11Ch14 – MBA 566

Bond Price, Yields, and Returns

Different Bond Types

Bond Price

Bond Yield

Bond Returns

Bond Risk Structure

22Ch14 – MBA 566

Face or par valueCoupon rate

Zero coupon bond

Compounding and paymentsAccrued Interest

Indenture

Bond Characteristics

33Ch14 – MBA 566

Accrued Interest

periodcouponinDays

periodAIinDayscoupondollarannualAI

___

___

2

__

Example on page 447

44Ch14 – MBA 566

Different Issuers of Bonds

U.S. Treasury

Notes and Bonds

Corporations

Municipalities

International Governments and Corporations

Innovative Bonds

Floaters and Inverse Floaters

Asset-Backed

Catastrophe

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Figure 14.2 Corporate Bond Listings

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Secured or unsecured

Call provision

Convertible provision

Put provision (putable bonds)

Floating rate bonds

Sinking funds

Provisions of Bonds

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Principal and Interest Payments for TIPS

The above is index bond.

See pages 451-452.

Compute real returns in year 1, 2, 3

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)1()1(1 rParValue

rCP T

T

T

tt

tB

PB = Price of the bond

Ct = interest or coupon payments

T = number of periods to maturity

y = semi-annual discount rate or the semi-annual yield to maturity

Bond Pricing

Accrued interest: page 459

99Ch14 – MBA 566

Ct = 40 (SA)P = 1000T = 20 periodsr = 3% (SA)

Price: 10-yr, 8% Coupon, Face = $1,000

77.148,1$

)03.1(

1000

03.1

140

20

20

1

P

Pt

t

1010Ch14 – MBA 566

Prices and Yields (required rates of return) have an inverse relationship

When yields get very high the value of the bond will be very low.

When yields approach zero, the value of the bond approaches the sum of the cash flows.

Bond Prices and Yields

1111Ch14 – MBA 566

Inverse Relation Between Prices and Yields

1212Ch14 – MBA 566

Yield to Maturity

Interest rate that makes the present value of the bond’s payments equal to its price.

Solve the bond formula for r

)1()1(1 rParValue

rCP T

T

T

tt

tB

1313Ch14 – MBA 566

Yield Measures

Bond Equivalent Yield

7.72% = 3.86% x 2

Effective Annual Yield

(1.0386)2 - 1 = 7.88%

1414Ch14 – MBA 566

Current Yield

Annual Interest / Market Price

$70 / $950 = 7.37 %

1515Ch14 – MBA 566

Yield to Call

For callable bonds

See example on page 460

1616Ch14 – MBA 566

Holding Period Return versus YTM

Reinvestment Assumptions

Holding Period ReturnChanges in rates affects returns

Reinvestment of coupon payments

Change in price of the bond

1717Ch14 – MBA 566

Horizon Analysis

Example 14.6 – page 462

1818Ch14 – MBA 566

Figure 14.6 Prices over Time of 30-Year Maturity, 6.5% Coupon Bonds

1919Ch14 – MBA 566

Holding-Period Return: Single Period

HPR = [ I + ( P0 - P1 )] / P0

where

I = interest payment

P1 = price in one period

P0 = purchase price

2020Ch14 – MBA 566

Example

CR = 8%

YTM = 10%

N=10 years

Semiannual Compounding

What is HPR when the rate falls to 7% in six months?

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Zero-coupon Bonds and Treasury Strips

Zero coupon bonds – page 465Short term treasuries

Long term zero coupons

Treasury may strip payments from treasury coupon bonds -- STRIPS

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The Price of a 30-Year Zero-Coupon Bond over Time at a Yield to Maturity of 10%

After-tax return – see page 478.

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Rating companies (P 467)Moody’s Investor Service

Standard & Poor’s

Fitch

Rating CategoriesInvestment grade

Speculative grade

Page 468

Default Risk and Ratings

2424Ch14 – MBA 566

Coverage ratios

Leverage ratios

Liquidity ratios

Profitability ratios

Cash flow to debt

Factors Used by Rating Companies

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Sinking funds

Subordination of future debt

Dividend restrictions

Collateral

Protection Against Default

2626Ch14 – MBA 566

Yields on Long-Term Bonds, 1954 – 2006

Understand default premium – page 473-474

2727Ch14 – MBA 566

Credit Risk and CDO

• Collateralized debt obligations (CDOs): a mechanism to reallocate credit risk in the fixed income markets (figure 14.12)

• SIV• Tranch• subprime market crisis