Post on 16-Dec-2015
Lecture 10Debt Securities
Ana Nora Evans 403 KerchofAnaNEvans@virginia.eduhttp://people.virginia.edu/~ans5k/
Math 1140 Financial Mathematics
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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.
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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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Problem 1Problem 2Problem 3
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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).
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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.
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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)
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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
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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
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Given:
Amount S
Proceeds P
Term t
D = S - P
D = Sdt
Discount rate
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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
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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.
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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
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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
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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
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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.
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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
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Find the investment yield of a 182-day T-bill auctioned at an average price of $9,659.30 per $10,000 face value.
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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
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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
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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