Derivation Aug 2021
M₀: The Deviation-from-Mean Matrix
How the deviation-from-mean matrix is constructed and what it does.
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NOTES / QUANTITATIVE FINANCE
Quantitative Finance
Factor models, portfolio construction, covariance estimation, and the linear algebra behind them.
17 pieces
Note Aug 2021
The Effect of Including a Constant Column in OLS
Deviations from means.
Derivation Aug 2021
Derivation of the Variance of the Sample Mean
A compact derivation of the variance of the sample mean.
Note Aug 2021
Newey-West Covariance Matrix (Part 2)
The multivariate case of the Newey-West covariance matrix.
Note Jul 2021
Central Limit Theorem (CLT)
The most prolific result in statistics.
Note Jul 2021
Newey-West Covariance Matrix (Part 1)
A covariance matrix that incorporates heteroskedasticity and autocorrelation.
Derivation Jun 2021
Partitioned Least Squares Derivation
Deriving the partitioned least-squares estimator by partialling out one block of regressors.
Derivation Jun 2021
Normal Equations for Partitioned Least Squares
The full derivation of the normal equations for partitioned least squares.
Derivation Jun 2021
The Beta Constraint for Active Portfolios
Why the beta of the benchmark component equals one, and what that implies for active weights.
Note Jun 2021
Benchmark Portfolio Optimization
Optimizing a portfolio relative to a respected benchmark.
Note Jun 2021
Providing an Active Portfolio
Supplying alpha to a benchmark portfolio.
Note Jun 2021
Solution for Constrained Weighted Least Squares
Full setup and solving for CWLS in the context of factor models.
Note Jun 2021
Partitioned Least Squares
Understanding what it means to "partial out" variable effects.
Definition Jun 2021
Projection Matrix
A short reference on projection matrices and why idempotence implies projection.
Note Jun 2021
Factor Models 101
A technique for approximating the covariance matrix.
Definition Jun 2021
Alpha
A working definition of alpha, its role in portfolio returns, and its formula relative to a benchmark.
Note Jun 2021
The Geometry of Ordinary Least Squares
Visualizing the workhorse model for regression analysis.