## Tuesday, June 29, 2010

### CAGR II

Recently, I was given an opportunity by a reader to explain more about CAGR. It's not a brand of cigar. It's refers to compounded annual growth rate - a calculation to find out the compounded returns per year (note that this is different from simple interest rate). I actually wanted to share how silly this calculation is about but I had a feeling that I've written about it donkey years ago. After searching, I realised I did write an article about CAGR here, so I'll just highlight or perhaps add some points to it.

Frankly, I've not used CAGR for years because of I realised that with one calculation, the whole story can be quite distorted. Basically the calculation of CAGR depends on three variables - Future value, present value and time period. The most significant gripe I have about CAGR calculation is the fact that you can get hugely wide differences in value by just changing the variables. Essentially it boils down to a GIGO (garbage in garbage out) system where the output depends firmly on the input that you put it.

 CAGR CIGAR is a stick used for smoking, giving a pleasurable feeling afterward

Take a look at this example. Let's say these are the figures for yearly profit from year 1 to year 4 respectively:

10, 15, 20, 25

Present value: 10
Future value: 25
Time period: 3
CAGR: 35.7% per yr

Here's another example of yearly profit from year 1 to year 4 respectively:

10, -2, 45, 25

For those who are synchronous with me in thought would have realised that the CAGR for the two examples are exactly the same. Why? The first example and second example looks very different but the three variables that affect CAGR calculation - namely present, future value and time period - are all the same.

So, what does that leave us?

1. Firstly, you must realise that the CAGR just draws a straight line between the start value (present value) and the end value (future value) and ignores all the ups and downs in between them. In a non-linear world, this assumption is just plain bullshit. I can make a good CAGR by carefully selecting my base year and my final year, so do be careful of it. Statistical calculation must be treated firstly as a blatant lie.

2. Secondly, it would be better to accompany CAGR calculation with the actual values of the data points in between the present and final values. To make it better, I would suggest a graph. It's like doing linear regression calculation in A'lvls - you must accompany each calculation with a scatter plot. This will give a bigger picture of the meaning of the CAGR value calculated.

3. Lastly, I simply do not use it anymore. From experience, projecting the past into the future is at best a guesstimate because the reality could be more optimistic but usually more pessimistic. Since it's a guesstimate, there's really no need to put a numerical figure to your guesstimate. I do not use it anymore because I fail to see the value of such calculations in fattening my wallet, though it might well do to fatten my ego.

Createwealth8888 said...

1) Total Invested Capital (Initial Value)

2)Current Portfolio Value (Current Stock Value + Realized P/L + Cash Availble)

3) No of years in investing

Very useful in measuring how well you use your capital and revise your investing strategy over your investing time frame

http://createwealth8888.blogspot.com/2009/08/measure-measure-measure-part-2.html

Createwealth8888 said...

Why are you trying to forecast your future using CAGR?

Createwealth8888 said...

Currently, how do you measure how well are you doing with your capital?

Anonymous said...

Hi LP,

Hmmm, I don't know if I've left any other reply before but I've definitely been reading your blog for about a year now, and enjoying your insights, ideas & analysis. Real good stuff. Keep posting =)

Cheers,
~K

la papillion said...

Hi bro8888,

I think cagr can be used to find out one's investing returns per year, compounded annually. However, it doesn't work if you inject or withdraw cash, affecting the initial value. I have such problems because I never did fix a investing capital and see how much it'll grow from there. I continually invest more over the years.

I'm not forecasting my future with CAGR. I'm forecasting data when analysing a company, e.g. revenues, cashflow etc. But that was in the past, I no longer do that now.

I did a unit trust method to calculate the NAV value of my holdings. By comparing the NAV value of my total portfolio from this period to the next, I can compute the returns. However, it suffers from the the same problem when I take out and inject cash into the system, the NAV would be distorted.

I figured that once I can set a fix amount each year, I can compute my returns on a yearly basis. That would have to wait till my major affairs are settled. Till then, I've all the data to calculate them (I keep a good record of changes in my portfolio on monthly basis) but I did not compute my returns.

la papillion said...

Hi K,

Createwealth8888 said...

If you not really concern on your investment performance and to measure returns on investment to review and refine investment and trading strategies, you might be better off in investing and re-investing in SGS (bonds)i.e. be a fixed income retail investor.

Createwealth8888 said...

CAGR III - an alternative view.

http://createwealth8888.blogspot.com/2010/06/cagr-iii.html

la papillion said...

Hi bro8888,

I disagree that if one is not concerned over investment performance, then one should be better off doing bonds. Bonds returns, esp treasury bonds, are pathetic and the money is locked over such a long period of time in order to earn that miserable returns. Corporate bonds are another different animal altogether.

It's also not true that I'm not concerned about performance. I did tabulate my returns in the form of NAV. It's just different from yours, which is using CAGR.

1. I didn't say that measuring is not impt. In the post, I am referring to CAGR calculation as a way to forecast trends, which is what I did in my valuation in the past. I no longer do that because forecasting trends is just pointless.

2. I saw how you adjusted the % for putting in cash and taking out cash. I wouldn't do that myself. I'll stick to my NAV way of measuring returns.

3. I don't know why we're talking about investment returns here. I thought the whole post is about using CAGR to calculate data like revenue, earnings, profit etc? I'm showing how unreliable using CAGR to forecast trend can be, and to warn readers about it. I think your first paragraph is quite uncalled for. You totally misquoted me out of context.

Createwealth8888 said...

You use CAGR to measure the past performance on investment returns and can also use CAGR to determine what sort of returns that is expected to get there.

e.g.

If I have 100K as capital and I want to have \$1M in 20 years. I will have to invest at CAGR = 12.2%

If I have 500K as capital and I want to have \$1M in 20 years. I will have to invest at CAGR = 3.5%

la papillion said...

Hi bro8888,

Ya, but there are always issues on how to maintain that rate for 10-20 yrs. I saw your post on trading here and there, I agree to that more than putting into someplace for long term at 10% pa. Sounds more do-able.

Grey said...

LP, the NAV of the unit trust method won't be distorted if you add units at the price of entry when you inject funds and subtract units at the price of exit when you withdraw funds;

WeoW!

la papillion said...

Hi Grey,

Yes, I remembered that you had shown me a post about it in your blog :) Thanks for the reminder :)

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