Definition of Macaulay duration

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.

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.

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.

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 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.

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.

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.

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.

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