Notebooks

Each notebook starts from an idea in the empirical asset pricing literature and turns it into a portfolio an investor could hold. All notebooks draw on the same data sources and report the same performance measures, so their results can be compared directly.

Minimum-Variance Portfolios

Implementing the Minimum-Variance Portfolio Estimate the global minimum variance portfolio of the 100 largest U.S. stocks from a rolling 60-month window, where the sample covariance matrix is singular, use short-sale constraints to make the problem solvable, and compare the resulting long-only portfolio to the value-weighted market with CRSP data.

Minimum-Variance Portfolios from Daily Returns Estimate the covariance matrix from daily returns for universes of 50 to 500 stocks and windows of 6 to 60 months, and show that what matters is the complexity c = N / (T - 1), the ratio of stocks to observations, rather than the frequency of the data.

Mean-Variance Portfolios

Can Regression Alphas Beat the CAPM? Hold the tangency portfolio of the 100 largest U.S. stocks with the alphas from index-model regressions or with zero alphas, as the CAPM says, and show that the regression alphas are sample means in disguise, overstate the Sharpe ratio by an amount predictable in advance, and lose to the market, while the zero-alpha portfolio earns about the market’s Sharpe ratio. Short-sale constraints and shrinkage limit the damage without beating the market.

Stochastic Discount Factors

An SDF for the Factor Zoo Estimate the maximum-Sharpe portfolio of 153 U.S. factors, which is also the stochastic discount factor that prices them, shrink it with a ridge penalty, and test whether the complexity c = N / T governs its out-of-sample Sharpe ratio as it governs the volatility of the minimum-variance portfolio.

Is There an Eigenvalue Cliff? Count how many principal components of the 153 factors grow with the number of factors, against the few dominant components above a bounded bulk that the arbitrage pricing theory assumes, and measure how much Sharpe ratio an SDF loses when it keeps only the leading components.

The Factor Zoo in Real Time Restrict the SDF of the factor zoo to the factors published at each date, measure how much of its Sharpe ratio came from factors no investor could have known about, and test whether returns fall after publication as in McLean and Pontiff.

Trading Costs

What Do Anomalies Cost to Trade? Rebuild six factors from stock-level data, measure their turnover, and price their trades with spreads estimated from daily prices, with effective spreads from TAQ, and with the market impact model of Frazzini, Israel and Moskowitz, to find how much of each factor survives costs and how large a fund it could support.

Momentum

Momentum Crashes Rebuild momentum from daily CRSP returns, show that its crashes come in market rebounds after bear markets as Daniel and Moskowitz find, test volatility-managed momentum out of sample and net of trading costs, and measure crowding with the comomentum of Lou and Polk, through the U.S. side of the 2026 momentum reversal.