 # Chapter 6. Risk and Term Structure of Interest Rates Risk Structure Term Structure Risk Structure Term Structure.

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Chapter 6. Risk and Term Structure of Interest Rates Risk Structure Term Structure Risk Structure Term Structure

Not all interest rates are created equal! many interest rates at one time interest rates move together over time many interest rates at one time interest rates move together over time

January 2004 3 mo Tbill2.33% 3 mo Commerical Paper2.52% prime rate5.25% 10 yr. Tnote4.23% 10 yr. AAA corporate5.46% 10 yr. BAA corporate6.15% 30 yr. mortgage 5.71% 3 mo Tbill2.33% 3 mo Commerical Paper2.52% prime rate5.25% 10 yr. Tnote4.23% 10 yr. AAA corporate5.46% 10 yr. BAA corporate6.15% 30 yr. mortgage 5.71%

measurementmeasurement difference between two interest rates  spread measured in  percentage points  basis points  1 percentage pt. = 100 basis pts. difference between two interest rates  spread 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% spread .19 percentage pts.  19 basis pts. 3 mo. Tbill 2.33% 3 mo. Commercial paper 2.52% spread .19 percentage pts.  19 basis pts.

example 2 10 yr Tnote4.23% 10 BAA corporate6.15% spread  1.92 percentage pts.  192 basis pts. 10 yr Tnote4.23% 10 BAA corporate6.15% spread  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 debt with same maturity, but different characteristics  default risk  liquidity  tax treatment

PatternsPatterns Baa always the highest yield Municipal’s always the lowest (1940) Baa > AAA > U.S. > municipal  size of the spread varies 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 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 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 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 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 Treasury yields AAA Corp yields BAA Corp 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. 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? higher liquidity lower yield

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 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 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 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 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 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. 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 muni has 10% coupon rate corp has 6.7% coupon rate muni can offer a lower yield and still be competitive

tax treatment explains Treasury yields muni 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 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 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 focus on Treasury yields  same default risk, tax treatment  similar liquidity  many choices of maturity -- 4 weeks to 30 years

Treasury yields over time

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

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

downward sloping (inverted) yield falls w/ maturity (rare) April 1980 yield falls w/ maturity (rare) April 1980 maturity yield

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 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. 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 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 assumptions about investor preference implications for maturity and yield check implications against 3 facts about yield curve assumptions about investor preference implications for maturity and yield check implications against 3 facts about yield curve

B. The Expectations Theory Assume: bond buyers do not have any preference about maturity i.e. bonds of different maturities are perfect substitutes Assume: bond buyers do not have any preference about maturity 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 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 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

exampleexample 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 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) expected one-year interest rates: 5%, 6%, 7%, 8%, 9% over next 5 years so 5-year bond must yield (approx)

maturity yield 1 yr.5 yrs. 5% 7% yield curve if ST rates are expected to rise, yield curve slopes up 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

ST rates expected to fall maturity yield

ST rates expected to stay the same maturity yield

ST rates expected to rise, then fall maturity yield

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) 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 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 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 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 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 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? 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 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 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

D. Liquidity Premium Theory assume: bonds of different maturities are imperfect substitutes, and investors PREFER ST bonds 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 higher yield = liquidity premium so if true, investors hold ST bonds UNLESS LT bonds offer higher yield as incentive higher yield = liquidity premium

so, LT yield = average exp. ST yields + liquidity premium so, LT yield = average exp. ST yields + liquidity premium

exampleexample 5 years 1 yr. bond yields: 5%, 6%, 7%, 8%, 9% AND 5yr. bond has 1% liquidity prem. 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 exp. about ST rates does the theory explain the 3 facts? 1. & 2? YES. LT rates are still based in part on exp. about ST rates

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. 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.

ProblemProblem How do we interpret yield curve? slope due to 2 things: (1) exp. about future ST rates (2) size of liquidity premium do not know size of liq. prem. How do we interpret yield curve? slope due to 2 things: (1) exp. about future ST rates (2) size of liquidity premium do not know size of liq. prem.

if liquidity premium is small, then ST rates are expected to rise if liquidity premium is small, then ST rates are expected to rise maturity yield yield curve small liquidity premium

if liquidity premium is larger, then ST rates are expected to stay the same if liquidity premium is larger, then ST rates are expected to stay the same maturity yield yield curve large liquidity premium

E. What does the yield curve tell us? expected future ST rates? expected inflation? business cycle? expected future ST rates? expected inflation? business cycle?

slope of yield curve is useful in predicting recessions slight upward slope  normal GDP growth steep upward slope  recovery from recession 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 flat curve  uncertainty  could mean recession, or slow growth inverted curve  exp. lower interest rates  followed by slowdown or recession

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