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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.

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.

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.

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.

breakingthemarket.com/stochastic-eff…

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.

breakingthemarket.com/stochastic-eff…

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.

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.

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 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 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.

-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.

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.

ergodicityeconomics.com/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.

ergodicityeconomics.com/lecture-notes/

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.

breakingthemarket.com/welcome/

breakingthemarket.com/welcome/

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.

breakingthemarket.com/stochastic-eff…

breakingthemarket.com/stochastic-eff…

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.

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.