What exactly is the concept of CAGR in returns?
Be it profits or sales or investments; the one thing you want to figure out is how they grew over time. When the growth is for a period of one year it is quite simple. But what if the capital appreciation of your investment is over a longer period of 3-5 years. That is when CAGR becomes applicable.
The most common one amongst the various measures to measure returns over a longer period is CAGR. In other words, CAGR is the annualized growth rate of investment over a period of time. It is a measure of how much your investments have grown during a given interval of time considering the impact of compounding on an annual basis.
The beauty of CAGR is that it considers the value of money. For example, if Rs.100 grew to Rs.130 in 3 years, then in simple terms the annual average return is 10%. But there is a flaw in that this does not calculate the power of compounding and hence gives the wrong picture of returns over a longer period of time.
Can CAGR be applied to calculate mutual fund returns?
In fact, one of the best measures of returns on a mutual fund over a period of time is CAGR. This is very simple in case of growth plans but can get complicated in the case of dividend pay-out plans and dividend reinvestment plans. One can use the concept of CAGR to estimate mutual fund returns and investment performance more effectively over a longer period of time. It considers time value and assumes that all intermediate returns are effectively reinvested into the portfolio. Thus is it is more scientific.
How to calculate CAGR of a mutual fund over time?
It is a very simple step by step process you need to follow as under
- In the first step, you take the NAV of the fund at the end of the investment period or what you call the closing value.
- As the second step, you must fetch the NAV of the fund at the beginning of the investment period, or what we call the starting NAV.
- The third steps is to calculate the CAGR as per the formula used to calculate the geometric mean. Here is how you go about it.
CAGR = {(Ending NAV of the fund / Starting NAV of the Fund) ^ (1/ No. of years)} – 1
Here is how it would work in practice. If the NAV of the fund at the time of investment is 100, which grows to 170 in 4 years. As per the formula using above, one may calculate CAGR to be 14.19%. In other words, it is assumed that the NAV appreciated in a compounded manner at 14.19% each year over a period of 4 years. The actual returns annually may be different.
Can you tell me how to calculate CAGR returns?
To calculate the compounded annual growth rate or CAGR, follow the following steps. These are very simple steps.
- Divide the investment value at the end of the period by the initial investment amount. Let us call the output as “X”.
- Calculate the nth root of “X”. That means if the period is 2 years then calculate square root of X and if it is 3 years then cube root of X and so on.
- From the output that you get from Step 2, deduct 1. The result is the CAGR in decimal terms. You can multiple by 100 to get CAGR in percentage terms.
You can convert the above explanation into a formula as under.
Here, FV is the future value of the investment, PV is the present value of the investment, and n represents the number of years of investment.
Can you explain CAGR to me with a real life example?
Let us assume that your investment of Rs.10,000 grows to Rs.13,000 in 2 years. Normally, the period is longer, but for the sake of simplicity of calculations, we are just using 2 years here. Let us apply the CAGR calculation formula here.
CAGR = {(FV / PV)1/n } – 1
Now let us impute the numbers in the formula and what do we get?
CAGR = {(13,000 / 10,000)1/2 } – 1 = 14.02%
You can verify if the CAGR calculation is correct. At CAGR of 14.02%, the investment of Rs.10,000 grows to Rs.11,402 at the end of 1 year and to Rs.13,000 at the end of 2 years. That matches with our final value of the investment.
So, that is how the CAGR can be calculated. For longer tenures like 5 years or 10 years, it is simpler to use a scientific calculator or to use an excel spread sheet.
Are there any shortcomings in the CAGR calculation?
While the CAGR is a good measure overall for compounded returns, it has some limitations. Here are a few of them.
- It does not give a true picture of the volatility of the returns since the returns are smoothed based on the starting point and the ending point. For example, let us look at two funds with NAV movements as under.
| Period | NAV of Fund A | NAV of Fund B |
|---|---|---|
| Start | 100 | 100 |
| Year 1 End | 115 | 90 |
| Year 2 End | 130 | 140 |
| Year 3 End | 145 | 145 |
In the above case, both Fund A and Fund B have moved from Rs.100 to Rs.145 in 3 years so in both cases, the CAGR returns would be 13.19%. However, in the second case, Fund B is extremely volatile and for any prudent investor Fund A is the obvious choice. The CAGR does not reflect this difference.
- Another limitation when assessing investments based on CAGR is that there is a tendency to assume that the CAGR will persist in the future also. However, that may not be the case in reality.
- CAGR is not effective for calculating returns from investments where the investing is periodic, as in the case of systematic investment plans or SIPs. In such cases, the IRR is a better measure.
Is CAGR the same as annualized returns?
No they are different. Annualized returns refer to simple annual returns generated by mutual fund scheme during the investment period. They use the arithmetic mean. Going back to our example of Rs.100 appreciating to Rs.170 in 4 years, the annualized returns would be 70% divided by 4 i.e. 17.5%. However that is not the correct picture.
If you use the CAGR method, you arrive at 14.19% which is more reflective of the correct picture since the time value and the power of compounding is factored in this calculation. CAGR is a better approximation compared to annualized returns.
Is CAGR the same as irr or internal rate of return?
The IRR (Internal Rate of Return) is a much better measure when the outflows are periodic or inflows are periodic. For example, in case of SIPs, dividend plans, money back plans, systematic withdrawal plans where there are intermediate flows, then IRR is a much better measure as it factors the time value of each intermediate flow.
CAGR considers only one investment amount while the IRR has the flexibility and the ability to calculate returns through various investment amounts made at different periods.
