1. Fixed Income Kuliah 8

2. Introduction to the Measurement of Interest Rate Risk

3. Introduction to the Measurement of Interest Rate Risk

4. Price – Yield Curve for an Option Free
At low yields, prices rise at an increasing rate as yield fall – a characteristic of positive convexity
Price/Discount Rate Relationship for an Option-free Bond
Price
At high yields, prices fall at a decreasing rate as yield rise – a characteristic of positive convexity
Yield
Positive convexity: Prices go up faster than they go down

5. Bond Price Volatility
For very small change in yield (less than 50 bps), the magnitude of the percentage price change for different bonds is about equal, whether the yield increases or decreases
For large changes in yield (more than 50 bps), the magnitude of the percentage price change depends on whether the yield increases or decreases.
Percentage price decrease associated with a given increase in yield is less than the percentage price increase associated with an equal decrease in the yield; This is a characteristic of positive convexity.
The magnitude of the percentage price change on a bond for a given change in yield depends on 3 features:
Bond’s coupon rates- the lower the coupon, the greater the bond price volatility
Its term to maturity – the longer the term to maturity, the greater the price volatility
Initial yield - the lower the initial yield, the greater the price volatility

6. Price Yield Function of a Callable Vs an Option Free Bond

7. The Price Volatility Characteristics of Putable Bonds

8. Effective Duration

9. Example : Calculating Effective Duration

10. Percentage Price Change for a Bond based on Effective Duration

11. Macaulay Duration

12. Portfolio Duration

13. Example : Calculating Portfolio Duration

14. About Convexity
A measure of curvature of price-yield curve (2nd derivative of the bond price function with respect to yield)
More curve  higher convexity
Straight line  zero convexity
Positive convexity  price increase at an increasing rate
Negative convexity  price increase at a decreasing rate

15. About Convexity

16. Convexity & option-free bond

17. Convexity of callable/prepayable bond

18. Convexity of putable bond

19. Percentage Price Change Based on Duration and Convexity Convexity2

20. Percentage Price Change Based on Duration and Convexity

21. Effective Convexity

22. PVBP Price Value of a Basis Point

23. Exercise Exercise 1 Exercise 2
Which of the following measures is lowest for a currently callable bond ?
A. Macaulay duration
B. Effective Duration
C. Modified Duration
Exercise 2
The effect on a bond portfolio value of a decrease in yield would be most accurately estimated by using :
A. is an option free bond
B. has an embedded put option
C. has negative convexity

24. Exercise Exercise 3 Exercise 4
A 14% semiannual pay coupon bond has six years to maturity. The bond is currently trading at par. Using a 25 basis point change in yield, the effective duration of the bond is closest to : A B C
Exercise 4
A bond has a convexity of The convexity effect if the yield decreases by 110 basis points is closest to :
A %
B %
C %

25. Exercise
Exercise 5
Assume a bond has an effective duration of 10.5 and convexity of Using both of these measures the estimated percentage change in price for this bond, in response to a decline in yield od\f 200 basis points, is closest to :
A %
B %
C %