Secrets of Compounding Returns

There’s a famous legend about the origin of chess that goes like this...

When the inventor of the game showed it to the emperor of India, the emperor was so impressed by the new game, that he said to the man.

“Name your reward!”

The man responded,

“Oh emperor, my wishes are simple. I only wish for this. Give me one grain of rice for the first square of the chessboard, two grains for the next square, four for the next, eight for the next and so on for all 64 squares, with each square having double the number of grains as the square before.”

The emperor agreed, amazed that the man had asked for such a small reward -- or so he thought. After a week, the king realized that he was unable to fulfil his promise because on the sixty-fourth square the king would have had to put more than 18,000,000,000,000,000,000 grains of rice, which is equal to about 210 billion tons. It was sufficient to cover the whole territory of India with a meter-thick layer of rice.

This story is likely apocryphal, but it makes a good point -- compounding can destroy an entire kingdom if it is not managed wisely.

Compound interest is also so powerful that it has been called "The Eighth Wonder of the World". It's so controversial that charging compound interest on loans was banned by the Qur'an.

It can work against you or for you.

Here are few inside tips on compounding:

The Rule of 72

This one goes back to the Italian Renaissance. It's a quick and easy "rule of thumb" for calculating the amount of time it takes for money to double when growing at a fixed rate of between 6% and 10% per year.

It is fantastically easy to use. Simply take "72" and divide it by the annualized rate of return. The result is the number of years that it will take to double in value. It takes about 7.2 years for a portfolio to double at 10% annually.

Subtract 1 from 72 for every three points of annual returns less than 8%, or add 1 to 72 for every three points above 8%. Therefore, at a rate of 5%, the Rule of 72 becomes the Rule of 71.

The Sequence of Gains and Losses Doesn't Matter....

It doesn't matter if you have a +20% gain followed by a -10% loss, or a -10% loss followed by a +20% gain. Mathematically, they are the same thing.

(1 + 0.20) * (1 - 0.10) = (1 - 0.10) * (1 + 0.20)

.... Unless It Does

It is more difficult to recover from a large loss when money is taken out after the portfolio has declined in value.

It's one reason why retirees are in less of a position to handle significant losses.

A Loss Is Not Offset by Its Equivalent Gain

If a portfolio was down -20% in 2022 and up +20% last year, it's still not back where it started. It's down -4%.

(1 - 0.2) * (1 + 0.2) = 0.96

and...

0.96 - 1 = - 0.04

With bigger losses, it is even more challenging to play catch-up.

Cryptocurrency is notorious for big swings. Up or down +/- 80% in a year is perfectly normal for Bitcoin.

Here's how the math works on an eighty-percent loss followed by an eighty-percent gain:

(1 - 0.80) * (1 + 0.80) = 0.36

and...

0.36 - 1 = - 0.64

If you are lucky enough to catch an +80% rebound after an -80% loss you could still be down -64%!

That's why I say that it is important to "keep your losses survivable". The goal is to avoid the -80% loss, because that is a hole in the ground that you aren't going to be able to climb out of.

Returns Are Not Additive, They Are Multiplicative

Which is better for a non-taxable account with no transaction costs -- one with a +30% gain or thirty +1% gains?

They are the same, right?

Nope.

In the first case, a $100 account grows to $130. That's great.

In the second case, a $100 account grows to $134.78. That's even better.

(1.01) ^ 30 = 1.3478

Time Is Sometimes More Important than Performance

If an enterprising 15-year-old can put aside $1,000 per year into a tax-free account earning 10% per year, each and every year, that money will grow to $1,280,000 by the time he/she is 65.

Now let's say that that this teen has a somewhat less ambitious brother or sister who doesn't start until age 25. He/she would need to generate annual returns of 13.4% to reach the same level by age 65.

How about the 35-year-old uncle? He would need William Buffett-esque returns of 19.5% every year to hit $1.2m by retirement age.

The moral of this story is simple… When it comes to building your portfolio, starting sooner is almost always better than later. Compounding returns can be amazing, if you can get them to work for you rather than against you.