Foundations

# Premium [Unlocked]: The Difference Between CAGR and XIRR Returns. How Much Did You Make?

Let’s begin by considering this investment illustration…

64K per quarter if you invest only Rs. 10 lakh! For six years! That’s like 16% a year! (You only get 64K per quarter for 6 years, and no principal is returned at the end)
But here’s what it really is. If you are an investor looking for capital appreciation (you don’t need the cash flow) then you just put the money in, and see how much you get at the end of 6 years. The answer? 15.38 lakh. For six years, that’s less than 7%.
Oh but wait, you can reinvest the money you get! Where can you put it? Something that gives you just 8% a year. And you need to pay some tax on the money you get each quarter. That will give you a net amount of 16.45 lakh after 6 years. You put in 10 lakh. So the return is a miserable 8.65%.

### What Just Happened?

The point was this: your Rs. 10 lakh became Rs. 16 lakh in six years. That’s all. And that is just 8.65%.
The problem was: they kept giving you back your money, and your alternative avenues to reinvest were only 8%.
That’s what you should look at as an investor focussed on Capital Appreciation. IF you are looking for cash flow (money to spend) then this is a good idea. Of course, anything that promises IRRs of 16% or more tends to be a scheme that has too much risk. (If you don’t know what the risk is, then it’s too high a risk to take)
For a capital appreciation investor, things are different. You have to calculate things as if you invest money and take it out only at the end. So lots of entries and one big exit.

### The Way to Calculate Returns: First, The CAGR

Let’s say you have a big amount of money. A lump-sum, say 10 lakh. You invest that into stocks. And it grows. You sell a little and use that money to buy other stocks. Whatever dividends come in, you use it to buy more stocks. And it grows, slowly, to Rs. 20 lakh in six years.
Your money doubled in six years. This is a 12% return per year.
This is a Compounded Annual Growth Rate. A CAGR. You put in money at one time, and that’s how much the portfolio grew.
You will compare this 12% return to the return of a mutual fund manager. This is how the fund growth is evaluated – the change between two NAVs (Net Asset Values) at two different dates, suitably annualized, is the “CAGR” of the Fund. So you have a 3 year CAGR (now minus 3 years ago, annualized)
But hardly anyone does anything like this. You don’t put money just one time. You put money every month. Every month, you buy a little more. You might call it an “SIP”. Or just a regular investment. But you don’t buy at one shot, you buy every month.
What’s your return now? It’s complex. If you invested Rs. 50,000 per month for two years, and stopped, then didn’t invest more for four more years. At the end you are at Rs. 18 lakh, your return is – what?
You invested 12 lakh. (24 x 50,000) It is now 18 lakh. So you made Rs. 6 lakh in profit. That is 50% in say 6 years. Does that mean your return is about 8% a year? (50/6)

### Enter the XIRR

We add another Four Letter Acronym to confuse you. The XIRR. The Internal Rate of Return. We’ll get to the “X” later.
It accounts for cash flows. You put 50,000 in month 1. It’s invested for 6 years. You put Rs. 50,000 in month 2, it’s invested for 5 years 11 months. And so on for each installment of Rs. 50,000 for 24 months. If you use a single rate of return for each installment, how much would that get you?
An XIRR would tell you how much return you actually got. For example at 6% such a cash flow would earn you Rs. 16.11 lakh. Too low, your portfolio is now worth 18 lakh. So you try 7%. That gave you a cash flow of Rs.16.89 lakh. Not big enough. You keep trying until you reach the answer: 8.34%.
That’s your XIRR. This is YOUR return. It’s not the same as the underlying portfolio CAGR, which is likely to be different.

### Forget that, show me an example: Capitalmind Momentum Portfolio

We have done it all. We started the new Momentum portfolio in 2016 november. We bought in four tranches. Each tranche was about 1.4 lakh. Then, we rejigged stocks every month. How do we get the portfolio’s return? Till now?
First, the CAGR. The portfolio plot looks like this:

This is of no use. You can’t use this bumpy chart. It has the cash flows as big “upjumps”. One for each tranche. So we adjust this curve. How?
We calculate the daily return for this portfolio. If you add more cash (buy another tranche) we back it out for that day. So when we bought the second tranche of Rs. 1.4 lakh, that day’s data would show a much higher number than for the earlier month. So we remove 1.4 lakh from that day’s number, and keep the daily return noted. This gives us a smooth equity curve. And here’s how the return curve (arrived at through the daily return method).

This is the return of the portfolio. No matter when you bought into this portfolio, you made the return curve after that point. If you bought on 21/12/2016 your return was 40% since then. If you bought in Feb 2017, you got in at 115 (a 15% return from start) and now it’s 140 (40% return) which to your portfolio is a return of 21%+.
(To be fair, this is pretty good as a return, but we digress.)
This one isn’t compounded or annualized. The portfolio has only been around about 6 months. If we annualized a 10 day return of 5% we would get some ridiculous annual return of 350%+. Even higher if you assume 10 day compounding. That makes no sense. So you compound only after a year (assuming profits are reinvested after one year). And you look at annualized returns only after you’re invested about one year or more.
However this is how the CAGR is calculated – you just annualize point to point returns on the absolute return graph.
And here’s how the portfolio works in terms of XIRR. You invested in four months (Nov, Dec, Jan, Feb). You got back money today. An amount of Rs. 7.74 lakh.
This is how your XIRR is, today:

The formula is in Excel (or online spreadsheets). You get the annualized return for these “cash flows”.
Note: This is why the “X” before the IRR. It’s a rate of return but for irregular cash flows. The distance between the dates is not uniform. So we use an XIRR to calculate this.
101.8% was for today. What was it yesterday? The day before? And so on?
We calculated them and show them to you in a graph:

As you can see this isn’t moving up. But that makes sense. If I want to make 30% i don’t want to start with 1% and keep going up to 30%. I want the return to be stable at 30% as much as possible.
Of course, markets are volatiles, so XIRR will at some point go up and then down. As we move on to longer terms, the XIRR will stabilize.
Let’s now say you invested in the same portfolio but only did two tranches. Your XIRR would be different. But your CAGR would be the same (the upper curve, but after you invested)

### Why CAGR or XIRR?

When you want to find out how much your money has made for you, you want to use an XIRR. If you invest in tranches, life gets complicated. You can’t just say I invested Rs. 1000 a month for five years, and now I’m at Rs. 100,000 so I have 66% return. The CAGR here doesn’t make sense because you invested at different times. The XIRR of the cash flows will help you.
(Btw, It’s fine to say it when you’ve only invested for six months – the time value of money isn’t so apparent)
When you evaluate a fund’s performance you will use it’s CAGR. The curve of the NAV over time tells you how stable the fund’s return is. The CAGR for multiple periods tells you the same thing. The fund manager’s prowess comes into play in a CAGR calculation.
When you evaluate your own performance, you will use XIRR. If you invested in a fund over 5 years, with investments done every month (an SIP), you will need to use XIRR to evaluate what you would have made.

Dividends are cash flow out. Into your bank account. If you reinvest them, then don’t bother recording anything. If you don’t reinvest them, they are cash flow out (kind of like selling and taking money out). Record these appropriately.
Buybacks are also cash flow out unless you reinvest.
Rights issues are fresh investments.
The idea is simple: Your returns are based on how much you put in and when. And how much you take out and when. And always, the last entry assumes you take out everything today, to give you the return picture.