Life and Investment Through the Lens of Uncertainty

Life and Investment Through the Lens of Uncertainty

Disclaimer: Opinions are my own. Not investment advice.

Decisions are not judged by results

Decisions and results are separate. The quality of a decision should not be judged by the quality of its result, which often depends on randomness.

If I drove drunk yet got home safely, I have made a bad decision with a good outcome. If I drove sober and careful but was rear-ended, I have made a good decision with a bad outcome.

If I rushed into $NIO upon open, dumped before close, and netted some decent gain, did I make a good decision? So much of one’s success was attributed to the research and painstaking, often confusing luck with skills, and signal with noise.

In the last 20 years, $SPY has a nontrivial mean daily return of 0.0338% but a standard deviation of 1.2405%, which is 37 times the return. Holding it for just a day is really speculating as opposed to investing.

We always make decisions under uncertainty, but our weapons are legions—probability, expectation, and Monte Carlo.

Vanish of randomness

Suppose we treat each daily return R1, R2, ..., Rn as a random variable from the same distribution—any distribution, especially not Normal. Suppose the distribution has a mean mu and standard deviation sigma. Then, the sum of R1, R2, ..., Rn has mean n * mu and and standard deviation sqrt(n) * sigma.

In layman’s terms, the longer you hold a stock, the narrower the distribution of its return. If you end up with a spike, it means you almost always make money.

This analysis is simplified and assumes the underlying distribution does not change. The real distribution is not observable, but with so many pension and retirement funds in the market, your investment positions are also a reflection of your confidence in the federal government.

Uncertainty has existed in the past

Uncertainty implies unknown and seems applicable only to future events. After all, I cannot predict the tomorrow price of a stock, but I know for sure what its price was yesterday. The past can only be learned but not altered.

Yet uncertainty has existed in the past. The price went up yesterday, but it could have gone down. Be very careful with past observations. What has happened is only one of the possibilities. Watch out for the “alternative” histories, cried Nassim Nicholas Taleb. If a certain kind of events—no one has seen a black swan, or the market has never gone down more than 20% in a day—has never been observed before, we cannot conclude it is impossible.

Stay in the game

The black swan is not scary as long as you can keep playing. Stay away from Russian roulette. No matter how lucrative the upside is, there is no come back if you get wiped out. Limit tail risk. Always fasten the seat belt.

Know your tools

Through what instruments, you asked. It is like choosing the tech stack for your startup: always the ones you know.

Call options have the leverage and convexity that bends in your favor regardless of the price going up or down, or so you have overheard in an anonymous web forum. Not entirely in apropos, but at what cost? What if the price remains stationary? Hint: look into theta risk.

Being reasonable, not rational

It is never about achieving the most optimal return, but a good enough one that allows me to sleep at night and achieves my life goals. Investing is a means to an end. Be patient and start living.

Warren Buffett’s skill is investing, but his secret is time.

– Morgan Housel, The Psychology of Money