A piece called Investing is More Luck Than Talent was upvoted to #1 in the prominent tech forum Hacker News. It’s fundamentally wrong, and here’s why it matters.
My career path has gone through tech and hedge funds, so I’m always interested when an investing-related article reaches the top of Hacker News. The tech community’s perspective is much needed in finance. That article, written by a business school professor and well-published academic, made a few interesting arguments:
- Extreme wealth inequality is a problem, and there are some mathematical models that might help explain it. This part I generally agree with.
- The observed distribution of wealth inequality implies, based on a simplistic model, that wealthy people are wealthy because of luck not skill. Many hardworking people would likely disagree with this.
- Even if an investor had some skill, it would barely make a difference. This is wrong.
That final key point in his argument turns out to be logically flawed, resulting in a dangerously misleading conclusion for anyone who invests or is thinking about investing.
Jack and Jill
Central to the last point, the article posed a thought experiment:
- Consider Jack and Jill, two investors. Jack is just a regular guy who gets market returns. Jill is an investing wizard.
- Each year there are 2 scenarios: either Jack is A) down 10% or B) up 30%. Both scenarios are equally likely. These scenarios are roughly consistent with long term stock returns of +10%/year and 20% volatility.
- Since Jill is a skilled investor, she has 1% of outperformance per year. So her scenarios are A) down 9% or B) up 31% — both equally likely.
- Both Jack and Jill start with $100k to invest.
The author concluded, with an abbreviated explanation, that after 20 long years of investing, Jill would only come out ahead of Jack 56% of the time, even with her certain 1%/year advantage. This seemed so counterintuitive. My investing experience has taught me that small advantages are huge over time. Naturally, I had to bury myself in a spreadsheet to figure this out.
The return scenarios are basically a tree and their probabilities follow a binomial distribution. As we expand this out to 20 years and plot the outcomes on the same scale we get an interesting picture:
It’s clear that over time there are a few scenarios were Jack and Jill both do really well. In fact, by Year 20, they both tend to do quite well in general:
However, the claim we’re investigating references the relative performance of Jack and Jill. This will involve an assumption about how Jack’s and Jill’s scenarios are correlated. This is where the author went off the rails. It seems he assumed the up and down scenarios for Jack and Jill were perfectly uncorrelated. That means the joint distribution of returns at the 20 year horizon would look like this:
Sure enough, this reconciles with the author’s claim that Jill only does better 56% of the time. However, there’s something very wrong with this. In reality, Jack’s and Jill’s return scenarios aren’t perfectly uncorrelated (as if they’re living in parallel universes, or different times, or exposed to entirely different markets). In fact their return scenarios are perfectly correlated, because they’re investing at the same time and exposed to the same market. Jack is invested in the broad market. Jill is exposed to that same broad market, plus she has her secret sauce which lets her consistently outperform by 1%/year.
If we correctly assume the returns are correlated, the joint distribution of returns looks like this:
This distribution is much “skinnier” — there are fewer scenarios where Jack outperforms Jill. In fact there are no such scenarios:
Wow, that author’s conclusion was WRONG — the truth is, as he framed the story, Jill the expert investor would outperform exactly 100% of the time, every year, because her outperformance is above and beyond the same market returns Jack experiences. In fact, her outperformance is on average +133% (or around $133k), although could be as little as +3% (around $3k) or as much +3,148% (or over $3 million).
Both of these extreme scenarios are highly unlikely, but they are, in fact, both positive. Also notably, in the scenario where Jill outperforms the most, Jack does quite well himself and is up over 189x (or up almost $19 million). Again this most extreme scenario is quite unlikely (0.0001% chance).
The key insight here is actually obvious based on how the author framed the example — no math necessary. Each year, Jill does better regardless of whether the market is up or down. So if she does better every year regardless of market conditions, how can she possibly ever fall behind?
Here’s What Matters
In reality these “certain” advantages generally don’t exist. There are uncertain ones though, and those too add up over long timeframes (although they might not put Jill ahead literally 100% of the time). I guess what really made me mad about this article is the dismissive, defeatist tone toward investing. As if it were effectively saying “the system is rigged, so why even try.” However, the more obvious, logical, and practical conclusions from his example, which the author failed to mention are:
- If you invest early, and stay invested, you can build a tremendous amount of wealth whether you have skill or you just invest in ETFs/indices. On average Jack was up +573% and Jill was up +706%
- Investing is not without risk — but if you stay invested for the long run, scenarios where you lose a lot of money tend to become less likely
- If you do happen to have skill, seemingly small advantages can actually add up tremendously over time
So is investing “More Luck Than Skill”? Wrong question. The right one is “Some portion of your performance is out of your control — fine — so should you invest anyway?” As this example suggests, whether you have an advantage or not, the answer is a resounding “Yes.”*
*Assuming you’ve paid off all your credit cards, high-interest debt, have an emergency fund, can tolerate some losses, etc. This is not investment advice.
The views expressed are solely those of the author at the time of writing. The author does not endorse any linked content or any other content in this publication. This communication is for discussion purposes only. Past returns do not guarantee future results. Nothing in this communication constitutes investment advice, an offer to sell, or the solicitation of an offer to buy securities.