The generalization of Kelly is (for the quants) essentially to maximize the expected logarithmic returns over the subperiods. One implication of this approach is that it seeks to avoid large drawdowns (as larger and larger drawdowns have unbounded negative logarithms).
So even a full-Kelly approach will tend to keep a substantial cash allocation or perhaps allocate some to puts (about the only strictly defensible 100% equity full-Kelly portfolio would treat conservative estimates of the price that would ensure a PE bid as cash equivalent: something like positive net-net (more current assets than total liabilities) might approximate that). Kelly bettors in games where there are definable odds generally practice half-Kelly which is exactly equivalent to 50% in cash and 50% in a full-Kelly portfolio (which itself will have some cash allocation!), if nothing else to help account for uncertainty around whether you've correctly figured out the payouts and probabilities.
The key point is not only to think about the odds and payout of success, but to consider the odds and payout in the worst-case scenario (and consider those at least as much as the success case). This is pretty easy to analogize to the Graham & Dodd "margin of safety" (and there's at least some research indicating that Buffett sizes bets in a Kelly-esque manner: he also endorsed Ed Thorp as a good manager for his limited partners who didn't follow him into Berkshire (someone who took their money from Buffett and put it into Thorp's fund and then bought BRK when Thorp stopped managing other people's money may actually have done better than someone who stayed with Buffett)).
I've toyed with the idea of an equal-weight portfolio that sells flowers and waters weeds but when the sales (plus dividends, covered call premiums, etc.) of a flower exceed what you put in by enough to have gotten an acceptable annual return, you exempt it from equal-weighting and only sell enough to keep that realized return profile (until you decide it doesn't deserve any weight).
There is a time element to it. I started my portfolio in 2012 more or less, I bought some stocks, and I still find new ideas in 2023, so I could not have started my portfolio with 15 equal weights Ideas. I did not even have 15 ideas when I started! So new ideas get added progressively, and their weight depends not only on confidence, but also on available funds and saving rates, and things to sell.
On top of that I am willing to add less weight on a new idea if I just discovered the company. I like to have followed it for two years to really feel confident to concentrate more.
Investing in taxable vs tax-exempt accounts is very different.
Size your positions, at least in the tax-exempt accounts, as if you woke up each day with all cash and were investing it from scratch. In taxable accounts strive for long-term compounders and low turnover.
Avoid big hits to the portfolio via choices concerning concentration and correlation of your investments.
From Kelly: confidence in winning is more important vs maximizing expected value.
Try to be tax efficient.
Consider difficult questions like: given a 60/40 binary bet with the outcome determined tomorrow, how much would you bet?
I have many positions, over 30, with 10% being considered unusually large and 4% - 5% being standard with some bits and pieces of smaller size. I will employ leverage at times when I believe the opportunity set is super attractive. My overall positions across strategies come together to, hopefully, limit downside over each year to an acceptable level while providing acceptable upside. I have found that I can absorb significant losses without too much stress as I have quite a bit of confidence in my process and long-term outcomes.
Thanks for sharing. Curious to know if the handful of companies you own are internally diversified across sectors, etc., and if you consider that when you think about weighting?
Yes I do. I only own a single stock from any one sector.
For instance, I like multiple banks that I see as worthy of owning, but one of my largest positions is a bank stock, so I don’t buy additional banks.
Likewise, I like a lot of defense companies right now, but my largest holding is in the defense industry, so I tend to quickly pass on new defense ideas because I can’t justify the additional concentration risk. If the US government is the primary customer for both, I’m not really diversified
I'm currently working as an investment Analyst. For my personal portfolio I bought two companies with a position size of 4%, 3.5% one of the position now has grown to about 16% of the portfolio (The Largest Position), and the other one also has become decent size. Usually on average I run ideas around 12%-10%. Also usually my smaller positions tends to have higher variability of outcomes and the characteristics of the names which became higher hasn't changed that much either. In general I don't like to play too much with my portfolio as I believe in low churn and compounding overtime. My question is how would think about managing your own portfolio when it's comes to position sizing (I allocate portion of my paycheck to this portfolio on monthly basis) as you don't have to answer clients over higher volatility and concentration risk would you let you winners to run or come back to your targeted allocation range.
Yeah, implementing a weighting strategy can be different for personal and professional accounts for the reason you suggest. Let's say you have a $50,000 portfolio and own 10 stocks, one of which grew to be a 10% position ($5,000 value). If you're contributing $1,000 a month for the next year or something similar, you can effectively reduce your weight in the 10% stock over time by allocating your new funds into other investments, holding all else equal. On the other hand, you could allocate new personal funds according to the target weights you have in your portfolio. $100 of each $1,000 addition would go to the 10% position, for example. Much more easily done now with low/zero commissions, but be mindful of trading costs if they exist. Could allocate to a few holdings rather than every holding each month.
Super thank you much for your thoughts I agree on the last statement too for an example I'm running a tracker position in Bergman & Beving but when I bought the stock realised Sweden charges a lot more than US. Nothing extraordinary just wanted highlight
A rule of thumb that I have been using for position sizing is: “The maximum cost basis for a holding can be no larger, in percentage terms, than the number of years of personal experience in this market.” For example, an investor with 6 years of experience can only build a position up to 6% of capital.
In my limited experience, large concentration is a bet between arrogance and confidence. The difference being that confidence, and by extension the right to more concentration, is only earned through experience.
I agree with the positive correlation between time following the company and maximum position size. That said, there are some companies that are easier to ramp up on than others.
What constitutes a large concentration is different for each investor. Some investors need to be reined in with position size, but I think most of us - maybe I'm speaking for myself here - need a nudge to be just a little more confident. Nick Train has a great line: "Identify your great investment idea. Buy as much of the idea as you feel comfortable with. Buy the same amount again, so you can no Ionger sleep at night, because of the size of your holding. Finally, tell everyone else about it." If nothing else, it's a great framework for pushing yourself to consider your risk appetite.
I started out with an equally weighted portfolio of 40 stocks. Once I saw some winners of >100% within 1-2 years, I decided a portfolio of 15-25 stocks might be a better choice with weightings ranging 2-10%. This approach pushes me to do deeper research as a result.
The generalization of Kelly is (for the quants) essentially to maximize the expected logarithmic returns over the subperiods. One implication of this approach is that it seeks to avoid large drawdowns (as larger and larger drawdowns have unbounded negative logarithms).
So even a full-Kelly approach will tend to keep a substantial cash allocation or perhaps allocate some to puts (about the only strictly defensible 100% equity full-Kelly portfolio would treat conservative estimates of the price that would ensure a PE bid as cash equivalent: something like positive net-net (more current assets than total liabilities) might approximate that). Kelly bettors in games where there are definable odds generally practice half-Kelly which is exactly equivalent to 50% in cash and 50% in a full-Kelly portfolio (which itself will have some cash allocation!), if nothing else to help account for uncertainty around whether you've correctly figured out the payouts and probabilities.
The key point is not only to think about the odds and payout of success, but to consider the odds and payout in the worst-case scenario (and consider those at least as much as the success case). This is pretty easy to analogize to the Graham & Dodd "margin of safety" (and there's at least some research indicating that Buffett sizes bets in a Kelly-esque manner: he also endorsed Ed Thorp as a good manager for his limited partners who didn't follow him into Berkshire (someone who took their money from Buffett and put it into Thorp's fund and then bought BRK when Thorp stopped managing other people's money may actually have done better than someone who stayed with Buffett)).
I've toyed with the idea of an equal-weight portfolio that sells flowers and waters weeds but when the sales (plus dividends, covered call premiums, etc.) of a flower exceed what you put in by enough to have gotten an acceptable annual return, you exempt it from equal-weighting and only sell enough to keep that realized return profile (until you decide it doesn't deserve any weight).
Great point about the odds and payout on the worst case scenario.
There is a time element to it. I started my portfolio in 2012 more or less, I bought some stocks, and I still find new ideas in 2023, so I could not have started my portfolio with 15 equal weights Ideas. I did not even have 15 ideas when I started! So new ideas get added progressively, and their weight depends not only on confidence, but also on available funds and saving rates, and things to sell.
On top of that I am willing to add less weight on a new idea if I just discovered the company. I like to have followed it for two years to really feel confident to concentrate more.
Very complicated.
I agree that there should be a positive correlation between time following the company and position size.
Investing in taxable vs tax-exempt accounts is very different.
Size your positions, at least in the tax-exempt accounts, as if you woke up each day with all cash and were investing it from scratch. In taxable accounts strive for long-term compounders and low turnover.
Avoid big hits to the portfolio via choices concerning concentration and correlation of your investments.
From Kelly: confidence in winning is more important vs maximizing expected value.
Try to be tax efficient.
Consider difficult questions like: given a 60/40 binary bet with the outcome determined tomorrow, how much would you bet?
I have many positions, over 30, with 10% being considered unusually large and 4% - 5% being standard with some bits and pieces of smaller size. I will employ leverage at times when I believe the opportunity set is super attractive. My overall positions across strategies come together to, hopefully, limit downside over each year to an acceptable level while providing acceptable upside. I have found that I can absorb significant losses without too much stress as I have quite a bit of confidence in my process and long-term outcomes.
In my opinion, the only way to outperform is to concentrate. All the greatest investors followed this philosophy.
I stick to owning 5 stocks so my average position size is 20%.
However, my largest position exceeds 50% of the portfolio as it’s grown from an initial base of 20%.
Top 2 stocks are 80% of the portfolio.
I think all of your factors have played a role. These stocks are each either the companies with my highest upside and/or least risk.
Thanks for sharing. Curious to know if the handful of companies you own are internally diversified across sectors, etc., and if you consider that when you think about weighting?
Yes I do. I only own a single stock from any one sector.
For instance, I like multiple banks that I see as worthy of owning, but one of my largest positions is a bank stock, so I don’t buy additional banks.
Likewise, I like a lot of defense companies right now, but my largest holding is in the defense industry, so I tend to quickly pass on new defense ideas because I can’t justify the additional concentration risk. If the US government is the primary customer for both, I’m not really diversified
Hi Todd,
I'm currently working as an investment Analyst. For my personal portfolio I bought two companies with a position size of 4%, 3.5% one of the position now has grown to about 16% of the portfolio (The Largest Position), and the other one also has become decent size. Usually on average I run ideas around 12%-10%. Also usually my smaller positions tends to have higher variability of outcomes and the characteristics of the names which became higher hasn't changed that much either. In general I don't like to play too much with my portfolio as I believe in low churn and compounding overtime. My question is how would think about managing your own portfolio when it's comes to position sizing (I allocate portion of my paycheck to this portfolio on monthly basis) as you don't have to answer clients over higher volatility and concentration risk would you let you winners to run or come back to your targeted allocation range.
Yeah, implementing a weighting strategy can be different for personal and professional accounts for the reason you suggest. Let's say you have a $50,000 portfolio and own 10 stocks, one of which grew to be a 10% position ($5,000 value). If you're contributing $1,000 a month for the next year or something similar, you can effectively reduce your weight in the 10% stock over time by allocating your new funds into other investments, holding all else equal. On the other hand, you could allocate new personal funds according to the target weights you have in your portfolio. $100 of each $1,000 addition would go to the 10% position, for example. Much more easily done now with low/zero commissions, but be mindful of trading costs if they exist. Could allocate to a few holdings rather than every holding each month.
Super thank you much for your thoughts I agree on the last statement too for an example I'm running a tracker position in Bergman & Beving but when I bought the stock realised Sweden charges a lot more than US. Nothing extraordinary just wanted highlight
A rule of thumb that I have been using for position sizing is: “The maximum cost basis for a holding can be no larger, in percentage terms, than the number of years of personal experience in this market.” For example, an investor with 6 years of experience can only build a position up to 6% of capital.
In my limited experience, large concentration is a bet between arrogance and confidence. The difference being that confidence, and by extension the right to more concentration, is only earned through experience.
I agree with the positive correlation between time following the company and maximum position size. That said, there are some companies that are easier to ramp up on than others.
What constitutes a large concentration is different for each investor. Some investors need to be reined in with position size, but I think most of us - maybe I'm speaking for myself here - need a nudge to be just a little more confident. Nick Train has a great line: "Identify your great investment idea. Buy as much of the idea as you feel comfortable with. Buy the same amount again, so you can no Ionger sleep at night, because of the size of your holding. Finally, tell everyone else about it." If nothing else, it's a great framework for pushing yourself to consider your risk appetite.
I started out with an equally weighted portfolio of 40 stocks. Once I saw some winners of >100% within 1-2 years, I decided a portfolio of 15-25 stocks might be a better choice with weightings ranging 2-10%. This approach pushes me to do deeper research as a result.
Hi Todd,
Your article is fantastic, Now a days I am feeling a lacking point specifically position sizing (Even after many years in the market).
It gains my knowledge more.