bus422 (ch 1& 2) 1 bond market overview and bond pricing 1. overview of bond market 2. basics of...
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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
BUS422 (Ch 1& 2) 3
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
BUS422 (Ch 1& 2) 5
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.
BUS422 (Ch 1& 2) 7
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
BUS422 (Ch 1& 2) 8
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
BUS422 (Ch 1& 2) 9
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)
BUS422 (Ch 1& 2) 10
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
BUS422 (Ch 1& 2) 11
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
BUS422 (Ch 1& 2) 12
Zero-coupon bonds
Price of zero-coupon bond: P0= M/(1+r)n
Example
BUS422 (Ch 1& 2) 13
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
BUS422 (Ch 1& 2) 14
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
BUS422 (Ch 1& 2) 16
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
BUS422 (Ch 1& 2) 17
Procedures of computing priceStep 1
Getting P’
Step 2
P’+30
Step 3
P=(P’+30)/1.025^0.33
BUS422 (Ch 1& 2) 18
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.
BUS422 (Ch 1& 2) 20
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%)
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