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Duration , Modified Duration, Convexity

Duration , Modified Duration, Convexity. 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 ?”. Example. 9900. 100. 6. 2.

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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

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