$$\begin{array} { | l | l | l | l | l | }
\hline \text { Rate } & \text { Maturity } & \text { Ask } & \text { Change } & \text { Ask yield } \
\hline 7.1250 & \text { Oct 15,2005 } & 102 : 08 & - 1 & 5.9156 \
\hline
\end{array}$$
-If yields increase by 10 basis points, what is the approximate price change on the $100,000 Treasury note? Use the duration approximation relationship.
A)+$179.39
B)+$16.05
C)-$1,605.05
D)-$16.05
E)+$160.51

Question

$$\begin{array} { | l | l | l | l | l | } 
\hline \text { Rate } & \text { Maturity } & \text { Ask } & \text { Change } & \text { Ask yield } \
\hline 7.1250 & \text { Oct 15,2005 } & 102 : 08 & - 1 & 5.9156 \
\hline
\end{array}$$
-If yields increase by 10 basis points, what is the approximate price change on the $100,000 Treasury note? Use the duration approximation relationship.
A)+$179.39
B)+$16.05
C)-$1,605.05
D)-$16.05
E)+$160.51

Quizplus · Accepted Answer

The duration approximation relationship is:$$\Delta Price = -Duration * \Delta Yield * 100,000$$where:* $\Delta Price$ is the change in price* $Duration$ is the duration of the bond* $\Delta Yield$ is the change in yieldIn this case, the duration of the bond is not given, but we can estimate it using the following formula:$$Duration = \frac{\sum_{i=1}^{n} PV_i * t_i}{Price}$$where:* $PV_i$ is the present value of the $i$th cash flow* $t_i$ is the time in years until the $i$th cash flow* $Price$ is the current price of the bondUsing the given information, we can calculate the present value of each cash flow as follows:$$PV_1 = 100,000 * e^{-0.059156 * 0.8479} = 94,084.63$$$$PV_2 = 100,000 * e^{-0.059156 * 1.8479} = 88,270.27$$$$PV_3 = 100,000 * e^{-0.059156 * 2.8479} = 82,559.26$$$$PV_4 = 100,000 * e^{-0.059156 * 3.8479} = 76,951.61$$$$PV_5 = 100,000 * e^{-0.059156 * 4.8479} = 71,447.33$$$$PV_6 = 100,000 * e^{-0.059156 * 5.8479} = 66,046.41$$$$PV_7 = 100,000 * e^{-0.059156 * 6.8479} = 60,748.85$$$$PV_8 = 100,000 * e^{-0.059156 * 7.8479} = 55,554.66$$$$PV_9 = 100,000 * e^{-0.059156 * 8.8479} = 50,463.83$$$$PV_{10} = 100,000 * e^{-0.059156 * 9.8479} = 45,476.36$$The duration of the bond is then:$$Duration = \frac{94,084.63 * 0.8479 + 88,270.27 * 1.8479 + 82,559.26 * 2.8479 + 76,951.61 * 3.8479 + 71,447.33 * 4.8479 + 66,046.41 * 5.8479 + 60,748.85 * 6.8479 + 55,554.66 * 7.8479 + 50,463.83 * 8.8479 + 45,476.36 * 9.8479}{102,080} = 6.848$$The change in yield is 10 basis points, or 0.001. Therefore, the change in price is:$$\Delta Price = -6.848 * 0.001 * 100,000 = -684.80$$The correct answer is A.

-If Yields Increase by 10 Basis Points, What Is the |