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Economics 434 Financial Markets Professor Burton University of Virginia Fall 2013

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Treasury Bills Anything issued with less than 1 year in original maturity Everything else is a note or a bond Three main types – 4 week bill (30 day bill) – 3 month (90 day bill) – 6 month (180 day bill) – Year bill (360 day bill) Also, from time to time – Cash management bills

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Key facts about treasury bills Always have “original maturity” less than one year Quotes are “discounts” Year is assumed to be 360 days long Actual annual yield higher than quote because – Quote is a discount – Year has more days than 360

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Example: The Year Bill Assume the quote is 0.40 % Assume the principal amount is $ 1 million (always assume this in this class for treasury bills) What is the price of this bill? – Discount is.004 times $ 1 million = $ 4,000 – Price then must be $ 996,000 What is the annual yield of this bill? – Yield for 360 days is 4/996 =.004016 % – Yield for 365 days is 365/360 times.004016 % or.004072 or.4072 percent

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Example: The Three Month Bill Assume the quote is.10 % Assume the principal amount is $ 1 million (always assume this in this class for treasury bills) What is the price of this bill? – Discount is (.001 divided by 4) times $ 1 million = $ 250 – Price then must be $ 999,750 What is the annual yield of this bill? – Yield for 90 days is 250/999,750 =.0250006 % – Yield for 365 days is 365/900 times.0250006 % or.101414 percent

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General Principles To calculate annual yield – First calculate the amount of the discount Quote times t/360 times $ 1 million where is t is the days remaining to maturity – Then note that the amount of the discount is your profit and $ 1 million minus the discount is your cost, so that the yield for t days is: Yield for t days = discount/($ 1milion – discount) – Then annualize: Annual yield = (365/t) times (Yield for t days)

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US Treasury Notes and Bonds Assume that principal (payoff) amount is $ 100,000, paid at maturity date of bond Two payments annually, approx. six months apart If coupon is 10 percent, each payment is $ 5,000; if coupon is 1 percent, each payment is $ 500 Name is: coupon (plus) maturity date For example: 2 ½’s of AUG ‘23

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2 ½’s of August 2023 Pays $ 100,000 on Aug 15, 2013 Also pays $ 1,250 on Feb 15, 2014 and Aug 15, 2014 Similarly for every year until payment of $ 1,250 on Aug 15, 2013 plus the $ 100,000 payment on that same date Yield? Price?

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