Fixed Income Kuliah 8

Introduction to the Measurement of Interest Rate Risk

Introduction to the Measurement of Interest Rate Risk

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

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

Price Yield Function of a Callable Vs an Option Free Bond

The Price Volatility Characteristics of Putable Bonds

Effective Duration

Example : Calculating Effective Duration

Percentage Price Change for a Bond based on Effective Duration

Macaulay Duration

Portfolio Duration

Example : Calculating Portfolio Duration

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

About Convexity

Convexity & option-free bond

Convexity of callable/prepayable bond

Convexity of putable bond

Percentage Price Change Based on Duration and Convexity Convexity 2

Percentage Price Change Based on Duration and Convexity

Effective Convexity

PVBP Price Value of a Basis Point

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

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. 0.389 B. 3.889 C. 3.970 Exercise 4 A bond has a convexity of 57.3. The convexity effect if the yield decreases by 110 basis points is closest to : A. -1.63% B. 0.693% C. 1.673%

Exercise Exercise 5 Assume a bond has an effective duration of 10.5 and convexity of 97.3. 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. 19.05% B. 22.95% C. 24.89%