Oh no! Not another variable… Wasn’t it enough already to know about the bond price, its maturity, its coupon, its yield and whatnot?!

Sorry, but duration is important… You know why the price of a bond can change, and why that influences its yield. But do you know by how much the price and the yield can change? In other words, can you measure the volatility of a bond? Yes, you can – with duration. High volatility means you might end up on a rollercoaster; with low volatility, you might have found more stability.

And depending on your investment strategy, you might willingly go after the rollercoaster, or on the other hand be content with a low volatility investment.

# Duration tells you whether your bond is a rollercoaster or a becalmed ship

Duration lets you know how exposed to volatility you are when buying a given bond. It is another measure of the amount of risk you are taking.

First of all, although you could be excused for confusing the two, duration is not synonymous with maturity! Maturity is the time until the capital of the loan is repaid and with each passing day, maturity shrinks to zero as the maturity date is fixed when the bond is issued. Duration, on the other hand, is variable

# How long before this bond pays for itself?

There are two types of duration, following two different calculations: let’s talk about Macaulay duration first. Macaulay duration measures the amount of time it takes before a bond “pays for itself”. That is, Macaulay duration represents the amount of time it takes for cash flow(s) from the bond (usually, coupon payments) to cover the gross “expense” of the bond.

When you buy a bond, you incur an expense: the bond has the potential to bring in money, of course, but on the day you buy the bond, you have to part with money in the first place. So the balance is negative: by buying the bond, you have made a dent in your money.

But a bond will bring in money, in coupons and capital repayment at maturity. Macaulay duration calculates how long it will take for money earned from the bond to cover your expenses, so to speak: how long before the balance is restored between the money that left your account when you paid for that bond, and the money coming into your account that the bond is bringing you.

That allows an investor to make sure that, given their investment strategy, a particular bond will not just be a “money pit” but will actually bring in money – and when.

In fact, the raw data of how many years it takes to recoup your investment often stops an investor taking an action that they hadn’t quite thought through!

# How sensitive is this bond to interest rate changes?

Modified duration on the other hand measures how sensitive a bond is to changes in interest rates. While Macaulay duration is calculated in years (which makes intuitive sense for a “duration”), modified duration is calculated in percentage (…which doesn’t make as much intuitive sense).

This percentage represents the percentage change of the bond price when interest rates change. Modified duration tells you how much of a swing the bond price will take for a 1% change in interest rates (whether up or down).

Now there are two things to remember:

When interest rates increase, this means lenders can charge more money in exchange for lending the money they have (borrowers, on the other hand, have to pay more for borrowing money).

When interest rates increase, new bonds that are issued at that time have to match the new, increased interest rates. This means that, on the market, there will be two types of bonds (simplifying a lot!): new bonds with a higher income potential (higher interest rate that lenders earn), and older bonds, issued at a time when interest rates weren’t so high.

These older bonds only had to match a lower interest rate at the time they were issued: this means their potential for generating a return (based on their coupon) is less than the new bonds. As a result, investors will choose the new, more rewarding bonds, and there will be less demand for old, less rewarding bonds. The price of those older bonds will decrease.

(Now this is just an explanation of the mechanism by which interest rates might influence bond prices – in reality, due to all the other things that happen in the markets, interest rate changes might have less of an impact on prices, yields, and indeed, duration!)

It’s the exact opposite if interest rates decrease: older, more “return generating” bonds will be more attractive and the demand for them will be higher than that for newer issues, all else equal, resulting in an increase in their price.

How much prices will decrease or increase when interest rates change will be reflected in each bond’s duration.

Modified duration allows you to analyse to a certain extent whether the yield will fluctuate a lot or a little if interest rates change at a later date. Modified duration is, then, a measure of the volatility of a bond’s price (and hence of its yield).

# “This bond will pay for itself in 17.54 years”

Let’s take an example; I buy a bond at face value, for €1000. Its maturity date is 20 years away. It has a coupon of 5,7%.

So when I buy the bond I part with €1000 (plus costs, but let’s leave those out for the sake of the example). Every year, I earn 5,7% of the face value, that is, €57. It will take (1000:57) = 17.54 years for the bond to pay for itself. After those 17.54 years I have earned back the €1000 I spent originally: €57 a year, times 17.54.

The rest of the money coming in from the bond after that (remaining interest payments and capital repayment at maturity) will represent my “profit”.

But if I sell the bond before the 17.54 years are elapsed, I have to ascertain whether I’m not, in fact, losing money on the sale – because I haven’t recouped my expenses yet. Of course I might be able to sell the bond at a premium and this would contribute to my profit. But what if I can’t?

On a technical note, the Macaulay duration examines only the “present value” of the coupons: that is, how much the coupons are worth when you don’t consider the impact of reinvesting them.

Indeed, a lot of calculations regarding bonds assume in their formula that interest is reinvested, earning bondholders interest on interest.

Admittedly, I have not examined what the impact of reinvesting the coupons would be on the payback period. If I am able to reinvest coupons at a similar rate, I would cover my expense more quickly and this could reduce duration.

But this would be assuming that I can, in fact, find another investment with a similar rate. However, in the current environment of “on the floor” interest rates and based on the fact of life that interest rates are always changing, that is something that I’m happy to mention, but not calculate in this example.

# How long will you be vulnerable, and how much?

So even before you buy a bond, you can look at its duration to know the amount of time before you recoup your costs, and how that bond’s price will be affected by changes in interest rates – should you want to sell this bond before it pays for itself, are you going to get your money back?

A longer time to maturity means there is a longer stretch of time during which a bond is sensitive to fluctuations in interest rates. Indeed, the longer you hold a bond, the more likely it is that interest rates will be changed in the meantime.

Take the above bond: 17.54 years duration means that, during 17.54 years, you the bondholder are exposed to changes in interest rates, since they might affect negatively the “profit” you were expecting from the bond. Should you sell the bond before the 17.54 years are up, you might make a loss on the sale.

And the longer the time to maturity, the riskier the investment. In fact, in most (but not all) cases, time and risk are “positively correlated” – in plain English, this means that if one goes up then so does the other.

Of course, if an investment is riskier you stand to lose a lot in adverse conditions… But you also stand to win a lot if conditions are favourable! Imagine interest rates go down, making your older bond more attractive: if it has a high duration, its price will increase by a lot!

But to a shrewd investor this will not come as a surprise, however pleasant: they will have calculated this before buying the bond, and they know how their bond is likely to react when interest rates change.

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