If everyone is society optimized for arithmetic return, or linear utility, then society would grow wonderfully at first. Society's geometric return would be high. Some people would win big, some would lose big, and the average would be good because many are involved.
Through time though, many people would get unlucky by losing a few times in row and would fall out of contributing because they don’t have much capital/resources/access any longer to help. So now the number of contributors to society’s growth is smaller.
If people keep basing decisions on linear utility, with fewer and fewer winners each round and more and more losers, a funny thing starts to happen. Probability says society stops growing as more people fall out of the game, leaving fewer people capable of creating growth.
After long enough of everyone using “linear utility” society will start to shrink. It will wither away due to a low geo return.

If everyone sizes their bets at the Kelly level though, society grows as a whole at its fastest rate possible (without any transfer payments).

Now this example is not dissimilar to what would happen on a financial market if every person based their bets on linear utility. At first it would be great. Some unlucky customers would lose a lot, others win more. Soon there’s less people and dollars bidding on the assets
Geometric returns turn negative, and prices fall as only a few people have any capital to play any longer. But if the participants in the market made their bets at Kelly, prices would grow forever, as would most of the investor’s wealth.
Linear utility, aka making decisions on the “expected value” (arithmetic average), is dangerous for an individual and society.

I wish economists would acknowledge it was a huge mistake to have compared rationality to it or evaluated behavior against it in the first place.

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More from @breakingthemark

17 Dec
I just re-read Bernoulli’s 1738 paper “Exposition of a New Theory on the Measurement of Risk” which is the foundational paper of Expected Utility Theory.

It’s Amazing

It’s so wildly different than EUT that its hard to believe this was its beginning.

Let’s see if you agree.
The paper isn't about utility. It’s about expected value.

Bernoulli used the utility concept to get the reader to abandon the traditional view of expected value(arithmetic average), and then used it to derive the equation for valuing risk.

The final equation doesn’t use utility
He starts out the paper identifying that tradition evaluation of risk come from expected values, which are calculated with the arithmetic average.

Notice the rule here in italics is about expected values. Image
Read 30 tweets
4 Jul
There are two side to the Kelly Criterion which I think often get equated as the same when they really are not.

Traditional Kelly betting is about limiting your exposure to a risky bet. The bet in question is usually a "bet" in that when you lose, you lose everything you expose.
So you scale back and don't risk everything. Most casino games fit this description as do some financial instruments like options.

The optimal leverage here is less than 1. You want to hold cash on the side to buffer the future losses.
But standard investment assets, don't work this way.

I showed here, that individual stocks are effectively full Kelly bets.

Just buying one stock is the appropriate "size", as they have an optimal leverage of 1.

Read 7 tweets
1 Jun
Lots of tail hedge articles these days. I feel many miss the point. They keep studying returns as if they add with each other through time. They don’t. The math of lose 3% in 9 calm years, make 25% in the one volatile year = -5% return is meaningless.
The average through time is meaningless because investment returns don’t ADD. They COMPOUND.

A tail hedge that reduce the average return of a portfolio (as a tail hedge often does) but reduces the portfolio variance by more than twice as much, leads to higher geometric returns.
Now is this really complicated and difficult to get right with options based tail risk hedges? Yes. There are so many ways to implement it and returns are skewed and convex. And if you don’t understand why tail hedges are useful, you could easily butcher the implementation.
Read 8 tweets
21 May
I’ve really enjoyed the Asness-Taleb feud. Some of the best parts are the comments by the people supporting their “guy”. I’m drawn to the similarity of their views:

-Both sides think they are the counterpuncher. Both sides think they were attacked first.
-Both sides think the other’s intellectual prowess is overrated.

-Both sides think their investment strategy is superior.

-Both sides think the other often acts like a bully.

-Both sides think the other is acting unhinged and triggered in their response.
-Both sides think the other often gets very angry and blocks people.

-Both sides think their “guy” is making clear obvious points.

-Both sides think the followers of the other are brainwashed, but are slowly coming around to the truth.
Read 4 tweets
20 Apr
A year ago today I started reading @ole_b_peters and @alex_adamou 's ergodicity economic lecture notes.

They were so good I finished it by the end of the next day.

There's lots of math, but as I've said before, this stuff is going to change the world.

My blog is about trying to create the best investment strategy, and isn’t EE centric. But the concepts I use are very similar to those EE discusses. I’m an engineer, so I’m focused more on application than pure theory.

Many posts come from similar concepts as EE does. This post on stochastic efficient is the most similar, as it’s my proof that EE’s work on the subject is correct.

Read 14 tweets
11 Dec 19
Let’s tweak the game a tiny bit: Flip a coin. Heads, Double money. Tails, lose 51%

Arithmetic return=24.5%

Geometric return= -1%

100 coin flips through time. Now the values trend downward toward 0.

Arithmetic mean, the dark blue straight line, leaves the picture early on.
Here is the average wealth of the 100 coin flips. It climbs, and climbs quite aggressively due to the positive arithmetic return. But the wealth ends up peaking, and then falling back down to where it started. The portfolio can’t escape the negative geometric return.
Three more random trials. These coins are a great examples of news traveling slowly between the coins. Early on some coins don’t realize others are landing heads. Once they do, they shoot up. Then later the coins hesitate to realize they are supposed to start losing money.
Read 7 tweets

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