There are three methods used to calculate the annual growth rate of an indicator. Average Annual Growth Rate (AAGR), Compounded annual growth rate (CAGR), and exponential trend function. Among the three, the most commonly used methods are AAGR and CAGR.

## What is Average Annual Growth Rate (AAGR)?

Average annual growth rate (AAGR) refers to the average increase in value of an individual’s investment portfolio over the period. This can be evaluated for any kind of investment, be it stocks, bonds, futures, options, retirements, savings, insurance, cryptocurrencies, etc. However, this calculated value does not include any risks involved in the investment, such as volatility of the market. Also, this does not account for the compounding of growth.

## Average annual growth rate formula

Average annual growth rate (AAGR) is calculated by taking the arithmetic mean of the growth rates over that period. Apart from this average annual growth rate formula, you can also use an average annual growth rate calculator available online.

AAGR = (G1 + G2 + G3 + …………… + Gn) / N

Wherein, G1 is growth rate over period 1

G2 is growth rate over period 2

G3 is growth rate over period 3

Gn is growth rate over period n

N is number of payments made, or the total number of periods

For computing growth rates in percentage over a period, the following formula is used:

G = {( FV / IV )-1} x 100%

Wherein, IV is the value of investment at the start of the period, i.e., initial value.

FV is the value of investment at the end of the period, i.e., final value.

NOTE: The length of each period remains the same (month, quarter, year, etc.) This value becomes useless if the length of the period is varied as the calculation then becomes faulty.

## What does Average annual growth rate mean? What does it signify?

It is a standard of measurement of growth over several periods of time. You will often find this figure on brokerage statements and mutual fund prospectuses. It is also used by financial analysts and economists to find changes in economic activity in a company, organization, or country (GDP).

In simple terms, AAGR is considered useful in defining the direction of the trend of growth of a commodity or investment. Whether the trend is growing upwards, or dropping down.

### Example

Below are the values of investments for the portfolio of XYZ.

Year 1: Rs. 250

Year 2: Rs.280

Year 3: Rs.320

Year 4: Rs.290

Year 5: Rs.250

Using the above formula, growth rates can be calculated as:

Year 1: 0, as no time period before this year

Year 2: {(280 / 250) – 1} x 100 = 12 %

Year 3: {(320 / 280) – 1} x 100 = 14.285 %

Year 4: {(290 / 320) – 1} x 100 = – 9.375 %

Year 5: {(250 / 290) – 1} x 100 = – 13.793 %

Average annual growth rate =  Sum of growth rates / Number of years

AAGR = [0 + 12 + 14.285 – 9.375 – 13.793] / 5 = 3.114 / 5 = 0.6234

So, the AAGR for the portfolio of  XYZ is 0.6234 %

However, we can clearly see that the overall growth rate of the company XYZ is 0% as revenue for year 1 is the same as the revenue generated in year 5, which is Rs.250,000.

Due to this phenomenon, AAGR is not considered the correct way to measure growth and thus is not commonly used for analysis. Most analysts use Compounded annual growth rate (CAGR) for their calculations.

## Limitations of AAGR

Let us take an investment that provides growth of 25% in its first year followed by 15% growth in the next year. So, the AAGR for the total period of these two years will be 20%.

While calculating the AAGR, any fluctuations that occur in the rate of return of the investment between the starting of the initial period and the ending of the final period are not taken into consideration.

This can be responsible for mistakes in estimating the value. Average annual growth rate is taken as the average of annual returns, hence it can not provide any information on fluctuations occurring in the price of the commodity, hence no insights are provided on the risk involved in investing and the volatility of the market.

Also, AAGR is not able to accommodate compounding and its effects, as this calculated value is linear in nature. An analysis may be able to draw out information such as growth of the commodity as x percent over a large period, but never be able to deduce fluctuations happening over smaller individual periods within that large period.

AAGR is useful for depicting the trends; however, it can be misleading as it is unable to depict changing financials accurately. Moreover, AAGR remains oblivious to volatility in the market and often tends to overestimate the change in value of the said investment.

To better understand the limitations, let us look back at the volatility of investments. Volatility is the degree of fluctuations or change occurring in the price of the portfolio over a given time period. For example, if the price of investment fluctuates very often for a given period, then the investment is considered highly volatile. On the other hand, if the price remains constant, then it is considered less volatile.

Two factors contribute to volatility: negative returns and distribution of returns.

### Negative returns

Let us assume our initial investment is Rs.100.

In case 1, you gain 15% in year 1 and lose 15% in year 2. The reverse of the same is in case 2.

 Impact of Negative returns Case 1 Case 2 Start 100 100 Year 1 15% 115 -15% 85 Year 2 -15% 97.75 15% 97.75 AAGR 0% 0% CAGR -1.13% -1.13%

This phenomenon is often termed as ‘Compounding’s Revenge’. Whenever you lose money, it takes even greater returns just to break even. So, if you lose say 20%, you will need to grow 25% just to break even.

### Distribution of returns

For the illustration below, AAGR is 10% for all the cases. As the distribution of returns grows, CAGR shrinks further.

 Impact of Distribution of returns Case 1 Case 2 Case 3 Start 100 100 100 Year 1 10% 110 15% 115 30% 130 Year 2 10% 121 10% 126.5 0% 130 Year 3 10% 133 5% 132.825 0% 130 AAGR 10% 10% 10% CAGR 10% 9.92% 9.14%

Upon combining the above two, it is evident that AAGR is not an efficient means for calculating annual growth rates and can often overestimate the value in growth.

## Conclusion

AAGR is a good tool to estimate the direction of trends and should be used carefully.