BUS422 (Ch 1& 2) 1

Bond Market Overview and Bond Pricing

1. Overview of Bond Market

2. Basics of Bond Pricing

3. Complications

4. Pricing Floater and Inverse Floater

5. Pricing Quotes and Accrued Interest

BUS422 (Ch 1& 2) 2

What is A Bond?

Bond: a debt instrument requiring the issuer (debtor) to repay to lender/investor the amount borrowed plus interest over a specified period of time

• Plain vanilla bonds

• Advanced debt contract – mortgage pass-through securities

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Most Generic Classification

Government bonds – low/no risk, low yield, low expected returns

-- return is high when yield goes down

Risky bonds – non-government bonds, including corporate bonds, municipal bonds, mortgage securities (subprime market securities)

BUS422 (Ch 1& 2) 4

Sectors of US Bond MarketTreasury Sector

have you heard of saving bonds?

Agency Sector

Municipal Sector

Corporate Sector

Asset-Backed Security Sector

Mortgage Sector

See: www.investinginbonds.com

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Billion Dollars.

Muni U.S.

Treasury Mortgage-

Related Corpe

Fed Agencies

Money Market

Asset- Backed

Bond Total

Stock Total

1985 859.5 1,437.7 372.1 776.5 293.9 847.0 0.9 4,587.6 2006.1

1986 920.4 1,619.0 534.4 959.6 307.4 877.0 7.2 5,225.0 2337.4

1987 1,010.4 1,724.7 672.1 1,074.9 341.4 979.8 12.9 5,816.2 2934.5

1988 1,082.3 1,821.3 772.4 1,195.7 381.5 1,108.5 29.3 6,391.0 2680.2

1989 1,135.2 1,945.4 971.5 1,292.5 411.8 1,192.3 51.3 7,000.0 2970.3

1990 1,184.4 2,195.8 1,333.4 1,350.4 434.7 1,156.8 89.9 7,745.4 3153.7

1991 1,272.2 2,471.6 1,636.9 1,454.7 442.8 1,054.3 129.9 8,462.4 3268.9

1992 1,302.8 2,754.1 1,937.0 1,557.0 484.0 994.2 163.7 9,192.8 4171.5

1993 1,377.5 2,989.5 2,144.7 1,674.7 570.7 971.8 199.9 9,928.8 4713.2

1994 1,341.7 3,126.0 2,251.6 1,755.6 738.9 1,034.7 257.3 10,505.8 5468.3

1995 1,293.5 3,307.2 2,352.1 1,937.5 844.6 1,177.3 316.3 11,228.5 5415.9

1996 1,296.0 3,444.7 2,486.1 2,122.2 925.8 1,393.9 404.4 12,073.1 7422.6

1997 1,318.7 3,441.8 2,680.2 2,359.0 1,022.6 1,692.8 535.8 13,050.9 9147.0

1998 1,402.9 3,340.5 2,955.2 2,708.6 1,300.6 1,977.8 731.5 14,417.1 11,430.9

1999 1,457.2 3,266.0 3,334.2 3,046.5 1,620.0 2,338.8 900.8 15,963.5 14,743.5

2000 1,480.9 2,951.9 3,564.7 3,358.6 1,854.6 2,662.6 1,071.8 16,945.1 17,941.8

2001 1,603.7 2,967.5 4,125.5 3,835.4 2,149.6 2,566.8 1,281.1 18,529.9 16,980.8

2002 1,763.1 3,204.9 4,704.9 4,094.1 2,292.8 2,546.2 1,543.3 20,149.2 14,138.9

BUS422 (Ch 1& 2) 6

Stocks vs. Bonds

1. Different Characteristics

2. Different Markets Stocks: traded on exchanges and OTC markets: NYSE, AMEX, NASDAQ Bonds: traded on OTC markets 3. Similarity: Buy stocks and bonds through online traders.

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Returns of Aggregate Stocks, Gov Bonds, Corporate Bonds

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

1985 1990 1995 2000 2005

Year

Re

turn

s

ret_stock ret_gov ret_credit

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Overview of Bond Features• Term to maturity• Coupon rate

– Fixed rate bonds– Floating rate bonds

—Reference rate + quoted margin• Principal/Face Value• Interest rate/yield to maturity• Price

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Example of a fixed payment bond

10 years, face value $1000, coupon rate 8%, semi-annually paid, interest rate 9%. What is the bond price?

45/(1+0.04)+45/(1+0.04)^2+… + 1045/(1+0.04)^10

There are many variations in bond designs: (1) deferred-coupon (2) amortizing securities: securities with a schedule of

periodical principle repayments. (3) options could be embedded (page 5)

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FV versus PV

Future Value: Pn= P0(1+r)n

Present Value: P0= Pn/(1+r)n

Future value for a regular annuity

Present value for a regular annuity

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Examples

1. Cash flow (1): you receive $100 in year 1, $200 in year 2, $300 in year 3. Interest rate is 9%. What is the value of the cash flow?

2. Cash flow: you need to pay $100 in year 1, $200 in year 2, and $300 in year 3. Interest rate is 9%. How much you need invest today to pay for this loan?

3. Coupon Bond: 2 years, face value $1000, coupon rate 8%, semi-annually paid, interest rate 9%. What is the bond price?

Using your financial calculator

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Zero-coupon bonds

Price of zero-coupon bond: P0= M/(1+r)n

Example

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Complications

• If the next payment is due in fewer than 6 months

• Cash flows may not be known

• What is the appropriate required yield and whether one discount rate can be applied to all cash flows

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Next Due Payment < 6 months

n

tnt rr

M

rr

CP

111 )1()1()1()1(

periodmonth -sixin days

couponnext and settlementbetween days

In fact, this is a 3-step approach to calculate bond price. (1) In the first step, we compute bond price if I buy the bond in the next payment date (i.e., I won’t get any payment for it):

1

11)1()1(

n

tnt r

M

r

CP

(2) Add in the payment I receive in the next payment date, then

n

tnt

n

tnt r

M

r

C

r

M

r

CCP

111

1

11 )1()1()1()1(

(3) Discount the above price back to the date I purchase the bond. The idea is to suppose I buy the bond right before the next payment day, thus I can have the next payment, then discount the value back to time 0.

BUS422 (Ch 1& 2) 15

Price Quoted and Accrued Interest

Price quoted: 100: meaning 100% of its par value/face value

Accrued interest: when an investor purchases a bond between coupon payments, the investor must compensate the seller of the bond for the coupon interest earned from the time of the last coupon payment to the settlement date of the bond.

for a treasury bond, accrued interest is based on the actual number of days the bond is held by the seller.

Full price/dirty price = price + accrued interest

Clean price

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Example

A bond face value $1000, YTM=5%, coupon rate=6% semiannually paid, maturity=5 years. The bond was issued on 7/1/2003, and bought on 11/1/2005. What is price of the bond.

v=? 0.33

n=? 6

FV=1000; I/Y=2.5; PMT=30; N=5 P’=1023.23

P=(P’+30)/1.025^0.33=1044.62

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Procedures of computing priceStep 1

Getting P’

Step 2

P’+30

Step 3

P=(P’+30)/1.025^0.33

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Example (cont’d)

What is the accrued interest of the bond?

30*2/3=20

What is the dirty price of the bond?

Dirty price=1044.68

Clean price=1044.68-20=1024.68

BUS422 (Ch 1& 2) 19

Floater and Inverse Floater

See Exhibit 2-4.Inverse’s price = collateral’s price – floater’ price

Collateral is the fixed-rate security from which the inverse floater is created

Floor: the minimum interest rate on the inverse floaterCap: the maximum interest rate on the floaterThe sum of interests paid on floater and inverse floater

must always equal interests on the collateral.

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Risk Associated with Bonds

1. Interest-rate risk2. Reinvestment risk3. Call risk4. Credit risk5. Inflation risk6. Exchange-rate risk7. Liquidity risk – institutional investor must trade

frequently in some extent8. Risk risk

BUS422 (Ch 1& 2) 21

Exercises1. Is there risk when investing in treasury bonds, supposing

there is no chance that the US government will default.

2. Ignore any complication, write down the formula for a 3-year fixed payment coupon bond. Annual coupon rate is c, and coupons are semiannually paid. Face value is m, interest rate/discount rate/yield to maturity is r.

3. Questions 9 and 10 of chapter 1

4. Questions 7, 9, and 11 of chapter 2 (7. $13,111,510; 9. A. 541.25; b. –5.94%; c. 1077.95; d. 1000, -7.23%)