43.1 Define discount factor and use a discount function to compute present and future
values.
1. Fundamentals of bond valuation: present-value-based bond valuation model
Step 1. Estimate the cash flows over the life of the bond.
Step 2. Determine the appropriate discount rate.
Step 3. Calculate the present value of the estimated cash flows.
where
Asimpleexample:
Suppose a 5-year fixed income security exists with $1,000 face value and a 20% coupon rate.
The appropriate discount rate is 16% and the coupons are paid on a semiannual basis.
The calculator solution is:
2. Quotation conventions: Bonds are quoted on a percentage basis relative to par value $100
Types of bonds
Quotation
U.S. Treasury notes and bonds
1/32
92-8
Corporate and municipal bonds
1/8
101-1
-12+
Example
(92+8/32)% of par value
(101+1/8)% of par value
(101+12.5/32)% of par value
2
3. Discount factors
where
discount function
0
the present value of $1 to be received at the end of the period t
t
1
Note: The future value of $1 invested for time t is
0
t
1
Example1:Calculatingdiscountfactors
Treasury bond
1
2
3
4
5
Prices are from 5/17/14, with t+2 settlement
Coupon
Maturity
4.25%
11/19/14
7.25%
5/19/15
2.00%
11/19/15
12.00%
5/19/16
5.75%
11/19/16
Please generate the discount factors for the dates indicated.
Ans:
0
0.5
0
0.5
Time to Maturity
0.5
1
1.5
2
2.5
1
Discount Factor
0.9939
0.9880
0.9825
0.9731
0.9633
3
Price
101-16
105-31+
101-07
120-30
110-13+
43.2
arbitrage argument, and describe
how it can be applied to bond pricing.
43.5 Identify arbitrage opportunities for fixed income securities with certain cash flows.
43.4 Construct a replicating portfolio using multiple fixed income securities to match the
cash flows of a given fixed income security.
1. Law of one price:
Two securities or portfolios that have identical cash flows in the future, regardless of future
events, should have the same price.
2. Arbitrage profit:
profit without investing any money or being exposed to any risk. (i.e. earn the riskless return)
Example2:Identifyarbitrageopportunities
Maturity
YTM
Coupon
(annual payments)
Price
(% of par)
1y
2y
2y
4%
8%
8%
0%
0%
8%
96.154
85.734
100.000
The 2-year spot rate is 8.167%. Is there an arbitrage opportunity? If so, describe the trades
necessary to exploit the arbitrary opportunity.
Ans:
8%<8.167% means the bond is trading rich i.e., the bond price is too high
Suppose that the par value is 1,000,000
:
(
)
Arbitragestrategyandcashflowdiagram
Strategy
Buy a $1,000,000 of 2-year, 8% coupon bond
-1,000,000
+80,000
Short sell a $80,000 of 1-year ZCB at 96.154
+76,923.20
-80,000
Short sell a $1,080,000 of 2-year ZCB at 85.734
Total
+925,927.20
+2,850.40
4
+1,080,000
-1,080,000
0
0
43.3 Identify the components of a U.S. Treasury coupon bonds, and compare and
contrast the structure to Treasury STRIPS, including the difference between
P-STRIPS and C-STRIPS.
1. STRIPS: to separate trading of registered interest and principle securities
Zero-coupon bonds issued by the Treasury are called STRIPS.
-STRIPS, TP, P) and coupon
(C-STRIPS, TINTs, INTs).
The Treasury can retire a STRIP by gathering the components to reconstitute the coupon
bond.
Advantages
Disadvantages
ZCB can be easily used to create any type of cash Illiquid ( created by larger financial institutions)
flow stream and thus match asset with liability
Shorter-term C-STRIPS tend to trade rich.
cash flows. This mitigates reinvestment risk.
Longer-term C-STRIPS tend to trade cheap.
ZCB are more sensitive to interest rate changes
P-STRIPS typically trade at fair.
than coupon bonds. This could be an issue for
Large institutions can potentially profit from
asset-liability management or hedging
STRIPS mispricing.
purposes.
2. Treasury STRIPS:
The Treasury does not issue zero-coupon notes and bonds. However, because of the demand
for zero-coupon instruments with nocreditrisk and a maturity larger than one year, the private
sectors have created such securities called Treasury STRIPS.
Example3:IdentifySTRIPS
Which of the following statements about STRIPS is correct? STRIPS:
I. have less interest rate sensitivity than coupon bonds.
II. tend to be highly liquid.
A. I only.
B. II only.
C. Both I and II.
D. Neither I nor II.
Ans: D
5
43.6
accrued interest with respec
ect to bond pricing.
43.7 Describe the common day--count conventions used in bond priciing.
Quoted price (Flat price/Clean price)
Full price
(Dirty price)
Accrued interest
Dirty price = Quoted p
price + Accrued interest since last coup
upon date
Fullprice: the price paid by a bu
buyer
Quotedprice: the price appeariing on trading screen
Accrued interest
106 days
Feb. 15, 2014
Previous coupon
payment date
75 days
Jun. 1. 201
2014
Settlementt
date
Aug. 15, 2014
Next coupon
payment date
Actual/Actual U.S. Treasury bond
bonds
onds, municipal bonds, and bonds issued
d by U.S. government
U.S. corporate bo
30/360
Actual/360
agencies
U.S. Money markket instruments
Example4:Computingaccruedin
nterest
A $1,000 par value U.S. corporate
e bond pays a semiannual 10% coupon. Assume
A
the last coupon
was paid 90 days ago and there a
are 30 days in each month. Compute the accrued
a
interest.
Ans:
6