Duration & Convexity

# Duration & Convexity

## Duration & Convexity

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##### Presentation Transcript

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

3. Bonds Risk & return tradeoff

4. Factors effect bond return

5. Risks of return

6. Maturity Effects Interest rate volatility risk

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

8. 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.

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

10. Duration

11. Duration

12. Duration is elasticity

13. 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

14. First derivative of price equation

15. Macaulay duration, Modified duration

16. 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:

17. Example 2: Using duration to approximate price change

18. When duration does not work well?

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

20. Reason of duration inadequacy Underestimation Price Overestimation Yield

21. Improvement in price change approximation

22. Convexity calculation

23. 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:

24. Example 5: Using convexity to approximate price change

25. Using duration and convexity simultaneously

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

27. Thanks