Kelly Criterion: How SBF’s Disdain for Bet-Sizing Formula May Have Led Alameda Research, FTX to Ruin

• Michael Lewis’ new book about Sam Bankman-Fried Going Infinite discussed the former FTX CEO’s training in probability theory.
• Looking back, it becomes apparent that the young SBF always had a unique approach to risk aversion.
• Considering past comments, it seems as if SBF justified risky investment strategies by twisting the assumptions of the Kelly Criterion.

If there is one takeaway from Michael Lewis’ new book about Sam Bankman-Fried (SBF) Going Infinite, it’s that the FTX founder was addicted to games and that his approach to risk and reward was a unique product of his background in finance.

From his student days at MIT, where he majored in physics, the biography charts Bankman-Fried’s journey to crypto billionaire via an internship at the trading firm Jane Street Capital. But with the benefit of hindsight, SBF’s Jane Street anecdotes look like major red flags that 

Bankman-Fried’s Jane Street Internship

It was at Jane Street that SBF honed the kind of game-theoretical strategies upon which he would found the FTX empire.

Although he minored in mathematics at MIT, the picture Lewis paints of his Jane Street days is one in which everything could be conceived as a bet and where interns were constantly encouraged to view the world through the lens of risk and reward.

In one passage, Lewis quotes SBF as saying that “the interns [were] all addicted to gambling, and to positive expected value gambling more than anything in the world.

Or, to put it another way, Jane Street taught SBF and his fellow interns always to take a bet when the odds were stacked in their favor.

However, regarding how much to risk given a probabilistically advantageous scenario, SBF’s gambling philosophy diverges from economic orthodoxy. 

SBF’s View of the Kelly Criterion

In probability theory, the “Kelly Criterion ” is a formula for calculating the optimal size of a bet based on the assumption that the gambler values their wealth logarithmically. 

In other words, the foundational assumption of any Kelly bet is that a dollar is worth more to someone who is only in possession of $10 than someone with a million bucks to play with. As such, it assumes that optimal bet sizing strategies will differ depending on the gambler in question’s starting wealth.

However, in a 2022 tweet, the financial analyst Matt Hollerback detailed an exchange with SBF that suggests he had a completely different understanding of bet sizing.

Explaining his position, SBF postulated a scenario in which a gambler wins 1,000 times the value of their bet with a 10% probability of winning.

According to a standard Kelly strategy, under these circumstances, the optimal strategy for someone with $100,000 to play with would be to bet no more than $10,000.

“But I, personally, would do more,” SBF stated, adding that he would up his bet to $50,000.

Explaining his rationale, SBF said, “My utility function isn’t really logarithmic. It’s closer to linear.” 

That is to say, he acknowledged that his aversion to risk doesn’t change just because his starting point is already rich.

Bankman-Fried Justified Risk in the Name of Altruism

Clearly, SBF’s all-in approach to gambling doesn’t lend itself to running a multi-billion dollar crypto empire that holds millions of customers’ deposits in its custody.

But Bankman-Fried claimed a higher purpose behind his risky strategies.

Noting that his end goal is philanthropy on a global scale, SBF notes that “Kelly tells you that when the backdrop is trillions of dollars, there’s essentially no risk aversion on the scale of thousands or millions.”

Ultimately, the kind of big-money altruism displayed in his conversation with Hollerback chimes with the idealistic but reckless young man depicted in Going Infinite.

Unfortunately for Bankman-Fried, the jury in his trial won’t judge him on his philanthropic ambitions but will need to assess whether his risky interpretation of Kelly-based economics extended to the management of FTX, and whether such an extension amounts to to fraud.