Last Updated on December 29, 2021 at 5:15 pm
A few months back we saw what a compounded annual growth rate (CAGR) is and how it is calculated in the case of a lump sum investment.
In this post, let us consider a mutual fund SIP and calculate the associated return.
First a quick recap.
Lump sum investment: Non-volatile instruments
When a lump sum is invested in a non-volatile instrument like a fixed deposit, the maturity value is clearly known even before the investment starts. This is because there is well defined compounding – quarterly in most cases.
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So the CAGR is a well defined number. For quarterly compounding, it is simply the effective annualized rate.
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Lump sum investment: Volatile Instruments
When the lump sum is invested in volatile investments like gold, real estate or stocks, the maturity value can be just about anything – a 100% more or 100% less!
So the CAGR can be calculated only when the current value is known (in contrast for a fixed deposit, the current value can be calculated with the CAGR).
For volatile instruments there is no compounding! There is only appreciation or depreciation of the underlying asset (stock, bond, commodity, real estate etc.)
We calculate CAGR by pretending the instrument compounds at a rate r
r = CAGR =(maturity value/investment)(1/years)-1
For more details on how this is related to annual returns, see here.
Recurring investment: Non-volatile instruments
The recurring deposit is an example of periodic investments in a non-volatile investment. It is nothing but a series of fixed deposits of reducing the tenure. For example, if you open an RD for 2 years, the 1st instalment is an FD of 24 months duration. The second instalment is an FD of 23 months duration and so on.
Therefore, here again the maturity value is known before the investment begins.
Check out the comprehensive recurring deposit calculators available @ freefincal
Recurring investment: Volatile Instruments
The monthly SIP is a classic example of this category. There are several ways to calculate the associated return. A couple of them can be found here: Mutual Fund SIP Returns Calculator
Before we understand how to calculate returns from a volatile instrument like a mutual fund SIP, I request you to stare at this spaghetti making machine for a few moments.
Photo Credit: cefeida (Flickr)
Now let us ‘draw’ some analogies
Investing in non-volatile instruments
Lump sum investments: A single spaghetti strand of known length
Recurring investments: Multiple spaghetti strands of known but different lengths
In both cases, since the lengths are known, there is nothing to calculate.
Investing in volatile instruments
Lump sum investment: A single spaghetti strand of unknown length
If I give you the strand, you can easily DETERMINE the length. No big deal.
Recurring investment: Multiple spaghetti strands of unknown length
Now, how will you go about determining the average length of the strands?
Here is another picture to drive home my point. Excuse my indulgence. I simply love spaghetti!
Photo Credit: renekyllingstad (Flickr)
Since it is not practical to measure the length of each strand and average it, you ESTIMATE the average length.
Similarly,
- for lump sum investments in volatile instruments, you can DETERMINE the CAGR if you know the current value of the investment. The answer in this case is exact (assuming there is compounding involved).
- for recurring investments in volatile instruments, you can only ESTIMATE the CAGR if you know the current value of the investment. The answer in this case is approximate (again assuming there is compounding involved).
Why the spaghetti analogy? Why estimate?
The reason will become clear when we realise that some SIP instalments may occur during market lows and some during market highs. So each instalment will have different current value depending on the date of purchase.
For example, when direct mutual fund plans were introduced, the value of my monthly investments in HDFC Top 200 regular plan was green (positive) while the value of monthly investments in the direct plan was red (negative) for a long time.
That is each instalment grows at an entirely different pace. Hence, the analogy with spaghetti strands of different and unknown lengths.
We will need to estimate CAGR because the investments were made at different points in time and we always look at the total value of all the instalments.
Don’t worry too much about the math that follows, it would suffice if you could appreciate the difference between determining CAGR for lump sum investments and estimating CAGR for SIP investments.
The CAGR for SIP investments is estimated by an iterative technique called Newton Raphson method. Excel implements this via an extraordinarily simple function known as XIRR.
Investors who have online accounts in portals like ICICI AMC, FundsIndia, Value Research and software packages like MProfit must be familiar with the use of XIRR for SIP investments. Xirr is also used in my mutual fund tracker.
Here is the formula (take a deep breath!)
Try to pull the CAGR to one side. That is, try writing this equation as
CAGR = (rest of the quantities)!
Well, you cannot. It is impossible. Therefore, the CAGR is estimated.
To estimate something, you need an approximation technique. There are several available. Each of them will have its own limitation!
If the current value is much lower than the total investment, that is if we suffer a loss and if it is a heavy one, XIRR usually gives an error.
This means the CAGR cannot be estimated or there are multiple solutions to the given problem!!
More about XIRR
- IRR/XIRR – Excel – Limitations of Calculating Complex Cash Flow Returns
- Excel IRR and XIRR: Spot bugs and understand errors with this cash flow returns analyser
Resources
Note
Sometimes people assume SIP installments are spaced 30 days apart, ignoring both the actual number of days in a month and number of business days. This is done using Excel functions IRR and RATE. See this Excel sheet. While it is one thing to assume investments are spaced 30 days apart while planning for a financial goal, it is quite another to make that assumption for ongoing SIPs. One must always use the XIRR function for ongoing SIPs.
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