Yield Duration Statistics: Price Value of a Basis Point (PVBP)

A bond provides investors a 5% coupon, paid semiannually. It has a yield-to-maturity of 6% and a face value of 100. If the bond has 12 years left until maturity, which of the following is _closest_ to its price value of a basis point (PVBP)?

Correct! The purchase price of the bond can be obtained by taking the present value of all the coupons and the face value: $$\displaystyle PV_{0}=\frac{PMT}{(1+r)^{1}}+\frac{PMT}{(1+r)^{2}}+\frac{PMT}{(1+r)^{3}}+......+\frac{PMT+FV}{(1+r)^{N}}$$ If the yield-to-maturity increases by one basis point, i.e., 0.01%, then the new price will be: $$\displaystyle PV_{+}=\frac{2.5}{(1+0.03005)^{1}}+\frac{2.5}{(1+0.03005)^{2}}+\frac{2.5}{(1+0.03005)^{3}}+......+\frac{2.5+100}{(1+0.03005)^{24}}=91.4522$$ If the yield-to-maturity decreases by one basis point, i.e., 0.01%, then the new price will be: $$\displaystyle PV_{-}=\frac{2.5}{(1+0.02995)^{1}}+\frac{2.5}{(1+0.02995)^{2}}+\frac{2.5}{(1+0.02995)^{3}}+......+\frac{2.5+100}{(1+0.02995)^{24}}=91.6124$$ Therefore, the price value of a basis point is: $$\displaystyle PVBP = \frac{(PV_{-})-(PV_{+})}{2} = \frac{91.6124 - 91.4522}{2}=0.0801$$ For PV+: [[calc: 24 n 2.5 pmt 100 fv 3.005 iy cpt pv, 24 n 2.5 pmt 100 fv 3.005 i pv]] For PV-: [[calc: 24 n 2.5 pmt 100 fv 2.995 iy cpt pv, 24 n 2.5 pmt 100 fv 2.995 i pv]]

Incorrect. This answer choice would be true if the bond wasn't paying the coupons semiannually.

Incorrect. One possible way to obtain this answer choice is to consider a one-basis-point change in the semiannual yield-to-maturity, while the proper way to do the calculation is to take a one-basis-point change in the annual yield-to-maturity—which is equivalent to a 0.5-basis-point change in the semiannual yield-to-maturity.

0.0792

0.0801

0.1602