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McGraw-Hill/Irwin Copyright 2006 by The McGraw-Hill Companies, Inc. All rights reserved.

Chapter 7

The Risk and TermStructure of Interest

Rates

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Bond Ratings and Risk

Bond Ratings - Moodys and Standard and Poors

Ratings Groups Investment Grade

Non-Investment Speculative Grade Highly Speculative

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Commercial Paper Ratings Moodys and Standard and Poors

Rating Groups Investment

Speculative Default

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Increased Risk reduces Bond Demand.The resulting shift to the left causes adecline in equilibrium price and an

increase in the bond yield.Risk spread (premium)

Bond Yield = U.S. Treasury Yield+ Default Risk Premium

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Long-Term Bond Interest Rates and Ratings

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Short-Term Interest Rates and Risk

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Tax Status and Bond Prices

Coupon Payments on Municipal Bondsare exempt from Federal Tax Payments.

Tax-Exempt Bond Yield= (Taxable Bond Yield) x (1- Tax Rate).

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Term Structure of Interest Rates

The relationship among bonds with thesame risk characteristics but different

maturities is called the term structure ofinterest rates.

A plot of the term structure, with the yield

to maturity on the vertical axis and thetime to maturity on the horizontal axis, iscalled the yield curve.

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Web Link:

US Treasury Bloomberg.com
http://www.ustreas.gov/offices/domestic-finance/debt-management/interest-rate/yield.htmlhttp://www.bloomberg.com/markets/rates/http://www.bloomberg.com/markets/rates/http://www.ustreas.gov/offices/domestic-finance/debt-management/interest-rate/yield.html

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Expectations Hypothesis

Bonds of different maturities are perfect

substitutes for each other.An investor with a two-year horizon. Buy a 2 year bond or

Buy a one year bond and another one yearbond in one year.

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Total return from 2 year bonds over 2 years

)2y2y i)(1i(1

Return from one year bond and then another one yearbond

)i)(1i(1 e1y1y

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If one and two year bonds are perfect substitutes, then:

)i)(1i(1)i)(1i(1 e1y1y2y2y

Or

2iii

e1y1y

2y

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n

iiiii

ent

et

et t

nt 1121111 ....

Or in general terms

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Expectations Theory can not explain whylong-term rates are usually above shortterm rates.

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Liquidity Premium Theory

The yield curves upward slope is explainedby the fact that long-term bonds are riskierthan short-term bonds. Bondholders face

both inflation and interest-rate risk. Thelonger the term of the bond, the greaterboth types of risk.

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Liquidity Premium Theory

n

iiii

rpi

ent

et

et t

nnt

1121111 ....

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Information Content of InterestRates

Direction of future rates Implied forward rate Direction of risk premium

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Forward Rates

Forward Rate is an implied non-observable short term rate.

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Forward Rate Example

Year Spot Rate1 5%2 6%3 7%4 6%

f2 = (1.06) 2 / (1.05) 1 = 7.0% Strategy 1:

Invest $1 in a 2 yr. zero coupon: $1 x (1.06)2

= $1.1236Strategy 2:Invest $1 in 1yr zero coupon receiving 5% 1 st yr. and 7.0%

2nd yr. = $ 1.1236 = (1.05)(1.07)

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Forward Rate Example

Year Spot Rate1 5%2 6%3 7%4 6%

f2 = (1.06) 2 / (1.05) 1 = 7.0%

f3 = (1.07)3 / (1.06)

2 1 = 9.03%

f2 = (1.06) 4 / (1.07) 3 1 = 3.06%

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Chapter 07w