uploads///Macaulay duration formula

Know how to calculate and interpret your bond’s duration



A bond’s price is affected by various factors like credit quality of the issuer, callability of the bond, coupon rate, and maturity. Duration, in effect, takes into account all these factors while providing with an assessment as to the price sensitivity of the bond to interest rate changes.

Macaulay duration

This is calculated by adding the results of multiplying the present value of each cash flow received by its time to maturity and dividing by the total price of the bond:

Macaulay duration formula

where n=number of cash flows, t=time to maturity, C=cash flow, i=required yield, M=maturity (or par) value, P=bond price.

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It attempts to take into account most of the factors that affect a bond’s price. For example, if you hold a five-year bond with a par value of $1,000 and a coupon rate of 5% (paid annually), your bonds’ duration would work out to be 4.55 years, which means that the bonds’ cash flows will pay back your $1,000 in 4.55 years. All cash flows you receive after that time period is what you’ve earned on your investment.

Modified duration

This measures the responsiveness of the bond’s price using Macaulay duration to account for the impact of changing interest rates on the bond price. It calculates how duration will change when interest rate increases by 1%.

In the above example, if the bond is currently selling at par, which gives us a yield-to-maturity of 5%, the modified duration works out to be 4.33 years. This shows that if the bond’s yield changes by 1%, which is from 5% to 6% in the above example, the duration of the bond will decline from 4.55 to 4.33.

Effective duration

This accounts for bonds with embedded options or redemption features as cash flows from these bonds change when interest rate changes. It uses a complex bond pricing models that adjust the value of the embedded options based on the probability that the option will be exercised.


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