# Understanding Macaulay Duration | CFA Level I Fixed Income

Duration is an essential concept to understand the interest rate risk of a bond. In this article, we’ll explore the concept of Macaulay duration and its importance in bond investing.

## Investment Horizons and Interest Rate Risks

Investors with different investment horizons experience varying effects on their returns due to changes in market interest rates. Short-term investors are more concerned with market price risk, while long-term investors worry more about reinvestment risk.

So, how can we find an equilibrium point where the effects of changes in yield-to-maturity on both market price and reinvestment return balance each other? Enter the concept of duration, particularly Macaulay duration.

## What is Macaulay Duration?

Macaulay duration measures the sensitivity of a bond’s full price to changes in its yield. A high duration means a high price fluctuation when the yield changes, and a low duration implies lower price fluctuations.

Macaulay duration is calculated as the weighted average of the number of years until each of the bond’s promised cash flows is paid. The weights are the present values of each cash flow as a percentage of the bond’s full value.

## Calculating Macaulay Duration: Steps

To calculate Macaulay duration:

1. Identify all the cash flows.
2. Discount each cash flow to its present value using the bond’s yield.
3. Divide each present value by the bond’s full value to get the weights for each year.
4. Calculate the Macaulay duration by summing the product of each weight and the number of years to the payment of the cash flow.

EXAMPLE

Let’s calculate the Macaulay duration of a bond with the following characteristics:

After following the steps above, we find that the Macaulay duration of this bond is 2.792 years.

## Duration Gap and Investor’s Returns

If an investor’s investment horizon matches the bond’s Macaulay duration, the changes in yield-to-maturity will have minimal impact on the investor’s net return. The difference between a bond’s Macaulay duration and the investor’s investment horizon is called the duration gap.

In conclusion, Macaulay duration is a crucial measure for understanding a bond’s sensitivity to changes in interest rates. However, there are other improved measures of duration that we’ll discuss in future lessons. Stay tuned!

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