Lecture 11 - Term Structure of Interest Rates
from last time
yield curve
segmented markets theory
expectations theory
preferred habitat theory
From Last Time
- When a flight to quality occurs with people shifting out of risky bonds into low risk bonds, the savings curve in the risky bonds market does shift to the left while the savings curve in the low risk market shifts to the right.
- People invest in junk bonds because they offer a higher interest rate as compensation for the additional default risk.
- Liquidity, the ease with which an asset can be converted into cash, is a desirable characteristic of an asset. Liquidity reduces the risks of holding an asset: I can sell it quickly if I need to. So, illiquid assets must offer a higher return to
induce people to hold them.
Yield Curve
The term structure of interest rates is the variation in yield for related debt instruments differing in maturity. It looks at bonds with common default risk, liquidity, information costs, and taxation characteristics but with different maturities.
The yield curve shows the relationship at any one instant between the yield to maturity and term to maturity on otherwise comparable bonds.
- yield curve generally slopes upward: long-term interest rates are usually higher than short-term rates
- yield curve typically shifts up or down rather than twisting: long and short-term
interest rates generally move up and down together
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Segmented Markets Theory
This theory assumes that markets for bonds of different maturities are completely separated and segmented. The interest rate for each maturity bond is determined by the supply and demand for that maturity bond only. It assumes that borrowers have
particular periods for which they want to borrow and lenders have particular holding periods in mind, e.g. saving for retirement, paying for your kid's college education.
The yield curve slopes upward because the demand for short-term bonds is relatively higher than the demand for longer-term bonds. People prefer to lend for short periods of time.
The segmented markets theory cannot explain why interest rates on bonds of different maturities tend to move together since the interest rate for each maturity bond is determined by the supply and demand for that maturity bond only.
Expectations Theory
Expectations theory assumes that bonds of all maturities are perfect substitutes. Lenders and borrowers are indifferent between, say, a 2-year bond and a succession of 1-year bonds.
So, for example, if people expect that short-term interest rates will be 10% on average over the next two years, then the interest rate on 2-year bonds will be 10% too.
Let i1t = interest rate for this year on a 1-year bond
ie1,t+1 = next year's expected interest rate on a 1 year bond
i2t = today's interest rate on a 2-year bond
If i1t = 8% and ie1,t+1 = 12%, then i2t = (i1t + ie1,t+1)/2 = (8 + 12)/2 = 10%.
Suppose a 2-year bond had an interest rate above 10%, say, 11%. A 2-year bond would bring the lender a total return of 22% over the two years while a succession of two 1-year loans would only bring a 20% return. Investors will shift to the 2-year bond
market and drive down the interest rate to 10%.
in,t = {i1t + ie1,t+1 + ... + ie1,t+n-1}/n
- can explain movements together by short-term and long-term interest rates since long-term rates are simply an average of short-term rates
The expectations theory predicts that the yield curve is upward sloping when interest rates are expected to rise. (Remember that yield curves generally slope upwards in the real world.) For example, suppose i2t = 6% and i1t = 4%.
What must ie1,t+1 (what we now expect next year's 1-year rate to be) equal?
Yield curves are usually upward sloping, but short-term interest rates are as likely to fall as to rise. So, this prediction of the expectations theory is inconsistent with the real world evidence. It cannot explain the usual upward slope of the yield
curve.
Preferred Habitat Theory
The preferred habitat theory combines the segmented markets and expectations theories by assuming that investors care about both expected returns and maturity. Investors prefer short-term to long-term bonds and will not buy a long-term bond if it offers
the same expected returns as a series of short-term bonds. Long-term bondholders need to be paid a term premium.
Suppose i1t = 6% and ie1,t+1 = 6%. i2t must be greater than 6% to induce people to hold 2-year bonds.
in,t = {i1t + ie1,t+1 + ... + ie1,t+n-1}/n + hn,t, where hn,t is the term premium for a n-period bond.
So, under the preferred habitat theory the yield curve has a natural upward slope due to the term premiums; also, since long-term rates are, in part, an average of short-term rates, the yield curve will tend to shift rather than twist.
if the yield curve slopes
- slightly upward, investors expect interest rates to stay about the same
- sharply upward, short-term rates are expected to rise
- flat, short-term rates are expected to fall slightly
- downward, a sharp decline in interest rates is expected
EC 230, Money and
Banking Files 
