Duration measures a bond's sensitivity to changes in interest rates and is used to assess interest rate risk. The higher the duration, the more sensitive the bond or bond fund is to changes in interest rates. Various methods have been developed to measure duration, such as Macaulay duration.
Macaulay duration can be calculated using the formula:
$$Macaulay\, duration \mmlToken{mo}[linebreak="auto"]{=} \left[\left(\sum_{i=1}^{t}\frac {i\times C_{i}}{(1+r_{i})^{i}}\right)+ \frac{t \times F}{(1+r_{t})^t}\right]\div P$$
F— face value;
ri— interest rate for period i;
Ci— coupon payment size;
P— market value (clean price).
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