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Economics 434 Theory of Financial Markets

Economics 434 Theory of Financial Markets. Professor Edwin T Burton Economics Department The University of Virginia. Treasury Auction Schedule. Treasury Bills 3 mo and 6 mo bills every Monday (unless holiday) 4 week bill every Tuesday (unless Monday or Tuesday is a holiday

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Economics 434 Theory of Financial Markets

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  1. Economics 434Theory of Financial Markets Professor Edwin T Burton Economics Department The University of Virginia

  2. Treasury Auction Schedule • Treasury Bills • 3 mo and 6 mo bills every Monday (unless holiday) • 4 week bill every Tuesday (unless Monday or Tuesday is a holiday • Year bill – once a month • Treasury Notes and Bonds • 3, 10, and 30 year monthly – early in the month • 2, 5, and 7 year monthly – end of the month

  3. Stripping Securities • Treat each payment of a note (or a bond) as a separate security • See the textbook for more information

  4. Duration – the measure of risk in a default free world

  5. Do the following • Calculate present value of entire bond • Calculate each separate present value of each separate coupon payment • Then create fractions • Pres Value of first coupon/Total present value • Pres Value of second coupon/Total present value • Etc. • Weight each maturity time by its fraction: • ½ (PresVal ½) + 1 (Pres Val1) +…..10 (PresVal 10) • This average of the maturity is called “McCauley Duration”

  6. Now ask the question • If the yield on the issue changed by a small amount, how much would the price change • That is the definition of duration • Equals, roughly, the minus of McCauley Duration

  7. Formally How much does the price of the bond change given a small change in yield Really interested in percentage change of price for a small change in yield This is called “duration” -- percentage change in bond price for a small change in yield

  8. Some mathematics By simple rearrangement Recall that P = the discounted sum of coupons:

  9. Continuing Rearranging gives: P P

  10. Duration Equals McCauley Duration for a treasury bond or note P P Duration McCauley Duration Is approximately equal to 1

  11. In the case of treasury bills or any zero coupon bond • Duration is especially easy to calculate • Duration, in this case, equals maturity • 3 mo bill on date of issue, duration is ¼ • 6 mo bill on date of issue, duration is ½ • Year bill on date of issue, duration is slightly less than one. • Duration of 30 year coupon on newly issued 30 year bond is 30 • 30 year coupon is riskiest of all, one day treasury bill is least risky

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