Two Key Principles of Effective Investing
Two key principles of investing that every investor should know. Read this issue if you don't read any others.
In this newsletter issue I’m going to share two powerful principles of investing that anyone who wants to be a decisive and effective investor must understand and internalize.
These two principles are intended for a reality where you can’t predict the future and aren’t right 100% of the time.
If you are an investor that believes you can predict the future without fail, then these two principles are not for you. However, if the future is as opaque to you as it is to me, then these two principles are of paramount importance.
🛟 Principle #1
Principle #1 is stupid simple but of utmost importance for not just investing, but how you live your life.
Ergodicity is a measure of the capability of a system to eventually visit all its possible states.
Don’t be intimidated by the big word, it’s quite a simple idea.
The more ergodic a system is, the more states it can visit. A system is less ergodic when it’s more likely to reach a terminal state where state transitions are no longer possible. Terminal states are bad.
In life and in investing, you want to be as ergodic as possible and you want to avoid the terminal states.
For investing, the quintessential terminal state is going bankrupt, but you could also end up in prison as Rupert Murdoch and Sam Bankman-Fried found out.
For life, a quintessential terminal state is dying early from non-natural causes.
Let’s focus on ergodicity in investing.
The basic idea of ergodicity in investing is that you want to avoid going bankrupt as much as possible. There are many ways you can do so, such as fractionalizing your bets, not taking on significant leverage, having a rainy day fund, etc.
Take, for example, John who has a job and a mortgage. John is basically living paycheque to paycheque to pay off his mortgage and doesn’t have a rainy day fund. Suddenly, there’s a major economic downturn and John is laid off. John now can’t meet his mortgage’s monthly payments, thus defaulting on the loan and losing the house. He has reached a terminal state. If John had kept a rainy day fund, he could keep paying his mortgage until he finds a new job in a few months. This rainy day fund would’ve helped him avoid the terminal state of defaulting on the loan and keep open the possibility of eventually fully owning the house.
To summarize, Principle #1 says you should ensure your financial situation is as ergodic as possible. You must avoid the terminal states at all costs.
⚖️ Principle #2
We’ve all heard the idiom “don’t put all your eggs in one basket”.
It’s usually uttered in the context of increasing financial ergodicity.
However, the idiom also has a surprising profit-increasing motive that’s much less understood.
Here’s an example of a game to start us off.
Imagine in this game you have a 70% chance of winning 200% (3x) and 30% chance of losing 99%. The game’s arithmetic expected value (EV) is quite high, at 2.103.
Now imagine playing this game 10 times in a row and fully reinvesting your returns each time.
Guess what are your chances of losing 95% of your money by the end of the 10 rounds? A whopping 61% of the time!
How could such a high arithmetic EV lead to such a terrible probabilistic outcome?
The answer lies in the difference between the arithmetic EV and the geometric EV.
In a game where you’re playing rounds sequentially and fully reinvesting returns each round, even though each individual round’s EV is the arithmetic EV, your overall EV is the geometric EV.
What’s the geometric EV? The equation is outcome_1 ^ chance_1 * outcome_2 ^ chance_2.
For the game above its geometric EV is 3^70% * 0.01^30% = 0.54.
Now you can see, 0.54 is a far cry from 2.103 and this is why after 10 games, you have such a high chance of losing basically your entire bank roll.
When you are growing your wealth, to enjoy the vast benefits of exponential growth, you have to reinvest more and more of your wealth over time.
So how does one do so without subjecting yourself to the geometric EV and instead benefit from the arithmetic EV?
The answer to this question lies in fractionalizing your bets, aka “don’t put all your eggs in one basket”.
The more you fractionalize your bets, and the more uncorrelated they are, the more your overall EV approaches the average arithmetic EV across all your bets.
Here’s an example to demonstrate this point.
Let’s use the same game we described above: 70% chance of winning 200% (3x) and 30% chance of losing 99%.
Suppose you have $100 when you start playing this game. If you bet all $100 on just one round, there’s a 30% chance you end up with just $1!
However, if you split your bet into 100 smaller bets of $1, then your aggregate returns across the 100 games approaches the arithmetic EV of $210.30.
This is the power of fractionalizing your investments.
This quick mental exercise reveals the deeper truth behind the idiom.
When you spread your eggs out among multiple baskets, you’re not only increasing your ergodicity, you’re also increasing your profitability!
One can go deeper into this concept by asking how one should size their fractional bets to further increase profits, since every bet has its own win rate and payout ratio.
A meditation on this question is beyond the scope of this issue but a good starting point is the famous Kelly Criterion.
When legendary investor Stanley Drunkenmiller was asked what his investing superpower is, he alluded to the Kelly Criterion by saying,
“One of my number one jobs, is to know whether I'm hot or cold. And when I'm hot, I'm supposed to turn the dial way up. Not say, okay, I'm a 40% this year, let's go, this will look good at the end a year ago, take a break. No, you got to make hay while you're hot. And then when you're cold, the last thing you should do is try and make big bets to get back to even.”
📈 Principle #3 (for paid subscribers)
So I lied. As I was writing the issue, I realized that I actually have a third investing principle that I should share.
However, this principle is more tactical, specific to my style, and not broadly applicable. As such, I’m going to put this behind a premium pay wall and I hope it’s fair to do so given that I’ve shared the first two principles.
A few months ago, when the FTX/Sam Bankman-Fried saga was coming to a head, there was an article from one of the major technology news publications that profiled Sam Bankman-Fried (SBF) in an attempt to frame his misguided actions in the context of his personality.
The article said that because SBF had worked at Jane Street, a large and venerated Wall Street hedge fund, for several years before starting FTX, it made sense that he’d make reckless decisions and maximize risk-taking.
This point piqued my curiosity.
Why would someone who worked at a hedge fund be inclined to maximize risk? After all, the “hedge” in “hedge fund” inherently suggests risk aversion.
After some pondering, the answer became clear. Conveniently, it builds upon Principles #1 and #2.
Many hedge funds use a “multi-manager” model where there are a series of pods led by a few portfolio managers and each pod executes their own unique strategy.
The hedge fund then divides its capital among the pods, allocating more capital to the winning pods and reducing capital from the failing ones.
This multi-pod structure is a direct application of Principle #1.
Then, within each pod, the hedge fund encourages risk maximization. The reason being, if the pod fails, the fund loses at most 1x but if it wins, it can make the overall fund a fortune.
The hedge fund has a risk management department that monitors trades across all pods to ensure that in aggregate, there aren’t too many correlated bets. Too much correlation puts the fund at risk of significant losses from a single market event, which decreases ergodicity.
In other words, the risk management department is a direct application of Principle #2.
In such a multi-pod model, the hedge fund is thus incentivized to maximize risk and reward within each pod in order to maximize its overall profit, assuming proper bet sizing and aggregate risk management.
Here’s how the math works.
Imagine one pod in the fund has a win-loss structure like so: 60% chance to win 300% and 40% chance to lose 90%.
The arithmetic EV is 4 * 60% + 0.1 * 40% = 2.44 while the geometric EV is 4^60% * 0.1^40% = 0.91.
Again, we see that the geometric EV sucks while the arithmetic EV is great. As discussed in Principle #1 above, the hedge fund can realize the arithmetic EV by fractionalizing its bets.
So this, I believe, is the secret sauce to hedge funds. And I’m going to make the assertion that ordinary investors can replicate this win-loss structure without needing to run a major and sophisticated multi-pod hedge fund.
The key to doing so is through options.
With options, the wins are exceptionally large (theoretically unbounded but practically 1-5x) and the losses are bounded at 1x.
This is the exact payout ratio that you need to replicate the strategies of a multi-pod hedge fund.
As such, an ordinary investor can fractionalize a portfolio across a series of ideas expressed as options trades and each trade replicates the characteristics of a pod in a multi-pod hedge fund without the messy overhead of company administration and personnel management.
This, in my opinion, is not just intellectually fascinating but also incredibly powerful as a tool to grow wealth.
And yes, options have a bad reputation given their high volatility but any tool used in the wrong way can be destructive. It just so happens that options are easily misunderstood and too often misused.
So there you have it, three powerful principles of investing that, when applied with sophistication, can allow investors of all sizes to make money.
These principles are designed for a reality where you don’t know the future, and thus have a non-trivial chance of being wrong. However, if you can size your bets well and are often right (doesn’t even have to be right most of the time), you can be significantly profitable.
With these principles, you are leaning on indisputable math to be both your backstop and your profit generator and all you need to focus on is being incredibly right without fear of being wrong.
To be a successful investor, you must let your ideas flourish so that they can become wealth.
Thanks for this, the arithmetic vs geo EV example is pretty enlightening.