lecture 37 - with inkans5k/math1140/lecture 37 - with ink.pdf · 18/11/2011 2 math 1140 -financial...

18/11/2011

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Lecture 37

Bonds

Ana Nora Evans 403 [email protected]://people.virginia.edu/~ans5k

Math 1140 Financial Mathematics

Math 1140 - Financial Mathematics

Last Time

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A bond is a legal promise to pay the owner of the

bond, regular payments, ending at a specified date

in the future.

On the bond are specified the face value (par

value), F, and the coupon rate (bond rate), r.

The coupon period is the time interval between

two payments.


Last Time

The regular payment, called coupon, is the interest

on the face value of the bond, F, for one coupon

period, at the coupon rate, r.

The coupon is equal to Fr.

The last payment is called the maturity value

(redemption value), R.

3 Math 1140 - Financial Mathematics

The issuer of the bond, usually a corporation, a

state, local or state government, sells the rights to

the coupon payments and the redemption value to

an entity (investor).

Who borrows money?

A) The investor.

B) The issuer of the bond.

C) Mickey Mouse.

D) Nobody.

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The price of the bond is the amount paid by the

owner of the bond to the issuer of the bond.

The price is calculated using the desired yield rate

per coupon period.

5

i

iFriRP

n

n

−

−+−

++=)1(1

)1(


A) When the yield increases, the price increases.

B) When the yield increases, the price decreases.

C) When the yield increases, the price does not

change.

D) None of the above.

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Math 1140 - Financial Mathematics7 Math 1140 - Financial Mathematics

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Bonds rating and junk bonds.

The book value of a bond.

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The credit rating of a bond is a financial indicator

to potential investors.

The credit rating of a bond is assigned by a credit

rating agency registered with the Securities and

Exchange Commission (SEC).

Examples: Standard & Poor's, Moody’s.


Moody’s S&P Capacity of the issuer to meet its obligations

Aaa AAA Extremely strong

Aa1 AA+ Very strong

Aa2 AA

Aa3 AA-

A1 A+ Strong

A2 A

A3 A-

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S&P Rating

US treasury bonds AA+

Germany AAA

Spain AA-

China AA

Home Depot A-

Middlesex Cnty, NJ AA+

Math 1140 - Financial Mathematics 11


Baa1 BBB+ Adequate

Baa2 BBB

Baa3 BBB-

Ba1 BB+ Less vulnerable

Ba2 BB

Ba3 BB-

B1 B+ More vulnerable

B2 B

B3 B-

S&P Rating

Romania BBB+

Mozambique B+

Ukraine B+



Caa CCC Currently vulnerable

Ca CC Highly vulnerable

C Highly vulnerable (a bankruptcy petition may have been filled)

C D Failed to pay one or more of its financial obligations when it

became due.

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S&P Rating

Greece C

Jefferson County's sewer

system bonds

C

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Greek Bonds Yield


Greece’s Bond Haircut

“Negotiators from the Institute of International Finance, a

consortium of Greek bondholders, have agreed to swap

their current bonds for new ones worth 50% of their

current value, though the final figure has still to be

thrashed out.”

The Guardian, 16 Nov 2011

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Junk Bonds

A junk bond is a bond with a rating of BB or lower.

A junk bond has a high risk of default and offers a

high-yield.

A junk bond is also called a high-yield bond or a

speculative bond.

15Math 1140 - Financial Mathematics

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The Book Value

The book value of a bond at a given time is the

value of the remaining coupons plus the

redeeming value at the given time.

Similar to the outstanding value of a loan.


The Book Value

Consider a bond with face value, F, coupon rate, r,

yield, i, and n coupon payments.

The book value of the bond after the kth payment

is

18

i

iFriR

kn

kn

)()( )1(1

)1(−−

−−+−

++

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Suppose that a $2000 12-

year par-value bond pays

interest at 9% convertible

semi-annually.

Find the book value

immediately after the 11th

coupon has been paid, if

the yield rate is 7%

convertible semi-annually.

F = $2,000

R = $2,000

r = 0.09/2 = 0.045

i = 0.07/2 = 0.035

n = 12×2 = 24

k=11

There are 13 payments left.

The book value is:

19

035.0

)035.1(1045.0000,2$)035.1(000,2$

1313

−

−−

×+


Suppose that we have a 14-year par-value bond that pays interest at 8% convertible semi-annually. If the book value immediately after payment of the 13th coupon is $1269.10 at a yield rate of 7% convertible semi-annually, what is the face value of the bond?

n = 14×2 = 28

r = 0.08/2 = 0.04

k = 13

BV13 = $1,269.1

i = 0.07/2 = 0.035

F = ?

20

i

iFriRBV

kn

kn

k

)()( )1(1

)1(−−

−−+−

++=

i

iFriFBV

kn

kn

k

)()( )1(1

)1(−−

−−+−

++=

Math 1140 - Financial Mathematics21 Math 1140 - Financial Mathematics

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lecture 37 - with inkans5k/math1140/lecture 37 - with ink.pdf · 18/11/2011 2 math 1140 -financial...

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