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# Compounded Annual Growth Rate (CAGR)

Unlike the Average Annual Return (AAR), the Compounded Annual Growth Rate (CAGR) computes a rate of return that accounts for the compounding effect of reinvesting all funds in subsequent years. By accounting for compounding, the CAGR metric provides a better comparison between two investments than a simple AAR.

While a CAGR is normally computed to compare annual returns of investments, there is no need to limit the calculation to one year intervals. In the calculation section, below, arbitrary start and end dates may be used in the calculation. The formula simply normalizes the metric to represent annual performance.

The ability to calulate an annual performance metric using arbitrary date ranges is very important for creating Rolling CAGR metrics as another way of evaluating performance of an investment.

At MCI, we design our products to have high CAGR values and low volatility. CAGR is one of the preferred metics used by the MCI Team to give an honest comparison to other investments.

# Calculation

We report CAGR on an annualized basis, as a percentage gain per year, using the following formula:

$$CAGR = (\frac{FV}{PV})^\frac{1}{n} - 1$$

where: $FV$ = the future value of the invested amount (ie the value on the ending date of the calculation) $PV$ = the present value of the invested amount (ie the value on the starting date of the calculation) $n$ = the number of years between the starting and ending dates

To compute the CAGR for an investment between two arbitrary dates, we will need the starting date, the ending date, the initial amount of the investment, and the ending amount of the investment. We start by determining the value of $n$, using the starting and ending dates to calculate the whole plus any fractional portion of a year.

Once we have the value of $n$, we can plug all of the numbers into the formula and calculate the CAGR.

We calculate the CAGR on our backtested strategies by using this formula with the starting and ending dates of the backtesting period, and the initial and final amounts of the investment over the backtesting period. As an example, we’ll calculate CAGR for our CTB1 strategy, using the currently available performance data:

$PV$ = 10,000 on 01/01/1990 $FV$ = 8,511,126 on 12/22/2017

$n$ = 27.97 years

$$CAGR = (\frac{8511126}{10000})^\frac{1}{27.97} - 1$$

CAGR = 0.2728, or 27.28% per year

The CAGR provides a smoothed, sustained average rate of return as if the starting equity were compounded annually. In this example, the initial 10,000 investement on 1/1/1990 grew into \$8.51 Million over the 27.97 years of the backetesting period. This was equivalent to a 10,000 investement that was compounded at an annual rate of 27.28% over 27.97 years.