If you invest in stock market you would have heard umpteen times the importance of “Power of Compounding”. It is a basic mathematical function – exponential – which leads to huge numbers as the compounding frequency increases. And the same is true about decay function, or negative compound as well. However, the world of investing is always in complete awe of power of compounding.

The principle has some value, but I think it is now one of the most misunderstood concepts. Some true stalwarts have quoted compounding, which are often used to sell the concept. For example, Albert Einstein famously said:

### “The greatest shortcoming of the human race is our inability to understand the exponential function.”

— Albert Allen Bartlett

This is very true – mathematically. It is also true in case of personal finance. That is how all Mutual Funds sell their Systematic Investment Plans (SIPs).

Then the same principle is used to create “inspiring” or “most motivational” message such as follows:

And this is where the misunderstanding of power of compounding lies. The message says that if you give your 99% everyday – for 365 days – you would end up at 0.03. If you give 100% everyday – for 365 days – you would end up at 1 (the message doesn’t mention it, but that’s the baseline case). And if you give “a little bit extra”, 101% everyday – for 365 days – the result is staggering! You would end up at 37.8! That is 37.8 times more than what you would achieve by giving 100% everyday! Just 1% extra effort and such a huge reward! Really motivating! But only for people who don’t understanding mathematics properly.

It is all good in pure numbers, but it doesn’t work in that manner in real life. CAGR (Compounded Annual Growth Rate) is a derived number – based on what you achieved over a period of time. It is not something which you can “chase” or “set as target rate”. Most of the life happens in non-linear manner and it would be foolish to chase a rate of compounding.

Also, “giving 1% extra or 1% less everyday” is all good in theory – what does it really mean? How does it translate into actions? It doesn’t make sense. It may motivate some people to start something but not to sustain it forever.

Does it mean that the idea has no utility? Absolutely not. It helps us understand that

1. Starting early and sustaining it for longer period has huge advantage
2. Having a trajectory is important. Purpose of CAGR should be just as a guiding path, not as a target. You will have to continuously monitor and revise the trajectory to achieve goal. Because things don’t happen in linear manner as planned

Here is another chart that is often cited by long-term investment community and advocates of “patience” and “power of compounding”

This is how Net Worth of Warren Buffett grew exponentially, after age of 50 or so. Yes, graphically it is true. And if you have read Buffett’s letters, he would talk of CAGR of ~19-20% for 50-52 years!

But that’s the backward-looking calculation. You cannot start today and say that you would earn 19-20% returns every year. That’s plain wrong. You cannot chase target in that manner. You’ll have to earn 30-40-50% returns for many years and limit bad years to lower returns (0-3-5%) or even occasional negative return years (-5 or -10%).

So the way compounding can help is by setting some intermediate milestones, say 5-10 years and setting different compounding return targets for those milestones. Remember, it is very easy to grow \$100 to \$200, but extremely difficult to grow \$1M to \$2 million (and far more difficult to turn \$1 Bln into \$2 Bln).

And yet, the idea of compounding is very appealing in investment world and lot of people try to apply it in different domains. Here is one interesting article I read today:

#### The Power of Compounding Small Daily Decisions

Intelligent Fanatics is an interesting initiative and you can read some interesting articles on their blog. It is also available in Book format.

Another interesting website you should follow for worldly wisdom is Farnam Street run by Shane Parrish. Farnam Street is the address where Warren Buffett lives. Though it is named after Buffett’s home, the blog is largely influenced by Buffett’s partner Charlie Munger‘s concepts of mental models.

Do check some interesting articles there and share more of such resources if you know.