Bond Prices and Interest Rates

Bond prices can be confusing. When the interest rate goes up, bond prices go down. Why is that the case?

Imagine that you’ve purchased a 10-year Treasury bond for $10,000 with a 2% coupon rate (i.e. it pays $200 of interest a year). Let’s say you hold onto that bond for five years, which means that now the Treasury bond is effectively a 5-year Treasury bond with a 2% coupon rate.

Now also imagine that interest rates have gone up over the five years such that a newly-issued 5-year Treasury bonds are paying 5% interest.

Would you be able to sell your Treasury bond for $10,000? It’d be pretty difficult (i.e. impossible) as nobody would want to buy your bond for $10,000 when they could buy a new bond in the market earning a 5% rate. You’d have to sell your bond for less than its face value. In other words, the price for your bond has gone down because interest rates have risen.

And the same result happens in reverse. If interest rates had gone down over the five-year period such that a newly-issued 5-year Treasury bond is paying 1% interest, people would be clamoring to buy your bond which pays at the 2% rate. In other words, the price for your bond would go up because interest rates have decreased.

How much does the price move? It moves exactly at the amount such that your bond offers the same yield to maturity as the newly-issued Treasury bond of the same duration. For example, in the hypothetical above, your Treasury bond paying a 2% coupon would only be worth $8,701 in the market. This discount not only reflects the lower coupon rate, but also takes into consideration the present value of money.

Break it down and make it even easier

Let’s use an easier example.

Consider a 1-year zero-coupon bond (i.e. one that pays no interest). It would be difficult to sell such a bond in the market as who would want to hand over money for one year only to get the same amount back at the end of the year?

To make such an offer attractive, imagine that the $10,000 1-year zero-coupon bond is trading at $9,500. The bond’s rate of return at the present time is about 5.26% since $10,000-$9,500 / $9,500 = 5.26%.

This would be a good deal to an investor who thinks a 5.26% return is attractive in the market. But what if the market currently paid 10% to similar bonds? Nobody in their right mind would hand over money to earn 5.26% when they could earn 10% with the same level of risk.

Therefore, the 1-year zero-coupon bond would fall in value from $9,500 to $9,099 (which gives a 10% yield).

Got it? Now it’s easy to see why bond prices move in inverse direction of changes in interest rates.

Joshua Holt is a former private equity M&A lawyer and the creator of Biglaw Investor. Josh couldn’t find a place where lawyers were talking about money, so he created it himself. He spends 10 minutes a month on Empower keeping track of his money. He’s also maxing out tax-advantaged accounts like 529 Plans to minimize his taxable income.

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    Five thoughts on Bond Prices and Interest Rates

    1. Thanks for the recap of bonds. I think people make it seem like bonds are really difficult to understand but it’s a pretty easy concept if you can do simple math. Personally, I do not own any bonds because I like the asset allocation that I have in my portfolio. In the future once interest rates start to rise I may consider buying bonds if it makes sense for me.

      1. Bonds are definitely a little more confusing than stocks, but I agree that once you get the concepts they aren’t too difficult to understand. I don’t own very many bonds either, but I wonder if that’s more of a factor of this low interest rate environment. I wonder if we’d be having the same conversation with the same positions in the 1970s.

    2. I think because people tend to gloss over the inverse relationship between bonds and interest rates, they fail to see in inherent capital risk of being investing in bonds at these historically low rates.

      If interest rates move up substantially, we will see a huge decline in bond prices.

      1. I completely agree, with one major caveat, which is that if you intend to hold the bond through duration you will not suffer any capital loss assuming the bondholder pays back the bond. I probably should have added that and made it clear in the article. A more complex topic would be a discussion of the relationship between interest rates and bond funds.

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