Investment Horizon, Macaulay Duration, and Interest Rate Risk

There is an important link between investment horizon and Macaulay duration of a bond that relates to the balance of these two risks. The difference between Macaulay duration and investment horizon is called __duration gap__. Duration gap can be positive, negative or zero. For example, an investor might own a bond with a long duration but have a short investment horizon. In this case the duration gap is positive.

Ned Neutral is interested in the same bond as Mary Short and Dr. Long. He has an investment horizon of nine years. Since this is equal to the duration, his duration gap is zero. If interest rates fall, any gains that Ned will realize from an increase in price will be offset by losses from dividend reinvestment. The reverse is true if interest rates rise.

To summarize: [[summary]]

Who has the larger duration gap?

A positive duration gap leads to risk that interest rates rise and a negative duration gap has risk that interest rates fall. When do the risks fully offset each other?

Incorrect. This is a negative duration gap, so the dominant risk is from interest rates falling.

Correct! The impacts offset for an investor with an investment horizon equal to the Macaulay duration of the bonds.

Incorrect. This is a positive duration gap so the dominant risk is to interest rates rising.

Incorrect. Be sure to look at investment horizon and Macaulay duration.

Incorrect. The duration gaps are different.

Correct! Mary Short has a duration gap of 4 years, while Dr. Long has a duration gap of -3 years.

As an example, there are two investors, both interested in a bond with a nine-year Macaulay duration. Mary Short has an investment horizon that is five years and Dr. Long has an investment horizon that is 12 years. The risk for each of these investors comes from different sources.

The risk for Mary Short comes from higher interest rates. Since she is going to sell her bonds in five years, her biggest risk is from a loss in value if interest rates rise. The biggest risk for Dr. Long is reinvestment risk. Since he is holding the bonds almost to maturity, a fall in interest rates is the dominant risk.

Dr. Long

Mary Short

Both are the same

-5 year duration gap

0 year duration gap

10-year duration gap

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