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The full form of CAGR is a Compound Annual Growth Rate. It measures the annual growth of an investment over some time. It is used to ascertain and compare the past performance of investments, or to project their expected future returns.
An investment that works on the principle of Power of Compounding, is the only investment that lets your investment grow manyfold and build wealth for you. You can say it is the growth rate that gets you from the initial investment value to the ending investment value.
It determines the real return on investment (ROI) by calculating the year over year returns, compounding them, and considering the investment values.
It is a far more realistic way to measure the overall return on investment than using an average returns method.
What is CAGR
CAGR shows how much a person’s investment grew over a specific period. In other words, it is the average returns an investor has earned on the investments after a given interval say one year. The bank or the financial institution calculates this rate in terms of percentage.
Any specific mutual fund plan would not provide a constant rate of return every year. The rates change from year to year.
Besides, when we make repeated investments, we want to know the return earned on all the investments together.
Say, for example, you invested in ELSS with a 5-year tenure. CAGR will tell you how much return this fund has earned you every year during this period.
Remember, this is applicable only for Growth Funds, that is, when the gains are re-invested. Not for Dividend Mutual Funds, where you get to withdraw your gains.
How to Calculate CAGR
The calculation of the compound annual growth rate formula is a bit complicated. You need to first divide the ending value by the beginning value of your Mutual Fund Investment. You get the total percentage of growth rate with that. Now you compute the nth root of that rate where n is the total number of years in the investment period. Then subtract one. It might be easier to look at the equation. Here it is.
CAGR Formula: WealthBucket
CAGR Formula Explained
To understand the CAGR Formula, let’s first begin by defining Growth.
Growth = End Value – Start Value
Example: If an investment of Rs. 2,00,000 grows to a value of Rs. 5,00,000, the growth is Rs. 5,00,000 – Rs. 2,00,000 = Rs. 3,00,000.
Now comes the Growth Rate. It is calculated as the Growth divided by the Start Value.
Growth Rate = Growth/Start Value = End Value/Start Value – 1
Example: Continuing the above example, the Growth Rate is Rs. 3,00,000/Rs. 2,00,000 = 1.5 or 150%
Note: We can also use Return on Investment (ROI) for the Growth Rate if we want to account for the interest earned, dividends, fees, and commissions, or a series of investments. When using ROI, Growth = Net Profit and Start Value = Total Investment.
Now let’s calculate the Annualized Compound Growth Rate. This is derived by compounding the growth rate over the number of years that we had our investment, using the APY formula (substituting Growth Rate for r and 1/Years for n).
APY = (1 + r ) ^ ( n ) – 1
APY = (1 + Growth Rate ) ^ ( 1 / Years ) – 1
Example: Staying with the above example, if our investment was growing for 3 years, the annualized growth rate = (1+150%)^(1/3)-1 = 35.72%
CAGR = APY = (End Value / Start Value) ^ ( 1 / Years ) – 1
Example: We can see that the CAGR calculated in the previous step is the same as the
APY = (5,00,000/2,00,000)^(1/3)-1 = 35.72%
More Example
Let’s assume you put Rs. 5,00,000 into an investment today. A year from now it grows to Rs. 6,00,000. A year after that it grows to Rs. 6,50,000, and next year it grows to Rs. 7,50,000. In the last year, it was valued at Rs. 10,00,000. To calculate the CAGR, we first compute the change in value (Rs. 10,00,000/Rs. 5,00,000 = 2). We can now take the percentage change in investment and adjust it to the power of the number of years in the investment period ( 1/4 years).
So our CAGR equation would be 2 ^ 0.25 – 1 or 2 to the .25 power minus 1.
The CAGR for the 4-year investment comes to be 18.92%.
Another Example for Comparison with Average Annual Return
Although the Average Annual Return is a common measure to evaluate Mutual Funds, CAGR is a much better strategy to measure an investment’s return over time because it considers investment losses.
For example, take Year 1 and Year 2 of our hypothetical investment in Fund XYZ. At the end of Year 1, the portfolio value falls from Rs. 1,00,000 to Rs. 75,000 for a return of -25% [(75,000 – 1,00,000)/1,000 ]. By the end of Year 2, the portfolio value had grown by +33% [(1,00,000 – 75,000)/75,000 ].
Averaging the Year 1 and Year 2 returns over two years gives us an average return of 4% [(-25 + 33)/2 ]. But that doesn’t truly reflect what has happened. We started at Rs. 1,00,000 and ended at Rs. 1,00,000, which is a return of 0%.
With this example, we can understand why CAGR is a better measure of return over time. Average annual return ignores the Power of Compounding and it can overestimate the growth of an investment. Whereas, CAGR is a geometric average that represents the one, consistent rate at which the investment would have grown if the investment had compounded at the same rate each year.
Advantages of CAGR
The Compound Annual Growth rate is a useful tool for comparing different investments over a similar investment horizon.
Moreover, it is considered better than an average annualized rate of return is that it is not influenced by percentage changes within the investment horizon that may show misleading results.
For Example: An investment gave a 25% return in the first year, raising the value from Rs. 1,00,000 to Rs.1,25,000. If all capital was reinvested in the same mutual fund plan for the next year, which gave a -25% return, the value of the investment would fall to Rs. 93,750. This is less than the initial investment amount.
| Year | Amount | Return |
|---|---|---|
| 0 | Rs. 1,00,000 | – |
| 1 | Rs. 1,25,000 | 25% |
| 2 | Rs. 93,750 | -25% |
| Average Returns | 0% |
|---|---|
| CAGR | -3% |
This clearly shows that the investment generated losses over a two-year horizon. With averaging returns, you will feel that there was no change in returns over the two years.
Disadvantages
- Smoothing
Compound Annual Growth Rate assumes growth to be constant throughout the duration of an investment. This smoothing mechanism may produce results that differ from the actual situation for a highly volatile investment.
| Year | Amount | CAGR (in %) | CAGR (in Rs.) |
|---|---|---|---|
| 0 | Rs. 1,00,000 | – | Rs. 1,00,000 |
| 1 | Rs. 1,25,000 | -3% | Rs. 96,825 |
| 2 | Rs. 93,750 | -3% | Rs. 93,750 |
Example: The Compound Annual Growth Rate correctly shows the ending value of the investment if a -3% CAGR was applied over a 2-year compounding period. However, the Compound Annual Growth Rate assumes that the investment falls at a constant 3%, when, in fact, it grew by 25% in the first year.
CAGR can be used as a tool to make a quick comparison between different investment options. But the final decision should be made by considering the trade-offs between risk and return.
Investor Actions
CAGR does not take into account a change in the value caused by investor decisions to further fund or liquidate the asset.
| Year | Amount | Change by Returns | Change by Investor |
|---|---|---|---|
| 0 | Rs. 1,00,000 | – | Rs. 1,00,000 |
| 1 | Rs. 1,20,000 | Rs. 20,000 | – |
| 2 | Rs. 2,30,000 | Rs. 10,000 | Rs. 1,00,000 |
| 3 | Rs. 2,00,000 | Rs. (-)30,000 | – |
As seen in this example, the source of value is important. In this case, zero returns have been generated by the asset. CAGR is coming to be 26%. Because the losses in the final year cancel out the gains in the first and second years. However, the value of the investment increased as a result of adding more funds to the initial investment. This raised the value of the investment although that increase was not generated by a matching performance. But the compound annual growth rate did not consider the reason for the change of value.
Points to Note
- The CAGR does not indicate any sale that happened from the starting year to the last year.
- In some cases, all the growth may be focused only during the initial year or in the last year.
- Sometimes, two investments may have the same CAGR. Though one is more lucrative than the other. This could be because the growth was faster in the initial year for one, while the growth happened in the last year for the other.
- Compound Annual Growth Rate is generally employed for investment periods ranging from 3 to 7 years. If the tenure is more, say 10 years, then the CAGR may hide the sub-trends in between.
- Remember, CAGR is different from year-on-year (eg: return on 30th August 2018 vs that on 30th August 2019) growth rate.
A Brief About Other Returns
There are other types of returns, besides CAGR, that help in analyzing the performance of Mutual Funds. A few have been explained below:
1. Annualized Returns
It is the geometric average amount of funds that investment creates every year for a fixed time. Annualized Returns signify the return rate an investor earns for a given period, considering the annual compounding. This shows how the investment would perform without focusing on the market volatility of markets.
2. Trailing returns
This is used for calculating the historical performance of funds on a daily, weekly, monthly or annual basis. Trailing returns method is ideal for a one-time investment. If you invest an amount on 30th August 2019, the 1-month trailing return period will range from 30th August 2019 to 30th September 2019.
3. Return since launch
The value of Return Since Launch is ascertained from the time an NFO (New Fund Offer) gets closed. They calculate it at an opening Net Asset Value of Rs. 10.
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