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Matt Hollerbach Profile picture
@breakingthemark
Dec 31, 2021 • 7 tweets • 2 min read • Read on X
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Who was the first to advocate using the geometric return in investing? Both Mark Spitznagel and I agree it was Daniel Bernoulli.

Most investors would benefit from understanding the true message from his brilliant 300 year old paper on measuring risk.

breakingthemarket.com/the-earliest-a…
The thread from last December where I first approached the topic.

A few sections from Spitznagel's book:

Risk aversion is not necessary with Bernoulli's framework
Academics missed the point
mapping to the geometric average
The big idea, hidden by a slick function.
Bernoulli was first, and his findings change everything.

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More from @breakingthemark

Matt Hollerbach Profile picture
Nov 11, 2022
Two years ago SBF wrote a thread on bet size and Kelly betting.

I questioned him on it. He engaged with me.

Let’s take a look at this thread and SBF’s views on bet sizing in light of the events with FTX and Alameda this week.
First off, nearly all financial blow ups arise from too much leverage. Too much leverage is a killer. So right away, you should question the idea that “better is bigger”.

Often bigger requires leverage. Often “bigger” is bigger than a fully Kelly bet therefore it's not better.
SBF goes into a coin flip type bet. A red flag comes up right away because he uses “utility functions” to determine the answer.

This is typical economic thought, but it's dangerous and I’m going to show you why.
Read 25 tweets
Matt Hollerbach Profile picture
Jun 10, 2022
Some of it is probably because of my geometric reference point.

I view everything through Geometric return. It's what I focus on, so anything that is critical to maximizing CAGR is really important to me. And if it’s that critical, then how can it not be “real”?
From my perspective, if rebalancing maximizes CAGR, and not rebalancing produces less CAGR, then that is a “premium” that is earned from rebalancing

Now if you view the market from an arithmetic view, nothing was harvested. But you don’t experience the arithmetic return, you experience the geometric, and therefore, its where I believe the “premium” should be measured.
Read 12 tweets
Matt Hollerbach Profile picture
Apr 13, 2022
I've written before about how multiplicative games (like investing) begin as arithmetic averages, but as time and repetitions increase, trend more and more to the geometric average.

This great game shared by @10kdiver shows the effect beautifully.
On the first card draw, the "edge" for that draw alone is clearly the arithmetic edge, and it's really really large.

But as you pull more and more cards, that edge decreases.

Ultimately, if you pull every card rolling the outcome from one round to the next, the edge disappears.
Since you played every card, the outcome you will received without question is the geometric average of the game.

So if you played one round-you get the arithmetic growth

Play every round, get the geometric growth

Play a few rounds, you get something in-between.
Read 12 tweets
Matt Hollerbach Profile picture
Mar 13, 2022
I made a conjecture a couple years ago that very often gets a lot of push back:

That the optimal leverage of individual stocks is 1.

The evidence I found supports this theory, but many people really hate it.

breakingthemarket.com/stochastic-eff…
The actual math is often criticized as controversial because I presented it though the lens of @ole_b_peters and @alex_adamou 's work on Ergodicity Economics.

But it's not really a new equation. A version has been used before by titans of finance and investing.
Bill's Sharpe's 1990 Nobel speech includes the equation to describe the risk premium in equation 6.

nobelprize.org/uploads/2018/0…

Tau in the equation is the investor's risk preference.

Tau=2 means the investor follows natural log utility, aka maximizes geometric growth.
Read 16 tweets
Matt Hollerbach Profile picture
Mar 12, 2022
Let’s dive into this idea further.

There isn’t a subject in the entire world that can only be correctly viewed from one perspective. Investing is one of the most complex fields out there.

Investing certainly doesn’t only have one correct, view point.
Traders, long term investors, value investors, quants, asset allocators, etc, none on them have a monopoly on truth in terms of investing.

None of these styles are necessarily superior to the others. They just approach the market from a different perspective.
It’s not uncommon for dogma and “common sense” in one area to be absent or shunned in others.

Investors will often take the dogma in their field as gospel and not challenge it. They assume its correct just because.
Read 14 tweets
Matt Hollerbach Profile picture
Mar 10, 2022
Three years ago today I started my blog. How time flies.

I wasn't on twitter then, and therefore I never put the first post on here. Since I didn't complete a new anniversary post, here's the one that started it all:

breakingthemarket.com/welcome/
And since this the blogs birthday I'm going to reminisce about a few of the comments that meant a great deal to me.

First, if you've ever read @moretothat 's own ridiculously high quality writing, you'll understand why I'll always remember this one:

I re-wrote the entire welcome page from scratch after reading a @TaylorPearsonMe thread on the hero's journey. That thread has impacted much of the blog's structure, so I really appreciated this comment:

Read 5 tweets

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