# Definition of __Macaulay duration__

## Macaulay duration

A widely used measure of price sensitivity to yield

changes developed by Frederick **macaulay** in 1938. It is measured in years and

is a weighted average-time-to-maturity of an instrument. The **macaulay**

**duration** of an income stream, such as a coupon bond, measures how long, on

average, the owner waits before receiving a payment. It is the weighted

average of the times payments are made, with the weights at time T equal to

the present value of the money received at time T.

## Macaulay duration

The weighted-average term to maturity of the cash flows from the bond, where the

weights are the present value of the cash flow divided by the price.

# Related Terms:

The expected life of a fixed-income security considering its coupon

yield, interest payments, maturity, and call features. As market interest rates

rise, the **duration** of a financial instrument decreases. See **macaulay duration**.

The ratio of **macaulay duration** to (1 + y), where y = the bond yield. Modified **duration** is

inversely related to the approximate percentage change in price for a given change in yield.

The **macaulay duration** discounted by the per-period

interest rate; i.e., divided by (1+rate/frequency).

The product of modified **duration** and the initial price.

A common gauge of the price sensitivity of an asset or portfolio to a change in interest rates.

The weighted average of the time until maturity of each of the

expected cash flows of a debt security

The time it takes for a policy or annuity to reach maturity.

The **duration** calculated using the approximate **duration** formula for a bond with an

embedded option, reflecting the expected change in the cash flow caused by the option. Measures the

responsiveness of a bond's price taking into account the expected cash flows will change as interest rates

change due to the embedded option.

A modification of standard **duration** to account for the impact on **duration** of MBSs of

changes in prepayment speed resulting from changes in interest rates. Two factors are employed: one that

reflects the impact of changes in prepayment speed or price.

A situation in which the price of the MBS moves in the same direction as interest rates.

A yield curve for zero-coupon bonds;

zero rates versus maturity dates. Since the maturity and **duration** (**macaulay**

**duration**) are identical for zeros, the zero curve is a pure depiction of supply/

demand conditions for loanable funds across a continuum of **duration**s and

maturities. Also known as spot curve or spot yield curve.

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