BC INVESTING
Saved by @zmbnski

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.
6) The genie knows you like investing. So he sets up a @RobinhoodApp account for you, and finances it with a princely sum of ... wait for it ... $1.

He also enrolls you in Robinhood's fractional share trading program, but not in margin or options trading.
7) Then the genie gives you a "stock tip": Aladdin Enterprises (NYSE: ALAD).

ALAD is a very special stock. Each month, the stock either exactly doubles or exactly halves in value. There's a 50/50 chance of either outcome, and no way to predict it in advance.
8) At the start of each month, you can rebalance your Robinhood portfolio between cash and ALAD however you like.

At the end of 20 years, all the stock in your account will be liquidated, the account will be closed, and its entire value will be given to you in cash.
9) Your goal, of course, is to maximize the end-value of the Robinhood account (20 years from now).

The only thing within your control is the portfolio rebalancing at the start of each month.

So what should your rebalancing strategy be?
10) Let's start by looking at the first month.

During this month, ALAD can either double or halve.

So, for every $1 you invest in ALAD at the beginning of the month, you'll have either $2 or $0.50 at the end.

On average, you'll have ($2 + $0.50)/2 = $1.25.
11) That's an average 25% monthly return on whatever money you invest in ALAD, vs 0% for whatever you keep in cash.

This is beginning to look like a no-brainer.

Clearly, the best way to proceed is to go "All In". Put your entire initial $1 in ALAD, and hold it for 20 yrs.
12) How will this "All In" strategy do over 20 years?

Best case: ALAD doubles every single month. That leaves you with many, many billions of dollars.

Worst case: ALAD gets halved every single month. That leaves you with an insignificant fraction of a penny.
13) But neither the best case nor the worst case are remotely likely.

These are like tossing a coin 240 times (once a month for 20 years) and expecting to get heads (or tails) every single time.

So what does the *average* case look like?
14) It turns out, for the "All In" ALAD strategy, the average case is not bad either.

Remember that on average, you make 25% per month? Compounded over 20 years, that turns your $1 into many billions.

So, in all likelihood, you'll make out like a bandit, right?

Not so fast.
15) Here's a table showing various "wealth brackets", and your chances of ending up in each one at the end of 20 years if you followed the "All In" strategy:
16) As you can see, there's more than a 50% chance that you'll end up with less than $1 at the end of 20 years.

And a 67.4% chance that you'll end up with less than $100.

And only a 3% chance that you'll end up a billionaire.
17) But how's that possible?

It's because outliers skew the average.

The billion dollar plus outcomes are so good that they lift up the entire average.

Kind of like one winning lottery ticket compensating for thousands of duds.
18) When you think about it, the *most likely* outcome is that ALAD doubles in some months and gets halved in others.

These doublings and halvings cancel each other, leaving you with roughly the same $1 you started with.
19) Key lesson: the *most likely* outcome can be dramatically different from the *average* outcome.

*Most likely* outcomes are not swayed by outliers. *Averages* are.

In this case, you will *most likely* end up with just $1. But *on average*, you expect to end up with billions.
20) So, you need a way to escape this "lottery ticket" situation.

You need a strategy that maybe gives up some of the unlikely billions in potential upside, but buys you a very good chance of turning that $1 into $100K or $1M.

That's the genius of Kelly. He found that strategy.
21) For this situation, Kelly's strategy is wonderfully simple:

At the start of each month, rebalance your portfolio so that exactly half of it is in cash and the other half is in ALAD stock.
22) So, how does this "Kelly strategy" do in comparison to "All In"?

The difference is night and day.

Just take a look at this table:
23) With "All In", there was a 50+% chance of ending up with less than the original $1. Kelly reduces that to just a 0.4% chance.

Kelly also gives you a 50+% chance of ending up a millionaire, and a 11% chance of ending up a billionaire!
24) Also, if you follow Kelly, the *most likely* outcome is that you'll end up with north of $1.3M.

The *average* outcome is still in the many billions, although Kelly does sacrifice some of the tail-end mega-billions.
25) But how did Kelly know to keep exactly 1/2 the portfolio in cash and 1/2 in stock? Why not 2/3 and 1/3? Or 3/5 and 2/5?
26) The answer is that Kelly built an entire mathematical theory to figure out the "best" possible strategy for a variety of situations like this.

When you apply the math to this particular problem, it so happens that you get 1/2 and 1/2 as the optimal strategy.
27) Indeed, you can think of more complicated portfolio allocation situations.

What if ALAD could quadruple, double, stay the same, or halve?

What if there was more than 1 stock: Aladdin Enterprises and Jasmine Enterprises?

Kelly's theory is applicable to all this and more.
28) I'll close this thread with a few references and resources:

"Fortune's Formula" by @WPoundstone is an excellent non-technical book that covers the Kelly Criterion in some detail.
https://t.co/soE2dFHDTH
29) "The Dhandho Investor" by @MohnishPabrai has many practical examples of how Mohnish has applied the Kelly Criterion to inform his own investment strategies.
https://t.co/76dL3uu0Ot
30) "The Kelly Capital Growth Investment Criterion" by Leonard MacLean, @EdwardOThorp, and William Ziemba is a comprehensive collection of articles about the Kelly Criterion (for the mathematically inclined).
https://t.co/dagvcvorZo
31) And of course, there's Kelly's original paper. You can read it in full here:
https://t.co/QAypqSA5N5
32) This thread on ergodicity by @borrowed_ideas is also pretty good; it contains some related ideas on probabilistic thinking, and was one of the inspirations behind my deciding to write this thread.
https://t.co/tplsgSr2mG
33) And speaking of ergodicity, @ole_b_peters has some good lecture notes that he's made available for free. His blog and Twitter feed are also pretty good.
https://t.co/FQDocNUnL4
34) If you're still with me, congrats! You have more persistence than most!

/End
A1) Hey, what do you know?

Turns out there’s actually some interest in the core mathematical theory behind the Kelly Criterion.

So, with a shout out to @borrowed_ideas who encouraged me to include this, here’s an appendix to the tweetstorm that gets into the math.
A2) The key mathematical idea that Kelly had was:

Instead of maximizing the wealth you expect to have at the end of each round, maximize the logarithm of this wealth.
A3) Why logarithm?

It’s a bit involved. I’ll let Kelly take this one:
A4) Let’s look at the “cash + ALAD” portfolio rebalancing problem from this angle.

At the start of a particular month, suppose our portfolio is worth $X. We divide this into two fractions: $f*X and $(1-f)*X.

We put $f*X in ALAD and keep $(1-f)*X in cash.
A5) What happens one month later?

If we’re lucky, the ALAD part of our portfolio would have doubled. So the whole portfolio will be worth $f*X*2 + $(1-f)*X.

But if we’re unlucky, the ALAD part would have halved, leaving us with $f*X/2 + $(1-f)*X.
A6) This simplifies to:

Lucky case: $X*(1+f)
Unlucky case: $X*(1-f/2)
A7) Kelly suggests that we take the logarithm of this. So here goes:

Lucky case: log(X*(1+f))
Unlucky case: log(X*(1-f/2))
A8) These cases are 50/50. Equally likely. So, on average, what’s the logarithm expected to be? It’s:

0.5*log(X*(1+f)) + 0.5*log(X*(1-f/2)),

which simplifies to:

log(X) + 0.5*log(1 + f/2 - f^2/2).
A9) Kelly suggests we now choose f to maximize this.

That’s the same as maximizing 1 + f/2 - f^2/2, which happens to be:

9/2 - 2*(f - 1/2)^2.

Maximizing this means minimizing (f - 1/2)^2.

And that means choosing f = 1/2.
A10) Remember that f was the fraction of our portfolio that we allocated to ALAD stock?

So choosing f=1/2 means we put half the portfolio in ALAD stock.

The other half, (1-f), goes to cash.

And that’s how you do the math behind the Kelly Criterion.
A11) For more complicated probabilistic outcomes, it’s usually a good idea to use a computer to figure out the Kelly strategy.

But the key idea is the same: maximize the expectation of the logarithm of your wealth at every step.
A12) If you got this far, you’re even more persistent than the readers who got to the end of the original thread. Kudos!

/End

More from 10-K Diver

10-K Diver
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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.
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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.
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10-K Diver
10-K Diver
@10kdiver
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*.
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10-K Diver
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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.
ASSET PRICE VS INTEREST RATE INFLATION
10-K Diver
10-K Diver
@10kdiver
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%).
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BEST VALUATION FACTOR

Price to earning below:10

Price to book below:2

5 years ROE:more than 20%

If you follow these points then you won’t overpay & your return would be bigger than anyone

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(1) Trailing EPS
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TAM is a sizing of how big your market is. A good way to estimate this is - if you can get to all potential buyers and based on how much $$ they are worth to you, how much money can your company make if you took the whole mkt?

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-1000 zoos have on average 3 hippos = 3000 hippos.
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4) But, we'll come back to this.

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A) how hard it is to get customers
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