| formula_id,concept_id,formula_latex,variable_definitions,interpretation | |
| FORM_e252ce63d2,PMC_0004,"\min_w \; w^\top \Sigma w \quad \text{s.t.} \quad \mu^\top w \ge r^*, \sum_i w_i = 1",w = portfolio weights; Sigma = covariance matrix; mu = expected return vector; r* = target return,Core optimization framework for balancing portfolio risk against target return. | |
| FORM_727112246d,PMC_0007,E[R] = \left[(\tau \Sigma)^{-1} + P^\top \Omega^{-1}P \right]^{-1}\left[(\tau \Sigma)^{-1}\Pi + P^\top \Omega^{-1}Q \right],tau = uncertainty scalar; Sigma = covariance; P = pick matrix; Omega = view uncertainty; Pi = implied excess returns; Q = views,Bayesian posterior expected returns used to produce more stable institutional allocations. | |
| FORM_7ef820cf7d,PMC_0010,\sigma_p = \sqrt{w^\top \Sigma w},sigma_p = portfolio volatility; w = weights; Sigma = covariance matrix,Canonical measure of total portfolio variability. | |
| FORM_e8b7e05ccf,PMC_0015,\text{Sharpe} = \frac{R_p - R_f}{\sigma_p},R_p = portfolio return; R_f = risk-free rate; sigma_p = portfolio volatility,Measures compensation received per unit of total risk. | |
| FORM_f17754b073,PMC_0016,\text{TE} = \sqrt{\mathrm{Var}(R_p - R_b)},R_p = portfolio return; R_b = benchmark return,Key metric for benchmark-aware mandates. | |
| FORM_d6d5d7986c,PMC_0017,\text{IR} = \frac{R_p - R_b}{\text{TE}},R_p = portfolio return; R_b = benchmark return; TE = tracking error,Risk-adjusted measure of active management skill. | |