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How can a bond have a negative yield?

Eric Jacobson  |  26 Sep 2016Text size  Decrease  Increase  |  

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Observers have noted that owning a bond with a negative yield is akin to paying someone else to hold your money, but how?


There's currently a heated debate about the long-term impact of negative rates on global economic growth, the financial sector, and investor behaviour, and some of the early evidence isn't comforting.

Observers have noted that owning a bond with a negative yield is akin to paying someone else to hold your money, but how?

Although bond maths is messy, it's easy enough to understand that if you buy a plain-vanilla bond for $1,000 and it pays 10 per cent per year--a coupon of $100--and you get your $1,000 back at maturity, you've made money on the investment.

But how can you lose money on a bond if it's making regular interest payments?

For starters, it's important to remember there's a big difference between the very basic interest rate of a bond and its yield to maturity.

The first one is a very simple expression of the payments a bond makes periodically, relative to its face value. On its own, it really doesn't tell you anything about a bond's overall return.

A bond's yield to maturity, however, is meant to provide a snapshot of its expected annualised total return, taking into account how much an investor pays for the bond, how much income it produces, and how much the investor gets back at the end.

That's crucial because whether you pay more or less than a bond's face value up front will have a very important impact on what your ultimate yield to maturity, and thus your ultimate return, will be.

How price rises and yields fall

Consider some very basic examples using an even simpler hypothetical government bond with a 1 per cent coupon and exactly 10 years left until maturity.

Take the most basic case first. If the market rate for that bond is a 1 per cent yield to maturity, its price should be $1,000.

What would happen to the price of the same bond if market yields were to go all the way to zero?

Remember, it's the same bond, so it's still paying coupons and will still return $1,000 at maturity. All other things equal, the value of those coupon payments would go up.

In fact, if an investor were to purchase that bond when market yields are at zero, the price would actually rise all the way to $1,100.

Put another way, the investor has to pay an extra $100 in order to make the transaction worthwhile to whomever is selling it, because the seller is giving up claim to the bond's future coupon payments.

The maths is a little trickier once you get to a negative yield. In fact, the thought of it was evidently so outlandish that it seems to have left the designers of Microsoft Excel thinking it would never happen: Its standard functions won't accommodate negative yields.

We can still approximate the price one would wind up paying for a bond marked to a negative 1 per cent yield to maturity.

Although bond calculators can help produce the number, the trick is essentially to push up the bond's price high enough that, at a certain point, receiving the bond's principal and interest payments will represent a loss equal to a negative 1 per cent annualised yield to maturity.

In other words, if yields were to fall all the way to negative 1 per cent in the marketplace, our hypothetical 10-year government bond with a 1 per cent coupon would actually command a large premium--$211 in this example--to its face value in order to compensate a seller enough to give up its future coupons.

Can a bond be born negative?

Those are examples of how transactions might look in the secondary market for bonds that have already been issued.

You might wonder, though, how a government would structure a brand new bond when market yields are negative.

It's not necessarily an issue of a government simply wanting to sell a bond with a negative yield, of course. Somebody still has to want to buy it.

As such, each government's central bank generally prices its new bonds based on auctions whose prices affect, and are affected by, market rates.

As you might guess from the secondary market example, it all comes down to price. It remains fundamentally true that the more an investor pays for a bond the lower its return will go.

So, when the market is trading such that a new 10-year government bond should carry a negative yield in order to match the market, the easiest path would be to sell new bonds without coupons--that is, zero-coupon bonds. Some European governments have done this.

After all, in practical terms, you probably don't want to ask a bondholder to send coupons back to the government.

Unlike a normal zero, though, which is originally priced at a discount to its maturity value so investors earn the difference, an investor who pays more than the maturity value of a zero-coupon bond will get back less at the end of its term.

And the deeper the negative yield, the higher that bond's issuing price will be as well.

How does this even happen?

Of course, the question of why an investor would agree to buy a bond with a negative yield is a messy one of its own, and there are several explanations.

The most harrowing scenarios involve a dramatic economic slowdown and the deflation that would typically accompany one.

In such cases, large investors without the luxury to hide billions of dollars under the mattress, might put it into "safe" assets that charge a premium for that safety.

In today's environment, though, the most common causes involve central bank activity.

When economies are sluggish and central banks are anxious to try and generate inflationary pressure and economic activity and job growth, one of the first levers they turn to is to charge for commercial banks to deposit money with them overnight.

That has the effect of pushing down short-term interest rates, and the impact typically ripples out to longer maturities depending on the market's reaction.

The other big factor most at play these days is quantitative easing. In effect, central banks are buying longer-term bonds out in the marketplace and doing so in such large quantities that they dramatically pull down supply.

Doing so, and indicating that more is coming, also encourages investors to try and buy bonds before the central banks do.

More from Morningstar

• Why China's debt-fuelled economic expansion can't keep happening

• India, China hold pockets of investment opportunity


Eric Jacobson is a US-based senior analyst covering fixed-income strategies on Morningstar's manager research team.

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