 Financial Terms Macaulay duration

# 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:

## Duration

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.

## Modified 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.

## Modified duration

The macaulay duration discounted by the per-period
interest rate; i.e., divided by (1+rate/frequency).

## Dollar duration

The product of modified duration and the initial price.

## Duration

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

## Duration

The weighted average of the time until maturity of each of the
expected cash flows of a debt security ## Duration

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

## Effective duration

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.

## Mortgage duration

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.

## Negative duration

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

## Zero curve, zero-coupon yield curve

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