You are a portfolio manager who has presented a report to a client. The report indicates the duration of each security in the portfolio. One of the securities has a maturity of 15 years but a duration of 25
The client believes that there is an error in the report because he believes that the duration cannot be greater than the security's maturity. What would be your response to this client?
Unfortunately, market participants often confuse the main purpose of duration by constantly referring to it as some measure of the weighted average life of a bond. This is because of the original use of duration by Macaulay where the cash flow for each period divided by the market value formed a weight with the weights adding up to one. If you rely on this interpretation of duration, it will be difficult for you to understand why a security with a maturity of 15 years can have a duration greater than 25 years. For example, consider collateralized mortgage obligation (CMO) bond classes. Certain CMO bond classes have a greater duration than the underlying mortgage loans (because CMO bond classes are leveraged instruments whose price sensitivity or duration are a multiple of the underlying mortgage loans from which they were created). That is, a CMO bond class can have a duration of 25 although the underlying mortgage loans from which the CMO is created can have a maturity of 15 years.
The answer to the puzzle (about duration being greater than maturity) is that duration is the approximate percentage change in price for a small change in interest rates. Thus, a CMO bond class with a duration of 25 does not mean that it has some type of weighted average life of 15 years. Instead, it means that for a 100-basis-point change in yield, that bond's price will change by roughly 40%. Similarly, we interpret the duration of an option in the same way. A call option can have a duration of 25 when the time to expiration of the option is much less than 25 years. This is confusing to someone who interprets duration as some measure of the life of an option.
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