Lecture 10 Debt Securities Ana Nora Evans 403 Kerchof [email protected] ans5k/ Math 1140 Financial Mathematics

Lecture 10Debt Securities

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

Math 1140 Financial Mathematics

Math 1140 - Financial Mathematics 2

Who won the men’s soccer game last night?

A) UVa

B) Liberty

C) I don’t know, I was

doing homework.

D) I don’t know,

I was out partying.

E) What’s soccer?

Correct answer: B, Liberty won 2-0.

3Math 1140 - Financial Mathematics

Extra credit opportunity

I will give extra credit to students finding errors in the class slides, class notes and homework solutions!


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Treasury Bills

A treasury bill (T-bill) is a short-term debt obligation backed by the U.S. government with a maturity of less than one year. The face value or par amount of a T-bill is the amount paid at maturity. The term of a T-bill can be 4 weeks (28 days), 13 weeks (91 days), 26 weeks (182 days) or 52 weeks (360 days).


T-bill priceT-bills are auctioned. First auction took place on December 17, 1929.

The price or bid of a T-bill is a percentage of the face value.

The purchase price is the money paid for the T-bill.

Example: To buy a $1,000 T-bill priced at 98.8 you pay $988.00 . The purchase price is $988. The return is $1,000 - $988 = $12.


The discount yield is the discount rate of the T-bill using Banker’s rule.

Amount = face value (FV)

Proceeds = purchase price (PP)

Term = term of the bill (28, 91, 182, 360 days)

We calculate the discount rate.

Discount Yield (Bank Discount)


Banker’s rule is a rule for calculating the term using exact time and ordinary interest.

Exact time – calculate the precise number of days

Ordinary interest – divide by 360

If m be the number of days of the term then

t = m/360

Banker’s Rule


Price or bid (B) is the percentage of the face value paid.

Purchase price(PP) is the money paid for the T-bill.

PP= B/100 * FV

The purchase price of a $1,000 T-bill bought with a bid of 99.8 is:

PP = (99.8/100)* $1000

= $998

Purchase price


Given:

Amount S

Proceeds P

Term t

D = S - P

D = Sdt

Discount rate


Amount(S) = FV

Proceeds(P) =

PP = (B/100)*FV

The term =

t = m/360

d = (S-P)/(St)

d = (S-P)*360/(Sm)

d = (FV- B/100 * FV)*360/(FVm)

d = (1- B/100)*360/(m))

1001(

360 B

md

)1(360

FV

PP

md


The discount yield is called rate of return in the textbook.

Find the rate of return of a 182-day T-bill auctioned at an average price of $9,659.30 per $10,000 face value.


Questions


Monday 11:00 – 12:30

Tuesday 3:30 – 5:00

Friday 2:30 – 3:30

Example:

If you can make it to office hours Monday 12:00 – 12:30 you should answer A.

Answer B only if are committed for the entire session for all days.

Choose one of:

A) I can come at least one of the sessions (this includes part of a session)

B) I can not make any of the scheduled office hours

New Office Hours


A) I received an email on Monday with subject ‘lecture 9 slides and homework 4’

B) I did not receive an email on Monday with subject ‘lecture 9 slides and homework 4’

Emails


Would you be interested in extra review sessions of chapters 1 and 2 to help you improve your grade?

A) Yes

B) No

Review Sessions


Investment Yield (Coupon Equivalent)The investment yield is the interest rate of the T-bill using exact interest.

Maturity value = face value

Principal = purchase price

Term = term of the bill (28, 91, 182, 360 days)

We calculate the interest rate.


Maturity Value(S) = FV

Principal(P) = p FV

Let m be the number of days of the term.

Use exact interest.

t = m/365

I = S – P = Pit

i = (S-P)/(Pt)

i = (S-P)*365/(Pm)

PP

PPFV

mi

365

B

B

mi

100365


Find the investment yield of a 182-day T-bill auctioned at an average price of $9,659.30 per $10,000 face value.


Questions



Alice bought a 4-week $10,000 T-bill at a discount yield 0.02%. What is the price of the T-bill?

9/1/2011


What about 09/07/2011?


What does the 0% bank discount rate tell you?



Questions


Treasury notes, or T-notes, are issued in terms of 2, 3, 5, 7, and 10 years, and pay interest every six months until they mature. The interest is called coupon.

The price of a note may be greater than, less than, or equal to the face value of the note.

When a note matures, you are paid its face value.

Why would anyone pay more than the face value for a T-note?

Treasury Notes



References

http://www.treasurydirect.gov/indiv/research/indepth/tbills/res_tbill.htmhttp://www.newyorkfed.org/aboutthefed/fedpoint/fed28.htmlhttp://www.treasurydirect.gov/indiv/research/indepth/tnotes/res_tnote.htm

http://www.treasurydirect.gov/indiv/research/indepth/tbills/res_tbill.htm

http://www.treasurydirect.gov/indiv/research/indepth/tbills/res_tbill.htm

http://www.newyorkfed.org/aboutthefed/fedpoint/fed28.html

http://www.newyorkfed.org/aboutthefed/fedpoint/fed28.html

http://www.treasurydirect.gov/indiv/research/indepth/tnotes/res_tnote.htm

http://www.treasurydirect.gov/indiv/research/indepth/tnotes/res_tnote.htm


Next time

Compound Interest

Friday

Read sections 3.1, 3.2

First Exam (max 15 points):

26 September 2011 at 7pm

Location to be announced

Charge

Documents

Lecture 10 Debt Securities Ana Nora Evans 403 Kerchof [email protected] ans5k/ Math 1140 Financial Mathematics