Macaulay duration formula
Financial acronyms
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Description of the Macaulay duration formula
Formula for the calculation of a bond's Macaulay duration.
Formula
\[ D=\frac{\sum_{t=1}^{N}\frac{t \cdot C_{t}}{\left ( 1+i \right )^{t}}}{\sum_{t=1}^{N}\frac{C_{t}}{\left ( 1+i \right )^{t}}} \ \]
Symbols
\(C\ \)
Cash flow (coupon or principal)
\(i\ \)
Yield
\(N\ \)
Total number of annuities (number of years times number of payments per year)
\(t\ \)
Time until the payment of the cash flow (full years and year fraction)