Question

Consider the same 3 year bond with a $100 par value and a 5% annual coupon where comparable bonds are yielding 6% (assume continuous compounding). If the yield goes up 1%, then according to the duration formula for a bond's price change, the bond price will change by: (Present decreases as negative values, increases as positive values)

Answer 1

Price of a 3 year bond with a $100 par value and a 5% annual coupon where comparable bonds are yielding 6% (assume continuous compounding) = 5*e^(-0.06) + 5*e^(-0.06*2) + 105*e^(-0.06*3) = $96.85

duration of the bond as calculated earlier = 2.86 years

So modified duration of the bond = duration*e^(-r) = 2.86*e^(-0.06) = 2.69 years

So change in price dP = -P*D*dr = -96.85 * 2.69 * .01 = -2.61

So change in price = -2.61/96.85 = -2.69%