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Duration & Convexity

Duration & Convexity. Hossein Abdoh Tabrizi Maysam Radpour. June 2011. Table of Contents. Bonds; risk & return tradeoff Maturity effect; interest rate volatility risk Duration Convexity. Bonds. Risk & return tradeoff.

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Duration & Convexity

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  1. Duration & Convexity Hossein Abdoh Tabrizi Maysam Radpour June 2011

  2. Table of Contents Bonds; risk & return tradeoff Maturity effect; interest rate volatility risk Duration Convexity

  3. Bonds Risk & return tradeoff

  4. Types of bonds based on option granted to the issuer or bondholder

  5. Factors effect bond return

  6. Risks of return

  7. Maturity Effects Interest rate volatility risk

  8. Price volatility in option-free bonds Price Yield to maturity

  9. Factors affecting interest rate volatility • Coupon rate • maturity • Yield to maturity • All other factors constant, the lower the coupon rate, the greater the price volatility. • All other factors constant, the longer the maturity, the greater the price volatility. • All other factors constant, the higher the yield level, the lower the price volatility.

  10. Percentage price change for Four Hypothetical BondsInitial yield for all four bonds is 6%

  11. Duration

  12. Duration

  13. Duration is elasticity

  14. Price equation of an option-free bond • P: price • C: periodical coupon interest • Y: yield to maturity • M: maturity value (face value) • N: number of periods

  15. First derivative of price equation

  16. Macaulay duration, Modified duration

  17. Example 1: Duration calculation • Duration for a 9% 5-year bond selling to yield 6% with semiannual coupon payments and face value of 100$ is:

  18. Example 2: Using duration to approximate price change

  19. When duration does not work well?

  20. Example 3: When duration does not work well? • For the previous example, the real and approximate price change when yields change are as follows:

  21. Reason of duration inadequacy Underestimation Price Overestimation Yield

  22. Improvement in price change approximation

  23. Convexity calculation

  24. Example 4: convexity calculation • Convexity for a 9% 5-year bond selling to yield 6% with semiannual coupon payments and face value of 100$ is:

  25. Example 5: Using convexity to approximate price change

  26. Using duration and convexity simultaneously

  27. Example 6: Comparing approximate price change using duration and convexity and real price change

  28. Thanks

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