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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%