what is average annual growth rate aagr 
the average annual growth rate aagr reports the mean increase in the value of an individual investment portfolio asset or cash flow on an annualized basis it doesn t take compounding into account formula for average annual growth rate aagr aagr gra grb grnnwhere gra growth rate in period agrb growth rate in period bgrn growth rate in period nn number of payments begin aligned aagr frac gr a gr b dotso gr n n textbf where gr a text growth rate in period a gr b text growth rate in period b gr n text growth rate in period n n text number of payments end aligned aagr ngra grb grn where gra growth rate in period agrb growth rate in period bgrn growth rate in period nn number of payments understanding the average annual growth rate aagr the average annual growth rate helps determine long term trends it applies to almost any kind of financial measure including growth rates of profits revenue cash flow expenses etc to provide the investors with an idea about the direction wherein the company is headed the ratio tells you your average annual return the average annual growth rate is a calculation of the arithmetic mean of a series of growth rates aagr can be calculated for any investment but it will not include any measure of the investment s overall risk as measured by its price volatility furthermore the aagr does not account for periodic compounding aagr is a standard for measuring average returns of investments over several time periods on an annualized basis you ll find this figure on brokerage statements and in a mutual fund s prospectus it is essentially the simple average of a series of periodic return growth rates one thing to keep in mind is that the periods used should all be of equal length for instance years months or weeks and not to mix periods of different duration aagr examplesthe aagr measures the average rate of return or growth over a series of equally spaced time periods here are two examples assume an investment has the following values over the course of four years the formula to determine the percentage growth for each year is simple percentage growth or return ending valuebeginning value 1 text simple percentage growth or return frac text ending value text beginning value 1simple percentage growth or return beginning valueending value 1thus the growth rates for each of the years are as follows the aagr is calculated as the sum of each year s growth rate divided by the number of years aagr 20 12 5 18 5 25 4 19 aagr frac 20 12 5 18 5 25 4 19 aagr 420 12 5 18 5 25 19 in financial and accounting settings the beginning and ending prices are usually used some analysts may prefer to use average prices when calculating the aagr depending on what is being analyzed as another example consider the five year real gross domestic product gdp growth for the united states over the last five years the u s real gdp growth rates for 2018 through 2022 were 0 7 1 8 3 9 7 0 and 2 6 respectively thus the aagr of u s real gdp over the last five years has been 3 2 or 0 7 1 8 3 9 7 0 2 6 5 1aagr vs compound annual growth rateaagr is a linear measure that does not account for the effects of compounding the above financial investment example showed that growth over four years averaged 19 per year the average annual growth rate is useful for showing trends however it can be misleading to analysts because it does not accurately depict changing financials in some instances it can overestimate the growth of an investment for example consider an end of year value for year 5 of 100 000 for the aagr example above the percentage growth rate for year 5 is 50 the resulting aagr would be 5 2 however it is evident from the beginning value of year 1 and the ending value of year 5 the performance yields a 0 return depending on the situation it may be more useful to calculate the compound annual growth rate cagr the cagr smooths out an investment s returns or diminishes the effect of the volatility of periodic returns cagr ending balancebeginning balance1 years 1cagr frac text ending balance text beginning balance frac 1 text years 1cagr beginning balanceending balance years1 1using the above example for years 1 through 4 the cagr equals cagr 200 000 100 00014 1 18 92 cagr frac 200 000 100 000 frac 1 4 1 18 92 cagr 100 000 200 000 41 1 18 92 for the first four years the aagr and cagr are close to one another however if year 5 were to be factored into the cagr equation 50 the result would end up being 0 which sharply contrasts the result from the aagr of 5 2 limitations of the aagrbecause aagr is a simple average of periodic annual returns the measure does not include any measure of the overall risk involved in the investment as calculated by the volatility of its price for instance if a portfolio grows by a net of 15 one year and 25 in the next year the average annual growth rate would be calculated to be 20 to this end the fluctuations occurring in the investment s return rate between the beginning of the first year and the end of the year are not counted in the calculations thus leading to some errors in the measurement a second issue is that as a simple average it does not care about the timing of returns for instance in our example above a stark 50 decline in year 5 only has a modest impact on total average annual growth however timing is important and so cagr may be more useful in understanding how time chained rates of growth matter 