How can I determine if my stock picking performance was due to luck or due to skill?

I've had that exact same question myself, though usually in the opposite direction (am I unlucky or an idiot :) )

One thing I've looked at is large components of return. If you have one or two investments that dominate your returns, that's more an indication of luck versus skill. If you remove the best performing stock or fund, how different is your return profile?

As an example, I've seen stock sites that say they consistently beat the market, but their highlighted picks consist of FANG stocks (Facebook, Amazon, Netflix and Google), which have increased by many multiples since 2010. My question has been - how have you done other than those picks? Not that picking those stocks early is completely luck - certainly one could look at their businesses and see potential, but do they get excess returns on other stocks as consistently?

Ask yourself the same question - do you have one or two stocks or indices that dominate your returns? What separates them from the other stocks/indices that would indicate skill versus luck?

If you remove the FANG stocks from the S&P 500, the average returns since 2010 drop from 10.2% to 8.9%. How much does removing the largest contributors from your portfolio change your returns?

At the end of the day it may not matter - sometimes being lucky is better than being good - but it can be hard to distinguish the two.

From a qualitative point of view, it helps to keep notes on why you buy a certain stock/bond (or derivative). It keeps you honest as you'll see when you got the call right and whether it was for the right reason.

For a more quantitative assessment, you want to look at what's driving your gains/losses: is it really alpha or is it beta (correlated with the overall market, for example the S&P500)?

The rising tide lifts all boats, as the moniker goes. Conversely, when it goes out, you'll see who was swimming naked, to paraphrase Buffett.

Also, it could be due to good/bad luck with timing the market.

Investing is about making informed guesses. Skill vs luck is a continuum and having a robust process you can stick to is as important, if not more important, than the outcome.

To answer your specific questions: professionals either look at absolute performance or relative performance compared to a benchmark and/or risk (measured by standard deviation of returns).

To compute the return you can look at time-weighted returns, which accounts for the addition/withdrawal of funds, or money-weighted returns.

Once you know your rate of return, you can compute the Sharpe ratio or risk-adjusted excess return compared to the risk-free rate or other benchmark.

If you bought S&P 500 with 3x Leverage in 2000, does a CAGR of ~20% outperform a S&P 500 with 1x Leverage (i.e. no leverage)? No. Outperformance is on a risk-adjusted basis.

For an individual, the easiest way to determine outperformance is by finding the Mean weekly return (in %) and its Standard Deviation (in %). Then find the leverage of S&P 500 that achieves exactly the same Standard Deviation. For example, if your portfolio standard deviation is 8% and S&P 500 (with no leverage) is 6%, then the equivalent leverage is 1.33x. Then compare the portfolio Mean return (in %) against 1.33x the Mean return of S&P 500.

To determine whether it is by chance that there is outperformance, it requires alpha and beta as you suggested. Specifically, it is the p-value / confidence interval / statistical significance of the estimated alpha, which most statistics software or Python (Scipy Stack) can calculate it for you. Having a positive estimated alpha does not guarantee that it was not by chance.

Without your data, there is not much that we can discuss.

Here is a calculation of luck and skill:

Determine the percentage of profitable years. Then luck is a 50% result but set luck at 0% skill and set maximum positive-skill at 50%. So luck is ((50 - 50) / 100) or 0% skill while maximum positive-skill is ((100 - 50) / 100) or 50% skill.

For example, a 50% result is 0% skill, a 53% result is 3% skill, a 99% result is 49% skill, and a 100% result is 50% skill.

Then a 47% result is -3% skill, a 1% result is -49% skill, and a 0% result is -50% skill.

Then luck, as a 50% result, plus skill equals to the underlying result. Also, a 100% result only claims 50% skill and thus 50% luck while a 0% result only suggests -50% skill and thus 50% luck. There is always a significant percentage of luck and therefor no 100% skill.

There is no 100% skill while 0% skill is 100% luck. Wow, a 50% result is 100% luck which is 0% skill !

Now suppose that a five-year investment result is positive due only to the fifth year result. An investor could claim all five years as profitable based on an average return. There are choices of accounting methods.

In fact I set investment gain against a year-beginning balance plus an average deposit/withdrawal balance as projected to year-end. That's a version of a modified-Dietz.

Now a money-market investor might wonder why they don't have 100% skill but are they setting their investment result against the inflation rate ? An investment is not really successful unless the result is greater-than-or-equal-to inflation. A comparison of investment return to inflation is not particularly required but the point is that 100% skill is not likely.

The simple answer is that it's luck, because no-one seems to be able to pick stocks and always outperform the market with it (considering their leverage). That's not how any fortunes are made in finance that I know of.

For instance take Warren Buffett. He's outperformed the market a lot, I believe, and for decades on end. And yet, he likes a certain kind of company to invest in. It's probable that he's just lived in a period of time when--in retrospect--that kind of company was the right kind of company to be in. Put Buffett in previous or future decades, where other kinds of companies were the fastest growing, and would he recognize that and invest in those companies instead? Or would he still be interested in what he's interested in today, and only be a modest success or even failure?

Here is the question you want to ask: Is the mean return of your portfolio (excluding fees) relative to the index significantly different from zero?

First, determine a time-weighted return series P(t) for your portfolio, such that P(t+1)/P(t) - 1 is your return in each period excluding contributions, withdrawals, and fees. (Exclude those things because they aren't relevant to your stock-picking skill.)

Then, determine the total return series I(t) for the index, and define R(t) = P(t)/I(t).

Consider the series s(t) = R(t+1)/R(t) - 1. You want to test the null hypothesis that the underlying mean of s(t) is zero (i.e., your returns are consistent with luck in an efficient market). You can reject this (and find evidence of skill) if the empirical mean of s(t) has a magnitude more than a few times its standard error (the empirical standard deviation of s(t) divided by the square root of the number of samples).

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Why is s(t) the right metric? Consider a professional investor who is holding the index by default and is trying to decide whether to reallocate any capital to track your portfolio (and they can do so with negligible fees). If they find your portfolio useful in improving their return, that's equivalent to your having skill.

If at time t, out of a notional 1 dollar of assets, they allocate a fraction f to your portfolio (leaving 1-f in the index), then their wealth at time t+1 will be W = (1-f) I(t+1)/I(t) + f P(t+1)/P(t). Using the standard log-wealth utility and expanding to first order in f, we get the utility ln(W) = ln(I(t+1)/I(t)) + f s(t). The dependence on f is only in the last term.

Thus, befitting intuition, if the mean of s(t) is positive, then expected utility is increased by taking f > 0 (how big f should be depends on higher-order terms) -- i.e., going long your portfolio is desirable. Somewhat less intuitively, if the mean of s(t) is negative, then your portfolio is still useful because expected utility is increased by taking f < 0 -- i.e., going short your portfolio is desirable.

It may be surprising that creating a portfolio with negative mean s(t) is as hard as positive mean s(t). You can't just buy high-fee funds or throw money away on trading costs, because we've excluded fees. You can't just buy out-of-the-money options that almost always expire worthless, because even if you lose everything, s(t) can't be less than -1, so its mean will be counterbalanced by the small chance of a big gain.

The answer is extremely simple, "have you outperformed the market?" (Over and over.)

The definition of not-luck is very simply "outperformed the market consistently many times."

Good answers above, the unfortunate truth is: you can't be certain. Given the relative efficiency of equity markets, it's more likely that you were just lucky (after risk adjustment) by standard measures.

A general rule of thumb is: the more obscure your area, the more likely your success is due to skill.

Say you mainly trade on mid-cap commodity stocks traded on the Zimbabwean Stock Exchange. This is not the most efficient of markets so you make take advantage of these inefficiencies. This could be more skill than luck: it took "skill" to identify the market and skill to exploit the inefficiencies. But on US large-cap equities the excess performance is almost certainly due to luck.

Under @DStanley's answer there is a comment from Philipp: "[...] Luck can run out any moment, while skill (hopefully) does not. [...]" Your skill might not run out, but its effectiveness might: I'm certain some traders in the 50s were successful "simply" for being very quick in their calculations and order placements; when computers came to the party, they still had the skill, but the skill did not give them an edge. So in some way if you are skilled, one could say you were lucky your skill is still relevant !

The only investors with stellar long term records use fundamental analysis (value investing) in their practice. To use FA means you can make accurate estimates of a companies value, and understand when estimates can't be made accurately.

If you don't understand how to value companies, you don't have enough skill to beat the market. If you do understand, you still need to be able to have the other soft skills necessary to beat the market (patience, resistance to outside bias, work ethic, etc).

In both of these scenarios, what method can I use to determine whether the performance was due to good luck, bad luck, good skill, or bad skill? What established methods do financial professionals use to separate luck from skill?

Statistics.

Scenario A: I have outperformed the S&P 500 nearly every year for the last 20 years. My CAGR is about 12%. I turned every $1 in 2000 into about $10 by 2020.

If probability of outperforming in a year is 50%, in 20 years it is 0.00000095367 or about one in a million.

The world has 3.3 million stock market indexes: https://www.businesswire.com/news/home/20180122005183/en/Index-Industry-Association-Surveys-Index-Universe

If you have prior reasons to believe your strategy is superior, chose it because of it and found it is a winning strategy afterwards, then you probably have a market-outperforming strategy.

However, if you search through the 3.3 million stock market indexes, you are likely to find approximately three that outperform the most commonly used market benchmark index every year in 20 years, so most likely the outperformance was caused by selection bias if selecting the index suitably.

(Edit: Oops, it had the world "nearly". If you outperform market 19 times in 20 years, probability is 20 in a million; if you outperform market 18 times in 20 years, probability is 380 in a million; if you outperform market 17 times in 20 years, probability is 6840 in a million or in other words 0.7% -- so high that e.g. in medicine a drug that might have produced the observed results by sheer chance with 0.7% probability might be rejected.)

Scenario B: I have occasionally outperformed and occasionally under-performed the S&P 500 for the last 20 years. My CAGR is about 5%. I turned every $1 in 2000 into about $2.70 by 2020.

In the long run, stocks yield about 8%. Thus, you are consistently underperforming the market (however, in 2000 there was a stock market bubble and in 2020 there was a low point due to coronavirus crisis, so pick the dates suitably and 5% CAGR would be about average for the 2000-2020 period).

Are these methods easily adopted by individual investors?

Yes. Learn about statistical tests. Calculate the probability that the outcome would happen due to blind chance instead of superior strategy. If the probability is let's say less than 0.1%, then you have with a high probability a good strategy.