PRMIA 8006 Exam With Confidence Using Practice Dumps

Statement I is not correct because the 4% bond with the same modified duration as the zero coupon bond will have a maturity much later in the future than the zero coupon, and the final repayment coming much later will cause its convexity to be greater than the equivalent duration zero coupon bond.

Statement II is not correct as the convexity of a bond increases not in a linear fashion but in proportion to the square root of time as the maturity of the bond is increased.

Statement III is not correct as mortgage based bonds bring negative convexity even in the case of long positions,

Statement IV is not correct as the duration of a zero coupon bond maturing in 10 years has a modified duration greater than that of a coupon bearing bond of the same maturity, which means its convexity is higher and not lower (note this is different from statement I where the modified durations were identical. Here, the maturity is identical which has different implications.)

Therefore none of the statements is correct and Choice 'd' is the correct answer.

Short calls and short puts have negative gamma, ie their delta increases at a decreasing rate as the price of the underlying change. Likewise, remember that long calls and long puts have positive gamma.

Since Macaulay duration is 6 years, the modified duration is 6/(1+5%) = 5.71. This means that if interest rates were to rise by 1%, the bond price would decrease by 5.71%. Since interest rates have risen by 10 bps, (100bps = 1%), the bond's price would fall by roughly 0.571%, or 57 basis points