Lecture 5 II The Risk and Term Structure of Interest Rates -- Term structure  Term structure of interest rates  bonds with the same characteristics,but different maturities  focus on Treasury yields same default risk, tax treatment many choices of maturity -- 4 weeks to 10 years

Treasury yields over time

Relationship Between Yield & Maturity  relationship between yield & maturity is NOT constant sometimes short-term yields are highest, Most of the time, long-term yields are highest

A. Yield curve  plot of maturity vs. yield  slope of curve indicates relationship between maturity and yield  The living yield curve The living yield curve

upward sloping  yields rise w/ maturity (common) maturity yield

flat  yield varies little with maturity maturity yield

downward sloping (inverted)  yield falls w/ maturity (rare) maturity yield

Term Structure Facts to Be Explained Besides explaining the shape of the yield curve, a good theory must explain why:  Interest rates for different maturities move together.  Yield curves tend to have steep upward slope when short rates are low and downward slope when short rates are high.  Yield curve is typically upward sloping.

3 theories of term structure 1. Expectations Theory Pure Expectations Theory explains 1 and 2, but not 3 2. Market Segmentation Theory Market Segmentation Theory explains 3, but not 1 and 2 3. Liquidity Premium Theory Solution: Combine features of both Pure Expectations Theory and Market Segmentation Theory to get Liquidity Premium Theory and explain all facts

1.The Expectations Theory  Assume: bond buyers do not have any preference about maturity i.e. bonds of different maturities are perfect substitutes, R e on bonds of different maturities are equal.

A.The Expectations Theory  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

A.The Expectations Theory  but investors hold both short-term an long- term bonds  so,  must EXPECT similar return: long-term yields =average of the expected future shorttern 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

1.Expectations Theory The important point of this theory is that if the Expectations Theory is correct, your expected wealth is the same (a the start) for both strategies. Of course, your actual wealth may differ, if rates change unexpectedly after a year. We show the details of this in the next few slides.

 expected one-year interest rates: 5%, 6%, 7%, 8%, 9% over next 5 years so 5-year bond must yield (approx) 1.Expectations Theory

yield curve  if ST rates are expected to rise,  yield curve slopes up maturity yield

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). 2. ST rates are more volatile YES. If LT rates are an average of ST rates, then they will be less volatile

theory vs. reality 3. yield curve usually slopes up NO. Under expectations theory, this means we would expect interest rates to rise most of the time. BUT we don’t. (rates have trended down for 20 yrs.)

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

2.Segmented Markets Theory Key Assumption: Bonds of different maturities are not substitutes at all Implication: Markets are completely segmented: interest rate at each maturity determined separately Explains Fact 3 that yield curve is usually upward sloping People typically prefer short holding periods and thus have higher demand for short-term bonds, which have higher price and lower interest rates than long bonds Does not explain Fact 1 or Fact 2 because assumes long and short rates determined independently

3. Liquidity Premium Theory  assume: bonds of different maturities are imperfect substitutes, and investors PREFER ST bonds Less inflation risk, less interest rate risk

 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

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 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.

Problem  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 maturity yield yield curve small liquidity premium

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

C. What does the yield curve tell us?  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

 flat curve uncertainty could mean recession, or slow growth  inverted curve exp. lower interest rates followed by slowdown or recession