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8/8/2019 Interest Rates & Yield Curves
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Interest Rates & Yield Curves
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What four factors affect the cost
of money?
Production opportunities
Time preferences for consumption
Risk
Expected inflation
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Real versus Nominal Rates
k* = Real risk-free rate.
T-bond rate if no inflation;1% to 4%.
= Any nominal rate.
= Rate on Treasury securities.
k
kRF
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k = k* + IP + DRP + LP +
MRP.Here:
k = Required rate of return on adebt security.
k* = Real risk-free rate.
IP = Inflation premium.
DRP = Default risk premium.
LP = Liquidity premium.
MRP = Maturity risk premium.
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Premiums Added to k* for Different
Types of Debt
ST Treasury: only IP for ST inflation LT Treasury: IP for LT inflation, MRP
ST corporate: ST IP, DRP, LP
LT corporate: IP, DRP, MRP, LP
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What is the term structure ofinterest rates? What is a yield
curve?
Term structure: the relationship betweeninterest rates (or yields) and maturities.
A graph of the term structure is called the
yield curve.
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Treasury Yield Curve
0
5
10
15
10 20 30
Years to Maturity
Interest
Rate (%)1 yr 6.3%
5 yr 6.7%
10 yr 6.5%
30 yr 6.2%Yield Curve
(May 2000)
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DEBT INSTRUMENTS
Commercial Paper
Treasury Bills
Treasury Notes
Treasury Bonds
Municipal Bonds Corporate Bonds
Junk Bonds
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Hypothetical Treasury Yield Curve
0
5
10
15
1 10 20
Years to Maturity
Interest
Rate (%) 1 yr 8.0%
10 yr 11.4%
20 yr 12.65%
Real risk-free rate
Inflation premium
Maturity risk premium
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What factors can explain the shape
of this yield curve?
Th
is constructed yield curve is upwardsloping.
This is due to increasing expected
inflation and an increasing maturity risk
premium.
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Corporate yield curves areh
igh
er th
an th
atof the Treasury bond. However, corporateyield curves are not neces-sarily parallel tothe Treasury curve.
The spread between a corporate yield curveand the Treasury curve widens as thecorporate bond rating decreases.
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Hypothetical Treasury and
Corporate Yield Curves
0
5
10
15
0 1 5 10 15 20
Years to
maturity
InterestRate (%)
5.2% 5.9%6.0%
Treasury
yield curve
BB-Rated
AAA-Rated
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Debt Instruments
Have a certain maturity period
Pay stated interest periodically
Are redeemed at maturity i.e.
Purchased back at maturity by the issuer from
the investor
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0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
7.00%
8.00%
0 5 10 15 20 25 30 35
R
IP
MRP
Maturity R* IP MRP Yield
1 Year 2.50% 5.00% 0.00% 7.5%
5 Years 2.50% 4.60% 0.18% 7.28%
10 Years 2.50% 4.00% 0.28% 6.78%
20 Years 2.50% 3.5% 0.42% 6.42%
30 Years 2.50% 3.33% 0.53% 6.36%
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0.00%
1.00%
2.00%
3
.00%
4.00%
5.00%
6.00%
7.00%
8.00%
9.00%
0 5 10 15 20 25 30 35
R
IP
MRP
Maturity R* IP MRP Yield
1 Year 2.50% 3.00% 0.00% 5.5%
5 Years 2.50% 3.40% 0.18% 6.08%
10 Years 2.50% 4.00% 0.28% 6.78%
20 Years 2.50% 4.5% 0.42% 7.42%
30 Years 2.50% 4.67% 0.53% 7.70%
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0.00%
1.00%
2.00%
3
.00%
4.00%
5.00%
6.00%
7.00%
8.00%
9.00%
0 5 10 15 20 25 30 35
R
IP
MRP
Maturity R* IP MRP Yield
1 Year 2.50% 3.00% 0.00% 5.5%
5 Years 2.50% 3.40% 0.18% 6.08%
10 Years 2.50% 4.00% 0.28% 6.78%
20 Years 2.50% 4.5% 0.42% 7.42%
30 Years 2.50% 4.67% 0.53% 7.70%