Macaulay duration is basically the average time it takes for a bond’s cash flows to pay off, weighted by how much each cash flow is worth today compared to the bond’s price. Portfolio managers often rely on this concept when they want to protect their investments.
Formula of Macaulay Duration
You can figure out Macaulay duration like this:
\(\text{Macaulay Duration}=\frac{\sum_{t=1}^{n}\frac{t*C}{\left( 1+y \right)^{t}}+\frac{n*M}{\left( 1+y \right)^{n}}}{\text{Current Bond Price}}\)where:
- t=Respective time period
- C=Periodic coupon payment
- y=Periodic yield
- n=Total number of periods
- M=Maturity value
Learn more about Macaulay Duration
The metric is named after its inventor, Frederick Macaulay. You can think of Macaulay duration as the economic sweet spot for a set of cash flows. Another way to look at it is that it’s the weighted average time an investor needs to hold onto a bond until the present value of its cash flows matches what they paid for it.
Factors Affecting Duration
The price, maturity, coupon, and yield to maturity of a bond all play a role in figuring out its duration. Generally, the longer the time until maturity, the longer the duration. If a bond has a higher coupon, its duration tends to be shorter. When interest rates rise, the duration decreases, making the bond less sensitive to future rate hikes. Additionally, having a sinking fund, scheduled prepayments before maturity, and call provisions can all reduce a bond’s duration.