# How do you optimally allocate your portfolio concentration?

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So I had been thinking about this problem for a long time - that if you had 3 variables defined for a set of securities - downside, upside, and odds(confidence), you should be able to figure out how many % of your portfolio to put into each.

For example - say I have 3 securities:

A - downside 20%, upside 100%, confidence 90%

B - downside 80%, upside 600%, confidence 70%

C - downside 50%, upside 300%, confidence 75%

I am by nature a doubter of using models to describe a situation but in the recent couple years I had a gut feeling that models can help you create a trading plan and do execution a lot better.

I know the Kelly Criterion as it applies to single bets, and making these single bets continuously.  But we are talking about allocation in a portfolio, so we are really making simultaneous bets.

I don't exactly know how the above situation can be described as beautifully as the Kelly Criterion as it applies to single bets, but I tempered around with some optimization models and I did some backtesting, which basically have produced more consistent, better returns than I have achieved and it did so with better diversification.

Does anyone know of a good way to describe the above situation? As I feel that covers the essence of what I am trying to do - reducing risk and increasing return.

I never really doubted my ability to find good values consistently and my ability to make the odds, but where I usually fail is in how much to bet while facing a myriad of choices.  I also fail because I refuse to sell a stock that has run up, but has not reached intrinsic value, while other more undervalued stocks are available.  So I decided to create a framework that enforces me create more disciplined trading plans.

I would appreciate anyone's thoughts on this subject!

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Isn't this an expected value exercise?

A) .9 * 100 - .1 * 20 = \$88

B) .7 * 600 - .3 * 80 = \$396

C) .75 * 300 - .25 * 50 = \$212

So one would reasonably put 100% into B?

I would think the bigger question is how you get the confidence levels, people pull these out of a hat, but there is no way to tell that one is right or wrong about these weightings.

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Isn't this an expected value exercise?

A) .9 * 100 - .1 * 20 = \$88

B) .7 * 600 - .3 * 80 = \$396

C) .75 * 300 - .25 * 50 = \$212

So one would reasonably put 100% into B?

I would think the bigger question is how you get the confidence levels, people pull these out of a hat, but there is no way to tell that one is right or wrong about these weightings.

Well, this is expected return but I don't think anyone would put 100% into a situation where there is possibility for 80% loss and say that is reasonable.  So that's my main point, that you can't use expected return only and put every egg in a single basket based on that.  You have choices, and you may put more of your portfolio into B than A or C.

In a realistic optimal allocation scenario, not only do you have to get returns but also guard against the small chance of large losses.  Expected return, like using average volatility, or using standard deviation, do not guard against the rare cases of large unexpected losses.  So to have a realistic allocation, expected return can only be PART of the consideration.

With regard to how do you get to confidence levels - well you are doing this even if you are not using a model.  When you put a large part of your portfolio into a security, that implicitly means you must have high confidence for that security.  So this model does not really help you with that, it merely takes the confidence level that you already have made a judgement on.  There is of course the prudent action of doing more research to increase your confidence level in a security, but that's something you should be doing and not the model.

I want to be clear that when I made this scenario, I assumed you only would be thinking about this scenario if you have already done your homework on your risk and return.  This is a mental model that is a tool to help you with the next step - how to allocate.

So faced with this scenario, how would you guys allocate your capital?

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Yudeng, you have identified the fundamental problem, the solution to which separates the great investors from the merely good investors.

Thoroughly understanding the Kelly Criterion or related heuristics about how and when to concentrate bets or investments is crucial to success.  Understanding the practical limitations of the Kelly Criterion is even more important than understanding the criterion itself.  Use of the criterion without profound understanding of its limitations, especially considering human nature, can be a  trap.

There was a fund manager not long ago who ran a very concentrated portfolio of no more than a handful of stocks with allocations according to his use of the criterion.  He is now an ex fund manager.  There were three fatal flaws in his approach:  First, his estimation of margin of safety for each stock was flawed because it was based on relative value, not absolute value, and his stocks were incapable of returning substantial value to shareholders through workouts, large dividends, buybacks or other distributions in a down market.  Second, all of his holdings were highly correlated with the market, the hidden flaw in most diversification schemes.  Third, he didn't have a substantial cash reserve, and had to sell shares when there was a run on the bank during the down market.

You have correctly reasoned that there is less risk in holding a few concentrated positions simultaneously than holding the same positions serially.  However, as most financial markets and securities within those markets now have a high degree of correlation in their movements, it would be wise to use the Kelly Criterion as if these were serial investments.

We are all subject to overconfidence and other biases.  Therefore, those who use the Kelly Criterion successfully generally only use a "half Kelly", in other words, taking only half the position size specified by the formula as being optimal for long term capital growth.  :)

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interesting topic.

Allocation to each category-Would it not depend on ones risk tolerence + his confidence in estimating in estimating upside, downside etc ?

I would think that you would want to invest in more than one stock...the less confidence + competence you have the more securities you would need.(i.e. the extreme of the average person who does no work should stick to indexes vs the business man/owner/jockey investor can have one stock e.g. young bill gates owning early microsoft stock or sam walton + WMT)

If I had 5-10 stocks that fit category A -that would be appealing...90% chance of earning 100% assumimg over 3 years (I am making up the time frame, assuming that the average company takes ~ 3 years to reach IV as per Pabri).

Again depending on your age, financial situation (college tuitions coming do) adding some from the other categories (added risk + return depending on your risk tolerence)would be fine. How much would depend on your appetite for risk. It would appear that you re being compensated for taking the risk.

I may be out to lunch, but am putting the thoughts out for my own education.

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100% in few A's.

You might do very well for decades with B's, but in the end if you have a zero (you tought it would be 0,2, but you get 0...that's the 30% uncertainty) because of an economical storm (see 2008), you still end up with zero. 7*7*7*0= 0.

Cheers!

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Buffett in his early days - if they liked something, they were comfortable with 4 or 5 positions.

Mohnish - why invest in your 10th best idea?

I may be twisting these, but I only own one stock, so let it be.

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One thought would be to define an over-arching template that your comfortable with which will assure you a minimum level of diversification. Say you're comfortable with 5 stocks. Your template may then look like this:

1 - 35%

2 - 25%

3 - 20%

4 - 12.5%

5 - 7.5%

You could then use expected returns to fill in the blanks. Best outcome gets a 35% weight. Next best outcome gets 25% weight and so on... Overtime, you'd continue to calculate expected returns and rebalance accordingly.

* I don't do this. Just a thought to throw into the discussion.

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Buffett in his early days - if they liked something, they were comfortable with 4 or 5 positions.

Mohnish - why invest in your 10th best idea?

I may be twisting these, but I only own one stock, so let it be.

Same here. One or two  positions typically amount to more than half of our holdings.  Confidence is the key to having long term success with a concentrated portfolio, but confidence is deceptive because we are so easily deceived.  One of the best reality checks on confidence is failure analysis -- how have others failed in a particular realm or in related realms; how have we failed within our frame of reference.  There is a track record of experience related to failure in most fields and in general.  Pilots have their checklists to use before take off and for use when experiencing various emergencies.  These checklists are compiled from errors or other factors that increase risk that have been noted after crashes or circumstances that might cause failure.

Practice with the Kelly formula reveals that the optimalization of returns is much more sensitive to the probability of large losses than to the amount of likely gains.  Commonsense affirms this; a lifetime of investing success may be wiped out by doing one incautious thing such as using unsupportable leverage.

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A - downside 20%, upside 100%, confidence 90%

B - downside 80%, upside 600%, confidence 70%

C - downside 50%, upside 300%, confidence 75%

How one should actually allocate capital to these three examples depends on the person and the portfolio (managing your own vs. other people's money). The Kelly Criterion can be adjusted for multiple investments at a time -- it just makes for a more complicated model. Here are the Kelly allocations for the above 3 investments at the same time:

A - 8%

B - 67%

C - 25%

In reality, there is some chance of every investment losing 100%, so in this case Kelly would say to put 99% and never 100% into all investments. This is all theoretical, and obviously in practice it's much different with many more variables to consider.

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Investing is a very humbling business where the evaluation of risk is very hard. That is why you need a huge margin of safety.

I had a nice example of this today as my largest holding, EasyHome declared that an employee comitted fraud for 3.4M or about 15% of their loan book. A checklist is one of the most usefull weapon against mistakes but there will always be some unexpected events. I don't even think it's possible to implement employee fraud into a checklist.

I'm still bullish on the stock tough, no long term impairment.

BeerBaron

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Twacowfa - it is very tough to trust these days.  That is why I invested in a stock whereby the management team have their mom's money at stake.

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Twacowfa - it is very tough to trust these days.  That is why I invested in a stock whereby the management team have their mom's money at stake.

Exactly, The CEO of our biggest holding has most of his wealth tied up in the company, and he has a long term record of dealing fairly with investors whose funds he's managed and returning enormous value to them.  His CFO worked for Jack Byrne and was mentored by him.  Plus his returns are almost entirely not dependent on how well financial markets are doing.  :)

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Kelly ofrmula is fine but you should never forget the worst case scenario and make sure that you do survive to fight another day even if worst case scenario comes true.

Assume a gun with 1000 chambers has only one bullet and 999 of them are empty. I wouldn't pull the trigger on myself even for billions of dollars payout but with kelly formula your expected return might be in trillions and you are supposed to go for it.

So, allocating the higher % in higher risk adjusted ideas is good but you need to make sure that even in worst case situation you are not out of the game.

As some one else mentioned , allocation might vary depending on if it's only your money or pooled one. Different people have different reaction to fluctuations.

Cheers,

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Investing is a very humbling business where the evaluation of risk is very hard. That is why you need a huge margin of safety.

I had a nice example of this today as my largest holding, EasyHome declared that an employee comitted fraud for 3.4M or about 15% of their loan book. A checklist is one of the most usefull weapon against mistakes but there will always be some unexpected events. I don't even think it's possible to implement employee fraud into a checklist.

I'm still bullish on the stock tough, no long term impairment.

BeerBaron

I agree that the possibility of substantial financial fraud always exists, but it is far less likely to occur with some companies than with others.  Thus with BRK the risk effectively would be zero, with a startup managed by people of uncertain reputation, the risk might be high, with  some other companies, too hard to call.

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Kelly ofrmula is fine but you should never forget the worst case scenario and make sure that you do survive to fight another day even if worst case scenario comes true.

Assume a gun with 1000 chambers has only one bullet and 999 of them are empty. I wouldn't pull the trigger on myself even for billions of dollars payout but with kelly formula your expected return might be in trillions and you are supposed to go for it.

So, allocating the higher % in higher risk adjusted ideas is good but you need to make sure that even in worst case situation you are not out of the game.

As some one else mentioned , allocation might vary depending on if it's only your money or pooled one. Different people have different reaction to fluctuations.

Cheers,

A good point.  It's not a good idea to have all of your eggs in one basket, even if you watch that basket very carefully.

But the truth is that risk happens.  There is a small chance of being hit by lightening every time I take a walk on a cloudy day.  There is about one chance in a million that I'll wind up DOA when I drive across town at night in my car, no matter how careful I am.  The Kelly formula in theory doesn't provide for taking a fatal risk, but always holds back some capital to live to fight another day.  That's the theory.  In practice . . . . well, as the bard said : "Aye, there's the rub."

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You guys are hilarious.

The Kelly Criterion--where do I begin? When applied to investing, as opposed to cards, it has all of the drawbacks of qualitative reasoning combined with the arrogance of quantitative reasoning. It's the worst of all worlds.

As Templeton said, if you think you have all of the answers, you're not even asking the right questions.

How about a nuclear attack? I don't care how good a stock picker you are--you're screwed--end of story. The risks that end up killing you are the risks you don't even consider.

If you think rationally, you will realize that you can apply the Kelly Criterion to closed loop systems--cards--not the probability of exogenous events, such as some guy in a saloon pulling a gun on you if you win too much. And please, don't give me a lecture on your confidence level of getting shot. In other words, you can apply the system to things that can be definitely measured--cards--not the risks outside things that can be definitely measured, because those must be estimated, and the estimates are what throw a wrench in your calculations. It's a fun theory, but if you think you can blindly apply it--or even apply it to stocks at all in its original or 1/2 Kelly form, I have a great ice pond in Florida to sell you.

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HarryLong you are much more eloquent than me. Thanks for the closed vs open loop comparison.

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HarryLong you are much more eloquent than me. Thanks for the closed vs open loop comparison.

Myth, you flatter me. Merci, bien.

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I sometimes use the Kelly formula as part of my last check-up round partnered with a dcf calculation, naturally with conservative input. If they don't give me numbers to drool over, I know that I have deluded myself somewhere along the line and been blinded by my own enthusiasm. In making percentage allocation decisions it's pretty worthless, though.

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You guys are hilarious.

The Kelly Criterion--where do I begin? When applied to investing, as opposed to cards, it has all of the drawbacks of qualitative reasoning combined with the arrogance of quantitative reasoning. It's the worst of all worlds.

As Templeton said, if you think you have all of the answers, you're not even asking the right questions.

How about a nuclear attack? I don't care how good a stock picker you are--you're screwed--end of story. The risks that end up killing you are the risks you don't even consider.

If you think rationally, you will realize that you can apply the Kelly Criterion to closed loop systems--cards--not the probability of exogenous events, such as some guy in a saloon pulling a gun on you if you win too much. And please, don't give me a lecture on your confidence level of getting shot. In other words, you can apply the system to things that can be definitely measured--cards--not the risks outside things that can be definitely measured, because those must be estimated, and the estimates are what throw a wrench in your calculations. It's a fun theory, but if you think you can blindly apply it--or even apply it to stocks at all in its original or 1/2 Kelly form, I have a great ice pond in Florida to sell you.

Well put, Harry.  Application of the Kelly formula may lead to false confidence, and probably does lead to overconfidence in most uses as with the overconfident fund manager mentioned earlier.  Like the black scholes model for options pricing with all its limitations, it may be useful as a starting point for starting to think about all aspects of risk.  This can stimulate thought about what are the risks  that are out of the box and what is their estimated magnitude and probability.  I'm reminded of an old card counter I once knew.  He would agree with you that the risks of making a big score may be greater than leaving your money on the table and walking away for good.

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100% in few A's.

You might do very well for decades with B's, but in the end if you have a zero (you tought it would be 0,2, but you get 0...that's the 30% uncertainty) because of an economical storm (see 2008), you still end up with zero. 7*7*7*0= 0.

Cheers!

Get 600% a few times and who cares if you lose 80% :)

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You guys are hilarious.

The Kelly Criterion--where do I begin? When applied to investing, as opposed to cards, it has all of the drawbacks of qualitative reasoning combined with the arrogance of quantitative reasoning. It's the worst of all worlds.

As Templeton said, if you think you have all of the answers, you're not even asking the right questions.

How about a nuclear attack? I don't care how good a stock picker you are--you're screwed--end of story. The risks that end up killing you are the risks you don't even consider.

If you think rationally, you will realize that you can apply the Kelly Criterion to closed loop systems--cards--not the probability of exogenous events, such as some guy in a saloon pulling a gun on you if you win too much. And please, don't give me a lecture on your confidence level of getting shot. In other words, you can apply the system to things that can be definitely measured--cards--not the risks outside things that can be definitely measured, because those must be estimated, and the estimates are what throw a wrench in your calculations. It's a fun theory, but if you think you can blindly apply it--or even apply it to stocks at all in its original or 1/2 Kelly form, I have a great ice pond in Florida to sell you.

If you have a good way to handle the situation outlined I am all ears.

The risks you don't consider would end up killing you even if you do not use a model to do allocation, since you are subject to them as long as you bought stock. For every security you buy, you are implicitly making a statement about the downside, upside, and expressing some form of confidence in it.  The question is when you have multiple choices, what are good techniques you would use to decide how much to put into each choice?  It would be immensely helpful to know how you approached this.

For example with Buffett and Korean stocks - he got a basket of them trading at PE of 2-5 and didn't know much about them individually, but that basket did well overall for him.  Just because North Korea might attack South Korea(a risk Buffett acknowledged) it still didn't stop him from committing some money.

The situation with the Korean stocks was that if North attacked, they would all tank pretty much close to 0.  If North did not attack, then they would no longer remain cheap and probably can go up 100-200%. I doubt anyone can really know the chance that North Korea will attack South Korea, but I guess Buffett assumed it was small.

The main question is how many % of your portfolio would you put into the Korean stocks if you were in Buffett's shoes?  The answer would be a combination of:

1) depends on how comfortable you feel about the Korean situation

2) depends on what your other choices are, and their respective upside/downside/confidence level

That's what I am curious about - how people handle allocation so I can do it better.

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You guys are hilarious.

The Kelly Criterion--where do I begin? When applied to investing, as opposed to cards, it has all of the drawbacks of qualitative reasoning combined with the arrogance of quantitative reasoning. It's the worst of all worlds.

As Templeton said, if you think you have all of the answers, you're not even asking the right questions.

How about a nuclear attack? I don't care how good a stock picker you are--you're screwed--end of story. The risks that end up killing you are the risks you don't even consider.

If you think rationally, you will realize that you can apply the Kelly Criterion to closed loop systems--cards--not the probability of exogenous events, such as some guy in a saloon pulling a gun on you if you win too much. And please, don't give me a lecture on your confidence level of getting shot. In other words, you can apply the system to things that can be definitely measured--cards--not the risks outside things that can be definitely measured, because those must be estimated, and the estimates are what throw a wrench in your calculations. It's a fun theory, but if you think you can blindly apply it--or even apply it to stocks at all in its original or 1/2 Kelly form, I have a great ice pond in Florida to sell you.

If you have a good way to handle the situation outlined I am all ears.

The risks you don't consider would end up killing you even if you do not use a model to do allocation, since you are subject to them as long as you bought stock. For every security you buy, you are implicitly making a statement about the downside, upside, and expressing some form of confidence in it.  The question is when you have multiple choices, what are good techniques you would use to decide how much to put into each choice?  It would be immensely helpful to know how you approached this.

For example with Buffett and Korean stocks - he got a basket of them trading at PE of 2-5 and didn't know much about them individually, but that basket did well overall for him.  Just because North Korea might attack South Korea(a risk Buffett acknowledged) it still didn't stop him from committing some money.

The situation with the Korean stocks was that if North attacked, they would all tank pretty much close to 0.  If North did not attack, then they would no longer remain cheap and probably can go up 100-200%. I doubt anyone can really know the chance that North Korea will attack South Korea, but I guess Buffett assumed it was small.

The main question is how many % of your portfolio would you put into the Korean stocks if you were in Buffett's shoes?  The answer would be a combination of:

1) depends on how comfortable you feel about the Korean situation

2) depends on what your other choices are, and their respective upside/downside/confidence level

That's what I am curious about - how people handle allocation so I can do it better.

The Kelly Criterion comes into play for us, but it's the last thing we do.  It's far more important to understand all aspects of risk.  Some risks can be ignored if you like because they may have little relevance to asset allocation, for example, asteroid strike.  However, nuclear war is one thing we take into consideration.  We have a moderate position in a New Zealand company mainly to help provide a new start if we should flee there if a big war looms.  New Zealand would probably be about the safest place to be in that unfortunate event.

First degree relatives in our core family have unmortgaged houses.  That gives a lot of comfort, especially to the members of the gentler sex.  We have zero debt.  That's a good way to be, less worry, better sleep.  So we build a base of prudent security first, and then it doesn't seem quite so risky to put a third or half of one's investable assets into a really good idea if one thoroughly understands it, and the idea is much better than anything else that's well understood.

When we have an investment, there is a continual process of calculating and recalculating the estimated weighted probabilities of how the investment will do. This is a Bayesian analysis.  It's not perfect, but the ongoing process helps keep the evaluation objective as new information appears and is evaluated.  It's much easier to do this with a concentrated portfolio than with a widely diversified portfolio, and the returns will be much better if well executed than with a large portfolio that will be subject to "diworseification".  :)

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