“”Wednesday, August 12, 2026

Minimax

\max_{x \in \Delta} \min_{y \in \Delta} \, x^\top\! A \, y = v^*

§Zero-Sum

\textstyle\sum_{i=1}^{n} u_i(s) = 0 \;\; \forall \, s \in S

§Nash Eq.

x^{*\top}\! A y \geq x^{*\top}\! A y^* \geq x^\top\! A y^*

§Expected

\mathbb{E}[u_1] = x^\top\! A \, y

§Regret

R_T = \max_i \sum_{t=1}^{T} u_i^t - \sum_{t=1}^{T} u_{a_t}^t

§LP Dual

\min_{y,w} w \;\; \text{s.t.} \;\; Ay \leq w \cdot \mathbf{1}

§Payoff

u_1(i,j) = a_{ij}, \;\; u_2(i,j) = -a_{ij}

§Minimax

\max_{x \in \Delta} \min_{y \in \Delta} \, x^\top\! A \, y = v^*

§Zero-Sum

\textstyle\sum_{i=1}^{n} u_i(s) = 0 \;\; \forall \, s \in S

§Nash Eq.

x^{*\top}\! A y \geq x^{*\top}\! A y^* \geq x^\top\! A y^*

§Expected

\mathbb{E}[u_1] = x^\top\! A \, y

Sector Analysis

S&P 500 cross-sector correlations, valuation signals, and hedging insights

Cap-Weight — larger companies move the sector more. Matches how sector ETFs (XLK, XLV, XLE) actually behave, so correlations reflect what you'd experience when hedging with real instruments. Downside: mega-caps like AAPL or NVDA can dominate an entire sector. Based on all S&P 500 constituents.

Computing sector correlations…