 yr. BAA corporate 6.15%
• 30 yr. mortgage 5.71%
measurement
• difference between two interest rates
• measured in
• percentage points
• basis points
• 1 percentage pt. = 100 basis pts.
example 1
• 3 mo. Tbill 2.33%
• 3 mo. Commercial paper 2.52%
• .19 percentage pts.
• 19 basis pts.
example 2
• 10 yr Tnote 4.23%
• 10 BAA corporate 6.15%
• 1.92 percentage pts.
• 192 basis pts.
I. Risk Structure of Interest Rates
• debt with same maturity,

but different characteristics

• default risk
• liquidity
• tax treatment
Patterns
• Baa always the highest yield
• Municipal’s always the lowest (1940)
• Baa > AAA > U.S. > municipal
• size of the spread varies
A. Default Risk
• risk of not receiving timely payment of principal and interest
• depends on
• creditworthiness of issuer
• structure of bond
U.S. government debt
• zero default risk
• backed by “full faith and credit”

of U.S. government

• why?
• power to tax largest economy
• power to issue stable currency
Other issuers
• private
• foreign
• municipal
• all have some default risk
• rated for default risk
Bond ratings
• bond issuer pays rating agency
• Moody’s, S&P, Fitch
• p. 123
• high credit rating
• low default risk
• bond ratings may change over time
default risk & yield
• investors are risk averse

higher

default

risk

lower

credit

rating

higher

yield

so default risk explains

BAA

Corp

yields

AAA

Corp

yields

Treasury

yields

<

<

default risk is not constant!
• varies over the business cycle
• higher in recessions
• lower in expansions
• Baa vs. Treasury bond yield
• 12/99 191 basis pts.
• 12/01 296 basis pts.
B. Liquidity
• how quickly/cheaply can bond be sold for cash?

lower

yield

higher

liquidity

liquidity is not rated
• Treasuries most liquid
• depends on size of issuer
• related to default risk
• bonds in default very illiquid
• higher-rated bonds tend to be more liquid
C. Tax treatment

Q. why do municipal bonds have lower yields than Tbonds?

• muni’s less liquid
• muni’s not default-free

A. tax treatment

municipal bond interest
• exempt from federal income tax
• possibly exempt from state income tax
• if issuer & bondholder are in same state
Treasury bond interest
• exempt from state income tax

Corporate bond interest

• fully taxable
example: federal taxes
• bond where F=\$10,000
• coupon rate = 10%
• annual coupon pmts = \$1000
municipal bond
• before taxes:
• \$1000 in interest pmts.
• after taxes:
• \$1000 in interest pmts
Corporate bond
• before taxes:
• \$1000 interest pmts.
• after taxes
• (33% marginal rate)
• \$1000(1-.33)

= \$670 interest pmts.

So, after taxes
• muni has 10% coupon rate
• corp has 6.7% coupon rate
• muni can offer a lower yield and still be competitive
tax treatment explains

muni

yields

Treasury

yields

Corp

yields

<

<

impact of tax rates
• higher tax brackets derive more benefit from muni’s
• changing tax rates will affect the corporate-municipal yield spread
II. Term structure of interest rates
• bonds with the same characteristics,

but different maturities

focus on Treasury yields
• same default risk, tax treatment
• similar liquidity
• many choices of maturity

-- 4 weeks to 30 years

relationship between yield & maturity is NOT constant
• sometimes short-term yields are highest,
• sometimes long-term yields are highest
A. Yield curve
• plot of maturity vs. yield
• slope of curve indicates relationship between maturity and yield

yield

maturity

upward sloping
• yields rise w/ maturity (common)
• July 1992, currently

yield

maturity

downward sloping (inverted)
• yield falls w/ maturity (rare)
• April 1980
3 facts about the yield curve
• based on historical data on U.S. Treasury yields

1. interest rates on bonds of different maturities generally move together

2. If short-term rates are low, the yield curve slopes up.

If short-term rates are high, the yield curve slopes down.

3. The yield curve usually slopes up.

Understanding the yield curve
• what causes the 3 facts?
• what does the shape of the yield curve tell us?
• must understand why/how maturity affects yield
3 theories of term structure
• implications for maturity and yield
• check implications against 3 facts about yield curve
B. The Expectations Theory
• Assume:

i.e.

bonds of different maturities are perfect substitutes

if assumption is true,

then investors care only about expected return

• for example,
• if expect better return from short-term bonds, only hold short-term bonds
but investors hold both short-term an long-term bonds
• so,
• must EXPECT similar return:

long-term yields =

average of the expected

short-term yields

example
• 5 year time horizon
• investors indifferent between

(1) holding 5-year bond

(2) holding 1year bonds, 5 yrs. in a row

as long as expected return is same

expected one-year interest rates:

5%, 6%, 7%, 8%, 9%

over next 5 years

so 5-year bond must yield (approx)

yield

7%

5%

maturity

1 yr. 5 yrs.

yield curve
• if ST rates are expected to rise,
• yield curve slopes up
under exp. theory,
• slope of yield curve tells us direction of expected future short-term rates
theory vs. reality
• does the theory explain the 3 facts?

1. interest rates move together?

YES.

If ST rates rise, then average will rise (LT rate)

2. interest rates low, slopes up

interest rates high, slopes down

YES.

ST rates low, must be expected to rise,

so yield curve slopes up

ST rates high, must be expected to fall,

so yield curve slopes down

3. yield curve usually slopes up

NO.

Under expectations theory,

we would expect the yield curve to slope up only about 50% of the time

but it slopes up most of the time

what went wrong?
• back to assumption:

bonds of different maturities are perfect substitutes

• but this is not likely
• long term bonds have greater price volatility
• short term bonds have reinvestment risk
C. Segmented Markets Theory
• assume:

bonds of different maturities are NOT substitutes at all

if assumption is true,
• exp. return of ST bonds does not affect demand for LT bonds,

and vice versa

• separate markets for ST and LT bonds
theory vs. reality
• does the theory explain the 3 facts?

1. interest rates move together?

NO.

if they are not related, why would they move together?

2. interest rates low, slopes up

interest rates high, slopes down

NO.

ST yields do not affect LT yields,

so they will not affect the slope

3. yield curve usually slopes up

YES.

LT bonds have greater interest rate risk.

• LT bonds have lower demand
• LT bonds have a higher yield

so LT yield > ST yield,

and yield curve slopes up

• assume:

bonds of different maturities are imperfect substitutes,

and investors PREFER ST bonds

so if true,

investors hold ST bonds

UNLESS

LT bonds offer higher yield as incentive

so,

LT yield = average exp. ST yields

example
• 5 years
• 1 yr. bond yields:

5%, 6%, 7%, 8%, 9%

• AND 5yr. bond has 1% liquidity prem.
theory vs. reality
• does the theory explain the 3 facts?

1. & 2?

YES.

LT rates are still based in part on

3. yield curve usually slopes up

YES.

IF LT bond yields have a liquidity premium,

then usually LT yields > ST yields

or yield curve slopes up.

Problem
• How do we interpret yield curve?
• slope due to 2 things:

(1) exp. about future ST rates

• do not know size of liq. prem.

yield

maturity

yield curve

• if liquidity premium is small,
• then ST rates are expected to rise

yield

maturity

yield curve

• if liquidity premium is larger,
• then ST rates are expected to stay the same
E. What does the yield curve tell us?
• expected future ST rates?
• expected inflation?
slope of yield curve is useful in predicting recessions
• slight upward slope
• normal GDP growth
• steep upward slope
• recovery from recession
flat curve
• uncertainty
• could mean recession,

or slow growth

• inverted curve
• exp. lower interest rates
• followed by slowdown or

recession