CAGR – A Parable

‘Hey! I made 3.2% on my investments last week,’ my friend came running to me all jubilant and brimming with pride.

 

‘That’s pretty good,’ I replied.

 

‘Pretty good! The sandwich I had this morning was pretty good. 3.2% in a week means 166.4% in a year. And that’s not even considering the compounding effect. My week was brilliant.’

 

‘That’s a very nice thought,’ I say. ‘However, that’s not how investments work. Or math works for that matter.’

 

‘Huh?’

 

‘Take a step back. How did your portfolio perform in the week before this one?’

 

‘Something like a negative 1%.’

 

‘So shouldn’t your projection for the next 52 weeks take at least the past 2 weeks into consideration? You know they say the best way to predict the future is to look to the past.’

 

‘So you’re saying that in the next year I’ll make only 3.2% - 1% = 2.2% per week? That’s still a pretty good year.’

 

‘That’s not what I’m saying. I’m saying that if you use CAGR to project in time periods ahead, you’re going to end up with very weird answers. CAGR is a tool for averaging the past, not projecting the future. When you have long time periods and you want to understand them, CAGR comes in handy. It tells you your average gain (or loss) every year which will take you to the same result. It’s basically the same concept as IRR, only in reverse.’

 

My friend looked confused. ‘So when mutual fund houses tell us that they made 80% annualized returns this quarter because they made 20% this quarter…’

 

‘They’re thinking you’ll be dumb enough to buy into that crap. Most reputed funds will not present annualized numbers to you unless the return period is over a year. For most major funds and analysts, daily, weekly, monthly, or quarterly returns are not annualized but only the nominal values are presented. If a fund were to present these numbers on a day when the market moved 1%, their monthly returns would be say 30% while the annual returns would be…’

 

‘365%! That’s insane!’

 

‘Precisely.’