Estimating Modified Duration

Modified duration can be estimated from bond price changes (assuming no changes to cash flows) due to changes in yield as follows:

$D_{Mod}=\dfrac {P_--P_+}{2P_0\Delta y}$

• $\Delta y$ : yield change used in the calculation
• $P_-$ : bond price when YTM decreases by $\Delta y$
• $P_+$ : bond price when YTM increases by $\Delta y$
• $P_0$ : bond price at initial YTM

Substituting the values, we have:

$D_{Mod }=\dfrac {1150.25-1051.3}{2\times 1100 \times 0.01}=0.044977=\boxed {4.49\%}$