## Negative Bond Interest Rates & NAV

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Topic Author
BolderBoy
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### Negative Bond Interest Rates & NAV

Bonds are strange critters to me.

I understand that as a bond fund's interest rate goes up the NAV of the bond fund goes down. And vice-versa.

What happens to the NAV as the interest rate approaches zero? What happens to the NAV if the interest rate goes negative?

Uh, oh. Is this a calculus question?
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nisiprius
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### Re: Negative Bond Interest Rates & NAV

The important thing to keep in mind is that a bond that you have bought is (usually) a contract to pay a specific number of dollars on specific days, and the contract doesn't change. If you paid \$1,000 for a 20-year Treasury with a coupon rate of 2%, that bond will pay you \$10 every six months for 20 years, and at the same time as that last payment it also pays back your principal of \$1,000.

If interest rates fall to zero, your bond's interest rate doesn't fall to zero. It doesn't stop making those \$10 payments.

If interest rates double, your bond's interest rates don't double. It still keeps paying about \$10 every six months.

The market value only comes into play when you try to sell your bond on the market. If interest rates drop to zero, your bond, which pays \$10 every six months, is competing against fresh-issued bonds that pay nothing. So, obviously, your bond is worth more than the freshly-issued competition.

This gain is not permanent, though. To keep things simple... well, at a zero interest rate, they are simple... if the interest rate is zero, then you don't discount future payments. A \$10 payment five or ten or twenty years from now has a present value of \$10.

Which is weird, but not because bonds are strange critters but because a 0% interest rate is very weird.

So, if interest rates drop to zero at a time when your bond has 15 years left to maturity, your bond is going to be paying a total of 30 x \$10 = \$300 in interest, plus \$1,000 in principal when it matures, so its value is \$1,300.

But if you wait until there are 10 years left, there will only be \$200 in interest payments left and its value will only be \$1,200.

When there are 5 years left, \$1,100.

When there are six months left, \$1,010.

So if interest rates drop exactly to zero, your bond instantly becomes worth the grand total of all its future interest and principal payments... and as time progresses, that value declines until it is down to \$1,010.
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whodidntante
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### Re: Negative Bond Interest Rates & NAV

Let's say there is only one bond in the world. It's a one year bond. I want it, you have it. I've just got to have it. It's for \$100 and pays 1% in a year.

I offer you \$100, which for me would be a 1% yield, same as it is for you. You refuse.

I offer you \$101, which for me would be a 0% yield, and an immediate 1% profit for you. You think a little harder, but still refuse.

So I offer you \$102, which for me would be a -1% yield, and immediate 2% profit for you. You think really hard, but still say no.

So I say "fine, I have things to do so take \$110 and give me my bond." You cheerfully agree and we do the transaction. Then the United States economy collapses because we only had one bond and rates are -10%.

oldcomputerguy
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### Re: Negative Bond Interest Rates & NAV

This topic is now in the Investing - Theory News & General forum. -- mod oldcomputerguy
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Topic Author
BolderBoy
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Joined: Wed Apr 07, 2010 12:16 pm

### Re: Negative Bond Interest Rates & NAV

Okay, thank you both for the explanations so far.

With what you both said in mind, why would anyone buy a bond with a negative interest rate to start out? Can you please explain the rationale using the same type of explanations above?
"Never underestimate one's capacity to overestimate one's abilities" - The Dunning-Kruger Effect

Phineas J. Whoopee
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### Re: Negative Bond Interest Rates & NAV

BolderBoy wrote:
Fri Sep 13, 2019 11:10 am
Okay, thank you both for the explanations so far.

With what you both said in mind, why would anyone buy a bond with a negative interest rate to start out? Can you please explain the rationale using the same type of explanations above?
Because they, which includes large institutions, conclude they have no better options to store the value. They, which includes large institutions, would rather take a small, known loss than risk an unknown larger one. The former facilitates business planning and the latter doesn't.

Imagine Apple, Inc., trying to make payroll out of thousands of safe deposit boxes filled with \$100 bills.

PJW

MotoTrojan
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### Re: Negative Bond Interest Rates & NAV

BolderBoy wrote:
Fri Sep 13, 2019 11:10 am
Okay, thank you both for the explanations so far.

With what you both said in mind, why would anyone buy a bond with a negative interest rate to start out? Can you please explain the rationale using the same type of explanations above?
While the most obvious reason is the one stated above, where many institutions have nowhere else to go, you could also do so if you were speculating that interest rates would go further negative and wanted to make a profit as the NAV increased further (while also being exposed to the risk of losing even more than the negative rate).

Topic Author
BolderBoy
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Joined: Wed Apr 07, 2010 12:16 pm

### Re: Negative Bond Interest Rates & NAV

Ahhhhh. So if rates go negative and then go further negative the NAV would continue to rise.

Didn't know that. Thanks.
"Never underestimate one's capacity to overestimate one's abilities" - The Dunning-Kruger Effect

MotoTrojan
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### Re: Negative Bond Interest Rates & NAV

BolderBoy wrote:
Fri Sep 13, 2019 8:51 pm
Ahhhhh. So if rates go negative and then go further negative the NAV would continue to rise.

Didn't know that. Thanks.
Yup. And due to convexity the NAV gets even more sensitive as you approach, and pass zero.