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.

So the CAGR is a well defined number. For quarterly compounding, it is simply the effective annualized rate.

Check out the comprehensive **fixed deposit calculators** available @ freefincal

**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 1^{st} 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.

Dear Pattu

Thanks for sharing this article. Could you please write a comprehensive article in which the entire gamut of your investment philosophy is covered? A step-by-step right from the Frugal approach till the investment strategy at micro level.

Thanks. Will do this soon. I have however covered different aspects at different times. See:

http://freefincal.com/the-contended-investor/

http://freefincal.com/personal-financial-audit/

Thank you Pattu! Since I have been visiting this site and reading your articles, sometimes I felt that where to start, what to read first and next to implement it in our financial planning. Even a sequence of articles will help. Thanks again!

Well, first would the financial plan creator as it can gives you a sense of perspective on where you stand. You could also implement based on how much you need to invest etc.

Dear Pattu

Thanks for sharing this article. Could you please write a comprehensive article in which the entire gamut of your investment philosophy is covered? A step-by-step right from the Frugal approach till the investment strategy at micro level.

Thanks. Will do this soon. I have however covered different aspects at different times. See:

http://freefincal.com/the-contended-investor/

http://freefincal.com/personal-financial-audit/

Thank you Pattu! Since I have been visiting this site and reading your articles, sometimes I felt that where to start, what to read first and next to implement it in our financial planning. Even a sequence of articles will help. Thanks again!

Well, first would the financial plan creator as it can gives you a sense of perspective on where you stand. You could also implement based on how much you need to invest etc.

Sir wrt sip-cagr investor version-1, in sip calculator how come there is a high variation in the corpus accumulated when sip date falls in the beginning of the month or at the end of the month?

Sir wrt sip-cagr investor version-1, in sip calculator how come there is a high variation in the corpus accumulated when sip date falls in the beginning of the month or at the end of the month?

Hi

Thanks for the article on cagr and xirr

I have seen that software like mprofit do not calculate xirr for a particular period

They do it since inception.

How does one do it for a selected period like a quarter or a year. What do you suggest. .is they’re an online calculator

Can do it for a particular fund. I have rolling returns sheets for that. Cannot do it for entire folio.

Dear Pattu

CAGR calculation for a SIP is explained. Hence we get different CAGR for different SIPs in each MF. If I get 5 CAGRs viz 7%, 10%, 12%, 19% and 15% in 5 different MF with estimates value at the time of calculation as Rs. 90,000- First MF , Rs. 80,000-2nd MF , Rs. 60,000 3rd MF, Rs 85,000 4th MF, 1,00,000 for 5th MF then what is the calculation of aggregate CAGR for all folios,