1. Economics 434 – Financial Market Theory Tuesday, August 25, 2009 Tuesday, August 24, 2010Tuesday, August 26, 2010 Tuesday, August 31, 2010Tuesday, Sept 27-29, 2011 Economics 434 Theory of Financial Markets Professor Edwin T Burton Economics Department The University of Virginia

2. Economics 434 – Financial Market Theory Tuesday, August 25, 2009 Tuesday, August 24, 2010Tuesday, August 26, 2010 Tuesday, August 31, 2010Tuesday, Sept 27-29, 2011 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. Economics 434 – Financial Market Theory Tuesday, August 25, 2009 Tuesday, August 24, 2010Tuesday, August 26, 2010 Tuesday, August 31, 2010Tuesday, Sept 27-29, 2011 Stripping Securities Treat each payment of a note (or a bond) as a separate security See the textbook for more information

4. Economics 434 – Financial Market Theory Tuesday, August 25, 2009 Tuesday, August 24, 2010Tuesday, August 26, 2010 Tuesday, August 31, 2010Tuesday, Sept 27-29, 2011 Duration – the measure of risk in a default free world

5. Economics 434 – Financial Market Theory Tuesday, August 25, 2009 Tuesday, August 24, 2010Tuesday, August 26, 2010 Tuesday, August 31, 2010Tuesday, Sept 27-29, 2011 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. Economics 434 – Financial Market Theory Tuesday, August 25, 2009 Tuesday, August 24, 2010Tuesday, August 26, 2010 Tuesday, August 31, 2010Tuesday, Sept 27-29, 2011 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. Economics 434 – Financial Market Theory Tuesday, August 25, 2009 Tuesday, August 24, 2010Tuesday, August 26, 2010 Tuesday, August 31, 2010Tuesday, Sept 27-29, 2011 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. Economics 434 – Financial Market Theory Tuesday, August 25, 2009 Tuesday, August 24, 2010Tuesday, August 26, 2010 Tuesday, August 31, 2010Tuesday, Sept 27-29, 2011 Some mathematics By simple rearrangement Recall that P = the discounted sum of coupons:

9. Economics 434 – Financial Market Theory Tuesday, Sept 27, 2011 Continuing Rearranging gives: P P

10. Economics 434 – Financial Market Theory Tuesday, August 25, 2009 Tuesday, August 24, 2010Tuesday, August 26, 2010 Tuesday, August 31, 2010Tuesday, Sept 27-29, 2011 Duration Equals McCauley Duration for a treasury bond or note PP Duration McCauley Duration Is approximately equal to 1

11. Economics 434 – Financial Market Theory Tuesday, August 25, 2009 Tuesday, August 24, 2010Tuesday, August 26, 2010 Tuesday, August 31, 2010Tuesday, Sept 27-29, 2011 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