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
10-K Diver
@10kdiver
1/

Get a cup of coffee.

In this thread, I'll walk you through 2 probability concepts: Standard Deviation (SD) and Mean Absolute Deviation (MAD).

This will give you insight into Fat Tails -- which are super useful in investing and in many other fields.


2/

Recently, I watched 2 probability "mini-lectures" on YouTube by Nassim Taleb.

One ~10 min lecture covered SD and MAD. The other ~6 min lecture covered Fat Tails.

In these ~16 mins, @nntaleb shared so many useful nuggets that I had to write this thread to unpack them.

3/

For those curious, here are the YouTube links to the lectures:

SD and MAD (~10 min): https://t.co/0TwubymdE6

Fat Tails (~6 min):

4/

The first thing to understand is the concept of a Random Variable.

In essence, a Random Variable is a number that depends on a random event.

For example, when we roll a die, we get a Random Variable -- a number from the set {1, 2, 3, 4, 5, 6}.

5/

Every Random Variable has a Probability Distribution.

This tells us all the possible values the Random Variable can take, and their respective probabilities.

For example, when we roll a fair die, we get a Random Variable with this Probability Distribution:
DS
10-K Diver
10-K Diver
@10kdiver
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.
ALL
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10-K Diver
10-K Diver
@10kdiver
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.
ALL
10-K Diver
10-K Diver
@10kdiver
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.
FUNDAMENTALS
10-K Diver
10-K Diver
@10kdiver
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

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Ram Bhupatiraju
Ram Bhupatiraju
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My biggest mistakes in the last decade & what I learned.

There are 2 types of Investors in the Market. Those who make mistakes & admit them openly while learning, and those who give the illusion that they never make mistakes. I want to be firmly in the former camp.

Here we go⬇️


Putting those mistakes/examples/lessons down again in the thread below for easy reading.

Note that the lessons learned are very subjective. They are not recommendations. It depends on each person's Portfolio goals & strategies.

OK let's go. ⬇️⬇️

1⃣ Mistake : Actions not aligning to goals & competencies.

Ex : Mainly during 2010-14 - Dabbling in cheap (low quality) stocks & Options (LEAPS, but w/o clearly identified catalysts)

Lesson : Make sure your process and actions are leveraging your interests/strengths and aligned to your Portfolio goals. For me, that was leveraging my patience and interest in quality Cos. Monitor & improve the process over time.

2⃣ Mistake :Confusing between Quality/Durability and Temporary Business momentum or ST stock momentum.

Ex : Buying GILD/SAM in 2016, PTON/FVRR etc in early 2021.
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Nick Huber
Nick Huber
@sweatystartup
I got serious about Twitter on April 12th 2020.

Since that day:

I've raised $5MM and met with over 200 future investors in my real estate deals.

I've done $75k worth of consulting.

And I've met mentors and friends I'll carry with me for life.

What worked for me 👇👇👇

First of all I tried the mainstream advice and built my own blog, podcast, email list, YouTube. Spent 2 years. 500k downloads. Some success.

Got more value out of Twitter in 30 days.

If raising money or in business THIS is the platform.

Okay let’s go:

1. Stay on topic.

The most valuable folks here are here to learn. They curate their feed. They want business and to LEARN.

No fantasy football. No gifs. No pop culture. No one liner jokes.

Be an expert at what you do. Stay on brand.

2. No politics.

At all. Ever. It’s a great way to piss off (and say goodbye) to 1/2 the folks here.

Not everybody feels the way you do and the smartest folks don’t want your opinion. Nothing good comes of it. So avoid it.

3. Be incredibly open

Nobody will steal your ideas. Yes it’s uncomfortable and yes you’ll get challenged.

I shared my profit and loss statements on here. It led to discussions with many brilliant folks in the DMs and several folks who wanted to partner reaching out.
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Teji Mandi
Teji Mandi
@TejiMandiApp
In this post, we discussed the top most important #banking #ratios for #investors. If you're looking for some more additional ratios/terms, comment below and we will get back to you. Stay tuned for more updates like these!

#TejiMandi #TMLearn #TejiMandiLearn #DidYouKnow [1/8]


[2/8]


[3/8]


[4/8]


[5/8]
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J. Tuominen
J. Tuominen
@CapcentResearch
THREAD, PM EXIT STRATEGY

I sometimes get the question “At what price do I liquidate my PM portfolio?” The short answer is:

A) I´ll never sell all of it

and

B) I don´t have a PT. I could start selling at $1900 or at $100000, it depends.

For the longer explanation, 👇

Albert Einstein once famously said “Everything is relative”. I find that quote very useful in the world of investing as well.

First off, my preferred style of investing is more influenced by macro than micro (macroeconomics vs company specific).

That means I often buy a commodity, an ETF or a basket of companies operating in the sector of interest.

I frequently look at certain ratios, or said another way, instrument X relative to instrument Y.

By analyzing historical data, I´ve set up different “ratio milestones” for when history tells me to start unwinding the ratio. As these milestones are triggered, I sell 25% of the relatively stronger instrument. For every additional 10% skew in the ratio, I sell another 25% etc.

This means I´ll never pick the absolute top nor the bottom, but I should extract much of the value while keeping my emotions out of it.

An example where this principle is adopted is shown in the Gold/Silver ratio -graph below.
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Dollar Cost Averaging 101

Many of the brightest minds in the investing world share one common trait: they recommend dollar cost averaging as an investment strategy.

But what is dollar cost averaging and how does it work?

Here's Dollar Cost Averaging 101!

👇👇👇


1/ Dollar cost averaging, or "DCA" for short, is a simple investment strategy in which an investor splits the total amount to be invested in a given asset across regular periodic purchases.

The regular purchases occur regardless of price, volatility, or economic conditions.

2/ The goal is to remove the complexities of market timing from the process, allowing an investor to build their desired position without concern for external factors.

Its simplicity removes behavioral and psychological biases from the equation.

Let's look at an example.

3/ Imagine you want to build a $10,000 position in bitcoin. You have done your research and believe in the long-term story.

You aren't sure if it will go up or down in the near-term, so you decide to dollar-cost average.

Great decision! How will you do it?


4/ You split the $10,000 up into 20 pieces ($500 each). You could have done any number of pieces, but 20 felt right.

You decide on a weekly DCA, so every Monday, you buy $500 of $BTC, regardless of price. After 20 weeks, you have built your desired $10,000 cost basis position.
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@HiteshAwasthi89
Sri Devi Karumariamman mandir, Chennai, Tamilnadu

Sri Devi Karumariamman mandir is in Thiruverkadu, a suburb of Chennai. It is said that God Muruga came here and obtained the 'Vel' (spear) from His mother, Goddess Karumari (an avatar of Parvathi) 1/n


to fight the demon Suran and hence this place was called as 'Vel kadu' and became as Verkadu. As per legend Devi Karumariamman once disguised as a soothsayer visited Bhagwan Surya, the Sun God, to predict His future. 2/n


Not realising that the soothsayer is none other than Sakthi Matha, Surya ignored Her. Angered by his indifference, Devi Karumariamman immediately retreated. Bhagwan Surya lost His glory and the earth plunged into darkness. 3/n


Bhagwan Surya then realised His folly and pleaded forgiveness from Devi Karumariamman. In order to pacify mother Karumariamman, Suryadev said that His rays would fall on Her directly twice in a year and touch her feet. (in the month of Panguni (March- April) & during (Sep - Oct)


Mother Karumari Amman is worshipped here in two forms.A swayambu (self manifested) with only head visible above the ground and another one in a graceful sitting posture with all Parasakthi features,with four arms holding skull, sword, trishul, udukkai (damru). 5/n
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@JayneshKasliwal
ULTIMATE GUIDE TO 21 and 200 Moving Average
SUNDAY THREAD 🔖
A trend Following System That will Help You Improve Trading immensely.

RETWEET AND SHARE 🔄
@kuttrapali26 @AmitabhJha3
#stocks #StockMarket
1/n

Moving averages
EMA and SMA
1. Exponential Moving Average (EMA) is similar to Simple Moving Average (SMA), measuring trend direction over a period of time.
2. However, whereas SMA simply calculates an average of price data, EMA applies more weight to data that is more current
2/


21 EMA : SHORT TERM TREND
1. Calculates the Average Price of past 21 days
2. A stock above 21 ema is in strong momentum , which will give pullbacks to 21 ema again and again.
3. Stock above 21 ema should never be shorted so as to stay with the trend
3/n

3. A stock which moves 10-15% above 21 ema will be too extended and hence will generally pullback
Stocks take dynamic support on 21 ema
4. You can Short only if its too extended like 15 to 20% from 21 ema ( Not advised )
#ADANIPOWER:
#pnbhousing
4/n


1. Whenever 21 ema is sloping upwards its called uptrend
2. Whenever 21 ema is sloping downwards its called dowtrend
3. Whenever 21 ema is sideways its called consolidation
⏫Buy in uptrend
⏬Sell in downtrend
Examples:
5/n
MOVINGAVERAGES , MOVING AVERAGE 20021 , ALL
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Aditya Todmal
Aditya Todmal
@AdityaTodmal
A Thread on the Boss himself @Mitesh_Engr

Mitesh Sir's Positional Option Selling 101:

• How to find direction
• Which options to sell
• How to deploy capital
• Exit criteria
• What ROI he targets weekly
• What % risk he takes

Done with the help of @niki_poojary


How @Mitesh_Engr Sir finds the direction?

• Daily charts S/R
• 75 min charts S/R
• Intraday trend
• Always play directional
• Never trades in strategies


Which options to sell in weekly expiry according to @Mitesh_Engr?

• Weekly candle High/Low
• Sell 1% away options from those
• Exit when levels breached


Position Sizing by @Mitesh_Engr Sir.

How to deploy your capital?

• First sell 20%
• Pyramid the next day
• When to exit
• What to do when view goes wrong
• What to do with idle capital


Some important tweets of @Mitesh_Engr Sir

• What Data to look at
• ROI for safe players per month
• Max risk per day
• Gather knowledge and play directional
• Never play strategies
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Mitesh Patel
Mitesh Patel
@Mitesh_Engr
Again sharing bank nifty intraday weekly straddle. How to play by selling straddle.
Mostly will work on Monday to Wednesday. Sometimes on Friday.
Why to pay your money to learn this if u can get it here.
U need only practice.
Let’s go.

Say bank nifty future is at 32000.
Sell both 32000 call and put.
Considering current volatile market lest say premium on Monday morning is 350 on both sides.
Sold with 700 points combine premium.
If bank nifty will trade in narrow range say +\- 100 hold it.
If moving 200 points

then exit previous sold straddle. Sell new one. Let’s say BN moved +200
Now sell 32200. If bank nifty will move here within range then u will get profit through theta decay. Follow same procedure for next 150-200 pts move.

This is only for single straddle sell position.

Now in second case sell three straddle. 31900/32000/32100
In case of 100 points move no need to change.
If 200 + then future is 32200.
Exit 31900 and sell 31200 straddle.
If moving another 100 then exit 32000 and sell 32300. Continue same with 100 points move.
If no move then

it will consolidate between 32000-32200 or 32100 to 32300 and u will get theta decay.

This is for normal move. Sudden big move may come anytime. So keep SL in system.
If u r selling at 350-350 then keep SL in system 475 for both legs.
Practice it. No need to attend webinar.
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Matthew Panzarino
Matthew Panzarino
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New iPad Pro has Face ID, thinner bezels, squared off edges. A new touch sensitive Pencil that magnetically attaches to the edges. Thin enough to have a camera bump. Uses the XR's LCD cornering techniques.


The new 12.9" iPad Pro is physically smaller than the old one with the same screen size. It's roughly the same size as an 8.5 x 11 piece of paper. 5.9mm thick.

10 billion transistors in the A12X. 8-core CPU. 7-Core GPU. 35% faster single-core performance. 1000x faster GPU. iPad Pro is Xbox One S class GPU performance in "94% smaller" package, Ternus jokes.

Apple's silicon team is just dropping bombs every event.

live shot of Apple's silicon team


iPad Pro gets USB-C for up to 5K external displays and enables charging out to iPhones. Wild.
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