If you really want to know your bonds, know your duration.

(Photo: Getty Images)

There’s an old joke that still occasionally floats around the fixed income markets these days. It goes like this: What’s the difference between a bond and a bond trader? The answer: a bond matures. *Ha!*

If we wanted to get a little more sophisticated about it, we could say the difference between a bond and a bond trader is that a bond is there for the duration. That’s also a play on words, since duration, as it applies to fixed income securities, is a great measure of the potential price volatility of a particular bond or debenture, or even of a portfolio of bonds and debentures. It’s an easy calculation that can do wonders to help a do-it-yourself investor choose the right fixed income securities.

To explain this concept a bit further, we already know that the longer a bond’s term to maturity, the more sensitive its price is to changes in interest rates. It’s therefore good to own long-term bonds when interest rates are falling, because they’ll go up more in price than short-term bonds.

Alternatively, it’s best to shorten the average term to maturity of your bond portfolio as interest rates enter into a rising cycle, because the shorter the term, the less their price will be affected. Whenever that happens, for diversification reasons it’s better to shorten your average term than to get out of bonds altogether, although the latter may initially sound more attractive.

We also already know that the higher a bond’s coupon rate, the less its price will be affected by interest rate swings. So, putting the two together, we want to own short-term high-coupon bonds when rates are rising, and low-coupon long-term bonds when rates are trending down.

That’s all fine and dandy in theory; the problem arises when a do-it-yourselfer has to choose between two specific bonds. Suppose an investor has narrowed her choices down to two issues, a 4% four-year bond and a 5% five-year bond, and she needs to identify which is the less volatile of the two, because interest rates are expected to rise.

That’s not an easy task. She might assume the four-year bond is less volatile, because of its shorter term. She might equally assume the five-year bond is less volatile because it has the higher coupon rate. But the simple fact is she just doesn’t know, because she doesn’t know when the effect of a higher coupon has a more powerful effect on a bond’s price than does a shorter term.

This is exactly the situation where knowing the duration of each of the bonds is so helpful. Duration is a calculation, expressed in years, that measures a bond’s coupon-weighted term-weighted price volatility. The lower a bond’s duration, i.e. the less ‘years’ of duration it has, the less volatile its price will be.

So, how can a do-it-yourself investor find out what the duration of a bond is? Happily, some of the better discount broker websites will tell you, but only of the bonds they are offering for sale.

Alternatively, you can do an Internet search for ‘bond duration calculator’ and you’ll find lots of choices. Try to find a Canadian site, because in the U.S. they do things a little differently, including using a 360-day year (we use 365).

Finally, if you like this sort of thing, you can enter the duration formula into your home computer spreadsheet and calculate away to your heart’s content. It’s a bit involved: you have to take the present value of each of the bond’s cash flows, divide each by the total present value of all the cash flows, and then add up all of these individual durations to get the total duration of the bond. But once it’s programmed in, it’s a breeze to try out all kinds of bonds.

However you go about getting the durations, I encourage you to use this useful tool in your future bond selections, and even to use it on any bonds you already hold. It’ll give you a much clearer picture of what you own than you had before.

By the way, the duration of the five-year 5% bond (using a current yield of 3% and semi-annual compounding) is 4.68 years (calculated on my spreadsheet). The duration of the four-year 4% bond is 3.74 years, so there’s quite a difference between the two.

Blogs & Comment

## Bonds: Fixed income duration explained

If you really want to know your bonds, know your duration.

By David West

(Photo: Getty Images)

There’s an old joke that still occasionally floats around the fixed income markets these days. It goes like this: What’s the difference between a bond and a bond trader? The answer: a bond matures.

Ha!If we wanted to get a little more sophisticated about it, we could say the difference between a bond and a bond trader is that a bond is there for the duration. That’s also a play on words, since duration, as it applies to fixed income securities, is a great measure of the potential price volatility of a particular bond or debenture, or even of a portfolio of bonds and debentures. It’s an easy calculation that can do wonders to help a do-it-yourself investor choose the right fixed income securities.

To explain this concept a bit further, we already know that the longer a bond’s term to maturity, the more sensitive its price is to changes in interest rates. It’s therefore good to own long-term bonds when interest rates are falling, because they’ll go up more in price than short-term bonds.

Alternatively, it’s best to shorten the average term to maturity of your bond portfolio as interest rates enter into a rising cycle, because the shorter the term, the less their price will be affected. Whenever that happens, for diversification reasons it’s better to shorten your average term than to get out of bonds altogether, although the latter may initially sound more attractive.

We also already know that the higher a bond’s coupon rate, the less its price will be affected by interest rate swings. So, putting the two together, we want to own short-term high-coupon bonds when rates are rising, and low-coupon long-term bonds when rates are trending down.

That’s all fine and dandy in theory; the problem arises when a do-it-yourselfer has to choose between two specific bonds. Suppose an investor has narrowed her choices down to two issues, a 4% four-year bond and a 5% five-year bond, and she needs to identify which is the less volatile of the two, because interest rates are expected to rise.

That’s not an easy task. She might assume the four-year bond is less volatile, because of its shorter term. She might equally assume the five-year bond is less volatile because it has the higher coupon rate. But the simple fact is she just doesn’t know, because she doesn’t know when the effect of a higher coupon has a more powerful effect on a bond’s price than does a shorter term.

This is exactly the situation where knowing the duration of each of the bonds is so helpful. Duration is a calculation, expressed in years, that measures a bond’s coupon-weighted term-weighted price volatility. The lower a bond’s duration, i.e. the less ‘years’ of duration it has, the less volatile its price will be.

So, how can a do-it-yourself investor find out what the duration of a bond is? Happily, some of the better discount broker websites will tell you, but only of the bonds they are offering for sale.

Alternatively, you can do an Internet search for ‘bond duration calculator’ and you’ll find lots of choices. Try to find a Canadian site, because in the U.S. they do things a little differently, including using a 360-day year (we use 365).

Finally, if you like this sort of thing, you can enter the duration formula into your home computer spreadsheet and calculate away to your heart’s content. It’s a bit involved: you have to take the present value of each of the bond’s cash flows, divide each by the total present value of all the cash flows, and then add up all of these individual durations to get the total duration of the bond. But once it’s programmed in, it’s a breeze to try out all kinds of bonds.

However you go about getting the durations, I encourage you to use this useful tool in your future bond selections, and even to use it on any bonds you already hold. It’ll give you a much clearer picture of what you own than you had before.

By the way, the duration of the five-year 5% bond (using a current yield of 3% and semi-annual compounding) is 4.68 years (calculated on my spreadsheet). The duration of the four-year 4% bond is 3.74 years, so there’s quite a difference between the two.