Why bond prices fall when interest rates rise

It is the most important rule in fixed income and the one that surprises people most: when rates rise, the price of existing bonds falls, and vice versa. That is why a “fixed income” fund can show losses, and why your investment statement moves even when nobody has stopped paying.

The idea in one sentence

A bond promises fixed payments. If new bonds that pay more come out tomorrow, nobody will pay the same for the old bond that pays less. Its price has to fall until its return matches the market’s.

An example in pesos

You hold a bond with a face value of COP 10,000,000 that pays a 10% annual coupon (COP 1,000,000) for 5 years. If the market rate is 10%, it is worth exactly COP 10,000,000. See what happens if the rate changes:

The price is the present value of all the payments, discounted at the market rate:

How much does it fall? It depends on duration

The longer the bond, the more sensitive its price. That sensitivity is measured by modified duration: the bond in the example has a modified duration of about 3.8, which means that if rates rise 1 point, its price falls around 3.8%. A 10-year bond can fall twice as much with the same move in rates.

What happened in 2022

Between 2021 and 2022 Banco de la República (Colombia’s central bank) raised its rate from 1.75% to 12%, and the 10-year TES yield reached 15.43% in October 2022. Prices of TES and long-term bonds fell sharply, and many fixed income funds had weeks of negative returns. Those who held their securities to maturity received what was agreed; those who sold at the worst moment locked in the loss.

What to do with this

• If you will need the money soon, prefer short terms or securities you will hold to maturity.
• In a fund, check the duration in its fact sheet: it tells you how much it will move if rates change.
• If you expect rates to fall, longer-duration bonds will gain more in price.