Lecture 6 - Yield Curve

Outline
• How do interest rates vary across debt
instruments?
• What is the risk structure of interest rates
• What is the term structure of interest rates
• What is the yield curve?
• How does the term structure relate to the
yield curve?
7/13/2020 GONZAGA UNIVERSITY 2

Links
• Treasury data on the yield curve
https://www.treasury.gov/resource-center/data-
chart-center/interest-
rates/pages/textview.aspx?data=yield
• Monetary policy and the yield curve
https://www.bloomberg.com/news/articles/202
0-06-30/yield-curve-control-bets-are-getting-
more-obvious-in-treasuries

Understanding Interest Rates
• Commercial paper: Short-term note (1-270 days),
money market (follows federal funds rate)
• Federal funds rate: Short-term overnight lending
market between banks
• Corporate bonds: Long-term note (different
yields, following treasury notes)
• Governments bonds: Varying maturities (riskless)
• Conventional mortgages; 30 year maturities
(follow 10 year bond)

Commercial Paper
• Commercial paper is a short-term version of a
bond.
– The borrower has no collateral so the debt is
unsecured.
• Commercial paper is issued on a discount basis,
as a zero-coupon bond specifying a single future
payment with no associated coupon payments.
– Has maturity of less than 270 days.
• More than one third is held by money-market
mutual funds.

Commercial Paper

Short-term Rate

Mortgage Rates

Long-term Rates

Term Structure

Risk Structure of Interest
Rates
• Risk Structure of Interest Rates
– Relationship among interest rates
• Default risk - Occurs when the issuer of the
bond is unable or unwilling to make interest
payments or pay o the face value
• Risk premium - The spread between the
interest rates on bonds with default risk and
the interest rates on T-bonds

Bond Ratings

Commercial Paper Ratings

Enron and the Bond Market
• Enron's bankruptcy increased the spread
between Baa and Aaa rated bonds.
• Aaa bonds became more desirable (Rates fell
from 6.97% to 6.77%)
• Baa bonds became less desirable (Rates
increased from 7.81% to 8.07%)
– The spread increased from .84% to 1.28%

Determining Interest Rates
• Liquidity
– Demand increases with liquidity
– U.S. long term bonds are very liquid
– Corporate bonds are less liquid. There are fewer
bonds for anyone corporation
• Income Taxes and Municipal Bonds
– Not risk free and less liquid than U.S. bonds
– Tax free status increased the demand for municipal
bonds

Municipal Bonds

Flight to Quality

Term Structure
• Bonds with identical risk, liquidity, and tax
characteristics may have different interest rates
because the time remaining to maturity is different
• Yield Curve is plot of the yield on bonds with differing
terms to maturity but the same risk, liquidity and tax
considerations
– Upward-sloping means long-term rates are above short-
term rates
– Flat means short- and long-term rates are the same
– Inverted means long-term rates are below short-term rates

Term Structure
• Theory of the term structure must explain:
– Fact 1: Interest rates on bonds of different maturities
move together over time
– Fact 2: When short-term interest rates are low, yield
curves are more likely to have an upward slope; when
short-term rates are high, yield curves are more likely
to slope downward and be inverted.
– Fact 3: Yield curves are almost always upward sloping

Expectations Theory
• The interest rate on a long-term bond will equal an
average of the short-term interest rates that people
expect to occur over the life of the long-term bond.
• Buyers of bonds do not prefer bonds of one maturity
over another.
• They will not hold any quantity of a bond if its
expected return is less than that of another bond with
a different maturity.
• Bonds like these are said to be perfect substitutes.

Expectations Theory -
Example
• Let the current rate on one-year bond be 6%.
• You expect the interest rate on a one-year
bond to be 8% next year.
• Then the expected return for buying two one-
year bonds averages (6% + 8%)/2 = 7%.
• The interest rate on a two-year bond must be
7% for you to be willing to purchase it.

Expectations Theory – Yield
Curve
• A rising trend in short term rates increases the
long term bond rates
• When the yield curve is upward sloping, short
term rates are expected to rise in the future, long
term rates increase today
• When the yield curve is downward sloping the
average of future short terms rates is expected to
be lower than current short term rates
• When the yield curve is at, short term rates are
not expected to change on average

Expectations Theory
• Explains why interest rates on bonds with different maturities move
together over time (fact 1)
– An increase in short term rates today will increase future expected
short term rate and thus long term rates today
• Explains why yield curves tend to slope up when short-term rates
are low and slope down when short-term rates are high (fact 2)
• When interest rates are low (high), people expected higher (lower)
future short term rates which cause higher (lower) current long
term rates, thus the yield curve is upward (downward) sloping.
• Cannot explain why yield curves usually slope upward (fact 3)

Segmented Markets Theory
• Bonds of different maturities are not substitutes at all
• The interest rate for each bond with a different maturity is
determined by the demand for and supply of that bond
• Investors have preferences for bonds of one maturity over
another
• If investors have short desired holding periods, as it seems,
they generally prefer bonds with shorter maturities that
have less interest-rate risk
• Demand decreases for long term bonds, decreasing price
but increasing the interest rate
• Explains why yield curves usually slope upward (fact 3)

Segmented Markets Theory
• Cannot explain facts 1 and 2
– Because bonds are not substitutes there is no
reason to believe interest rates on long term and
short term bonds move together.
• It is not clear how demand and supply change
for long vs short term bonds with the current
short term interest rate

Liquidity Premium Theory
• Liquidity Premium: The interest rate on a long-
term bond will equal an average of short-term
interest rates expected to occur over the life
of the long-term bond plus a liquidity
premium that responds to supply and demand
conditions for that bond (compensation for
interest rate risk)
• Bonds of different maturities are substitutes
but not perfect substitutes

Liquidity Premium
• Bonds are substitutes
– Returns on short terms bonds will influence long term
rates
• Because bonds are not perfect substitutes it
allows investors to prefer one bond maturity over
the another
– Investors prefer short-term bonds
– Less interest rate risk and are more liquid
• Investors are credited with a liquidity premium
for holding long-term bonds

Preferred Habit Theory
• Investors have a preference for bonds of one
maturity over another
• They will be willing to buy bonds of different
maturities only if they earn a somewhat
higher expected return
• Investors are likely to prefer short-term bonds
over longer-term bonds

The Facts
• Interest rates on different maturity bonds move
together over time; explained by the first term in the
equation
• Yield curves tend to slope upward when short-term
rates are low and to be inverted when short-term rates
are high; explained by the liquidity premium term in
the first case and by a low expected average in the
second case
• Yield curves typically slope upward; explained by a
larger liquidity premium as the term to maturity
lengthens

Term Structure and the
Economy
• Expectation over future interest rates drives
the yield curve.
• During a recession, future short-term interest
rates will decline.
• What happens to the yield curve and term
spread during a recession? Expansion?

Yield Curve

Monetary Policy and the YC
• Open market operations move the short end
of the yield curve
• QE programs move the long end of the yield
curve.

MP and YC

Lecture 6 - Yield Curve

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