10-K Diver Profile picture
Dec 19, 2020 25 tweets 7 min read Read on X
1/

Get a cup of coffee.

In this thread, I'll walk you through the Rule of 72 -- and related "mental math tricks" for investors.
2/

As humans, we tend to think *linearly*.

When we see a curve, we like to mentally approximate it by a straight line.

This helps us cope with changes in the world around us. Changes that happen a *constant* pace. Changes that don't need our attention for very long.
3/

But in finance/investing, we need to think *exponentially*, not *linearly*.

Money compounds. Growth doesn't happen at a constant pace; it *accelerates* over time.

Most of us are not programmed to intuitively "get" compounding -- over the long run. Image
4/

So we need some "mental shorthands".

Rules of thumb that help us develop intuition about exponential growth.

Tricks that help us do "compounding math" in our head.

One such trick is to think of compounding as a process that *doubles* our money every so many years.
5/

So the question is: how long does the compounding process take to double our money?

The Rule of 72 gives us a simple approximate formula for this: Image
6/

As you can see, our rate of return appears in the *denominator* of the Rule of 72.

This makes intuitive sense: as our return increases, it takes less time to double our money.
7/

Also note: the Rule of 72 doesn't need to know *how much* money we start with.

For example, suppose our return is 9% per year. The rule then says we'll double our money in approximately 72/9 = 8 years.
8/

If we start with $100, we'll have $200 in ~8 years.

If we start with $1M, we'll have $2M in ~8 years.

It doesn't matter how much we start with. Whatever it is, it gets doubled in ~8 years -- as long as we can compound at 9% per year. That's the Rule of 72.
9/

The Rule of 72 encourages us to *think* in terms of repeatedly doubling our money.

This kind of thinking is powerful. It can help us do various compounding calculations just mentally -- no need to reach for a calculator or computer.
10/

For example, in this excellent ~40 min video, @MohnishPabrai demonstrates one such calculation.

At the age of 18, Mohnish's daughter Monsoon (@Typhoon_Girl) did an internship. From this, she saved $5K.
11/

She gave this $5K to Mohnish to invest.

Mohnish -- being the skilled investor he is -- feels confident that he can compound this money at 15% per year for 50 years.

The question is: at the end of 50 years (when Monsoon turns ~68), what would this $5K have grown into?
12/

We can do this calculation mentally -- just by thinking in doublings and using the Rule of 72.

Step 1. At our 15% per year return, the Rule of 72 says it will take roughly 72/15 = about 5 years to double Monsoon's money.
13/

Step 2. Over 50 years, that means the money will get doubled 10 times.

(50 years total)/(5 years per doubling) = 10 doublings.
14/

Step 3: From the "doubling table" below, we can see that after 10 doublings, every $1 turns into $1024. That's roughly a 1000x growth.

As Monsoon originally started with $5K, she will therefore end up with roughly 1000 * $5K = ~$5M at the end of the 50-year period. Image
15/

In this way, we can use the Rule of 72 and the process of "thinking in doublings" to work out approximately how much a given sum of money will grow into after many years of compounding.

Here's a quick summary of the steps involved: Image
16/

We can also use these ideas to quickly estimate our rate of return from an investment.

For example, let's take the excellent book "100 baggers" by @chriswmayer. The book is about companies that have delivered superb returns to long term shareholders. amazon.com/100-Baggers-St…
17/

Let's take one example from the book: NVR, a home builder.

Suppose we bought this stock about 10 years ago. At the time, the stock was at ~$700/share. Today, it's at ~$4200/share.

Suppose we held our shares over these 10 years. What's our annualized return? Image
18/

Again, we can estimate this using the idea of doublings and the Rule of 72.

Step 1. $700/share to $4200/share is a ~6x growth.

We know that "2 doublings" means ~4x growth and "3 doublings" means ~8x growth. So our ~6x growth is roughly 2.5 doublings.
19/

Step 2. These ~2.5 doublings have happened over 10 years. So 1 doubling has taken roughly 10/2.5 = 4 years.

Step 3. From the Rule of 72, we calculate our annualized percentage rate of return to be roughly 72/(years to double) = 72/4 = ~18%. Image
20/

Key lesson: With practice, the Rule of 72 and "thinking in doublings" can help us do "compounding math" mentally.

This can give us a real appreciation for exponential growth and the power of compounding -- what Einstein called the 8'th wonder of the world.
21/

Buffett habitually thinks like this. His hurdle rate for stocks is around 15% per year -- that's a doubling every 5 years.

Early in life, he realized that if he could keep this up for 80 years or so, he would double his money 80/5 = 16 times.
22/

That's a 2^16 = ~65000x growth.

Over a lifetime, this growth would turn $10K into ~$650M -- a phenomenal result achieved by steady compounding.

And we know Buffett has done even better than that -- because his returns have been better than 15% per year.
23/

Armed with mental techniques like the Rule of 72 and "thinking in doublings", even seemingly ordinary people can achieve extraordinary results -- if they're patient and disciplined.

For example, here's an inspiring story from "The Psychology of Money" by @morganhousel: Image
24/

In addition to Mohnish's video above, I also recommend this ~21 min video by @FocusedCompound.

Here, Andrew and Geoff discuss the Rule of 240 -- a variant of the Rule of 72 for "10x-ing" (rather than merely doubling) one's money.
25/

Thanks for reading to the end of another long thread.

Readers like you double my joy every week on Twitter!

Stay safe. Enjoy your weekend!

/End

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More from @10kdiver

Jan 1, 2023
1/

Get a cup of coffee.

In this thread, I'll walk you through "Gambler's Ruin".

This is a classic exercise in probability theory.

But going beyond the math, this exercise can teach us a lot about life, business, and investing.
2/

In my mind, Gambler's Ruin is the math of "David vs Goliath" ("Skill vs Size") type situations.

Here, David is a "small" player. He only has limited resources. But he's very skilled.

Pitted against David is Goliath -- a "big" player who has MORE resources but LESS skill.
3/

The battle between David and Goliath rages on for several "rounds".

Each round has a "winner" -- either David or Goliath.

David -- because of his superior skill -- has a higher probability of winning any individual round. That's David's advantage over Goliath.
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Dec 11, 2022
1/

Get a cup of coffee.

In this thread, we'll explore the question:

As investors, how often should we check stock prices?

To answer this, we'll draw on key ideas and concepts from many different fields -- probability, information theory, psychology, etc.
2/

Imagine we have a stock: ABC, Inc.

Every day that the market is open, our stock either:

- Goes UP 1%, or
- Goes DOWN 1%.

For simplicity, let's say these are the only 2 possible outcomes on any given trading day.
3/

Suppose we think ABC is a "good" investment.

That is, the company has a wide moat, good returns on capital, decent growth prospects, etc. And the stock trades at a reasonable price.

So, we buy the stock -- expecting to make a very good return on it. Say, ~15% per year.
Read 40 tweets
Oct 23, 2022
1/

Get a cup of coffee.

In this thread, I'll walk you through 2 key portfolio diversification principles:

(i) Minimizing correlations, and
(ii) Re-balancing intelligently.

You don't need Markowitz's portfolio theory or the Kelly Criterion to understand these concepts. Image
2/

Imagine we have a stock: ABC Inc. Ticker: $ABC.

The good thing about ABC is: in 4 out of 5 years (ie, with probability 80%), the stock goes UP 30%.

But the *rest* of the time -- ie, with probability 20%, or in 1 out of 5 years -- the stock goes DOWN 50%.
3/

We have no way to predict in advance which years will be good and which will be bad.

So, let's say we just buy and hold ABC stock for a long time -- like 25 years.

The question is: what return are we most likely to get from ABC over these 25 years?
Read 23 tweets
Sep 11, 2022
1/

Get a cup of coffee.

In this thread, I'll walk you through the P/E Ratio.

Why do some companies trade at 5x earnings and others trade at 50x earnings?

When I first started investing, this was hard for me to understand.

So, let me break it down for you.
2/

Imagine we have 2 companies, A and B.

Let's say both companies will earn $1 per share next year.

And both companies will also GROW their earnings at the SAME rate: 10% per year. Every year. Forever.
3/

Suppose A trades at a (forward) P/E Ratio of 10. So, each share of A costs $10.

And B trades at a P/E Ratio of 15. So, each share of B costs $15.

Which is the better long term investment: A or B?
Read 31 tweets
Sep 4, 2022
1/

Get a cup of coffee.

In this thread, I'll walk you through a fundamental business concept that may be counter-intuitive to some of you:

Just because a business has made $1 of PROFIT, it does NOT mean the business's owners have $1 of CASH to pocket.
2/

To understand why, let's start with how PROFIT is defined.

PROFIT = SALES - COSTS

That is, we take all sales (or revenues) the company made during a quarter or year.

We back out all costs incurred during this period.

That leaves us with profits.

Seems straightforward.
3/

Here's the problem:

The way a "lay person" understands words like SALES and COSTS is completely different from the way an *accountant* uses these same words.

These discrepancies can create enormous confusion.
Read 20 tweets
Aug 28, 2022
1/

Get a cup of coffee.

In this thread, I'll walk you through a framework that I call "Lindy vs Turkey".

This is a super-useful set of ideas for investors.

Time and again, these ideas have helped me think more clearly about the LONGEVITY of the companies in my portfolio.
2/

Imagine we're buying shares in a company -- ABC Inc.

ABC is a very simple company. It earns $1 per share every year. These earnings don't grow over time.

And ABC returns all its earnings back to its owners -- by issuing a $1/share dividend at the end of each year.
3/

Suppose we buy ABC shares for $5 a share.

That's a P/E ratio of 5.

We know we get back $1/year as a dividend.

So, for us to NOT lose money, ABC should survive AT LEAST 5 more years.

If something happens and ABC DIES before then, we'll likely lose money.
Read 32 tweets

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