Previously: The Kelly Criterion
Last time I said, never go full Kelly.
In practice, I strongly agree with this. Either one should go far over full Kelly because the core Kelly assumptions have broken down and you want to throw the rules out the window, or you are trying to responsibly grow a bankroll and full Kelly betting on what you believe your edge to be would be massively overly aggressive.
This time we go over the second category with practical examples. What are situations in which one should engage in what appears to be massive over betting?
Four main scenarios: Not winning is catastrophic, losing is acceptable, and losing is impossible, losing is inevitable.
When you play the game of thrones, you win or you die. If playing it ‘safe’ with your resources means you don’t win, then it means that you die. Either don’t play, or don’t hold back.
In Rounders (spoiler alert, movie is recommended), the star finds himself owing $15,000 to the Russian mob, and his best efforts could only get him $10,000. Without better options and unwilling to run for his life, he walks into the poker club of the man he owes the money to, and says “I owe you that money tomorrow, right? I’ve got $10,000. I’m looking for a game.”
Famously, early in the company’s history, the founder of UPS once found himself without the funds to make payroll. He knew that if he missed payroll, that would be the end of UPS. So he flew to Vegas with what funds he had, bet them all on black, won, made payroll, and now we have a UPS.
Magic players often select ‘safe’ decks instead of ‘risky’ decks. This is exactly backwards. If you flame out of a tournament and lose all rounds, you get nothing. If you win half of them, you still get nothing. If you win three quarters, you usually still get almost nothing relative to winning. Extra variance is great.
If you believe that the fate of everyone depends on crossing a threshold or hitting an impossibly precise target, no matter how bad the odds, you deploy everything you have and take your best shot.
There’s a deadline. We don’t have time for Kelly.
Losing not being so bad, or continuing to play not being so good, is effectively very similar to losing being catastrophic but not safely avoidable. In both cases, surviving is not a worthwhile goal.
A classic mistake is the gambler who forgets that they are using their bankroll to pay the rent. On forums I would often read stories of hard working sports gamblers with mid-five figure bankrolls. They make sure to make only ‘responsible’ wagers on sporting events, risking only 1-3% of their funds each time. When they have a good month, they could eat and make rent, but that ate up most of the profits.
What they continuously failed to realize was that this was not a sustainable situation. Being ‘responsible’ only ensured that, even if they were good enough at picking winners, they would never succeed due to their fixed costs. They were being ‘responsible’ with their sizing relative to their bankroll, but completely irresponsible when sizing relative to fixed costs of their time.
When I first started gambling on sports, I put aside a fixed bankroll I committed not to replenishing, but then acted what any Kelly-style formula would call completely irresponsible with that bankroll until after my first few double ups. As the operation became clearly worth my time, I scaled back and did more ‘responsible’ sizing, knowing that I wouldn’t be eaten alive by fixed costs.
Later, when exploring if it was worthwhile to return to wagering, I did a similar thing, struggled, and eventually lost everything I’d set aside. This was very good. It let me move on. To this day, we can never know for sure whether I had an edge during that second attempt – I suspect my luck was quite perverse – but I do know it wasn’t the best use of my time to find out.
Fail fast is a well-known principle for start-ups. I broke this rule once, with MetaMed, and it was an expensive mistake. Even if you have segregated your potential losses in dollar space, you need to contain them in time space, and emotional space, and social space.
There’s no deadline. But we don’t have time for Kelly.
You can’t lose everything if you can’t risk everything.
Most people’s resources are mostly not money, or even things at all, most of the time. When someone ‘loses everything’ we talk of them losing their friends, their family, their reputation, their health, their ability to work. And for good reason.
There is a scene in Defending Your Life where we flash back to the main character paying over $2,000, a third of all the money he has, to avoid a middle seat on an international flight. In context, this is to his credit, because it was ‘brave’ to risk spending so much. In a sense it was brave, in a more important general sense it was stupid, but in the most important sense he was spending a very small fraction of his resources, so the relevant questions were: Was this transaction worth it? No. Did this put the character at risk of having a liquidity crisis where not having any cash could be expensive? A little.
The best reason to do ‘safe’ things with money, and to maintain liquid savings, is to avoid paying the cost of needing liquidity and not having it, or paying the costs of avoiding scenarios where that liquidity might become necessary. This includes the ability to take advantage of opportunity. Avoiding extra costs of having to borrow money, which is expensive in time and in emotional well-being and social capital, not only in money, is by most people largely underestimated. Slack is vital.
There is also a benefit to having no cash. For some people, and in some families and cultures, one who has cash is expected to spend it, or inevitably will quickly spend it. Sometimes this is on one’s self, sometimes on others, but the idea that one can have money and conserve it by spending only responsibly isn’t a thing. The only socially acceptable way to not spend money is to not have money. Thus, there is a high effective ‘tax’ on savings.
In such situations, not only is risk not so bad, it can be actively great. If your risky bet pays off, you can have enough money for big purchases or even to escape your poverty trap. If it fails, you would have wasted the money anyway, and now you can conserve slash mooch off others. Thus, your goal is to find a way to translate cash, which one will inevitably lose, into inalienable property that can be protected, or skills and connections and relationships, or at least experiences one can remember.
This isn’t just for poor people. Start-up culture works this way, too, and the only way to get things at reasonable prices, including labor, or to be able to raise money, is to clearly have spent everything you have and have no spare resources. This is a large portion of why start-ups are so stressful – you are not allowed to have any slack of any kind. I’m likely about to start a new company, and this is the thing that I dread most about the idea.
This is all in contrast to the grand project we have been assigned, of ‘saving for retirement.’
Older people saving for retirement in modern developed countries, or at least some of those saving for retirement, face a special situation. Unable to earn additional funds, and without families or friends they can count on, their survival or at least quality of life depends entirely upon their ability to save up money earlier in life to spend later.
If they run out of money, they’ll still get some amount of government support, and perhaps some amount of familial support, but any remaining years are going to suck. If they die with money in the bank, that money can be passed on to others, but this is mostly a small benefit relative to not running out of cash to spend.
Compound this with large variance in remaining life span, and highly variant needs for health care and assistance during those remaining years, and you have an entire population pressured to furiously save every dollar they can. Any other use of one’s resources is looked at as irresponsible.
This is profoundly weird and profoundly messed up.
It is handled, by most people and by those we trust to advise us, mindbogglingly badly.
That’s true even in the cases where the problem definition mostly applies to one’s situation, if one is willing to assume the world will continue mostly as it is, and one is unable to invest in other types of resources and expects to have little assistance from them.
It also leads us, as a society, to treat our savings as the savings, the retirement savings, and to apply the principles of that problem to all saving problems, and all risk management problems. Young people take ‘risks’ and buy stocks, older people play it ‘safe’ and buy bonds.
If the world were a much more certain place, where we knew how long we would live, in what state of health, and how the economy and world would do, and everything else we might need money for, and how much money we needed to engage in various activities and consume various goods, we could kind of have a target number of dollars. There was an ad a few years back that was literally this. Each person had a giant seven-figure red number they would carry around from place to place, with an oddly exact number of dollars they ‘needed’ in order to be ‘able to’ retire. Implied was that less than this was failure and would be terrible, more than that would be success and no further funds required. Now you can rest.
Instead, at best we have a probabilistic distribution of how much utility one would be able to get from various amounts of capital, in various scenarios involving one’s life and how the outside world is working. Even in this simplified problem, how does one then ‘play it safe’? At best one can reduce variance from some ‘normal’ shocks like a decline in the stock market, while still being exposed to others, and likely not protect much at all from bigger risks. No matter what, the bulk of what you have will probably go to waste or be passed on to others, or else you are risking disaster. At a minimum, you’re ‘betting’ on what to do with and where to spend the rest of your life, and there you are very much all-in. Odd for someone who is about to die to even try to ‘play it safe.’
Fact check: it appears it was Fred Smith, founder of FedEx, who gambled $5000, won $27,000, and paid the fuel bill. Wiki pointed to this Huffpo article: https://www.huffingtonpost.com/2012/10/15/fred-smith-blackjack-fedex_n_1966837.html
if you drop the gambler's presentation of kelly, and just maximize expected log utility, you immediately get the correct answer for the "win or die" scenario. the second scenario lightly touches on kelly, and would also be aided by considering the situation as log utility maximization. (expenses going out every month like clockwork, decision is work (small guaranteed return), and/or how much to allocate to various bets.)
some of your concerns in the last post can also be modeled properly.
Expected log utility? Kelly says to maximize expected log money. (The fact that wealth-derived utility seems to go roughly like log of wealth is largely coincidence, so far as I can see, though I wonder vaguely whether, precisely because of Kelly, brains that value things logarithmically tend to accumulate most in the long run, in which case the Kelly criterion might actually explain why utility is roughly logarithmic in wealth. I'm pretty sure I don't actually believe that, though.)
Maximizing expected utility also gives the right answer in "win or die", of course.
The section on retirement savings spends a lot of space criticizing what people actually do, and rather little saying what they should do instead. Clearly you're suggesting playing-it-less-safe in some sense, but the ploddingly straightforward "keep investing in hopefully-high-return assets like stocks rather than hopefully-safe assets like bonds, even when growing old" seems (1) not like advice that's actually justified by anything else you've written and (2) to be missing a bigger point (which I take to be related to Ben's in "Against the barbell strategy").
It feels like this would benefit from being more explicit. But I get the impression (as I did from Ben's article) that you are deliberately avoiding being clear and explicit about something here, and I wonder what. (Perhaps nothing! My impression could be wrong.)
Mumble mumble "not investment advice" mumble mumble!
So there's at least *a little* deliberately avoiding being clear and explicit on exactly what to do, because legally one can't give investment advice safely, especially if the advice would be something riskier than standard. There's also 'what to actually do comes later and is a distinct and complex and heavy topic'.
You are correct that this series is in part a response / building upon "Against the barbell strategy." Not a coincidence there. I certainly am pointing out that choosing a weird form of "safety" as measured in dollars under 'normal' world conditions as represented by bonds is, even under the best of assumptions, a false security not worth sacrificing much for in expected value terms under most circumstances.
I think this paper, which models winner-takes-all, public knowledge situations (ex. the space race between the US and USSR) by «Guess Who?» game, is interesting formal model of the first half of this post.
“Guess Who?” is a popular two player game where players ask “Yes”/“No” questions to search for their opponent’s secret identity from a pool of possible candidates. This is modeled as a simple stochastic game. Using this model, the optimal strategy is explicitly found. Contrary to popular belief, performing a binary search is not always optimal. Instead, the optimal strategy for the player who trails is to make certain bold plays in an attempt catch up. This is discovered by first analyzing a continuous version of the game where players play indefinitely and the winner is never decided after finitely many rounds.