# Bond Duration – How To Calculate Interest Rate Risk For a Bond

January 5th, 2012 by David Waring**Bond Duration** is a measurement of how long it takes for the price of a bond to be matched by the money it generates. Here is a video overview, and you can find the longer text version below.

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Measured in years, duration is important information for investors, because a bond with a higher duration also has more interest rate risk (more time for things to go wrong) and higher price volatility, compared to one with a lower duration.

#### However, higher risk means higher potential reward:

A bond with higher duration will have larger gains when interest rates fall than a similar bond with a lower duration.

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The impact of a change in interest rates on a bond’s price, or its interest rate risk, is measured by the bond’s duration. If a bond’s duration is 8 (meaning that it will take 8 years for the bondholder to receive back the purchase price of the bond), you can also use that number to calculate how much the price will move if interest rates change.

In the case of a bond with a duration of 8, a 1% rise in market interest rates would cause the bond to decrease in value 8%. Conversely, a 1% fall in interest rate would cause the bond’s value to increase by 8%. The bigger a bond’s duration number, the greater the impact an interest rate move will have a bond’s price, and therefore the higher the bond’s interest rate risk.

Bond Duration is a very useful tool for estimation. However, it should be said that it tends to underestimate the change in market price as interest rate drop to near zero, and overestimate the impact on price for rising interest rates at high levels. This concept is called convexity.

### Here are a couple of rules of thumb for bond duration:

- Interest bearing bonds will have durations less than their term (time to maturity)
- A zero-coupon bond (paying no interest) will have a duration equal to its term
- Bonds with higher higher current yields will tend to have lower durations than those with lower current yields, because an investor holding a bond with a higher current yield receives repayment for the bond faster. In other words, the higher the current yield, the lower the duration. Similarly, the longer the maturity, the higher the duration.

## How bond duration changes with time

In a bond that pays interest, an interest payment that is made to an investor is no longer a future cash flow (it’s now already in the investor’s bank account). When such a payment is made, the duration of the bond will change. It can be recalculated by considering the amount of money still left to be generated. Whatever the result in terms of number of years, the time interval corresponding to the duration will shift forward in time: the date when the remaining cash flows match the price of the bond will now be later.

When buying a bond after its initial issue, duration for the new holder may not be the same as duration calculated by the original holder at the time of issue.

This lesson is part of our free Guide to the Basics of Investing in Bonds. To continue to the next lesson go here.

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a duration calculator for us govts would be helpful

Hi John,

Thanks for the comment. Will see about getting one added, here is one you can use in the meantime.

http://www.investopedia.com/calculator/bonddurcdate.aspx#axzz2DuhIQ3BR

Best Regards,

Dave

The most helpful exlpanation I have heard/read so far! Thanks!

Not quite sure why the bond value will fall when the interest rate rises.

I felt the cost of borrowing goes up and makes the bond more lucrative for the bond-holder.

So if i buy a bond below Par , with 5 years left to maturity paying a 5% coupon [implying YTM > Coupon Rate], how would i use duration in trying to figure out if it is a good investment?

If the company is creditworthy and will “most likely” pay facevalue at maturity, my net returns is coupons total 25 [5% a year] and the +30 dollars i made on the bond [paid 70 received par so very roughly 55/70 = 79%].

Obviously rough calcluations and rough example but in general what bond is going to return 42% higher in “coupon” payments over those 5 years.

Is that the POINT of duration, if there is a bond out there that will return a similiar return in a shorter time frame than my example, that comparison is made using duration?

Sure i would get 79% over 5 years, but if i can get similar return quicker than obviously that is better?

Thanks

I am just trying to see how to relate that example wih duration.

Thanks