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Thinking in Bets: Making Smarter Decisions When You Don't Have All the Facts by Annie Duke. A poker book but makes you think hard about position sizing with randomness and uncertainty.

 

Man For All Markets: Thorp's book and how he uses Kelly Criterion.

 

Buffett's investments in AMEX or Li Lu in BYD: -> Knowing when to plunge. As an inverse case, see Mark Sellers in Contango Oil and Gas -> when plunging goes wrong.

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Look up Kelly Criterion.  Never bet full Kelly.  1/3 is probably best. 

 

Nothing beats experience.  Figure out what industry you really know.  Figure out what industry has low impact if you get it wrong.  If you buy a grower at 10x revenue, if it turns out you are wrong, that downside is probably pretty high.  If you buy Union Pacific, you probably don't get a zero.  Do some pre-mortem on what could go wrong.  If you see a chance where it is a zero, then you need to size it very differently.  Obvious stuff, but people get caught up in the weed. 

 

Over time, you will get better.  The books are guidelines, experience helps. 

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Buffett Jan. 1966 Partnership Letter

“How much do I put in number one (ranked by expectation of relative performance) and how much do I put in number eight?” This depends to a great degree on the wideness of the spread between the mathematical expectation of number one vs. number eight. It also depends on the probability that number one could turn in a really poor relative performance. Two securities could have equal mathematical expectations, but one might have .05 chance of performing fifteen percentage points or more worse than the Dow, and the second might have only .01 chance of such performance. The wider range of expectation in the first case reduces the desirability of heavy concentration in it.

 

 

 

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whether it is Kelly or Buffett, I think you will find that position sizing is what I call a missing variable phenomenon...meaning that these rules all assume that you have ex ante the investment sizing a valid assessment of the risks/return of the investment that can only be really gleaned ex post.

 

Kelly uses the illegal mob time delayed wireline from the track to premise its baseline; Buffett in the 1966 letter posits a distribution curve not knowable at time of setting the investment sizing. so it is all skirting around the issue...which is you cant size for risk if your estimate for risk is uncertain and especially if faulty

 

you do want to avoid ruin. ergodicity helps some, but not much (Taleb's example of one person betting all or nothing on 100 coin flips vs 100 people betting all or nothing on a single coin flip...ruin will occur in first example with 100% certainty to the single player, less than 100% across the 100 players). beyond this there is not much to rely upon imo

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Age and your overall net worth is important as well.  People quote Buffet and Munger all the time.  But you are not Buffett nor Munger. None of us are.  Yes, you maybe an Autist like Roaring Kitty. But that's a special breed of special.  If you are in your early 20s, have a good job and good prospect in life and have good safety net, you can probably do a few 30-50% bets.  If you are in your 40s, 50s, and this is a lot of your nest egg, you probably want to be a lot more diversified. 

 

Personal story, in 2011, 2012 ish.  I put 30-50% into my top ideas in my IRA.  The balance was $30k or so.  I was buying a cash box at 1/2 of liquidation value.  That sizing really helped as I got a payout that was almost double.  I did that a couple times and got my IRA into the med to high 5 figures.  But once I crossed over 6 figures, something in my mind mentally changed and I realized that I need to be more diversified.  I have 15 positions in my IRA now.  6 figures is real money and I am in my late 30s.  So I was much more aggresive in my early 30s and now that my balance is about 8x (some contributions, not all performance) from 2011ish, I manage the IRA a lot different.  I manage money for other people and it never reached the level of concentration that it did in my IRA.  Ironically, it is the stuff that I size in 1-5% that tend to out perform lately.  So all this talk about concentrating on your best ideas, sometimes it is good to get some "right tail" exposure to some Saasy companies that doesn't make sense using 2021 P/FCF multiples.  But if you understand the business and realize that this is a "winner take all" category that could be worth 5x the current price in 5-8 years, it's not a bad portfolio allocation strategy to put 1-5% into it.  I prefer 1-2%. So I have a basket of what Peter Lynch call multi-baggers that I don't necessarily have a ton of confidence in like my Griffin Realty idea.  But allocating 10-20% to a basket like that is a wise way to catch some of that "right tail" return.  I do think there is something about digital market places, software, and other digital native businesses that are different than traditional manufacturing that makes it different this time around.  Famous last words. 

 

There are others that are much smarter than me who have evolved and developed the skills to invest in purely compounders and YOLO investments, I am not there yet.  Not sure if I want to be fully there.  As Robert Downey Jr said in Tropic Thunder "You never go full retard."  I never go full compounder.  Sometimes the stuff that you size at 2% wind up returning the same as the stuff that you size at 10% because the former is a 5 bagger the latter is a double.  Nothing wrong with that outcome as your degree of confidence is likely much higher in the latter. 

 

Happy investing, good luck compounding, and may your mind be exposed to wonderful growth. 

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Couple of takeaways ….

 

There are some very good approaches (Kelly), but they almost always treat every bet as an isolated once and done transaction, settling in near real time. In the real world the bet is relative to your risk tolerance at the time, the time horizon, and familiarity with the company you’ve bet on.

 

At most, most people can keep up with maybe 10-12 companies, and 2-4 industries. The reality is that the investor is really swing trading the same group of companies across different cycles and time horizons, and using his/her depth of knowledge to minimize the adverse risk. Risk tolerance, and time horizons changing, as personal circumstance and industry prospects change. Fewer vs more choices, higher maximum weightings, and ongoing risk mitigation.

 

Eye on the prize, not the process. If the objective is a fully paid off house in < 25 years (via mortgage repayment), do you really need compounders? Or is an ongoing string of 3-15 baggers better? Even if it takes 15 years to do, the incremental reward is 10 years of interest savings. Risk vs reward.

 

Human vs algo. The algo can apply mechanical formula a lot more reliably and faster than you can, you’re just a liability.

Do only what you’re good at, and where you have the advantage.

 

SD

 

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Totally agree with BG's point above.  The risk has to be related to your overall net worth and your ability to grow your net worth organically.

Take the two examples below:

 

Person 1-30 years old

Able to save 30K/year

50K net worth-all in stocks

largest position is 40%

While 40% is a huge position by most standards it's only 20K-this individual is saving that amount in like 8 months. So unless the position grew at a very high rate or he kept buying more this would become a smaller % of his net worth pretty quickly.

 

Person 2-63 years old

Able to save 50K/year

600K net worth-300K/stocks/300K in home

largest position is 40%

In this case, the individual has a position of ~120K representing 20% of his overall wealth as he nears retirement.  If this position goes belly up it significantly changes his retirement picture. 

 

I'm in my early 30's and generally keep no more than 5% of my overall net worth in a single position. 

 

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Concentrated bets are not for beginners because you need to ensure your bets are all low risk and learning to do that takes experience. I like to own 3 to 5 stocks which puts me at the extreme concentration end of the spectrum. But I’ve been at this a long time and experience has shown me that I have good enough judgement of risk to do it. You have to be able to judge the durability of the business. Factors that increase risk are leverage, financial and operational and a short history. Factors that reduce risk are being in a business that is more at the core of the economy and serve basic unchanging needs. Some companies are low risk because they are more like holding companies and are highly diversified (think Berkshire). I currently own three stocks, two are highly diversified and involved in real estate and infrastructure. The third is a preferred stock in a similarly stable business.

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The variable that needs to be considered is what you're buying. If your three positions are Mastercard, Union Pacific, and Berkshire, bought at not-crazy prices, you're going to be fine.

 

If your three positions are Twitter, XYZ Gold, and Tesla, I wish you great luck.

 

So before you ask, how many positions can I have - I would ask, how many positions are you >90% sure won't fail?

 

What I think gets lost in these discussions is that if you have 3 stocks and one triples, the others can go to ZERO and your portfolio will retain its value. The key is that the three don't overlap with each other and all go to zero at once. You have to understand something about fragility. This last year was instructive.

 

Six positions is more than enough if you know what you're buying and have an intelligent view of their correlations. More than enough.

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Concentrated bets are not for beginners because you need to ensure your bets are all low risk and learning to do that takes experience. I like to own 3 to 5 stocks which puts me at the extreme concentration end of the spectrum. But I’ve been at this a long time and experience has shown me that I have good enough judgement of risk to do it. You have to be able to judge the durability of the business. Factors that increase risk are leverage, financial and operational and a short history. Factors that reduce risk are being in a business that is more at the core of the economy and serve basic unchanging needs. Some companies are low risk because they are more like holding companies and are highly diversified (think Berkshire). I currently own three stocks, two are highly diversified and involved in real estate and infrastructure. The third is a preferred stock in a similarly stable business.

 

Rod,

 

Care to share your ideas?  Private messages open.  Anyone who's got 3 positions in RE and Infrastracture as their complete portfolio, I want to get to know. 

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Sure sounds like Brookfield to me.

 

Concentrated bets are not for beginners because you need to ensure your bets are all low risk and learning to do that takes experience. I like to own 3 to 5 stocks which puts me at the extreme concentration end of the spectrum. But I’ve been at this a long time and experience has shown me that I have good enough judgement of risk to do it. You have to be able to judge the durability of the business. Factors that increase risk are leverage, financial and operational and a short history. Factors that reduce risk are being in a business that is more at the core of the economy and serve basic unchanging needs. Some companies are low risk because they are more like holding companies and are highly diversified (think Berkshire). I currently own three stocks, two are highly diversified and involved in real estate and infrastructure. The third is a preferred stock in a similarly stable business.

 

Rod,

 

Care to share your ideas?  Private messages open.  Anyone who's got 3 positions in RE and Infrastracture as their complete portfolio, I want to get to know.

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yep. One is Brookfield (actually Partners Value Fund), the others are Dream Unlimited (DRM.TO) and Brookfield Office Properties Preferred (BPO.PR.N).

 

I could be accused of being Real Estate heavy.

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I always tend to hold a lot of stocks, more and more as time goes on, I used to be more concentrated. I find I'm getting less risk tolerant as I get older (late 40s now :( ).  And all of my regrets are stocks I've sold way too early.  Right now I hold 36 stocks.  My largest position (BAM) is about 13% and I hold a lot of 1-10% positions.  I tend to take small positions and add over time.  Whenever something grows past 10% I tend to trim a little (but not always).  I try never to sell completely unless there is a good non-valuation based reason to sell, which makes me not want to own it at all.  I'm trying to only trim on valuation, but never get rid of a great company entirely on valuation alone.  I don't do this for a living, so I think the diversification gives me some sense that not all of my eggs are in one basket and stops me from doing something dumb out of fear or worry.  If any one of my stocks takes a nose dive it isn't a huge deal.  More and more I like the Peter Lynch type approach of holding a lot of great companies and never selling.  Probably limits my gains, but limits my downside as well.  And sometimes I have great years like 2020 where I demolished the S&P500.  I also tend to hold very little cash, about 5% cash right now which is about where I usually keep it, (although I've been 0% cash in the past)  I also try to make sure I have at least 5% in something on the safe side like BRKB.  BRKB is about 8% now, so cash and BRK is 13%.  I used to count Apple as one of my almost as safe as cash stocks, but with it's valuation now I no longer consider it to be in that category.  I recently trimmed Apple back down to under a 10% position.  Anyway that's my current methodology, like always, subject to change.  And then there's crypto, which I haven't decided what to do with, so I'm just Hodling for now.  It has grown to about half the size of my stock portfolio and is almost all in two coins (BTC & ETH).  So it is about 1/3rd of my combined stock/crypto portfolio.  That means both BTC and ETH are larger than I usually let stocks get.  So I am obviously not managing that portion of my portfolio in the same way.  My cost basis there is so small though that I think I'm just going to continue to do nothing and see what happens in the coming years/decades.

 

 

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Agree with everyone above, but just to add I would rather own one stock that I paid a great price relative to future cash flow/margin profile, then 100 overpriced/overvalued stocks.

 

I essentially own a two stock portfolio that's 90% of my net worth. While the third is about 5% and the rest is a basket of workouts about 5%.

 

There are great opportunities in the market. I found an under-the-radar stock that has a couple of businesses and a liquid stake in a grower that's also under the radar, where it has long runway. Priced under cash per share, not even book, but because it's a small company under $100M, and circumstances the screeners are not updated yet.

 

I think position sizing has to relative to price paid, ability to generate more capital for dollar-cost averaging, and stage of your life.

 

My portfolio hasn't had a drawdown yet, but when running portfolios for others, I've experienced 50%+ drawdowns in a holding, but overtime it worked out, especially if you bought at the dips. While the other two holdings haven't gone down.

 

EDIT: Philosophy can change on a dime. Not a portfolio manager/financial advisor, when running portfolio, I meant my family. 

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At any one time, most everyone is a lot more diversified that they realize. Equity portfolio, FI portfolio, house(s), partnerships, crypto, pension, interest/dividend income, etc. Equities as a % of the total asset pool, and dividends as a % of total income, are far from 100%. Most are actually TOO diversified. 

 

Draw downs of 50%+ every 5-7 years (or more often) is pretty common. Capital exists to be used, and nothing cures 'invincibility' faster than getting rid of the 'excess' money. 50% every 5-7 years, is annual compounding of 10-15% (ROE); but the actual YOY returns will of course  look very different. Relying on diversification, and portfolio growth, to manage the return volatility is just not effective.

 

Most can manage small portfolios very well, but become utter sh1te when the portfolio is 3-4x that.

 

Different POV.

 

SD

 

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good thread!

 

one other small point is how you get to the targeted size....I like dollar cost averaging. you never know for sure whether you are buying cheap or dear, so buy steady, more when down and less when up

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I've dabbled with Kelly mostly as a tool to determine relative allocation between competing ideas (could also just use expected value which tends to correlate reasonably well with the kelly allocation and is easier to remember). Qualitatively have been guided simply by this dictum - size it sufficiently big that it makes a difference to your life but not so big that you lose sleep over it.

 

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Agree with all of the points mentioned above.There was a reading in CFA level three that really changed the way I approach my personal portfolio  as well.The reading was about asset allocation for human and financial capital .The idea is that early in your life most of your net worth is in human capital which are cash flows distant in the future and your financial capital is little.

 

So, if you consider your financial capital allocation only ,you might be underinvested and not concentrated as you may think. It touched on the correlation between human capital and financial capital. for-example ,you work in wall street and most of you pay is variable and equity like, by concentrating say on financial stocks you are actually more concentrated than you think because at worst you may lose your job (human capital) and your financial capital (stocks go down ).i think now it's being revised under risk management for individual portfolios worth a read .

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I read this book written by two NY Times reporters years back called "Blind Man's Bluff" about the Cold War that involved true stories about submarine espionage.  One of the stories involves the USS submarine Scorpion that disappears in 1968 to the bottom of the Atlantic with all hands lost.  This sets off a frantic search by the US Navy to find its lost sub.  All they knew was its last reported position, the path it was on (it was heading back to base at Newport News, VA after a tour of duty in the North Atlantic) and only vague other bits of information.  The area to be searched was a large part of the North Atlantic near the US coast.  It was kind of hopeless that the sub would ever be located.

 

https://en.wikipedia.org/wiki/USS_Scorpion_(SSN-589)

 

So the Naval Officer in charge of the search operation (a kind of Hunt for Red October Jack Ryan type of guy, I guess) comes up with a novel plan.  He doesn't just reach out to experts like other submarine commanders.  He assembles a wide range of folks - some with submarine knowledge, mathematicians, salvage ops men - basically a diverse set of knowledgeable people but not all experts in subs.  He briefs them with all the information and data that the Navy has related to the USS Scorpion's last voyage.  He then asks them to go off on their own, sift through the data and independently offer their best opinion on why the submarine ran into trouble, its speed and its steepness of descent so as to locate where it might have touched bottom.  He makes it interesting by offering a reward and prizes to the winner who comes closest to the actual location if/when the sub is located.

 

The individuals' guesses were assembled on a map and using some fancy math (Bayes Theorem) -- a composite guess of the "crowd" was isolated based on the collective estimate of the group as to where the sub might be located.  The location was not a spot any individual member came up with or picked.  But a search was started focusing on the spot identified by this collective method and five months later the sub was located within 220 yards from where the group's estimate said it would be.

 

Ok - why tell this story.  Because collective wisdom is what the stock market operates on.  It is why it is generally an efficient market.  The various participants individually all have guesses about the fair value of a stock.  These guesses are made up of lots of random guesses + a tiny bit of signal information in each guess.  As these guesses are aggregated, the random parts cancel each other out and what remains is mostly pure signal.

 

I long ago gave up on using the Kelly Criterion.  That is because according to the Kelly Criterion the size of the bet is determined by the formula:  Edge/Odds = size of bet.  But here's the thing - according to the formula if your Edge = zero, then the size of bet is "Don't Bet!"

 

If most of us are truly honest with ourselves, do we really have an edge in picking an individual stock vs the market.  Do we think our guess as to where the "missing sub" is located is going to be more accurate and correct than the collective wisdom of a diverse group of actors with money on the line?  Are we really just punters when we think we are experts?

 

The good news is that unlike most gambling games (which are negative sum), the stock market is a positive sum game.  All we need is to go with the market via diversification in a group of 10-15 high quality businesses and we will do fine.  So my recommendation is to put away the Kelly position sizing stuff because if you think you have an edge then you are making big bets that you alone can locate a "missing sub" better than the market can.

 

wabuffo

 

p.s. the USS Scorpion story is also featured in James Surowiecki's "Wisdom of Crowds" book.

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I read this book years back called "Blind Man's Bluff" about the Cold War that involved submarine espionage based on true stories written by two NY Times reporters.  One of the stories involves the USS submarine Scorpion that disappears in 1968 to the bottom of the Atlantic with all hands lost.  This sets off a frantic search by the US Navy to find its lost sub.  All they knew was its last reported position, the path it was on (it was heading back to base at Newport News, VA after a tour of duty in the North Atlantic) and only vague other bits of information.  The area to be searched was a large part of the North Atlantic near the US coast.  It was kind of hopeless that the sub would ever be located.

 

So the Naval Officer in charge of the search operation (a kind of Hunt for Red October Jack Ryan type of guy, I guess) comes up with a novel plan.  He doesn't just reach out to experts like other submarine commanders.  He assembles a wide range of folks - some with submarine knowledge, mathematicians, salvage ops men - basically a diverse set of knowledgeable people but not all experts in subs.  He briefs them with all the information and data that the Navy has related to the USS Scorpion's last voyage.  He then asks them to go off on their own, sift through the data and independently offer their best opinion on why the submarine ran into trouble, its speed and its steepness of descent so as to locate where it might have touched bottom.  He makes it interesting by offering a reward and prizes to the winner who comes closest to the actual location if/when the sub is located.

 

The individual's guesses on a map were assembled and using some fancy math (Bayes Theorem) -- a composite guess of the "crowd" was isolated based on the collective estimate of the group as to where the sub might be located.  The location was not a spot any individual member came up with or picked.  But a search was started focusing on the spot identified by this collective method and five months later the sub was located within 220 yards from where the group's estimate said it would be.

 

Ok - why tell this story.  Because collective wisdom is what the stock market operates on.  It is why it is generally an efficient market.  The various participants individually all have guesses about the fair value of a stock.  These guesses are made up of lots of random guesses + a tiny bit of signal information in each guess.  As these guesses are aggregated, the random parts cancel each other out and what remains is mostly pure signal.

 

I long ago gave up on using the Kelly Criterion.  That is because according to the Kelly Criterion the size of the bet is determined by the formula:  Edge/Odds = size of bet.  But here's the thing - according to the formula if your Edge = zero, then the size of bet is "Don't Bet!"

 

If most of us are truly honest with ourselves, do we really have an edge in picking an individual stock vs the market.  Do we think our guess as to where the "missing sub" is located is going to be more accurate and correct than the collective wisdom of a diverse group of actors with money on the line?  Are we really just punters when we think we are experts?

 

The good news is that unlike most gambling games (which are negative sum), the stock market is a positive sum game.  All we need is to go with the market via diversification in a group of 10-15 high quality businesses and we will do fine.  So my recommendation is to put away the Kelly position sizing stuff because if you think you have an edge then you are making big bets that you alone can locate a "missing sub" better than the market can.

 

wabuffo

 

p.s. the USS Scorpion story is also featured in James Surowiecki's "Wisdom of Crowds" book.

 

Wabuffo,

 

I think you're pretty good with this Garret Motion stuff.  So I think you are underselling yourself a bit. 

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I actually think the Kelly Criterion can be useful to play around with a bit if you have never done that - just to get a feel for the theory of position sizing and to compare relative position sizes (i.e. why do I have a 5% position in Google but only a 0.5% position in Microsoft even though my thought process about both names is about the same), but I agree that in practice in the stock market its application is limited and I hardly ever use it. l I think for me there are three prime drivers of position sizing:

 

1. Your personal situation (age, net worth, do you have a job, etc). If you are young and have a good job you can afford to take some risks. It doesn't work out? Write it off as a life lesson, worst case. But if you are a relatively poor retiree? You are fucked.

2. (downside) Risk. What happens if your thesis does not work out as expected? Are you buying a cash box or a growth story at 200x price / sales? E.g. "never lose money". I'd be extremely hesitant to put a large amount of money in a warrant or equity stub or something with an equal risk profile.

3. Level of confidence - the most tricky one. How sure are you that this is a good idea? Do you think you can correctly estimate all tail risks? What's the chance that you are missing an important piece of the puzzle? Can you point out what mistake others are making in their valuation? Why does this opportunity exist? What would you do if the stock cratered 50% today?

 

The big problem with number 2 and especially number 3 is that they are very hard to quantify. A skeptical view of your own abilities is required. Often when I see people making huge bets / running concentrated portfolio's I feel like they are overestimating their own abilities. In that case Kelly isn't going to help you either because you will always overestimate your own edge and underestimate the risks.

 

I guess for me it often comes down to: buy as much as you feel 'comfortable with' - and probably a bit less. I know, that's a vague concept, but if you are thinking all the time about a specific position or are anxious something will go wrong it's probably too big. And (at least in my case) very often plans and ideas turn out to be shit, no matter how confident you are initially. So even if you think: I would be totally comfortable with this being a 5% position, why not start with 3%? Often the exact moment of buying is not that time-critical anyway. So you can take it easy. Nibble a bit, take a break.

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