fixed income

Topics: Price, Marketing, Bond Pages: 15 (643 words) Published: November 2, 2014
Chapter 1
Prices, Discount Factors, and 
Arbitrage

STARTING WITH COUPON BONDS
• Three aspects: In May 2010 the U.S. Treasury 
sold a bond with 
– a coupon rate of 2  % and 
– a maturity date of May 31, 2015
– a payment frequency of two a year, six 
months apart
s of May 31, 2015”
• This bond is called “
Coupon rate

9/5/2013

Coupon frequency, “s” 
is for “semi‐annual”
L. Wu

maturity

2

Cash Flow of the Bond
• The unit for bond purchasing is $1,000.
• Suppose that an investor purchases $1m face 
value of the bond, i.e., 1,000 units.
• The the coupon payment is calculated 
according to

Year fraction

9/5/2013

Coupon rate

Face value

L. Wu

3

Cash Flow of the Bond, cont’d
Table 1.1: Cash Flows of the U.S. 2 ⁄ from books of May 31, 2015 

Date
"11/30/2010"
"5/31/2011"
"11/30/2011"
"5/31/2012"
"11/30/2012"
"5/31/2013"
"11/30/2013"
"5/31/2014"
"11/30/2014"
"5/31/2015"
9/5/2013

Coupon
Payment
$10, 625
$10, 625
$10, 625
$10, 625
$10, 625
$10, 625
$10, 625
$10, 625
$10, 625
$10, 625
L. Wu

Principal
Payment

$1, 000, 000
4

Government Bonds
• US Treasury
• Exchange Fund Bills & Notes Fixings (Hong 
Kong)

9/5/2013

L. Wu

5

Mid‐Prices of Selected Bonds

9/5/2013

L. Wu

6

DISCOUNT FACTORS
• The discount factor for a particular term gives 
the value today, or the present value, of one 
unit of currency to be received at the end of 
that term. 
• Denote the discount factor for t years by d(t).  • Let d(.5) =0.99925, then the PV of $1 to be 
received in six months is 99.925 cents.
• The present value of the cash flow $1,050,000 
in six month is 
.
9/5/2013

L. Wu

7

Bootstrapping the Discount Factors
• A coupon bond can be considered as a 
portfolio of zero‐coupon bonds.
• Given the prices of coupon bonds of 
consecutive maturities with six months gap, 
one can bootstrap the prices of zero‐coupon 
bonds

9/5/2013

L. Wu

8

Bootstrapping the Discount Factors
• Each row of Table 1.2 implies an equation for 
discount factors:
.99925
.99648

.99135
9/5/2013

L. Wu

9

Discount Factors
Coupon
1.250%

Maturity
"11/30/2010"

Price
100.55

Discount Factors
0.999254658

4.8750%

"5/31/2011"

104.513

0.996483873

4.500%

"11/30/2011"

105.856

0.991350497

4.75%

"5/31/2012"

107.966

0.985315395

3.3750%

"11/30/2012"

105.869

0.975199189

3.500%

"5/31/2013"

106.76

0.96414441

2%

"11/30/2013"

101.552

0.946933188

2.25%

"5/31/2014"

101.936

0.931718009

2.1250%

"11/30/2014"

100.834

0.915836248

Table 1.2

9/5/2013

L. Wu

10

THE LAW OF ONE PRICE
• Consider another U.S. bond, the ¾s of 
November 30, 2011, which is NOT included in 
Table 1.2. How should it be priced?
• Using the discount factors just obtained, we 
can present value the cash flow: 
• But, the market price is 100.19!
• An opportunity!
9/5/2013

L. Wu

11

Market Prices vs. Fair Prices

Table 1.4: Market Prices for Three U.S. Treasury Notes as of May 28, 2010 

Bond
PV
Price
PV−Price

⅞s 5/31/11
100.521
100.549
 −.028

¾s 11/30/11
100.255
100.19
0.065

rich

9/5/2013

¾s 5/31/12
100.022
99.963
0.059

cheap

L. Wu

12

ARBITRAGE TRADE

9/5/2013

L. Wu

13

Profit and Loss
• If you 
– Long the ¾s at the market price of 100.19 
for the face value of 100
– Short the portfolio of the three bonds at 
their market prices with face value F1, F2
and F3 , at the cost of 100.255
• You make a profit of $0.065, or ¢6.5
• Not exciting at all.
9/5/2013

L. Wu

14

P&L
• However, if you trade $500m face value, then 
.

$325,000

That is likely to be exciting.

9/5/2013

L. Wu

15...
Continue Reading

Please join StudyMode to read the full document

You May Also Find These Documents Helpful

  • Fixed Income and Group Project Essay
  • Essay about Question on Fixed Income Securities
  • 644 Minor proj Essay
  • Fixed income securities Essay
  • Fixed Income Arbitrage Essay
  • W-Fixed Income Securities Essay
  • HBS Case Fixed Income Valuation Essay
  • FNCE 4820 Fall 2013 Midterm 1 with Answers Essay

Become a StudyMode Member

Sign Up - It's Free