How does duration and convexity impact bonds when rates fall?

With inflation slowing and converging to the 2% target, central banks have begun to set sail. Indeed, a terminal rate of close to 2% in Europe and 3.75-4% in the US is expected by 2025. It should be borne in mind that we are coming from 4.5% in the Old Continent and 5.5% on the other side of the Atlantic. 

It is true that, in addition to these downward rate trends, there are other aspects to take into account, such as the level of debt. However, it is just as true that for investors, a rate reduction scenario is a novelty they have not had for more than ten years, with interest rates falling sharply from 2018 to 2020. For this reason, the concept of duration and convexity of bonds must be well understood in order to understand the behavior of these assets in a scenario such as the current one.

The duration of a bond is not really the life of that bond, it is the sensitivity of the price of the bond to interest rates. There are three-year, five-year, ten-year and even thirty or more year bonds. But, in a scenario of falling rates, duration matters because bond prices are affected. 

When rates fall, bond prices rise for the simple reason that bonds issued at higher interest rates pay more coupon and therefore appreciate in value. That is, an investor can profit by selling a bond he bought in 2023 with rates at higher levels.

To see it with a more graphic example, the performance of the bond price varies according to the bond yield. In other words, if bonds issued between 2022 and 2023 offered a coupon (which is the percentage they pay on money borrowed in one year) of 4.5% because rates were at 4.5% and, one year later, rates fall to 3.5% and the coupon also falls, bonds issued before the fall will be more interesting to investors because they pay a higher coupon. For this reason, the price of the oldest bonds is rising.

As this is always the case, then in fixed income, if rates go down, the price of the bonds issued goes up. Whereas, when rates rise, the price of older bonds decreases because it is more attractive for the investor to buy new bonds -which will pay more coupon- than older bonds.

However, this is not the only concept to be taken into account. In addition, although what we have counted is the logical movement, many times the market moves driven by other criteria such as the level of debt or the expectations of interest rates and inflation. 

To better understand the interaction between the two concepts and their translation into reality, it is necessary to talk about the 1% rule. Generally, when rates go down, as they are now, bond prices go up, but by how much? It is estimated that for every 1% change in rates, the price changes by 1% per year of duration. 

For example, if interest rates in Europe fall from 3.5% to 2.5%, a ten-year bond will appreciate in price by 10%. This means that investors take less time to obtain the expected return on investment. But, as the market does not behave in such a linear and logical way, convexity helps to adjust this effect to give a more realistic view.

Convexity can be positive or negative, although for bonds there is usually no negative convexity, which tends to be typical of other more complex assets. For normal bonds, convexity is positive or neutral/zero. It is positive when the duration of a bond increases as its price decreases and negative when the duration increases along with its price. This is important because bonds with positive convexity are less sensitive to changes in rates and less harmful to investors.

In other words, the higher this convexity, the lower the price of the bond when rates go down, as is currently happening. Meanwhile, the price will also increase less when rate go up. In other words, there is less volatility. However, it may be in an investor's interest to bet on bonds with lower convexity when rates fall because they will rise more in price. 

In short, investors buy a bond with the intention that its price will appreciate, but also with the objective of earning a return on the coupon payment. If the bond lasts 10 years and the coupon is 4%, the investor will receive 4% each year on the total lent and this does not change if the price goes up or down.

The duration is used to measure the impact of the change in rates on the bond price and to know how many years an investor will take to recover their investment. For example, if the bond has a ten-year duration and rates fall, it will take the investor less than ten years to get his money back because the bond will appreciate in value.

To understand this concept, we must again bear in mind the premise that prices are rising when rates fall and vice versa. Thus, if an investor paid $50,000 for a 5-year bond with a 4% coupon, each year he will receive $2,000 per coupon. He would recover his money in the fifth year, in any case.

However, if rates fall in the second year, such a bond could cost $50,000 in the market. This means that if the investor sells it in that second year, he would get his money back at that time, in addition to having collected $4,000 ($2,000 each year for the coupon payment). Whereas, if rates rise, that bond could go to $46,000. This would mean that the investor would have to wait longer to recover their investment.

Convexity is the degree of sensitivity that each bond has to the fluctuation of interest rates. This is a very important measure because depending on the degree, the investor will have greater or lower volatility and will recover their money more or less quickly. If the investor's plan is to hold the bond to maturity, then these concepts are irrelevant because they will continue to collect the coupon payment regardless of what happens in the market. The importance of these concepts lies in buying and selling bonds without holding them to maturity by rebalancing or bond trading.

For the retail investor, this data is difficult to access, as it is generally information provided by the Bloomberg platform for investment professionals. Therefore, you would have to look at the historical performance of each type of bond and compare it with its performance against the evolution of interest rates/rates.