I.  Yield Curve

• what is the relationship between yield and maturity?
• complicated--sometimes the yield decreases with maturity, sometime it increases with maturity
• usually the yield rises with maturity but not always
• looking at bonds with same properties, except for different maturities
• Treasury securities--many maturities, all liquid, all default-free
• Tbills:  1 mo. (4 wk.) , 3 mo. (13 wk.), 6 mo. (26 wk), 1 yr. (52 wk.)
• zero coupon
• Tnotes: 2, 5, 10 years
• coupon
• Tbonds: 30 years (not since 2001)
• coupon
• yield curve is a picture of the term structure (the relationship between yield and maturity) at a given point in time
• upward sloping yield curve
• longer-term bonds have higher yields
• downward sloping yield curve
• longer-term bonds have lower yields
• flat yield curve
• yields do not vary with maturity
• changing slope yield curve
• yield/maturity relationship is not consistent

• Pure Expectations Theory  (broad interpretation)
• assume
• bonds of different maturities are perfect substitutes (investors care only about total return)
• implication
• long term bond yields are the average of current and expected future short term bond yields
• approximately an arithmetic average
• exactly a geometric average
• why?  because if investors expected long term bonds to have a better yield, then they would only hold long term bonds (because they are indifferent among maturities); if they expected short-term bonds to do better they would only hold short term bonds.  Since we observe that investors hold both short and long term bonds then it must be the case that they expect them to yield about the same.
• this argument ASSUMES that investors have no preference for short or long term bonds

• so the slope of the yield curve indicates investors expectations of future interest rates
• the yield curve slopes up, rates are expected to rise, if the yield curve slopes down, rates are expected to fall
• How does the expectations theory compare to reality?
• the yield curve usually slopes up but
• the expectations theory cannot explain this--it would predict an upward slope only about 50% of the time.
• What's the problem with the expectations theory?
• the assumption that bonds of different maturities are perfect substitutes is not realistic:
• long term bonds carry greater interest rate risk or price risk than short term bonds
• short term bonds carry greater reinvestment risk than long term bonds
• Liquidity Theory
• assume
• bonds of different maturities are imperfect substitutes and that investors prefer short term bonds to long term bonds
• long term bonds must include a positive liquidity premium over and above expected future short term interest rates
• implication
• long term bond yields = average of short term yield + liquidity premium
• this make the yield curve much more difficult to interpret, because its slope now depends on two things, and we do not know the size of the premium, only its sign
• an upward sloping yield curve could mean that interest rates are expected to rise, if the liquidity premium is small OR it could mean that interest rates are expected to stay the same if the liquidity premium is large.
• the liquidity theory DOES explain why the yield curve usually slopes up--since long term bond yields include a liquidity premium that is positive, they are likely to be larger than short term bond yields
• The Preferred Habitat Theory
• assume
• bonds of different maturities are imperfect substitutes and that investors prefer short term bonds to long term bonds sometimes, but sometimes they prefer long term bonds to short term bonds
• the liquidity premium can be positive or negative
• implications
• the yield curve under this theory is even more difficult to interpret since we know neither the sign nor the size of the liquidity premium.
• most evidence suggests that the liquidity premium is almost always positive.
• The Market Segmentation Theory
• assume
• bonds of different maturities are NOT substitutes at all.
• the long term and short term bond markets are separate or segmented.
• implications
• long and short term bond yields are not related, so the slope of the yield curve does not signal anything about future short-term interest rates.
• long and short-term yields are determined by supply and demand in totally separate markets
• it is very unlikely that investors are always unwilling to substitute across maturities