# Is there a term that better describes a compound annual growth rate (CAGR) when it is negative?

When calculating rates of return for an investment or portfolio over time, whether to report or compare performance, one frequently calculates the Compound Annual Growth Rate (CAGR).

I've got a situation where I want to describe the resulting rate for a sum of money that has decreased over time, and it feels odd to refer to the result as the compound annual "growth" rate. So:

Is there an idiomatic term in the domain of finance that better describes a compound annual growth rate (CAGR) when one expects the result to be negative?  i.e. when an amount shrinks over time instead of growing — deflation instead of inflation.

I've thought about "compound annual shrink rate" and "compound annual loss rate", etc. and I can think of a variety of other possibilities, but I'd like to know what wording is common usage, if any.

Not sure why CAGR is a problem for both directions.

I used to be a physicist, and, when I taught classes in graduate school, students always wanted to use the terms "accelerate" and "decelerate" to describe "speeding up" and "slowing down". But acceleration is just a vector with magnitude and direction. There's nothing special about slowing down that it needs a special name. It's just acceleration in a direction opposite to the direction of motion.

I think the same thing applies here. There's nothing special about negative growth rates that they need a special name. Just stick a minus sign in front of the number and you convey the required information.

My experience is in economics, so it may differ from an accounting or personal finance perspective somewhat; that being said, I find it perfectly acceptable to use a term like CAGR when the rate is positive or negative. Economists talk about negative growth rates all the time, and it's universally assumed that growth rates can be positive or negative.1 Ideally, the actual magnitude and sign of the value should be specified by the value itself. The term, whether it's "growth rate", some modified version of it like CAGR, or any label in a table or on a graph, should describe the calculation or source used obtain the value. I shouldn't need the name to indicate the sign of the number if the number is present; the name is only there to help me understand the value.

Unfortunately, I don't know of any specific term that represents the geometric averaging nature of CAGR and also eliminates the minor potential for semantic confusion. However, I think the minor problem of semantics needs to be balanced against the tradeoff of using a different term that isn't as common, if one were to exist. CAGR is a standard, well-known term that a) allows someone who is familiar with the term to instantly understand the procedure you're using, and b) allow someone who isn't familiar with it to quickly search and find an explanation, since searching for CAGR will numerous simple explanations of how it's calculated.

1. This is different from the concept of economic growth, which is usually assumed to be positive in informal discussions. In economic modeling, many of the first steps in creating a model are symbolic anyway, so "growth rate,", "change in output", and "economic growth" are used interchangeably to describe changes in GDP because the values either aren't known, irrelevant until later in the project, or pulled from data that describes it using one or several of the previously stated terms.

Same question had popped up in our office,and we got an answer from one of the senior colleague. He said that we can call it CARC (Compounded Annual Rate of Change).

• Welcome to Money.SE. I am the down vote. A search finds no reference to CARC as being in use, anywhere. I'd suggest caution when taking any personal finance from this person. Aug 23, 2017 at 12:17
• @JoeTaxpayer Compounded Annual Rate of Change returns 21,600 pages in Google, including at least one that uses the CARC acronym. That's nothing to CAGR's 6.5 million results, but it does appear to at least be used by some folk. Aug 23, 2017 at 15:51
• (Raises fist) "Damn you, google" - I searched the acronym, not the words. I appreciate the note. Aug 23, 2017 at 15:54