# Duration has 2 meanings?

I wish in the book they would be clear in their usage of duration. Isn’t there two meanings? One is maturity and the other is sensitivity?

Can someone help in explaning?

It measures interest rate sensitivity and doesn’t always correspond with maturity.

When they say a bond has a duration of 5years they mean it has same duration as a five-year zero coupon bond. Not that it matures in five years. Another example – a 10-year floating rate bond will have a duration of close to zero, not 10years.

The first few paragraphs of this (http://en.wikipedia.org/wiki/Bond_duration) are very useful. I had the exact same question. See the cut and paste job below:

"In finance, the duration of a financial asset that consists of fixed cash flows, for example a bond, is the weighted average of the times until those fixed cash flows are received. When an asset is considered as a function of yield, duration also measures the price sensitivity to yield, the rate of change of price with respect to yield or the percentage change in price for a parallel shift in yields.

The dual use of the word “duration”, as both the weighted average time until repayment and as the percentage change in price, often causes confusion. Strictly speaking, Macaulay duration is the name given to the weighted average time until cash flows are received, and is measured in years. Modified duration is the name given to the price sensitivity and is the percentage change in price for a unit change in yield. When yields are continuously compounded Macaulay duration and modified duration will be numerically equal. When yields are periodically compounded Macaulay and modified duration will differ slightly, and there is a simple relation between the two. Modified duration is used more than Macaulay duration."

Thanks that helps.

The original idea of duration was Frederick Macaulay’s: he wanted to know the weighted-average time to recieve his money, where each weight is the present value of the cash flow at a given time in the future. Macaulay duration , therefore, is measured in units of time, usually years.

Someone looked at Macaulay’s calculation and noticed that if you modify it slightly - dividing it by (1 + YTM) - you get a formula for the percentage price change of the bond given a 1% change in yield; thus was born modified duration. Modified duration is also measured in years, though most finance people drop the word “years” and use only the number. (Bad practice, in my humble opinion.)

Someone else looked at modified duration and noticed that it - like Macaulay duration - assumes that the cash flows never change, making it impractical for computing the interest-rate price sensitivity of bonds with embedded options. They decided to compute the price sensitivity directly - using market prices that allow for changes in cash flows - and called it effective duration. You guessed it: effective duration’s also measured in years (though almost nobody says so).

Then came spread duration and key rate duration , and goodness knows what other kinds of duration. All measured in years.

That’s about it.

Just curious - It seems coincidental that the weighted average time till receipt of cash flows (macaulay) and the derivative basd rate of change in the price of the security for a given change in yield (modified duration) are roughly the same, if not equal, such as for zeros. Why is this? They seem like two different calculations - never totally understood why modified duration is specified in years (I understand the impact that term has on duration)?

I don’t know if anyone has ever said this before - if not, I’m about to coin a phrase - but there are no coincidences in mathemetics.

I could take you through the calculus (it’s not particularly difficult), but suffice it to say that when you compute dP/dr, CF1 gets multiplied by 1, CF2 gets multiplied by 2, and so on. The difference between Macaulay duration and modified duration is that the latter is slightly shorter because you divide by (1 + r).

Not coincidental, but kinda cool.