Chapter Five
The Structure of
Interest Rates
What Explains Differences
in Interest Rates?
Different Types of Debt Securities
• Personal saving via indirect finance
– CDs and money market accounts
– Early withdrawals and/or minimum deposits
• Personal borrowing
– Include loans, mortgages, credit cards, etc.
– Collateral and/or adjustable interest rates may apply
• Saving via direct finance
– Purchasing of debt securities
– May be via securitization, guaranteed investment
contracts, and/or commercial paper
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Debt Securities &
Their Yields
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Secondary Market Supply & Demand
Why does yield to maturity vary?
– Risk…riskier securities must hold more promise
• Same holds true for interest paid on credit and interest earned
on bonds
– Liquidity…transactions costs are lower on securities
that are more liquid
• On-the-run (very liquid) vs. off-the-run securities (less liquid,
not recently issued)
– Taxation…corporate & government securities are
subject to different levels of taxation
– Time to maturity…longer terms must hold more
promise
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Secondary Market
Supply & Demand (cont’d)
Please insert Figure 5.1
• Market participants sometimes worry about the risk of
borrowers’ default
– eg. 1998 Russian debt default caused supply of securities to increase
(many owners looking to sell) and demand to decrease (new investors
did not want to take on risk of default)
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Secondary Market
Supply & Demand (cont’d)
Please insert Figure 5.2
• Borrowers are concerned with default, as are investors, to
ensure future borrowing opportunities
– eg. discontinuing of 30 year U.S. Treasury bonds in 2001 resulted in
price increase and decrease in yield to maturity
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Supply & Change in Yields to Maturity
Please insert Figure 5.3
The surprise announcement of the U.S. Treasury in
October, 2001 dramatically affected the yield to
maturity on U.S. Treasury securities
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The Term Structure of Interest Rates
• Can assist in analyzing the
economy and making
predictions about economic
growth
• Term structure of interest
rates = relationship
between interest rates with
differing times to maturity
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Short & Long Term Interest Rates
• Short and long term interest rates generally move in the
same direction
• Short term rates tend to be more volatile and lower than
long term rates
Please insert Figure 5.4.
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Yield Curves
• Plots interest rates on different securities of similar default risk for
a given day
– Used to demonstrate difference in interest rates based on time to maturity
– Upward sloping curves show securities with longer times/higher yields to
maturity
Please insert Figure 5.5
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Yield Curves (cont’d)
Please insert Figure 5.6
Same yield curve, different dates…
Can we explain behavior of interest rates overall?
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Short- vs. Long-Term Securities
Is it better to buy one two-year bond or two
one-year bonds?
Please insert Table 5.2
The choice depends on the interest rates!
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Short- vs. Long-Term Securities (cont’d)
Sometimes it’s more convenient to use an approximation rather than
calculating the average interest rate of each security.
Two important assumptions being made above
1.
Investor bears no transactions costs
2.
Investor is certain of return on one-year bond
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Term Structure of Interest Rates
in Equilibrium
Establishing a relationship between shortand long-term interest rates
• Assume zero transactions costs and
predictable short-term interest rates
• Long-term interest rate = average of current
and future short-term rates
• This theory is known as the expectations
theory of long-term interest rates
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Shifting Demand
• Investors compare long-term interest rates with
comparable successive short-term rates, choosing to
purchase those with highest yields
• As demand for higher yield bonds increases, the price
rises, bringing the group of short-term bonds back into
equilibrium
Please insert Figure 5.7.
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Expectations Theory & Yield Curves
• Yield curve shapes will vary based on
expectations theory of term structure
• Different shapes will result when
– Short term rates are not expected to change
– Short-term rates are expected to fall
– Short-term rates are expected to rise
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Yield Curves of Different Shapes
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How Accurate are Short-Term
Interest Rates?
Please insert Figure 5.A
Forecasts made the earliest tend to be the most inaccurate, based on
predictions one, two, and three quarters ahead. Overall, however,
accuracy may be a reasonable assumption.
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Equilibrium Rates & Differing Maturities
Please inert Table 5.5
Please insert Figure 5.9
• Expectations theory makes it possible to figure out future interest
rates on long-term bonds by calculating average interest rate of
shorter-term bonds
• Fluctuations in one-year interest rates over time result in a yield
curve of varying slope
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The Term Premium
• Common contradiction to expectations theory
– Theory suggests yield curves should remain flat when
short-term interest rates are not expected to change
– This is not always the case!
– Theory ignores how investors respond to risk. (Recall
the assumption of zero transactions costs…)
– Interest-rate risk is greater on longer-term bonds,
which could cause investors’ preferences to shift
toward shorter-term bonds
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Incorporating a Term Premium
• Reconsider the case of the investor choosing
between one two-year and two one-year
bonds
• A variable must be added to account for
interest rate risk
• A term premium is the difference between
longer-term and shorter-term interest rates to
account for the risk of inflation
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Interest-Rate Risk &
Long-Term Securities
• Interest-rate risk one of main sources of risk to
any security
• Rate of discount has a relatively greater effect
on the present value of long-term securities,
rendering them riskier
• Present value of bonds with longer time to
maturity are higher
• For a given change in interest rates on all
bonds, the prices of long-term bonds are
affected more than the prices of short-term
bonds
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Bond Price & Market Interest Rates
Please insert Figure 5.10.
• The longer the time to maturity, the larger the term
premium
• If market interest rate falls below 8%, all bind prices rise,
but longer-term bond prices rise relatively more
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Term Premiums Are Ever Present
• Even when forecasts suggest that short-term
interest rates will remain stable, longer-term
securities still carry a term premium
• Term premiums are (still) smaller the shorter the
time to maturity
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Yield Curves & Business Cycles
• People are less likely to save,
hence making money available
for investment, during a
recession
• Borrowing tends to decline even
more than saving
• Effects a greater supply shift
than demand shift
• As economies emerge from
recessions, the reverse trend
tends to occur
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Securities Equilibrium in Recession
• During a recession, both saving and borrowing decline, but
borrowing more so than saving. Thus, the supply of debt securities
decreases more than the demand for them.
• Yields to maturity of existing securities subsequently decline, while
the price of debt securities rises.
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Inverted Yield Curves
• Short-term interest rates change more
over the business cycle than long-term
• The result is an inverted (downwardsloping) yield curve
• Smaller term premiums cause more of a
downward slope
• Larger term premiums result in a flatter
yield curve; without the term premium,
long-term rates would be lower that shortterm rates
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Yield Curves & Recessions
• People expect short-term rates to rise as
the economy leaves a recession
• Long-term interest rates should therefore
exceed short-term due to term premium
and expectations for short-term rates
• In the middle of an expansion, there are
few expectations for increases in shortterm rates; upward slope of yield curves
results only from term premium
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Yield Curves & Recessions (cont’d)
Please insert Figure 5.12
Fairly flat slopes to yield curves above indicate
people were not surprised by this recession
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Yield Curves & Expansions
Please insert Figure 5.13
Steeper yield curves indicate an expectation of
rising short-term interest rates, typical in a period
of expansion
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Yield Curves & Expansions (cont’d)
Please insert Figure 5.14
Three years into an expansion, yield curves are
flattening, as the expectations for rising shortterm interest rates diminish
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Predictable Recessions?
• Difficult to plot yield curves over time due
to profusion of data points
• Term spreads can simplify the process
• A term spread is the interest rate on a
long-term debt security, minus the interest
rate on a short-term debt security
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Predictable Recessions? (cont.)
•
•
Negative or low terms spreads are sometimes
indicative of recession
Two possible scenarios can lead to
low/negative spread, both of which increase
the odds of recession
1) Rising short-term rates as the effect of tight
monetary policy to slow the growth of the economy
2) Reduction in bank lending as banks are squeezed
by higher short-term rates not counterbalanced by
their long-term loan rates
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Term Spreads & Recessions
Please insert Figure 5.15
The spread between short-term interest rates and long-term
rates gets smaller before and rises during recessions
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