Rolling the model back to a formation date two years before the end of the sample, drawing a random 30-stock portfolio, and reshaping it three ways with a small active-set QP. Every prediction is then graded on the 104 weeks the model never saw.
Estimating the factor covariance matrix with a decaying memory, repairing thin specific risk estimates with shrinkage, and assembling the model. Any portfolio's predicted risk then costs one pass over the holdings and a 20 × 20 sandwich.
Estimating factor returns from the exposure matrix. Sector dummies make the regression exactly singular, the constraint that repairs it decides what every factor return means, and the solver is fifty lines of Cholesky and back-substitution.
Turning raw financial data into the factor exposure matrix in DuckDB SQL: cross-sectional standardization, composite factors, rolling-window factors, and an OLS trend slope built out of nothing but rolling sums.
Setting up a client-side data pipeline for a Barra-style fundamental factor risk model. We load parquet files into DuckDB WASM and explore our security universe and financial data directly in the browser.
The efficient market hypothesis, its three forms, the evidence for and against it, the Grossman-Stiglitz paradox, and what it all means for investors.
The covariance matrix for N assets, why covariances dominate portfolio risk, alpha as a gradient for improving the Sharpe ratio, tilting toward positive alpha, and the CAPM as an optimality condition.
From tangent portfolio to market portfolio, why diversifiable risk earns no premium, beta, the CAPM and Security Market Line, alpha, multi-factor models (Fama-French), and arbitrage pricing theory.
Why volatility is costly, the Capital Allocation Line, the Sharpe ratio as the slope of the CAL, Two Fund Separation, scaling vs. tilting, the efficient frontier, and the tangent portfolio.
Covariance, correlation, the two-asset portfolio variance formula, the diversification curve, systematic vs. idiosyncratic risk, and why diversification is the closest thing to a free lunch in finance.
Portfolio weights, the weighted-average return formula, buying on margin, short selling, leverage, rebalancing, and how the major stock indexes are built.
Expected return, variance, standard deviation, the normal model, Value at Risk, the Sharpe ratio, and why measuring risk is harder than measuring return.
The dividend discount model, multi-stage growth, implied returns, P/E ratios, and why small input changes produce big price swings.
Macaulay duration, modified duration, and convexity: the math behind how sensitive a bond's price is to interest rate changes.
How to price a bond from first principles, why prices and yields move in opposite directions, and what the shape of the yield curve is trying to say.
Why a dollar today beats a dollar tomorrow, and how compound interest turns a small return into a large balance.
What financial assets are, how markets work, and why the bid-ask spread is the price of immediacy.