NOTES / REFERENCE

Reference

Short definitions and standalone derivations that support the longer notes.

9 pieces

Induced Norm

The definition of an induced matrix norm and how it measures the largest stretch a linear map can apply.

Why a zero conditional mean implies that the disturbance is uncorrelated with the regressors.

How the deviation-from-mean matrix is constructed and what it does.

A compact derivation of the variance of the sample mean.

Deriving the partitioned least-squares estimator by partialling out one block of regressors.

The full derivation of the normal equations for partitioned least squares.

Why the beta of the benchmark component equals one, and what that implies for active weights.

A short reference on projection matrices and why idempotence implies projection.

A working definition of alpha, its role in portfolio returns, and its formula relative to a benchmark.