Bonds - Wharton Finance

Bonds

Finance 100

Prof. Michael R. Roberts

Copyright ? Michael R. Roberts 1

Topic Overview

z Introduction to bonds and bond markets z Zero coupon bonds

? Valuation ? Yield-to-Maturity & Yield Curve ? Spot Rates ? Interest rate sensitivity ? DVO1

z Coupon bonds

? Valuation ? Arbitrage ? Bond Prices Over Time ? Yield Curve Revisited ? Interest rate sensitivity ? Duration & Immunization

z Forward Rates

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What is a Bond and What are its Features?

z A bond is a security that obligates the issuer to make interest and principal payments to the holder on specified dates.

? Maturity (or term)

? Face value (or par): Notional amount used to compute interest payments

? Coupon rate: Determines the amount of each coupon payment, expressed as an

APR

Coupon =

Coupon Rate ? Face Value

Number of Coupon Payments per Year

z Bonds differ in several respects:

? Repayment type ? Issuer ? Maturity ? Security ? Priority in case of default

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Repayment Schemes

z Bonds with a balloon (or bullet) payment

? Pure discount or zero-coupon bonds

? Pay no coupons prior to maturity.

? Coupon bonds

? Pay a stated coupon at periodic intervals prior to maturity.

? Floating-rate bonds

? Pay a variable coupon, reset periodically to a reference rate.

z Bonds without a balloon payment

? Perpetual bonds

? Pay a stated coupon at periodic intervals.

? Annuity or self-amortizing bonds

? Pay a regular fixed amount each payment period. ? Principal repaid over time rather than at maturity.

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Who Issues Bonds?

z US Government (Treasuries)

? T-bills: 4,13,16-week maturity, zero coupon bonds ? T-notes: 2,3,5,10 year, semi-annual coupon bonds ? T-bonds: 20 & 30-year, semi-annual coupon bonds ? TIPS: 5,10,20-year, semi-annual coupon bond, principal -adjusted ? Strips: Wide-ranging maturity, zero-coupon bond, IB-structured

z Foreign Governments z Municipalities

? Maturities from one month to 40 years, semiannual coupons ? Exempt from federal taxes (sometimes state and local as well). ? Generally two types: Revenue bonds vs General Obligation bonds ? Riskier than government bonds (e.g., Orange County)

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Who Issues Bonds? (Cont.)

z Agencies:

? E.g. Government National Mortgage Association (Ginnie Mae), Student Loan Marketing Association (Sallie Mae)

? Most issues are mortgage-backed, pass-through securities. ? Typically 30-year, monthly paying annuities mirroring underlying

securities ? Prepayment risk.

z Corporations

? 4 types: notes, debentures, mortgage, asset-backed ? ~30 year maturity, semi-annual coupon set to price at par ? Additional features/provisions:

? Callable: right to retire all bonds on (or after) call date, for call price ? convertible bonds ? putable bonds

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Moody's Aaa Aa

A Baa Ba

B Caa Ca

C D

Bond Ratings

S&P AAA AA

A BBB BB

B CCC CC

C -

Quality of Issue Highest quality. Very small risk of default.

High quality. Small risk of default.

High-Medium quality. Strong attributes, but potentially vulnerable. Medium quality. Currently adequate, but potentially unreliable. Some speculative element. Long-run prospects questionable. Able to pay currently, but at risk of default in the future. Poor quality. Clear danger of default.

High speculative quality. May be in default.

Lowest rated. Poor prospects of repayment.

In default.

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The US Bond Market ? Flows

Amount ($bil.). Source: Flow of Funds Data 2005-2007

Debt Instrument U.S. Gov. Municipal

Corporate

2005 307.3 195 53.6

Consumer Credit Mortgages

94.5 1417.5

2006 183.7 177.3 213.4 104.4 1397.1

2007 237.5 214.6 314.1 132.3 1053.2

Dollar volume of bonds traded daily is 10 times that of equity markets!

Outstanding investment-grade dollar denominated debt is about $8.3 trillion (e.g., treasuries, agencies, corporate and MBSs

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Zero Coupon Bonds (a.k.a. Pure Discount Bonds)

z Notation Reminder:

? Vn= Bn = Market price of the bond in period n ? F = Face value ? R= Annual percentage rate ? m = compounding periods (annual ? m = 1, semiannual ? m = 2,...) ? i = Effective periodic interest rate; i=R/m ? T = Maturity (in years) ? N = Number of compounding periods; N = T*m ? r = discount rate

z Two cash flows to buyer of a zero coupon bond (a.k.a. "zero"):

? -V0 at time 0 ? F at time T

z What is the price of a bond?

V0

=

B0

=

F

(1 + r )T

or

V0

=

B0

=

F

(1 + i)N

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Zero Coupon Bond Examples

z Value a 5 year, U.S. Treasury strip with face value of $1,000. The APR is 7.5% with quarterly compounding? ? Approach 1: Using R (APR) and i (effective periodic rate) ?

? Approach 2: Using r (EAR) ?

? Approach 3: Using r (periodic discount rate) ?

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