Effective duration example: Consider a 3-year, 9.4 percent coupon bond selling for $10,000 par to yield 9.4 percent to maturity. The Macaulay’s duration for the option-free version of this bond with semiannual coupons and compounding was calculated to be 5.36 semiannual periods, or 2.68 years at the market rate of 4.7 percent semiannually. The modified duration was 5.12 semiannual periods or 2.56 years. A 30 basis point increase in rate to 5 percent semiannually will lower the price to $9,847.72.
The callable bond’s effective duration for a 30 basis point (0.30 percent) semiannual movement in rates either up or down is 2.54: