Add ex-ante Tracking Error method to Portfolio

[chilango74]

Background

Issue #61 covers the ex-post Tracking Error for Portfolio — the realized TE computed from the historical time series of portfolio vs benchmark returns.

This issue is about the ex-ante (forward-looking, planned) Tracking Error, as defined in Hwang & Satchell, Tracking Error: Ex-Ante versus Ex-Post Measures (2001), eq. (1):

TE_ex-ante = sqrt((a − b)' Σ (a − b))

where:

• a — portfolio weights
• b — benchmark weights
• Σ — covariance matrix of asset returns

Scope

• Unlike the ex-post measure, ex-ante TE requires benchmark weights, not just benchmark returns. The benchmark must be expressed in the same asset universe as the portfolio (e.g. another Portfolio object over a shared set of symbols).
• First step: estimate Σ as the sample covariance matrix of historical monthly returns (annualized). Advanced estimators (shrinkage, EWMA) are out of scope.
• Per Theorem 1 of the paper, ex-ante TE systematically underestimates ex-post TE because portfolio weights are stochastic ex-post (they drift between rebalancings). This should be documented in the docstring.

Related

• Add ex-post Tracking Error method to Portfolio #61 — ex-post Tracking Error for Portfolio