1

Bond Price, Yields, and Returns

Different Bond Types Bond Price Bond Yield Bond Returns Bond Risk Structure

2

Face or par value Coupon rate

Zero coupon bond Compounding and payments

Accrued Interest Indenture

Bond Characteristics

3

Accrued Interest

periodcouponinDays

periodAIinDayscoupondollarannualAI

___

___

2

__

Example on page 447

4

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

5

Figure 14.2 Corporate Bond Listings

6

Secured or unsecured Call provision Convertible provision Put provision (putable bonds) Floating rate bonds Sinking funds

Provisions of Bonds

7

Principal and Interest Payments for TIPS

The above is index bond.

See pages 451-452.

Compute real returns in year 1, 2, 3

8

)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

9

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

10

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

11

Inverse Relation Between Prices and Yields

12

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

13

Yield Measures

Bond Equivalent Yield

7.72% = 3.86% x 2

Effective Annual Yield

(1.0386)2 - 1 = 7.88%

14

Current Yield

Annual Interest / Market Price

$70 / $950 = 7.37 %

15

Yield to Call

For callable bonds See example on page 454

16

Holding Period Return versus YTM

Reinvestment Assumptions Holding Period Return

Changes in rates affects returns Reinvestment of coupon payments Change in price of the bond

17

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

18

Holding-Period Return: Single Period

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

where

I = interest payment

P1 = price in one period

P0 = purchase price

19

Example (Single period analysis)

CR = 8%

YTM = 10%

N=10 years

Semiannual Compounding

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

20

Horizon Analysis (multiple period)

Example 14.6 – page 456

21

Mortgage Example

Say you are interested in buying a 2-bedroom condo in Boston. The price is $300,000. You have a 30-year 3.5% APR mortgage with 20% down payment.

(1)What would be the monthly mortgage payment?

(2)What if you have 15-year mortgage with the same APR?

(3)Suppose you could rent the place out and the rent you collect will cover your mortgage payment. What would be the annual return of your investment if the condo value stays constant.

22

Zero-coupon Bonds and Treasury Strips Zero coupon bonds – page 459

Short term treasuries Long term zero coupons Treasury may strip payments from treasury coupon

bonds -- STRIPS

23

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

After-tax return – see page 478.

24

Rating companies (P 461) Moody’s Investor Service Standard & Poor’s Fitch

Rating Categories Investment grade Speculative grade Page 462

Default Risk and Ratings

25

Coverage ratios Leverage ratios Liquidity ratios Profitability ratios Cash flow to debt

Factors Used by Rating Companies

26

Sinking funds Subordination of future debt Dividend restrictions Collateral

Protection Against Default

27

Yields on Long-Term Bonds, 1954 – 2006

Understand default premium – page 473-474

28Chapter 1: Overview

14-28

Credit Default Swaps

A credit default swap (CDS) acts like an insurance policy on the default risk of a corporate bond or loan.

CDS buyer pays annual premiums. CDS issuer agrees to buy the bond in a default or pay

the difference between par and market values to the CDS buyer.

29Chapter 1: Overview

14-29

Credit Default Swaps

Institutional bondholders, e.g. banks, used CDS to enhance creditworthiness of their loan portfolios, to manufacture AAA debt.

CDS can also be used to speculate that bond prices will fall.

This means there can be more CDS outstanding than there are bonds to insure!

30Chapter 1: Overview

14-30

Figure 14.12 Prices of Credit Default Swaps

3114-31

Credit Risk and Collateralized Debt Obligations (CDOs)

Major mechanism to reallocate credit risk in the fixed-income markets Structured Investment Vehicle (SIV) often

used to create the CDO Loans are pooled together and split into

tranches with different levels of default risk.

Mortgage-backed CDOs were an investment disaster in 2007

3214-32

Figure 14.13 Collateralized Debt Obligations