The quant
field — α over σ_excess.

Eugene Fama's Efficient Market Hypothesis says all available information is already in the price. If it were perfectly true, no one could ever earn excess return except by luck. It's not perfectly true — there are documented, persistent anomalies (value, momentum, size, quality, low-volatility) that have paid premiums for half a century. But it's true enough that most active managers, after fees, underperform the index. The job of the quant is to live in that 5% wedge between "completely efficient" and "wildly inefficient" — finding edges small enough that no one has bothered yet, durable enough to survive being known, and large enough to be worth implementing.

A strategy returning 50% sounds incredible — until you find it's 90% volatility and the path was harrowing. The Sharpe Ratio normalizes for risk: how much excess return are you getting per unit of volatility? An equity index sits around 0.4 long-term. Warren Buffett's lifetime number is roughly 0.75. Renaissance's Medallion is rumored to run 2–3 — and is closed to outside money for a reason. Above 2 in any backtest should make you suspicious. You may be measuring luck, hiding tail risk, or — most often — fooling yourself.

Harry Markowitz won a Nobel for proving the only free lunch in finance: combining assets that aren't perfectly correlated lets you reduce portfolio risk without giving up expected return. The catch most people miss: it's not about owning more things, it's about owning differently correlated things. A portfolio of fifty tech stocks is less diversified than a portfolio of five well-chosen ones across uncorrelated regimes — equity, bonds, commodities, currencies, volatility. Slide the correlation below and watch the frontier curve flex; that curvature is the diversification benefit you're earning.

A factor model decomposes returns into known risk premia plus true alpha. The Fama-French three-factor model adds size (small minus big) and value (high book-to-market minus low) to the market beta of CAPM. Carhart adds momentum. What's left after explaining your returns by these exposures is your actual edge. Run the decomposition on most "successful" managers and the alpha shrinks toward zero — they were earning a known premium and charging like it was secret sauce. The remaining alpha is rare, valuable, and worth paying for. Most "alpha" is just beta you didn't recognize.

Almost every systematic strategy reduces to one of two bets. Mean reversion says: prices that moved away from fair value will return. It works on short horizons and in calm, liquid markets. Momentum says: prices that have moved will keep moving. It works on longer horizons and in trending markets. They are not friends. A trending market punishes mean reversion; a choppy market punishes momentum. A strategy that profits in both regimes is either a real edge — or, much more often, an overfit. Below, the same synthetic price series under each regime, with each strategy's entries and exits.

There are three classic ways to fool yourself with backtests, and every blown-up fund has done all three. Survivorship bias: you ran your strategy on the universe of stocks that still exist today, and the ones that went to zero quietly vanished from your dataset. Look-ahead bias: you used data at decision time that wouldn't have been available at decision time — earnings, restatements, classifications fixed in hindsight. Overfitting: you tuned 47 parameters until the strategy perfectly explained the past, with zero predictive power for the future. Each one independently can turn a real Sharpe of 0.0 into a backtest Sharpe of 2.5. Together, they're how everyone learns the same lesson the same way.

The Kelly Criterion says: bet a fraction of your bankroll proportional to your edge. Bet less, you grow slower. Bet more, you grow faster — until you over-bet, then you grow nowhere because variance eats you. Past 2× Kelly, you go to zero. The cruel truth is that most pros bet half-Kelly: half the long-term growth, but a fraction of the path-drawdown. Edge and sizing are independent skills. A trader with an edge of 5% who sizes wrong destroys more capital than a trader with no edge who never bets. Most public examples of "blown-up traders" are sizing failures, not edge failures.