The Compound Annual Growth Rate (CAGR) is a frequently mentioned rate in investment analysis. When you hold investments for a number of years, in some years the rates are higher than in other years. The rates keep changing from year-to–year. The CAGR smoothens a number of annual rates that an investment may give over a period of time. For example, a share’s historical annual returns over a 5 -year period are as follows:
| Table 1 | |||
| Compound Annual Growth Rate Share A | |||
| Year | Share Price on 1 April | Share Price on 31 March | Annual rate of growth |
| 2015 | – | 100 | |
| 2016 | 98 | 105 | 7.14% |
| 2017 | 105 | 112 | 6.67% |
| 2018 | 112 | 124 | 10.71% |
| 2019 | 124 | 140 | 12.90% |
| 2020 | 140 | 101 | -27.86% |
| Compound Annual Growth Rate at the end of 2020 | 0.20% | ||
| Compound Annual Growth Rate at the end of 2019 | 8.78% |
How is CAGR Calculated?
Suppose an investor purchases a share worth Rs. 100 on 1 April 2015. Table 1 gives the annual growth in the share price for the next 5 years.
In the example, the Annual Growth Rate has fluctuated from 6.67 % % to -27.86 %, for various years. The question is how much have you earned on an annualised basis for the 5 years the investment was held? The answer to this question is provided by the Compounded Annual Growth Rate.
The formula for CAGR is
CAGR = {(Price at End – Price at the beginning) ^ (1/no. of years)}-1
To state the formula in notations, we can write it as,
CAGR = {(Pe – Pb) ^ (1/n)} – 1
Where
Pe = Price at the end of the period, in this case at the end of 5 years
Pb = Price at the beginning of the period, in this case the purchase price of Rs. 100
n = number of years that the investment has been held, in this case it is 5 years
Multiply the result by 100 to get percentage.
Substituting the data in Table 1 in the formula, we get,
CAGR = {(101-100) ^ (1/5)} – 1
= 0.0020
Expressed as a percentage, CAGR = 0.0020 x 100 = 0.20 %
CAGR tells us that the annualised compounded rate at which the investment grew during the 5 years of holding the investment, was 0.20 % p.a.
What is the advantage of knowing the CAGR?
The CAGR helps us to compare the result with other investments that may have been made and tells us whether we have earned more or less than other investments. On another share investment, suppose the annual rates of return are different as given below:
| Table 2 | |||
| Compound Annual Growth Rate Share B | |||
| Year | Share Price on 1 April | Share Price on 31 March | Annual rate of growth |
| 2015 | – | 100 | |
| 2016 | 100 | 110 | 10.00% |
| 2017 | 110 | 95 | -13.64% |
| 2018 | 95 | 98 | 3.16% |
| 2019 | 98 | 140 | 42.86% |
| 2020 | 140 | 97 | -30.71% |
If we want to compare the returns on Share A with that of Share B, so that we understand which of the two shares has given better returns, CAGR is the only method. The data in Table 2, for Share B, indicates that Share B has earned a CAGR of -0.61 %. We now know that Share A earned a CAGR of 0.20 % which is better than Share B, which earned a negative return of -0.61 %.
The CAGR earned by Share B is calculated as follows:
CAGR = {(Pe – Pb) ^ (1/n)} – 1
Substituting the data in Table 2 in the formula, we get,
CAGR = {(97-100) ^ (1/5)} – 1
= 0.0061
Expressed as a percentage, CAGR for Share B = 0.0061 x 100 = -0.61 %
What the CAGR does not tell us
It is equally important to know what the CAGR does not tell us.
- The CAGR is not an indication of the next year’s earning: Firstly, the CAGR is calculated at a point in time. It was calculated when the share prices fell substantially. The calculated CAGR for both Share A and Share B, indicate what the investor would have earned, if the investor sells the shares on 31 March 2020. In 2021 the CAGR would be different – either more or less than the CAGR of 2020. Therefore, it does not mean that the two shares will continue to earn the calculated CAGR for all times to come in future. The CAGR does not tell us the likely earning for the very next year.
1.1. Why is this important?
We often come across situations, where the financial advisor presents a high CAGR from past data and extends it to future years, as if the investment will earn a high rate in future also. This then gives a rosy picture to the customer who gets fooled into buying the risky investment.
Let us take the CAGR at the end of the financial year 2019 for Share A. It is 8.78 %. If one were to project 8.78 % for the future period, the earnings on Share A can be projected as quite high. But what happened in the very next year, in 2020? The CAGR fell to 0.20 %.
The current CAGR cannot therefore be taken to project the future. The CAGR is merely a convenient figure to compare past earnings of various investments. It has nothing to do with the future.
2. The CAGR hides volatility
If you observe the data in Table 1, the share price has fluctuated considerably, between 6.67 % to -27.86 % year to year. Similarly, in Table 2, the share price has fluctuated between – 30.71 % to 42.86 %. Such fluctuation is called volatility. In simple terms volatility is the extent of fluctuation of the price and the frequency of the fluctuations. That is,
• What is the upper and lower point of the share price in a given period? And,
• How frequently does the share price go up and down in that period?
The CAGR does not capture the volatility present in the share price movements.
2.1 CAGR is linear: In statistical terms, the CAGR is a linear representation of the compounded annual rate of return. It is a straight line. Flattening the fluctuations, the CAGR is a smooth linear curve. An example of the CAGR linear curve is graphically shown below:
Chart 1 above seems to suggest that the growth of the share price has been a smooth straight line starting from the year of investment, 2015. The reality is however different. The volatility is entirely missing in Chart 1. Risk in an investment is defined by the extent of volatility in the market prices. Chart 2 below shows how the CAGR of 0.2 % has been earned on a year to year basis.
Chart 2 shows the year-to year volatility in the price of Share A. Investors need to be told about volatility, not CAGR. CAGR merely gives a figure to compare two or more investments during a past period. Volatility gives an indication of the risk in the investment.
Why is it important to know that CAGR is linear?
Very often, there are articles in newspapers, and interviews on TV where the expert makes statements based on the CAGR. A representative statement is, for example,
Even if the investor earns a CAGR of 12 % on the investment in a (suggested) mutual fund, in 20 years’ time an investment of Rs. 100,000 will be Rs. 964,630!
WOW!
This represents an increase of 9.65 times! When this figure is dangled in front of the investor, the investor’s knees turn weak and he or she falls for the trap.
But CAGR does not work that way
CAGR does not grow in that linear fashion, on a year-to-year basis. There are ups and downs in the share price.
What is the impact of the share price volatility on the returns?
Let us go back to Table 1. Suppose an investor invests in the share when the price is Rs. 105 (2017). If the investor sells in 2019 for Rs.140, the investor’s CAGR is 5.92 %. If the investor keeps the share for one more year and sells it for Rs.101 in 2020, the CAGR is -0.97 %. This is the kind of impact that volatility has on returns. CAGR does not help you to understand this.
The only difference in CAGR of 2019 and that of 2020 is that the share prices crashed in 2020, bringing the overall return down considerably. In the crash the value of the investment has crashed considerably.
The timing is more important
In a high-risk investment, the timing of the buying and selling is more important than the period of holding. If the investor gets the timing wrong, the investment is unlikely to give adequate returns.
An investor wants to earn a decent return on investments. An investment in a high-risk instrument is made in the hope of earning more than normal returns. An investor investing in a bank deposit will not expect a high return. But an investor investing in a share will definitely expect; since the investor is bearing a risk. The investor is trading the higher risk for a higher expected return. While doing so, the market conditions are not in the hands of the investor. The investor, especially if the investor is a layman as far as investments are concerned, becomes a slave to the market forces.
It may be noted that in a low risk investment, there is no price crash. Value of the investment does not get eroded due to market conditions.
Which is why we
Sell risks not returns
Returns are Uncertain
Risks are Certain