Compounding is said to be the 8th wonder of the world. Rightly so. It is the fundamental phenomenon behind any long term success in any domain – evolution, investing, fitness, skill development, relationships and so on.
Here is a statement that I have probably made the most on Twitter…
Right from the Big Bang (which led to the advent of the universe, to formation of Solar System, to formation of Earth, to life, to human beings!) to the success of Facebook & Amazon, every success has undergone a compounding (every failure too has compounded at a negative growth rate!).
In plain English, the phenomenon of Compounding is that Success begets success. Every success:
1) makes a system inherently strong
2) opens new avenues, and paves way for future success
Amazon, which started as a e-store for books, built on initial success and expanded on reach, products, competitive strength etc.
Every time a species survived a period of crisis, it evolved into a stronger species. Even within a species, there were random mutations and exaptations. Every time, those with a particular trait survived, they continued the gene pool.
I intend to write on how to use this fundamental phenomenon in everyday life. I also want to delve into a misconception about Compounding which the best of best seem to be having.
But first, let’s get the mathematics out of our way…
Formula of Compounding
What is Compounding – Compounding is an iterative process, where the starting base P changes with a certain rate r over a number of iterations t. With every iteration, the changes made in P gets appended back to it, before the next iteration starts.
Suppose P = 100, r = 5%. After the first iteration, P becomes 105. Now, in the next round of iteration, it is 105 (not 100) that grows by 5%.
In the similar vein, if r = -5%. After the first iteration, P becomes 95. Successive r% works on 95.
The Objective – With P as a starting base, the objective is to grow it over time. As you can see there are three levers to grow – P, r and t. The question is which lever is more important.
P, the starting base, is obviously important. As many investors say, to make money, you need money. It’s easier to become a billionaire, if you are already a millionaire. However, the problem is that it is not in your control most of the time. It is a given state, the starting point.
r is more important than P, because it is something that you can control. Also, it is powered by t, so it carries more, well, power!
The most powerful lever is t as it forms the power in this function – the number of successful iterations. This is surely in your control (as long as you are not too hardpressed for time!).
Let me throw some examples about how compounding works in our day to day life.
Example1: Let’s say you want to learn swimming.
Formula:
Perfect Swimming = Current level of skill (1+(amount of practice or learning rate))(no.of practice sessions)
It will help, if you already know the basics of swimming and do not fear water. But, that is something which is (as we say in algebra) “given” in the problem.
Your amount of practice & learning rate surely matters. However, it is very difficult to put more than 1 hour in a serious practice session.
If you want to learn swimming quickly, the best way to do it is to practice daily, rather than only on weekends, which is better than practising once a month, which is better than practising only when you visit a resort once in 3 months!
Your current swimming skill is a given. There is a limit to how much you can learn in one session. The best way to learn swimming quickly is to practice everyday – daily compounding!
Example 2: Liver Damage because of alcoholism
Liver Damage = Current Liver Condition (1-(amount of alcohol consumed per session) (no.of sessions)
This is an example of negative compounding – how people, businesses, health, relationships etc get caught in a negative vicious cycle and head to ruin. In this particular example, if you get into a daily/regular habit of drinking, you are doomed at a fast pace. Your liver doesn’t even get time to recover. This is obviously worse than occasional binge drinking, where you drink like nuts with your old friends and get back to routine life till you meet them again in 3 months!
Example 3: Netflix = -r% Books = +r%
Again occasional binge watching is fine. But, if you squander your time, series after series, while your competitor/peer is spending the same time on honing her skills, or working on her project, or reading books…no prize for guessing, who’s emerging as a better person on the other side.
As Mark Minervini said,
“Right now, somewhere out in the world someone is tirelessly preparing for success.”
As you can see from these examples, why habits are so important. Habits are compounding iterations! Let’s see what such compounding iterations do for fitness.
Example 4: Fitness
Dwayne Johnson = Current You (1+(Resistance Training))(no. of training sessions)
You compound the current you through a regimented resistance training for several months/years and voila…You become Dwayne Johnson!
Example 5: Investing
Wealth = Initial Capital (1 + r)(no. of years)
You know the drill by now! I tell you the solution to create long term wealth. All you need is an Investment Process that gives you a consistent positive r. Once you have it, all you need is several iterations.
You don’t have to chase a big growth rate. You don’t need a big r, all you need to ensure that r is positive. You must have read about the 1.01 vs 0.99 rule – You get 1% better vs 1% worse everyday for 1 year. A small difference in r, +0.01% vs -0.01% makes so much of a difference is compounded everyday for an year. The final value of INR 1 is Rs.37.8 and Rs.0.03 in the respective cases.
(1+0.01)365=37.8
(1-0.01)365=0.03
I reiterate, it’s great if you have a high r, but all you need is a positive r, as long as you have enough number of iterations.
One Last Thing: A common fallacy
You will hear even the best proponents of compounding and long term investing say that “the problem with compounding is that most of the gains are back ended.” Often that famous example of Chinese Bamboo is given – they apparently don’t show any progress, while you keep watering them; and then after testing your patience, they grow to great heights.
Also, often the example of Warren Buffett is quoted saying that most of wealth got generated after he crossed 70 years (even though he started at the tender age of 11!). This statement is specious. It gives you an impression that Compounding is a slow way of gaining, it needs patience…and possibly there is a faster way of gaining other than compounding. Let me clarify here…with the exception of subatomic world, a lottery, or adoption by a wealthy person or any such plain luck, there is no quantum leap in real life. All gains happen one step at a time. You don’t become strong & powerful overnight. Your business doesn’t grow multi-fold overnight. Earth took billions of years to form. Amazon was not the largest company the day it was formed. And yes, Warren Buffett took all those years to compound all that wealth.
The quoted statement is correct in the absolute value sense. In absolute terms Warren Buffett has made far more money after 70s than what he made in 20s. When we look at a typical exponential graph of compounding, it appears that most of the gains have come recently. But, here is the myth buster…
Assume that someone started investing with $100. She compounded the money by 20% for 80 years (on similar lines with Warren Buffett). Her money grew into some astronomical figure in 80 years…the figure being irrelevant here. Look at the chart representing the growth of the wealth.
It appears that the wealth started growing only after 50 years, especially after 70 years. Until 50 years, the growth looks conspicuous by its absence. One may conclude that Compounding is slow and back ended. Let’s break up the chart, and look at the first 50 years and what happened there!
What do we see here! The first 50 years also saw equally phenomenal growth. But yet again, it appears that most of the growth came after the age of 20, especially after 40! One can again fall to the conclusion that Compounding is slow & back ended!
You know the drill by now. Let’s break it up again and see how the first 20 year look. You can guess what’s coming!
Yes, as you probably guessed, the growth is equally good in the first 20 years as well. This property of Scale Free Distributions is called “Self Similarity”. The distribution looks similar at all scales (Similar to the Fractal Nature of Stock Price Charts! – Those who look at stock charts would have a sense of deja vu. They would have experience the self similarity of stock charts in all time frames…more on that separately in a different Blog!)
As you may be coming to the realisation now…Compounding was never slow, it was never back ended, and it never needed your virtue of patience. It was always rewarding you, building over your base. You were always climbing up – one step at a time!
For an investor who started with a capital of 100, reaching 3195 in 20 years is equally good as reaching 758370 in 50 years and a humongous 180019039 in 80 years! Mind you, at the age of 20, the investor has not even imagined something like “180019039”. So her anchor is not this humongous final figure, it is the $100, she started with, isn’t it! When you start exercising, while you may have a goal of being fit like Dwayne Johnson someday, but you get motivated at every stage of the build up of muscles. That build up keeps you going through the grind session after session.
This settles the argument that Compounding is slow and back ended. This also settles the quest for finding an alternative faster quantum leap. I reiterate…there is no quantum leap in domains of fitness, success, skill development, investing etc. Compounding is not back-ended. It is the fastest and the only way to grow. Irrespective, of what your starting base is (P), all you need is a positive r and enough iterations!