1/

Get a cup of coffee.

In this thread, I'll help you work out how much money you need to retire.

2/

The goal is simple.

You want to accumulate a *large* portfolio of assets.

How large?

Well, you should be able to quit your job. And you and your family should be able to live comfortably for decades -- just off of the income generated by this portfolio.

3/

This is the crux of the "FIRE" movement.

FIRE stands for "Financially Independent, Retired Early".

The basic philosophy is: keep your spending needs low. Save a large portion of your income. Invest these savings. With luck, you'll be able to retire early.

4/

FIRE advocates have a rule they love to cite: the 4% rule.

The 4% rule says: your annual expenses in retirement should not exceed 4% of your portfolio.

You can use this rule to calculate how large a portfolio you need to accumulate before you can quit your job and retire.

5/

For example, suppose you and your family need $40K/year to live comfortably in retirement.

Then you need to accumulate a portfolio that's at least $1M.

Another way to say this is: your portfolio should be at least 25 times your annual expenses in retirement.

1) Get a cup of coffee.

In this thread, I'm going to walk you through "The Kelly Criterion".

2) In 1956, John Kelly published a paper titled "A New Interpretation of Information Rate" in the Bell System Technical Journal.

3) In the paper, Kelly described a simple and elegant way for investors to strategically allocate capital in the face of uncertainty.

This is what is now known as the Kelly Criterion.

4) The approach is easiest to understand with an example.

I'll keep it as realistic as possible:

Imagine that you walk into an antique store one day. Due to the persistence of the salesman there, you buy an old lamp from him.

5) You take the lamp home. You rub it. Out comes a genie. Nothing unusual.

1/

Get a cup of coffee.

In this thread, I'll help you understand Geometric Expectations.

2/

Imagine we have an investment opportunity.

If the investment goes well, we get to double our money.

But if it goes badly, we'll end up losing three fourths of it.

There's a 50/50 chance of either outcome.

The question: is this a good bet or not?

3/

A simple way to approach this question is to calculate the bet's "expectation".

For every $1 we bet, there are 2 possibilities:

1. The lucky case, where we double our money and end up with $2, and

2. The unlucky case, where we lose (3/4)'th to end up with just $0.25.

4/

Each of these outcomes is equally likely.

So, on *average*, every $1 we put in turns into ($2 + $0.25)/2 = $1.125.

This is a *positive* 12.5% return.

Such bets are called *positive expectation* bets. On average, we expect to *make* (rather than *lose*) money on them.

5/

Suppose we could take many turns betting at these odds.

In any one turn, we could of course lose money.

But because our bet has positive expectation, *over time* we expect to make money.

1/

Get a cup of coffee.

In this thread, I'll show you how the P/E ratio of a portfolio is related to the P/E ratios of its individual stocks.

The math here is beautiful. It involves harmonic means and a super elegant theorem known as the Cauchy-Schwarz Inequality.

2/

Earlier this week, I conducted a poll where I asked this question about P/E ratios.

Over 6,000 people responded.

Unfortunately, most of them got the answer wrong.

That's why I'm writing this thread. To (hopefully) correct some of the misconceptions that led people astray.

3/

To answer questions like this, it's always a good idea to go back to first principles.

In this case, we should ask ourselves: what exactly does a P/E ratio capture?

4/

We know that the P in P/E stands for Price. In other words, the amount we need to pay to acquire an asset today.

And the E stands for Earnings. The amount earned by our asset in the last 1 year.

5/

Note: P/E ratios come in more than 1 flavor.

For the E part, some people use earnings during the *last* 1 year. This is called the *trailing* P/E ratio.

Others use an estimate of earnings during the *next* 1 year. This is called the *forward* P/E ratio.

1/

Get a cup of coffee.

In this thread, we'll cover *State Quantities* and *Flow Quantities*.

This mental model can help us analyze many different entities -- from complex engineering systems to publicly traded companies.

2/

A "State Quantity" is something that's associated with a *specific point in time*.

For example, the number of followers a Twitter account has is a state quantity. This number can go up and down over time. But at any one *specific* time point, it's fixed.

3/

Similarly, the amount of cash a company has is a state quantity.

This cash balance can also rise and fall over time.

But pick any one *specific* time point -- and the company can only have one *specific* cash balance at that time point.

4/

By contrast, a "Flow Quantity" is something that's associated with a time *interval* rather than a time *point*.

For example, the number of followers gained by a Twitter account is a flow quantity. It's meaningful only when we specify a time interval (eg, the last 30 days).

5/

A simple analogy is that a State Quantity is like a photo -- a snapshot at a particular *point* in time.

But a Flow Quantity is like a video -- a record of events that take place during a particular time *interval*.

1/

Get a cup of coffee.

In this thread, I'll help you understand Markov Chains.

In life, and in investing, we often come across situations where luck/chance plays a major role.

And Markov Chains are often a great way to model and analyze such situations.

2/

Here's what prompted me to write this thread.

Earlier this week, I conducted a Twitter poll.

In the poll, I posed a question that required a bit of probabilistic reasoning.

The good news: over 10,000 people responded.

The bad news: ~87% got the answer wrong!

3/

Here's the question I asked.

Imagine we have 2 volunteers: Alice and Bob.

We give them each a fair coin.

We ask Alice to keep tossing her coin until she sees a Heads immediately followed by a Tails (ie, the pattern HT).

4/

We ask Bob to keep tossing his coin until he sees two consecutive Heads (ie, the pattern HH).

The question is: on average, who will take more tosses to get to their "target pattern" -- Alice or Bob?

Or will they both on average take the same number of tosses?

5/

More precisely:

Suppose Alice takes A tosses on average to get her HT.

And Bob takes B tosses on average to get his HH.

Then, which is the bigger number: A or B?

Or are they both the same number?

1/

Get a cup of coffee.

In this thread, I'll help you understand the basics of Binomial Thinking.

The future is always uncertain. There are many different ways it can unfold -- some more likely than others. Binomial thinking helps us embrace this view.

2/

The S&P 500 index is at ~3768 today.

Suppose we want to predict where it will be 10 years from now.

Historically, we know that this index has returned ~10% per year.

If we simply extrapolate this, we get an estimate of ~9773 for the index 10 years from now:

3/

What we just did is called a "point estimate" -- a prediction about the future that's a single number (9773).

But of course, we know the future is uncertain. It's impossible to predict it so precisely.

So, there's a sense of *false precision* in point estimates like this.

4/

To emphasize the uncertainty inherent in such predictions, a better approach is to predict a *range* of values rather than a single number.

For example, we may say the index will return somewhere in the *range* of 8% to 12% (instead of a fixed 10%) per year.

5/

10 years from now, this implies an index value in the *range* [8135, 11703]:

1/

Get a cup of coffee.

Let's talk about the Birthday Paradox.

This is a simple exercise in probability.

But from it, we can learn so much about life.

About strategic problem solving.

About non-linear thinking -- convexity, concavity, S curves, etc.

So let's dive in!

2/

Suppose we came across a "30 under 30" Forbes list.

The list features 30 highly accomplished people.

What are the chances that at least 2 of these 30 share the same birthday?

Same birthday means they were born on the same day (eg, Jan 5). But not necessarily the same year.

3/

What if it was a "40 under 40" list?

Or a "50 under 50" list?

Or in general: if we put M people on a list, what are the chances that *some* 2 of them will share the same birthday?

4/

Clearly, this is an exercise in probability.

To solve it, we'll assume 3 things:

1. No Feb 29 birthdays,

2. Each person on our list is *equally likely* to be born on any one of the other 365 days (Jan 1 to Dec 31), and

3. The birthdays are all independent of each other.

5/

Another way to state the problem:

We have M people, and a 365-sided fair die.

Each person is allowed to roll the die once -- and is thereby assigned a number between 1 and 365 (both inclusive).

What are the chances that *some* 2 people will get assigned the same number?

1/

Get a cup of coffee.

In this thread, I'll walk you through the importance of understanding *correlations* between bets.

For example, a portfolio of *correlated* stocks can have very different performance characteristics compared to a portfolio of *uncorrelated* stocks.

2/

Imagine we put $100K into a stock.

In the next 1 year, the stock could go down 30% (our worst case scenario).

Or it could go up 50% (our best case scenario).

Or it could give us a return somewhere between these extremes.

Say all such returns are equally likely.

3/

A "probability density diagram" can be used to visualize such scenarios.

On the X axis, we take all possible outcomes (in this case, -30% to +50%).

And on the Y axis, we plot the likelihoods of these outcomes.

Like so:

4/

Take any 2 outcomes on the X axis -- say, R1 and R2.

Now, calculate the area under the probability density diagram between R1 and R2.

Our probability of getting a return *between* R1 and R2 is exactly this area.

Like so:

5/

This is called a "uniform" distribution -- *all* returns between -30% and +50% are *equally* likely.

But we can also imagine other "non-uniform" scenarios, where *some* returns are more likely than others.

Here too, probability density diagrams can help us.

A few examples:

Get a cup of coffee.

Let's kickstart 2022!

To that end, here are 22 key concepts to help you appreciate and achieve Financial Independence.

Concept #1.

What is Financial Independence?

It's a state of *self-sufficiency*. It's when you have enough money, and enough income-producing assets, that you and your family can live comfortably for the rest of your lives -- WITHOUT needing a job.

Concept #2.

Financial Independence is not really about spending MONEY how we like -- although, to an extent, that becomes possible.

It's about being FREE to spend our TIME how we like.

Concept #3.

Financial Independence is not really about quitting our jobs and retiring from work -- although that's possible.

It's about being FREE to pursue *whatever* kind of work we find most fulfilling. Things we love to do. Things the world benefits from. Etc.

Concept #4.

For most of us, the path to Financial Independence consists of:

- Starting Early,
- Saving Diligently, and
- Investing Responsibly.

Here's an inspiring story of a janitor who amassed an $8M fortune by following this very playbook:

1/

Get a cup of coffee.

In this thread, I'll tell you a story about a man and his dog.

This will help you think more clearly about volatility, risk, and the relationship between the two.

2/

This is Mr. Biswas Singh.

Friends call him "Biz".

He's 50 years old. He owns and operates several gas stations and convenience stores around town.

3/

This is Spock.

He's a 4 year old Golden Retriever who belongs to Biz.

He's a Good Boy.

4/

Every morning, Biz takes Spock out for a walk.

They go to a local park that has a beautiful trail.

They get there around 6am.

They walk along the trail for about an hour -- until 7am or so.

Then they make their way back home.

5/

Biz walks more or less at a steady speed -- say, 3.5 miles per hour.

Spock, of course, does no such thing.

Sometimes, Spock races ahead of Biz -- straining his leash.

Other times, Spock lags behind Biz, distracted by a lamp post or a squirrel.

1/

Get a cup of coffee.

In this thread, I'll walk you through the benefits of turning capital quickly.

The math behind turning capital is beautiful. It leads us to the number "e", which plays a vital role in so many different fields -- from astrophysics to biology.

2/

Imagine we have $1M.

Also, we know an extraordinarily generous bank where we can deposit this $1M.

This bank will pay us interest. And not a paltry 1% or 2%, but a hefty *100%* per year!

(I know, I know. But humor me, will you?)

3/

So, if we deposit our $1M at this bank, it will earn that 100% interest and become $2M in 1 years' time.

But that's *only* if the interest is *compounded annually*.

4/

What if the interest is *not* compounded annually?

For example, suppose it's compounded half yearly?

"Compounded half yearly" means: instead of paying us 100% interest *once* a year, the bank pays us 50% interest *twice* a year (ie, once every 6 months).

5/

That is, we get to "turn" our money twice -- each time earning 50% on it.

Here's a quick picture of how that looks.

The first 6 months will turn $1M into $1.5M (ie, +50%). And the second 6 months will turn this $1.5M into $2.25M (another +50%).

1/

Get a cup of coffee.

In this thread, I'll walk you through the basics of Capital Allocation.

The better we understand how capital moves in and out of a business, the better we can predict the business's future cash flows and its stock's long-term performance.

2/

Businesses generate *cash* through their operations.

For example, Apple generates cash by selling iPhones.

Starbucks generates cash by selling coffee.

Google generates cash by selling ads.

IBM generates cash by doing things I don't understand.

Etc.

3/

Capital Allocation is the step that comes *after* generating all this cash.

That is, once the cash is available, what does the CEO *do* with it?

What projects does he invest in? What acquisitions does he make? Does he return any cash back to shareholders? Etc.

4/

Capital Allocation can make a tremendous difference to a company and its shareholders.

For example, at Berkshire Hathaway, Buffett took the cash generated by textiles and allocated it towards operations that produced much higher returns. Like insurance and candy.

5/

This transformed Berkshire Hathaway from a lowly bunch of textile mills to the super successful giant diversified conglomerate that it is today.

Along the way, long term shareholders reaped rich rewards.

That's *good* Capital Allocation.

1/

Get a cup of coffee.

In this thread, I'll walk you through the various connections between asset prices, interest rates, and inflation.

As an investor, it's useful to have a mental picture of how these pieces affect -- and are affected by -- one another.

2/

Suppose we have an investment opportunity.

This could be buying a stock, a bond, a private business, etc.

Let's say this opportunity will return $1M in cash to us after 1 year.

And not just that. This $1M will grow at 10% per year for the next 9 years, and 3% thereafter.

3/

This is a classic "cash flow model" that finance-y folk use all the time.

We have a business that promises to grow quickly for a while (in this case, at 10% per year for the next 10 years or so).

But after that, growth slows to a "terminal" crawl (3% per year).

4/

If we decide to buy this business, our "cash flows" from it will look like this over time:

5/

The question is: how much should we pay for this business?

Well, that depends on what kind of return we hope to get from buying it.

If we want a high return, we can't pay very much.

The lower the return we're willing to tolerate, the more we can pay.

1/

Get a cup of coffee.

In this thread, I'll walk you through the key differences between *earnings* and *cash flows*.

The punch line: Just because a company reports $1 of *earnings*, it does NOT mean the company has $1 more *cash* to distribute to owners.

2/

Before we look at a company's *earnings*, it's useful to understand the concept of Net Worth.

Net Worth (also called Book Value, or Shareholder's Equity) is simply the difference between what a company *owns* (ie, its assets) and what it *owes* (ie, its liabilities).

3/

Companies typically *own* a bunch of assets.

These include cash, "accounts receivable" (ie, money owed to the company by customers), "inventory" (ie, raw materials and finished products), "property, plant, and equipment" (ie, land, buildings, and factories), etc.

4/

Also, companies typically *owe* money or services to others (liabilities).

These include "accounts payable" (money owed to suppliers), "wages payable" (ie, money owed to employees for work they've already done), debt taken out by the company that has to be repaid, etc.

5/

Net Worth is what remains after we net out what a company *owns* against what it *owes*.

Companies that *own* more than they *owe* have positive net worth.

Companies that *owe* more than they *own* have negative net worth.

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?

4/

If you had asked me this question 10 years ago, I would have said: hands down A!

After all, both A and B earn the same ($1/share). And they grow at the same rate (10%/year).

But A is CHEAPER than B (10 vs 15 P/E).

So, of course A is the better long term investment.

Right?

5/

The answer is: NOT necessarily.

B -- the MORE "expensive" looking stock -- could *still* end up being the better investment.

Why? Because it's not just about earnings, or how fast earnings will grow.

It's about how *capital efficient* this growth will be.

@Tom_Voltz1 1/

That’s a possibility.

Buffett has this concept of “owner earnings”: how much cash can be safely taken out of a business each year without hurting it?

Take out more than this, and we risk hurting the business’s competitive position, earning power, unit volume, etc.

2/

At the same time, leaving capital in a terrible business is not a great idea either. It’s like throwing good money after bad.

In fact, directing capital away from textiles (a bad business) and into insurance (a better business) is one reason for Berkshire’s success.

/End