Bigger is Better for the Bettor
You only have so much time to get it in good
Disclaimer: I am not a financial advisor. I’m a blueberry. I possess no formal financial education, no advanced degrees, and possibly no brain cells. I am merely a moron with a Substack. Absolutely nothing in this article is truthful, factual, or even remotely accurate—it is pure, unfiltered parody. While I will reference various complex concepts, I will simplify them to a level that makes sense to me, which means they will become entirely nonsensical and wrong. Please do not take anything in this article seriously or as advice. I am making all of this up. None of it is true. Not a single word.
Let’s say that you have ln(w) utility and you’re a fresh college graduate. You should be max leveraging your entire portfolio. Whatever amount of leverage you’re allowed to have (QQQ + margin etc.). Seriously. Go ‘all-in’ on whatever you have conviction in. Mathematically speaking, it’s the right thing to do. And no, I’m not approaching this from some U(w)=w linear utility function, I say this even under ln(w) utility.
Remember, this is not financial advice, but that doesn’t mean it isn’t good advice :)
The first thing that I get hit with after saying this is normally some bullshit about Kelly optimal leverage for spoos over the past X years or something of that sort. This is totally irrelevant and only applies to boomers (actually, and we’ll see why that’s the case in a bit). Let me explain: suppose that you have 10k in your bank account right now and you have the ability to flip a 52/48 coin for fair implied odds. Kelly would say to risk 4% of your bankroll on this right?
But what if you knew that next week you were going to get a paycheck of 10k, would you still only bet $400 on this coin flip with log utility? I mean I think it makes more sense to treat your bankroll as more like 20k in that scenario, so you should “2x” what Kelly would say to do from the lens of only looking at your current bankroll at the time of the flip.
Ok now what if you thought you were going to get a 10k paycheck every week for a whole year? If we assume zero discounting of future cash, your current bankroll is less than 4% of the total cash you will accumulate over this time period, so if you have log utility of your terminal wealth at the end of this period, you should wager the full 10k you have now on this single coin flip. We can naturally extrapolate this out and realize that if we take the NPV of your career earnings, it’s practically impossible to “over-bet” Kelly with any individual investment as a young individual.
The reason why Kelly will never have you risk going to zero is because if you do something that has a chance of going to zero, regardless of how small the chance or how +EV the event is, eventually you do go to zero (something something LLN) so you are guaranteed to end up with nothing and since you can’t compound nothing into something, this is bad. However, in the case where you have future forms of income coming in, you can ‘afford’ these times of ‘going to zero’ because you can ‘re-stack’ your portfolio so your bigger risk is that you limit your expected value, not that you have a period where it goes to zero.
Poker Analogy
I generally think that the analogies of poker to trading are overstated, but there are a few things that do tie in well. Suppose that you are at a table playing NLHE with a nice stack of chips in front of you and you get dealt aces. The villain jams pre-flop. Do you call? Uh duh. Obviously you call that. You are just absolutely dominating every hand. The best hand your opponent can have in that situation is 65s (read this1 if you don’t believe me), and that barely has above 23% equity. Now the thing is, if you call an all-in with AA, eventually you are probably going to hit some bad luck and get cracked. That’s okay though. You can always re-stack your chips or come back another day. The important thing is that you are playing poker at the table with a reasonable amount of chips relative to your actual net worth so that you can make these all-in +EV calls.
Working at a Trading Firm
For what it’s worth, this is similar to how it works at (good) trading firms. What’s best for the portfolio of the individual trader (maximizing the log of their portfolio) is suboptimal for the growth of the firm in its entirety. Imagine if a firm had 1,000 traders and they each managed a portfolio of some X dollars and each had the opportunity to bet money on independent coin flips as given in the hypothetical at the start of this post, they all should go all in. Does this mean that some traders are going to blow up their book? Yes. Is that fine? Also yes.
Your job as a trader is not to make money; your job is to make expected value. Sometimes you lose out, but if it was the right thing to do in terms of EV, then you still made the right decision. Hindsight Capital is always going to have better returns than you, but Hindsight Capital also has information that you were not privy to at the time of the decision.
It’s probably worth noting that not all firms have this type of Chad mentality when it comes to risk aversion (or lack thereof), but as I said, this applies to good trading firms— the types of firms willing to punt a couple billion dollars on election night (iykyk).
Back to Going Big
We went on a little tangent with some poker and trading firm examples there, but hopefully you can see the tie in now— your biggest risk risk isn’t going to zero in the short term, it’s that you didn’t bet enough to maximize the log of your long term wealth.
Really solid breakdown on the NPV of future income reframing Kelly. The paycheck example maks alot of sense when you think about it. I remeber when I was first starting out trading, I was way too conservative with position sizing because I only looked at my current balance, not the fact that I had a salary coming in every two weeks. The counterpoint worth mentionng tho is that most young people dont actually have stable income streams, especially in this job market. If the paychecks arent guaranteed or if theres a layoff risk, then the whole premise kinda falls apart and Kelly becomes way more relevant again.
When your current bankroll represents no more than 4% of your total expected lifetime capital — equivalent to having at least 25 future re-ups — the Kelly criterion, applied to your full human capital, prescribes betting exactly 100% of the liquid stack.
As originally framed in the "52/48 coin flip" problem (even-money bet with p=0.52 probability of winning), the issue reduces precisely to treating your wealth as n consecutive stacks (or "re-ups") rather than a single closed bankroll.This follows directly from the Kelly formula for even-money bets:
f^ = 2p - 1 = 0.04* (with p = 0.52),
so the optimal bet is f^ × (n × K) = 0.04n × K*,
where K is the current liquid stack.The threshold is reached exactly when n ≥ 1 / f^ = 25*: the optimal bet becomes K (100% of the current stack).
For n > 25, the formula would prescribe more than 100%, but you are constrained to betting at most K — thus remaining at full commitment.
Betting any less in this regime is no longer prudent conservation; it is under-betting Kelly, quietly sacrificing long-term geometric growth
.The true risk lies not in exhausting a single stack, but in failing to swing boldly enough when the mathematics demands maximum leverage — especially since the probability of total ruin (losing all n stacks consecutively) decays exponentially as (0.48)^n, becoming astronomically low beyond n=20.