Duration , Modified Duration, Convexity

# Duration , Modified Duration, Convexity

## Duration , Modified Duration, Convexity

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1. Duration , Modified Duration, Convexity

2. Duration • Weighted time (in years) , weighted by the present value of the cashflows . loosely “How many years does it take for the PV of payments to meet the price ?”

3. Example 9900 100 6 2 It is correct to say that it will take 6 years for this loan to be repaid, but for an investor this number will be misleading , since the greatest portion of the loan is paid in two years and only a small amount remains after that .

4. Example 9900 100 6 2

5. Example 9900 100 6 2 Payment at year two represent 99.315% of loan amount While last payment is only 0.68%

6. Example 9900 100 6 2 Payment at year two represent 99.315% of loan amount While last payment is only 0.685185%

7. Example 2 G 5000 2000 1500 120 5 2 3 6

8. Example 2 G 5000 2000 1500 120 5 2 3 6

9. Example 2 G 5000 2000 1500 120 5 2 3 6

10. Duration • In General 1 5 2 3 4

11. Duration • In General (FOR CONSTANT PAYMENTS of 1 for n years) 1 5 2 3 4

12. Duration • In General (FOR CONSTANT PAYMENTS of 1 ) 1 5 2 3 4

13. Duration • In General (FOR BONDS priced at par) 1 5 2 3 4

14. Duration • In General (FOR BONDS priced at par with m-thly payments) 1 5 2 3 4

15. Exercise • A 20-year bond pays semiannual coupons of 7.4% and is priced at par . Calculate the duration.

16. Exercise • A 20-year bond pays semiannual coupons of 7.4% and is priced at par . Calculate the duration.

17. Exercise • A 20-year bond pays semiannual coupons of 7.4% and is priced at par . Calculate the duration.

18. Price as a function of Yield Rate

19. Price as a function of Yield Rate

20. Example The Macaulay duration of a 10–year annuity–immediate with annual payments of \$1000 is 5.6 years. Calculate the Macaulay duration of a 10–year annuity–due with annual payments of \$5000.

21. Example The Macaulay duration of a 10–year annuity–immediate with annual payments of \$1000 is 5.6 years. Calculate the Macaulay duration of a 10–year annuity–due with annual payments of \$5000.

22. Duration of A portfolio

23. Price as a function of Yield Rate

24. Price Sensitivity

25. Modified Duration/Volatility

26. Modified Duration and Duration

27. Modified Duration-Example

28. Modified Duration-Example =-171.0933986-1643.854213

29. Convexity

30. Convexity-Example

31. Convexity-Example