In a simulation of 3,000 portfolios of varying sizes (250, 100, 50, and 15 stocks), the 15-stock portfolios showed significant alpha and outperformance, but also significant underperformance relative to the market, demonstrating that fewer stocks increases both upside and downside volatility.

The democratization of investing through the Dutch East India Company in 1602 was as revolutionary as the invention of the limited liability corporation because it allowed commoners and poor people to participate in ownership of global enterprises.

Fearing volatility (as defined by modern portfolio theory) can actually lead investors to do very risky things, such as selling stocks at market bottoms or abandoning sound business analysis in pursuit of portfolio smoothness.

Markowitz's 1952 dissertation defining risk as variance was cited without reference to prior definitions of risk such as Ben Graham's margin of safety or John Burr Williams's dividend discount model approach, despite these being established frameworks in the field.

A correspondence theory of truth (believing you have figured out how markets work permanently) cannot adapt to change; when markets evolve, investors holding a correspondence theory are violating their own model but cannot recognize it.

When 10,000 people make market forecasts over a 3-6 month period, some will necessarily be correct due to pure randomness, but this success is attributed to forecasting skill rather than statistical inevitability.

Between 60-90% of active managers underperform the stock market over time, and this is because they are constructed with broadly diversified, high-turnover portfolios that make it mathematically impossible to beat the market after fees and expenses.

Kahneman and Tversky's prospect theory showed that people feel twice as bad about losses as they feel good about equivalent gains, and modern portfolio theory co-opted this finding to justify its variance-minimization approach without addressing the underlying economic returns.

Modern portfolio theory became the dominant approach to money management starting in the late 1970s and early 1980s following the 1973-74 bear market, when Wall Street needed a framework to explain market crashes and people adopted variance-as-risk as a solution.

Academic researchers at Yale School of Management (Martin Kmers and Antipodesto) published research on 'high active share' in 2009, validating Hagstrom's 1998 research findings about the benefits of concentrated portfolios approximately 20 years later.

Finding the right client-advisor fit is more important than finding a perfect client or perfect strategy—the key is alignment where both parties share the same worldview about what investing means and can tolerate the same drawdowns and time horizons.

Permanent loss of capital is the true measure of risk in investing, not price volatility; a business worth zero or a company in financial distress represents actual risk that modern portfolio theory completely ignores.

If you are a 'know something' investor who can think about stocks as businesses and do intrinsic value work, broad diversification makes no sense and you shouldn't do it; if you are a 'know nothing' investor, you should have a broadly diversified portfolio or just own an index fund.

Active managers using modern portfolio theory are not doing deep financial analysis and business valuation; they are too busy putting together portfolios with non-correlated stocks that keep them close to the market while keeping variabilities down.

If tracking error and benchmark deviation are the primary concerns of active managers, they must know what bets the benchmark is making and then make different bets; those with low active share become 'closet indexers' earning index-like returns while charging active fees.

Modern portfolio theory's only real value is to make investors feel emotionally comfortable with a smooth ride; it adds no actual value to returns and is purely a psychological comfort mechanism.

Darwin and biological evolution provide a more accurate model for understanding markets than Newtonian physics, because markets are complex adaptive systems that evolve and change rather than moving toward an equilibrium point.

The cathedral and the casino metaphor frames two opposing activities in markets: the cathedral is business ownership and intrinsic value analysis, while the casino is price speculation and gambling behavior.

Brian Arthur's 'El Farol Problem' demonstrates that as soon as you solve a prediction problem (find an exploitable pattern in market behavior), everyone learns it, changes their behavior in response, and the pattern ceases to exist.

There is no science that can predict a complex adaptive system; asking whether there is a science to predict the market and the answer from Santa Fe Institute researchers is definitively 'no'.