Magic Of Compounding

Let me share with you one of the stories of Tenali Rama. Rama was one of the eight poets in the court of Vijaynagar King Krishnadevaraya. Apart from being a poet, he was also very wise and clever. One day, King Dhananjay of another kingdom wishes to attack Vijaynagar. Rama takes it upon himself to visit King Dhananjay and tries to stop the war. Dhananjay is pretty adamant that he would not back down. However, he is also very pleased with Rama’s wisdom and hence, wishes to reward him. Since he is very proud of his wealth, he asks Rama to ask him for whatever he wants, except of course, for not attacking Vijaynagar. Rama puts out a very simple request. He asks for grains of rice on the 64 boxes of a chess board. For the quantity of rice, Rama has a simple condition that each successive box will have double the number of grains as the previous box. So, the first box would have just one grain, second box 2, third 4 and so on. Dhananjay sees this as a pretty low value request and actually starts laughing. He gives Rama another chance in case he wants to change his mind and ask for some jewelry or a part of his kingdom. Rama doesn’t show any greed and says he would be just fine with the rice. Dhananjay happily agrees.

As I was watching this particular episode of the show based on Tenali Rama, I was also trying to understand the reason behind Rama’s ask. Like King Dhananjay, it took me some time to understand the magnitude of this ask. It goes pretty smoothly till 11th box. The king is still amused and he’s seeing the boxes of the chess board being filled with small heaps of rice. After the 11th box, things start to take a turn as the huge board boxes are no longer able to contain the required number of grains. Huge bags of rice need to be brought to satisfy the condition. Warehouses and warehouses of rice start emptying in the kingdom. The king just starts to realize what he has promised. The kingdom only has rice till 25th box of the chess board and then his minister informs him that there’s nothing more that they can do. Just to give a sense, the 25th box alone required close to 17 million grains of rice and there were still 39 boxes more to go. The king being a very arrogant one, does not want to take defeat and he insists that they fulfill Rama’s request no matter what it takes. He’s ready to buy the rice from neighboring kingdoms. But then as his minister does the math, he tells him that even if we take the rice of entire country for the next 10 years (this is 16th century India we are talking about), the most they can reach is 38th box, with 26 boxes still left. The 38th box would require 137 billion grains of rice. Then it sinks into the the king Dhananjay that there was no way they could fulfill Rama’s request.

A screenshot of the episode showing all the rice that was brought in,c_limit,f_auto,q_auto:good,fl_progressive:steep/

Probably this is why Albert Einstein called compounding the 8th wonder of the world. It’s easier to think linearly where everything is growing by the same amount every period. In this case, if the number of grains was growing by 2 every box, it’s a simple calculation and even the final box would have just 128 grains of rice. But whenever the amount of growth depends on the base amount of previous period, we can highly underestimate what is possible. The results can be so extraordinary it can seem like magic. But it’s just mathematics. All that is needed is enough time, and in this case, enough boxes of a chess board for the “magic” to take place. If he had only 20 boxes to play with, even with this high grown rate of 100%, king Dhananjay would have been fine fulfilling this request of Rama.

This is something that Morgan Housel stresses in his book, The Psychology of Money. He writes that there have been a number of books written about Warren Buffet’s investing, but one thing that is often overlooked is how long he has been investing for. Warren Buffet’s net worth at the time of the author writing his book (mid-2020) was 84.5 billion dollars. Out of that, 84.2 billion dollars was accumulated after his 50th birthday, 81.5 billion came after he qualified for social security, that is, in his mid-60s. Of course, he’s a great investor, having had a return of 22% on average annually, but he also began investing seriously when he was just 10 years old. By the time he was 30 years old, he already had a net worth of 1 million or 9.3 million adjusted for inflation. If on the other hand, his net worth by the age of 30 was a more plausible 25,000 US dollars and he retired to play golf at 60, then even with his phenomenal return of 22%, his net worth would have been 12 million dollars, 99% less than what his actual net worth is.

To further convey the importance of time, the author also gives example of another investor, Jim Simons, whose hedge fund has compounded money at 66% annually since 1988. That is three times what Warren buffet has generated. Simons’ net worth at this time is around 21 billion dollars, 75% less than Warren buffet. Even though he has generated higher returns than Buffet, he did not find his investment side until he was 50 years old. In other words, he has had less than half as many years to compound as Warren buffet.

The main takeaway Morgan conveys is that good investing is not really about generating the highest returns and home runs which are hard to be repeated, it’s about earning decent returns which can be sustained for a long period of time for compounding to kick in. That’s also a reason much of the investment advice is against going for individual stocks and trying to beat the market. On the other hand, it’s likely better to regularly just keep buying broad market based index funds.