Fixed Income Volatility: Macaulay Duration

Understanding Macaulay Duration of a Bond

Macaulay duration helps us figure out how much a bond's price might change when interest rates move. It's like estimating the average time it takes to get back the money we invested in a bond, considering both interest payments and the return of the initial investment. Let's break it down in simple terms.

What is Macaulay Duration?

Macaulay duration is like an average timer for a bond. It looks at how soon we get back the money we put in, including interest payments. This helps us know how the bond's price might change when interest rates go up or down.

How to Calculate Macaulay Duration

We can find Macaulay duration using a formula. We look at each future cash payment, see when we get it, and consider its value today. We add up all these values, and that gives us the Macaulay duration. It's a bit like finding the average time it takes to get our money back.

Example

Imagine a bond with a face value of $1,000, a 5% interest rate, and it pays us $50 each year. If it takes 5 years to get all our money back, and the interest rate is 4%, Macaulay duration helps us find that, on average, it takes around 4.93 years to get our money back.

Why Macaulay Duration Matters

Knowing Macaulay duration helps us understand how sensitive a bond is to changes in interest rates. If the duration is higher, the bond is more sensitive. It's like saying, if interest rates change, the bond's price might go up or down more.

Benefits and Drawbacks

Benefits: Macaulay duration tells us when we might get our money back and helps us see how sensitive a bond is to interest rate changes.

Drawbacks: It might not be perfect. It assumes that changes in bond prices happen in a straight line when interest rates change a little. For big changes, it might not be so accurate.

Conclusion

Macaulay duration is like a tool helping us understand bonds better. It's not perfect, but it gives a good idea of when we get our money back and how bonds react to interest rate changes. This way, we can make smarter choices when dealing with bonds in the world of finance.

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