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.
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.
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.
Position Sizing: Optimizing for Better Returns
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.
Very complicated.
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.
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.
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.
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.