Yield Curve Valuation Duration Documentation About

Duration

Explore the sensitivity of US Treasuries to market interest rates.

Maturity:

From:

To:

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$Macaulay Duration formula$

$D_Mac$ = Macaulay Duration $C_t$ = Cash flow at time t $y$ = Yield to Maturity $P$ = Bond Price $t$ = Time period $n$ = Total number of periods

$Modified Duration formula$

$D_Mod$ = Modified Duration $m$ = Compounding periods per year

The formulae shown are used to represent the Macaulay Duration and the Modified Duration.

There is a subtle difference between the two. The Macaulay Duration is the weighted average time to receive all of a bond's future cash flows, measuring on average how long you are at risk of interest rate changes for. The Modified Duration measures the sensitivity of a bond's price to a change in interest rates; it represents the percentage change of a bond's price for a 100 basis point change in interest rates.

Since the data from FRED represents the CMT par yields of bonds, the assumption is that the coupon yield is equal to the discount rate. This makes the bonds par value. This means all calculations of duration are made from the standpoint of a par value bond.