Fixed Income Volatility: Convexity

Convexity Simplified: What You Need to Know

Understanding Convexity in Bonds

Convexity is like a special tool to measure how sensitive a bond is to changes in interest rates. Imagine you have a favorite snack, and its price changes when the weather changes. Convexity helps us figure out how much the price of the snack (or bond) moves when the interest rates change.

What is Convexity?

Convexity is a way of looking at how a bond's price reacts when interest rates go up or down. It goes beyond just looking at how long it takes to get back the money you invested (which is called duration). Convexity helps us see the curve in the road, so to speak.

How to Calculate Convexity

To calculate convexity, we use a fancy formula. But you don't need to worry about the formula itself. What matters is that it considers the money you get from the bond over time, how long it takes to get that money, the bond's current price, and the interest rate.

Positive and Negative Convexity

Think of positive convexity like a good surprise. When interest rates go down, the bond's price goes up faster. It's like getting a bonus. On the other hand, negative convexity is like a bit of a downside. When interest rates go up, the bond's price goes down faster. It's something to be aware of.

Benefits of Convexity

Convexity helps us understand the risk of owning a bond better. It's like having a map that shows where the tricky parts in the road are. This way, we can make smarter choices when it comes to our investments.

Drawbacks of Convexity

Convexity can be a bit tricky to figure out. Sometimes, it might not be super accurate, especially if the bond is complicated or not traded a lot. Also, it assumes that the relationship between interest rates and bond prices stays the same, which might not always be true.

When to Use Convexity

Convexity is handy when we want to know more about the risk of interest rates changing. It helps us see a fuller picture and make better decisions about our money.

Common Misuses

Using only convexity to understand risk is like looking at only one piece of a puzzle. We need to look at other things too, like how long it takes to get our money back (duration) and other risk measures. Otherwise, we might miss important details.

Properties of Convexity

Convexity is buddies with duration. If a bond has a long duration, it usually has more convexity. Also, bonds with lower interest payments tend to have more convexity. But, as interest rates change a lot, the effect of convexity becomes less noticeable.

Wrapping it Up

Convexity helps us see the ups and downs in the road of bond investing. It gives us a better idea of what might happen when interest rates change. While it's a useful tool, we should remember it's not the only tool in our toolbox. We need to use it together with other tools to make the best decisions for our investments.

This article takes inspiration from a lesson found in FIN 4243 at the University of Florida.