1. Economics 434 Financial Markets Professor Burton University of Virginia Fall 2015 October 20, 2015

2. Present Value is the most Crucial Concept in Finance Value of future stream of payments As valued today Emphasis on “discounting” future revenue streams Common practice to use higher rates to reflect higher uncertainty of receipt of future payments

3. Default Free Securites (Sovereign Debt) US Treasuries ($ 18 trillion outstanding) – Bills (less than one year in original maturity) – Notes (ten years or less, longer than one year) – Bonds (greater than ten years at issuance) Random facts – Bills are called coupon and/or discount issues: 3 mo, 6 mo, year bills. Year assumed to be 360 days. – Notes and bonds are “coupon” issues; pay fixed coupons twice yearly October 20, 2015

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

5. 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

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

7. Economics 434 – Financial Market Theory Tuesday, Oct 20, 2015 Continuing Rearranging gives: P P

8. Duration Equals McCauley Duration for a treasury bond or note PP Duration McCauley Duration Is approximately equal to 1

9. Duration Equals McCauley Duration for a treasury bond or note PP Duration McCauley Duration Is approximately equal to 1

10. 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

11. In words 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”

12. 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

13. National Debt in US $ 18,151,323 as of July 31, 2015 Funded debt: $ 13,135 Trillion (GDP 18) Trillion)

14. Yield curve Junk bonds TreasuriesCorp Bonds Rates Maturities

15. October 20, 2015