Can CAGR Be Negative? Here’s What It Means

The Compound Annual Growth Rate (CAGR) provides a smoothed, annualized rate of return. CAGR can be negative, indicating a decline in value over the specified period.

What is Compound Annual Growth Rate (CAGR)?

Compound Annual Growth Rate represents the average annual rate at which an investment or value grows over a defined period, assuming profits or earnings are reinvested. It offers a standardized measure of growth, smoothing out the volatility of year-to-year returns.

CAGR calculates the geometric mean of growth rates, providing a single, constant rate that leads to the final value from the initial value, assuming continuous compounding. It differs from a simple average because it accounts for the compounding effect, where returns generated in one period can earn returns in subsequent periods. This makes it a more accurate representation of growth over time. For example, comparing the performance of different investments over the same timeframe becomes more straightforward using CAGR. It is widely applied in finance to analyze investment funds, compare advisor performance, or evaluate business metrics like sales and market share.

How CAGR is Calculated

The calculation of Compound Annual Growth Rate involves a specific formula that considers the beginning value, the ending value, and the number of periods. The formula for CAGR is: CAGR = [(Ending Value / Beginning Value)^(1 / Number of Periods)] – 1. This formula effectively determines the constant annual rate of return that would connect the initial and final values over the entire duration.

To illustrate how a negative CAGR can result from this calculation, consider an investment portfolio that started with $10,000 at the beginning of a three-year period. At the end of the first year, the value was $11,000. By the end of the second year, it declined to $9,500, and by the end of the third year, the portfolio’s value was $8,000. In this scenario, the ending value ($8,000) is less than the beginning value ($10,000).

Applying the CAGR formula, the calculation would be: CAGR = [($8,000 / $10,000)^(1 / 3)] – 1. This simplifies to [ (0.8)^(0.3333) ] – 1. Calculating this, (0.8)^(0.3333) is approximately 0.93. Subtracting 1 from 0.93 yields -0.07, or -7%. Therefore, the CAGR for this investment over the three years is -7%.

Interpreting a Negative CAGR

A negative Compound Annual Growth Rate indicates that an investment or value has decreased over the specified period. For instance, if an investment portfolio shows a negative CAGR, it means the portfolio’s overall value has diminished from its starting point.

In practical terms, a negative CAGR for business metrics like revenue or market share suggests a contraction rather than expansion over time. It signals that the capital employed has not generated positive returns or that the business segment is shrinking. While a negative CAGR highlights this decline, it does not explain the underlying reasons for it, such as market downturns, operational inefficiencies, or increased competition. Understanding a negative CAGR is important for investors and financial analysts, as it prompts further investigation into the factors contributing to the decrease in value.