Axios Capital: The highest bidder wins

Auctions make the world better

Posted in Uncategorized | Leave a comment

Axios Capital: Theatre of the absurd

The fideist slogan credo quia absurdum (“I believe because it is absurd”) is the best way to make sense of the Trump administration.

Posted in Uncategorized | Leave a comment

Axios Capital: When society faces the unprecedented

Our febrile world is not normal.

Posted in Uncategorized | 1 Comment

Axios Capital: America’s rebound

It’s the rebound economists didn’t see coming.

Posted in Uncategorized | Comments Off on Axios Capital: America’s rebound

Axios Capital: Left out of the country

America’s cities are facing a historic shortage of two vital resources: money and immigrants.

Posted in Uncategorized | 1 Comment

Axios Capital: When stocks become ironic

There have been moments of market euphoria in the past, moments when stocks stop being a serious mechanism for the allocation of scarce capital, and start being a fun, positive-sum casino. 

There have also been moments of national crisis, with tens of millions on the unemployment rolls and an implacable enemy killing hundreds of thousands of innocent Americans. 

Posted in Uncategorized | Comments Off on Axios Capital: When stocks become ironic

Dice thoughts

A few weeks ago, while I was going for a walk in the woods, I came up with a thought experiment. Later, I tweeted it out, and later still, I asked the listeners of Slate Money to write in with their answers.

The question:

I will roll a die as many times as you like. Every time it comes up 1/2/3/4/5, I double your money. If it’s a 6 you lose everything. You need to specify ex ante how much your initial stake is, and how many times I roll. What do you choose?

The obvious conditions apply: I am a gazillionaire with no counterparty risk, and you can only play the game once, on your own, with no partners.

This question is interesting on a bunch of different levels.

First, by forcing you to state up front how many times I am going to roll, this question is mathematically equivalent to me just rolling that number of dice at the same time — with you getting zero if at least one of those dice comes up 6. Psychologically, however, there’s a big difference.

Let’s say you choose 5 rolls on a stake of $100. You immediately think of a scenario where your money doubles four times in a row — you’re up to $1,600 — and then a 6 comes on the fifth roll. It feels as though you’ve lost $1,600 rather than just $100, and that outcome is psychologically worse than if a 6 came on the first roll.

Second, the question forces people to think hard about what it means to “expect” a certain outcome. Take that choice of 5 rolls on a stake of $100 again. The median outcome is that you end up with $0: there’s roughly a 60% chance of that happening. On the other hand, you have a 40% chance of winning $3,200, which means the “expected value” of the bet is $1,286.

What’s more, the more rolls you specify, the higher the expected value becomes. If you roll 20 times, your 2.6% chance of winning $105 million works out to an “average” payout (whatever that means) of $2.7 million. But few of us would consider it rational to expect to win $2.7 million if we specified $100 and 20 rolls. In fact, one thing we know for certain is that we won’t win $2.7 million! It’s either $105 million or nothing.

Third is the utility of money. For most of us, the utility of having $40 million is not so far removed from the utility of having $20 million. So it doesn’t make a lot of sense to take an 86% chance of doubling $20 million into $40 million. Better to just stop at $20 million.

Indeed, for many people the utility of money turns negative after a certain point. Just ask most lottery winners, or Johnny Depp. Getting enough money to buy a house and thereby have shelter for the rest of your life — that’s great. But getting enough money to buy 10 houses — that can create more misery than happiness, and even surprisingly rapid bankruptcy.

Almost no one has the self-awareness to know their own utility-of-money curve. But it’s not hard to think of people, from gambling addicts to Warren Buffett, who would not be better off if they won this bet. Such people might well do best by not playing at all.

Fourth is the question of whether this is an investment or a gamble. Most people’s answers fall into one of two broad buckets: There are the people who will stake roughly as much as they might risk at a poker game, and then there are the people who will stake roughly as much as they might invest in the stock market.

For the people who choose a poker-sized bet, the obvious question is whether and why they would ever invest in, say, stocks. The expected return characteristics of this bet are vastly superior to anything you can get in the stock market, so if you’re OK with stocks, shouldn’t you be OK with this? Is the difference that stocks go to zero slowly, if they go to zero? But that still implies that most people have a point at which they will sell a stock that is slowly declining. Which in turn violates the tenets of buy-and-hold investing.

For people making an investment-sized bet, the obvious question is how much to bet. That’s where the Kelly criterion comes in. Ian Chan on Twitter helpfully did a bunch of the mathematics so I don’t have to, but if you have a set amount of money, then according to the Kelly criterion the amount you should bet starts at 67% of that amount for 1 roll, and then declines to 59% for 2 rolls, 52% for 3 rolls, and so on down to 2.6% for 20 rolls. (From about 6 rolls onwards, the Kelly criterion percentage is very close to the probability of winning.)

Ian works backwards from that number, and basically asks: How much are you willing to tolerate losing, expressed as a percentage of the amount of money you have? If it’s, say, 9% of your wealth, then you should work backwards from there and decide to go for 13 rolls.

I take a different tack, which is to ask: How much money would you like to win? This is, after all, by far the best and most generous opportunity you will ever receive in your life. If you could sell this opportunity on the open market, there’s any number of individuals who would pay you hundreds of millions or even billions of dollars for it. So it seems a bit of a waste to just try to win $100 or so.

So I start by asking: What is an amount of money that would significantly improve my life and livelihood? To bet for any less than that seems silly, given the incredible opportunity in front of me. But to bet for more than that also seems like a bit of a waste: I’m risking losing more money, or a higher probability of ending up with zero, for a relatively marginal improvement in utility.

Let’s say the amount I alight upon is the aforementioned $20 million. And let’s say I have $250,000 in liquid assets. (Should people include non-liquid assets, or expected future income, in this calculation? Let’s say no for the time being, although that’s a question that can be debated.)

In order to get to $20 million in 7 rolls I would need to bet $156,000, which is 62% of my wealth. But according to the Kelly criterion at 7 rolls I shouldn’t bet more than 27% of my wealth, so that’s a non-starter. So increase the rolls: To get there in 10 rolls I’d need to bet $19,531, which is 7.8% of my wealth. That’s well below the 16% Kelly criterion, so that’s one option.

On the other hand, at 10 rolls I only have a 16% chance of winning. I can improve that to 19% by betting $39,000 on 9 rolls. That’s 15% of my wealth, which is still within the Kelly criterion of 19%.

So in this case I would probably bet either $19,500 on 10 rolls, or $39,000 on 9 rolls. In both cases I’ll expect to lose a sum that I could easily suffer in the stock market. This bet, however, comes with much higher expected returns. It’s a gain that will really transform my life if I hit, so the bargain seems like a good one.

All of which raises the toughest question of all: How on earth am I going to persuade my wife that I should spend $39,000 on a roll of the dice?

Posted in Uncategorized | 2 Comments

Axios Capital: A brand-new Fed

Today is a truly historic day in Fed history — one that will have a transformative effect on U.S. monetary policy for the foreseeable future.

Posted in Uncategorized | Comments Off on Axios Capital: A brand-new Fed

Axios Capital: The government’s cash crunch

The age of ever-growing deficits has devastated one group of government entities in particular — the ones that have historically been self-sufficient, funding themselves directly from their own revenues.

Posted in Uncategorized | Comments Off on Axios Capital: The government’s cash crunch

Axios Capital: Humility at scale

Philanthropy is rarely associated with humility.

Posted in Uncategorized | Comments Off on Axios Capital: Humility at scale

Axios Edge: Only one car company matters

Tesla is the company of the moment — the prime exemplar of just about any big and important trend that you might care about.

Posted in Uncategorized | Comments Off on Axios Edge: Only one car company matters

Axios Edge: A new hegemon

All multinational companies and executives need to worry about breaking U.S. law, no matter where they’re based or doing business. Now, they need to worry about Chinese law, too.

Posted in Uncategorized | Comments Off on Axios Edge: A new hegemon

Axios Edge: Swimming in cash

There’s plenty of money. It’s just not moving to where it’s needed. (New jobs, in case you were wondering.)

Posted in Uncategorized | Comments Off on Axios Edge: Swimming in cash

Axios Edge: The amorality of finance

The disconnect between economic and moral imperatives lies at the heart of the biggest issues facing America today, from the rising appeal of socialism to the question of how to deal with the coronavirus outbreak.

Posted in Uncategorized | 2 Comments

The meta-crisis

America’s institutions are failing. They no longer command the respect they need to be effective.

Posted in Uncategorized | Comments Off on The meta-crisis

Axios Edge: Explaining the markets’ insouciance

There is no particular reason why America’s move toward authoritarianism should hurt the markets.

Posted in Uncategorized | Comments Off on Axios Edge: Explaining the markets’ insouciance

Axios Edge: Fancy a bet?

Never has the stock market seen so much gambling. 

Posted in Uncategorized | Comments Off on Axios Edge: Fancy a bet?

Axios Edge: How insurers dodged the crisis

It’s hardly original to point out that the rich have been able to survive this crisis much more easily than the poor — but it still bears repeating. 

Posted in Uncategorized | Comments Off on Axios Edge: How insurers dodged the crisis

Axios Edge: Saying no to free money

Even when businesses are legally entitled to bailout funds, they will often avoid taking that money when faced with political or popular opprobrium.

Posted in Uncategorized | Comments Off on Axios Edge: Saying no to free money

Axios Edge: The crash diet

Regional food is a kind of language. It can die of neglect. Or, it turns out, of COVID-19.

Posted in Uncategorized | Comments Off on Axios Edge: The crash diet

Axios Edge: Rewriting the rules of finance

A crisis is a terrible thing to waste. The coronavirus crisis is a dress rehearsal for the climate crisis: It will help show us not only what is possible, but also, crucially, whether or not those actions work.

Posted in Uncategorized | Comments Off on Axios Edge: Rewriting the rules of finance

Axios Edge: America’s other coronavirus superhero

Move over, Anthony Fauci. Fed chair Jay Powell has come into his own in recent weeks, acting with uncommon and entirely unexpected speed and boldness.

Posted in Uncategorized | 1 Comment

Axios Edge: The arrears economy

Just when you thought the Fed might be out of ammunition, out it comes with another $2.3 trillion from its “super bazooka.”

Posted in Uncategorized | Comments Off on Axios Edge: The arrears economy

Axios Edge: Is there an “on” switch?

What happens after a war? Two weeks ago, I asked that question and came away cautiously optimistic about America’s ability to bounce back from its current crisis. Now, I’m not so sure.

Posted in Uncategorized | Comments Off on Axios Edge: Is there an “on” switch?

Axios Edge: The arena of the unwell

The greatest decade in the history of mankind is over. (Well, the greatest bull market, anyway.) The old order changeth, yielding place to new.

Posted in Uncategorized | 1 Comment