# Lecture 10 Debt Securities Ana Nora Evans 403 Kerchof Math 1140 Financial Mathematics.

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Lecture 10 Debt Securities Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu http://people.virginia.edu/~ans5k/ Math 1140 Financial Mathematics

Math 1140 - Financial Mathematics Who won the men’s soccer game last night? A)UVa B)Liberty C)I don’t know, I was doing homework. A)I don’t know, I was out partying. A)What’s soccer? Correct answer: B, Liberty won 2-0. 2

Math 1140 - Financial Mathematics Extra credit opportunity I will give extra credit to students finding errors in the class slides, class notes and homework solutions! 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). 6

Math 1140 - Financial Mathematics T-bill price T-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. 7

Math 1140 - Financial Mathematics 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) 8

Math 1140 - Financial Mathematics 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 9

Math 1140 - Financial Mathematics 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 10

Math 1140 - Financial Mathematics Given: Amount S Proceeds P Term t D = S - P D = Sdt Discount rate 11

Math 1140 - Financial Mathematics 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) 12

Math 1140 - Financial Mathematics 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. 13

Math 1140 - Financial Mathematics Questions 14

Math 1140 - Financial Mathematics 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 15

Math 1140 - Financial Mathematics 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 16

Math 1140 - Financial Mathematics 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 17

Math 1140 - Financial Mathematics 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. 18

Math 1140 - Financial Mathematics 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) 19

Math 1140 - Financial Mathematics Find the investment yield of a 182-day T-bill auctioned at an average price of \$9,659.30 per \$10,000 face value. 20

Math 1140 - Financial Mathematics Questions 21

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Math 1140 - Financial Mathematics 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 23

Math 1140 - Financial Mathematics What about 09/07/2011? 24

Math 1140 - Financial Mathematics What does the 0% bank discount rate tell you? 25

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Math 1140 - Financial Mathematics Questions 27

Math 1140 - Financial Mathematics 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 28

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Math 1140 - Financial Mathematics References http://www.treasurydirect.gov/indiv/research/ind epth/tbills/res_tbill.htm http://www.newyorkfed.org/aboutthefed/fedpoin t/fed28.html http://www.treasurydirect.gov/indiv/research/ind epth/tnotes/res_tnote.htm 30

Math 1140 - Financial Mathematics 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 31

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