I have extensive experience in this realm, including both independently re-deriving Kelly before learning about it and then working extensively with variations of it, in nominally Kelly-optimal conditions. Kelly is only optimal under a very strict set of criteria, and those criteria de facto do not occur in practice. It’s a great guide to the landscape, but a terrible perscription in most situations. Common errors include misunderstanding what counts as a bankroll, inability to access large portions of the real bankroll, changing returns to investment size, the existence of limiting factors, having almost any real utility function, unknown unknowns and edge uncertainty which is almost always correlated, psychological impact and inability to precommit credibly to Kelly, outside perceptions and their impact on your bankroll or utility, not accounting for calculation errors, odds or outcomes that are impacted by bet size, and more.
I may write a top-level post going into more detail (feedback on this idea is appreciated), but here I will deal only with this particular case.
In a start-up, the bankroll definition and potential is one key. Your bankroll includes more than you think, and that’s especially true in a start-up world where you can, even in failure, get more investment and start again, or join someone else’s start-up, or just go back to a day job. Kelly assigns infinite disutility to going broke, and going broke is standard procedure in the startup world. Also, how you take your compensation is largely for motivation and signaling and to keep control of the company, all of which impact the result. In bankroll terms my investing in my own company, and taking $0 other than expenses from my start-up work was madness, but it was clearly the correct play and has paid off handsomely in numerous non-bankroll ways even if no money results!
Going full speed at a startup, even in failure, is often a winning play as you develop connections, reputation, experience, skills and other neat stuff like that, laying the groundwork for future success.
I’d be interested in reading that post! If you do, could you explain more about the grounds on which you’d be applying Kelly to this problem at all, though? I’m somewhat unclear on that—see my other comment in this thread for detail.
In this problem, you’re starting a business, and you can consider that business as a bet, out of which you hope to gain a job, income, investment money from your equity, reputation, experience, and so on, all of which can be abstracted. Alternatively, you can look purely at the equity vs. salary trade-off in the context of Kelly, which as I explained above is deeply flawed. It’s not a great scenario for such calculations, but they can still provide insightful context.
That’s kind of reassuring. I’m just starting to read about Kelly, and my first reaction was “and your knowledge of the final outcome comes from where?”.
It also occurs to me that “Invest in real estate, they aren’t making any more land” is an effort at Kelly prediction, and we all know how well that worked out.
It is a classic mistake to treat your estimates as known expected outcomes when calculating how much to bet. This is one reason why real world gamblers almost always use half Kelly or even quarter Kelly rather than full Kelly.
“Invest in real estate, they aren’t making any more of it” is, in effect, a prediction of the expected returns to investment and/or the reliability of investment. Kelly would advise you on how to take advantage of the expected returns from real estate, once you nailed down your beliefs more carefully. For real estate, Kelly is rather horrified, as it finds many people investing far more money than they have into a single house. That sounds insane when you say it like that! However, a richer understanding of all a person’s assets together with the tax advantages of mortgage interest, and the inability to cheaply adjust the size of that investment, can make that reasonable under Kelly if you think the bet is stable (e.g. that the house can’t go to zero if it’s insured, at least not in any scenario where you care much about that).
I have extensive experience in this realm, including both independently re-deriving Kelly before learning about it and then working extensively with variations of it, in nominally Kelly-optimal conditions. Kelly is only optimal under a very strict set of criteria, and those criteria de facto do not occur in practice. It’s a great guide to the landscape, but a terrible perscription in most situations. Common errors include misunderstanding what counts as a bankroll, inability to access large portions of the real bankroll, changing returns to investment size, the existence of limiting factors, having almost any real utility function, unknown unknowns and edge uncertainty which is almost always correlated, psychological impact and inability to precommit credibly to Kelly, outside perceptions and their impact on your bankroll or utility, not accounting for calculation errors, odds or outcomes that are impacted by bet size, and more.
I may write a top-level post going into more detail (feedback on this idea is appreciated), but here I will deal only with this particular case.
In a start-up, the bankroll definition and potential is one key. Your bankroll includes more than you think, and that’s especially true in a start-up world where you can, even in failure, get more investment and start again, or join someone else’s start-up, or just go back to a day job. Kelly assigns infinite disutility to going broke, and going broke is standard procedure in the startup world. Also, how you take your compensation is largely for motivation and signaling and to keep control of the company, all of which impact the result. In bankroll terms my investing in my own company, and taking $0 other than expenses from my start-up work was madness, but it was clearly the correct play and has paid off handsomely in numerous non-bankroll ways even if no money results!
Going full speed at a startup, even in failure, is often a winning play as you develop connections, reputation, experience, skills and other neat stuff like that, laying the groundwork for future success.
I’d be interested in reading that post! If you do, could you explain more about the grounds on which you’d be applying Kelly to this problem at all, though? I’m somewhat unclear on that—see my other comment in this thread for detail.
In this problem, you’re starting a business, and you can consider that business as a bet, out of which you hope to gain a job, income, investment money from your equity, reputation, experience, and so on, all of which can be abstracted. Alternatively, you can look purely at the equity vs. salary trade-off in the context of Kelly, which as I explained above is deeply flawed. It’s not a great scenario for such calculations, but they can still provide insightful context.
That’s kind of reassuring. I’m just starting to read about Kelly, and my first reaction was “and your knowledge of the final outcome comes from where?”.
It also occurs to me that “Invest in real estate, they aren’t making any more land” is an effort at Kelly prediction, and we all know how well that worked out.
It is a classic mistake to treat your estimates as known expected outcomes when calculating how much to bet. This is one reason why real world gamblers almost always use half Kelly or even quarter Kelly rather than full Kelly.
“Invest in real estate, they aren’t making any more of it” is, in effect, a prediction of the expected returns to investment and/or the reliability of investment. Kelly would advise you on how to take advantage of the expected returns from real estate, once you nailed down your beliefs more carefully. For real estate, Kelly is rather horrified, as it finds many people investing far more money than they have into a single house. That sounds insane when you say it like that! However, a richer understanding of all a person’s assets together with the tax advantages of mortgage interest, and the inability to cheaply adjust the size of that investment, can make that reasonable under Kelly if you think the bet is stable (e.g. that the house can’t go to zero if it’s insured, at least not in any scenario where you care much about that).
I think part of the situation is that naive investors don’t quantify—if real estate is a good investment, they don’t think about how good it might be.
It’s interesting to watch “Kelly” drift in and out of being personified.