# Question of Bond Markets, Analysis and Strategies by cob75748

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```									            Pricing of Bonds
Zvi Wiener
Based on Chapter 2 in Fabozzi
Bond Markets, Analysis and Strategies
Fall-02        http://pluto.mscc.huji.ac.il/~mswiener/zvi.html   EMBAF
Time value of money
How to calculate price of a bond
Why the price of a bond changes
Relation between yield and price
Relation between coupon and price
Price changes when approaching maturity
Floaters and inverse floaters
Accrued interest and price quotes

Zvi Wiener                Fabozzi Ch 2          slide 2
Time Value of Money
present value PV = CFt/(1+r)t

Future value FV = CFt(1+r)t

Net present value NPV = sum of all PV

-PV    5         5    5         5    105
4
5        105
PV                
t 1 (1  r ) (1  r )5
t

Zvi Wiener                        Fabozzi Ch 2          slide 3
Time Value
You have \$100 now and are going to deposit
it for 5 years with 6% interest.
What will be the final amount?
It depends on calculation method!
Yearly compounding: \$100*1.065
Semiannual compounding: \$100*1.0312
Monthly compounding: \$100*1.00560

Zvi Wiener              Fabozzi Ch 2               slide 4
Periodic Rate
Annual interest rateA
r=                             =
Number of periods in a year   n

Effective Rate
n
 A
1  r 
n
 1    1  R
 n
Zvi Wiener                  Fabozzi Ch 2       slide 5
Pricing of Bonds
T
Ct
PV  
t 1 (1  r )t

100
Zero coupon bond           price 
(1  r ) t

Zvi Wiener             Fabozzi Ch 2                   slide 6
Pricing of Bonds
T
Ct
PV  
t 1 (1  r )t

Term structure of interest rates

T
Ct
PV  
t 1 (1  rt ) t

Zvi Wiener                 Fabozzi Ch 2         slide 7
Yield
Yield = IRR = Internal Rate of Return
T
Ct
Pr ice  
t 1 (1  y ) t

How do we know that there is a solution?

Zvi Wiener                      Fabozzi Ch 2             slide 8
Example
Price calculation:

5    5     105
    2
    3  83.34
1.10 1.11 1.12
Yield calculation:

5       5          105
                        83 .34
1  y (1  y ) 2
(1  y ) 3

y  11.9278%
Zvi Wiener                 Fabozzi Ch 2               slide 9
Price-Yield Relationship
Price and yield (of a straight bond) move in
opposite directions.
price

yield
Zvi Wiener               Fabozzi Ch 2                slide 10
General pricing formula
n
Ct
P
t 1 (1  r ) v (1  r )t 1

days between settlement and next coupon
v
days in six months period

Zvi Wiener                        Fabozzi Ch 2            slide 11
Accrued Interest
Accrued interest = interest due in full period*
(number of days since last coupon)/
(number of days in period between coupon
payments)

Zvi Wiener                Fabozzi Ch 2                  slide 12
Day Count Convention
Actual/Actual - true number of days
30/360 - assume that there are 30 days in each
month and 360 days in a year.
Actual/360

Zvi Wiener               Fabozzi Ch 2                  slide 13
Floater

The coupon rate of a floater is equal to a

For example LIBOR + 50 bp.

Sometimes it has a cap or a floor.

Zvi Wiener                Fabozzi Ch 2             slide 14
Inverse Floater
Is usually created from a fixed rate security.
Floater coupon             = LIBOR + 1%
Inverse Floater coupon = 10% - LIBOR
Note that the sum is a fixed rate security.
If LIBOR>10% there is typically a floor.

Zvi Wiener                Fabozzi Ch 2                 slide 15
Price Quotes and Accrued Interest

Assume that the par value of a bond is \$1,000.
Price quote is in % of par + accrued interest
the accrued interest must compensate the
seller for the next coupon.

Zvi Wiener                Fabozzi Ch 2                 slide 16
Home Assignment
Chapter 2

Questions 2, 3, 7, 8, 11

Zvi Wiener                Fabozzi Ch 2   slide 17
FRM-99, Question 17
Assume a semi-annual compounded rate of
8% per annum. What is the equivalent
annually compounded rate?
A. 9.2%
B. 8.16%
C. 7.45%
D. 8%

Zvi Wiener              Fabozzi Ch 2            slide 18
FRM-99, Question 17
(1 + ys/2)2 = 1 + y
(1 + 0.08/2)2 = 1.0816 ==> 8.16%

Zvi Wiener                  Fabozzi Ch 2   slide 19
FRM-99, Question 28
Assume a continuously compounded interest
rate is 10% per annum. What is the equivalent
semi-annual compounded rate?
A. 10.25% per annum.
B. 9.88% per annum.
C. 9.76% per annum.
D. 10.52% per annum.

Zvi Wiener               Fabozzi Ch 2                 slide 20
FRM-99, Question 28
(1 + ys/2)2 = ey
(1 + ys/2)2 = e0.1
1 + ys/2 = e0.05
ys = 2 (e0.05 - 1) = 10.25%

Zvi Wiener                 Fabozzi Ch 2   slide 21
Mortgage example
You take a mortgage \$100,000 for 10 years
with yearly payments and 7% interest.
What is the size of each payment?
10
x
100 ,000  
t 1 (1  0.07 ) t

10
1
100 ,000  x          t              x  14.2378
t 1 1.07

Zvi Wiener                          Fabozzi Ch 2                 slide 22
Mortgage example
How much do you own bank after 3 first
payments?
7
14 .2378
 1.07 t  76 .7314
t 1

What is the fair value of your debt if interest
rates are 5%?
7
14 .2378
 1.05 t  82 .3849
t 1

Zvi Wiener                Fabozzi Ch 2                  slide 23

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