Closes #014 - System-wide handbook sweep, English consolidation & Crypto state persistence
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Antigravity Agent
135
components/modules/sandbox/SandboxMathModal.tsx
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135
components/modules/sandbox/SandboxMathModal.tsx
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import React from 'react';
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import { BookOpen, X, TrendingUp, BarChart2, ShieldAlert } from 'lucide-react';
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import 'katex/dist/katex.min.css';
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import { BlockMath, InlineMath } from 'react-katex';
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interface SandboxMathModalProps {
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isOpen: boolean;
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onClose: () => void;
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}
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export default function SandboxMathModal({ isOpen, onClose }: SandboxMathModalProps) {
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React.useEffect(() => {
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const handleKeyDown = (e: KeyboardEvent) => {
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if (e.key === 'Escape') {
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onClose();
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}
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};
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if (isOpen) {
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window.addEventListener('keydown', handleKeyDown);
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}
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return () => {
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window.removeEventListener('keydown', handleKeyDown);
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};
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}, [isOpen, onClose]);
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if (!isOpen) return null;
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return (
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<div className="fixed inset-0 z-50 flex items-center justify-center bg-slate-955/90 backdrop-blur-md p-4 sm:p-6 md:p-8">
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<div className="bg-slate-900 border border-slate-800/80 rounded-3xl w-full max-w-4xl h-[80vh] flex flex-col overflow-hidden shadow-2xl relative text-slate-350">
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{/* Modal Header */}
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<div className="flex justify-between items-center px-6 py-4 bg-slate-950/50 border-b border-slate-800/80">
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<div>
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<h2 className="text-base font-bold bg-gradient-to-r from-teal-400 to-emerald-400 bg-clip-text text-transparent flex items-center gap-2">
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<BookOpen className="w-5 h-5 text-teal-400" /> Portfolio Sandbox - Math & Sizing Handbook
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</h2>
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<p className="text-[10px] text-slate-500 font-mono">Institutional Portfolio Construction & Allocation Spec</p>
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</div>
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<button
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onClick={onClose}
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className="text-slate-400 hover:text-slate-200 bg-slate-955/50 border border-slate-800 hover:border-slate-700 p-2 rounded-xl transition-all cursor-pointer flex items-center justify-center"
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aria-label="Close modal"
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>
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<X className="w-4 h-4" />
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</button>
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</div>
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{/* Modal Body */}
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<div className="flex-1 overflow-y-auto p-6 sm:p-8 space-y-8 text-slate-300 scrollbar-thin">
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{/* Section A: Synthetic Portfolio Model & Asset Weightings */}
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<div className="space-y-3">
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<h4 className="text-xs font-bold text-teal-400 uppercase tracking-wider font-mono flex items-center gap-1.5">
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<TrendingUp className="w-3.5 h-3.5" /> A. Synthetic Portfolio Model & Asset Weightings
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</h4>
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<p className="text-xs leading-relaxed text-slate-400">
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The sandbox constructs a continuous synthetic asset representing your active weight allocations and its daily return track:
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</p>
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<div className="bg-slate-950/40 p-4 rounded-xl border border-slate-800/60 my-2 space-y-4">
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<div>
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<p className="text-xs text-slate-400 mb-1">Active Percentage Weighting (<InlineMath math="w_i" />) Calculation:</p>
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<BlockMath math="w_i = \\frac{\\text{Shares}_i \\times P_{\\text{current}, i}}{\\sum_{j} \\text{Shares}_j \\times P_{\\text{current}, j}}" />
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</div>
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<div className="border-t border-slate-850 pt-3">
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<p className="text-xs text-slate-400 mb-1">Synthetic Portfolio Log Return (<InlineMath math="R_{pt}" />):</p>
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<BlockMath math="R_{pt} = \\sum_{i} w_i \\times \\ln\\left(\\frac{P_{t, i}}{P_{t-1, i}}\\right)" />
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</div>
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</div>
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</div>
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{/* Section B: Linear Mixed Effects Panel Regression (LMM) */}
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<div className="space-y-3">
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<h4 className="text-xs font-bold text-teal-400 uppercase tracking-wider font-mono flex items-center gap-1.5">
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<BarChart2 className="w-3.5 h-3.5" /> B. Linear Mixed Effects Panel Regression (LMM)
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</h4>
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<p className="text-xs leading-relaxed text-slate-400">
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Solves the system-wide macro response model across all historical event instances <InlineMath math="j" /> using a Swamy-Arora GLS estimator:
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</p>
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<div className="bg-slate-950/40 p-4 rounded-xl border border-slate-800/60 my-2">
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<div>
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<p className="text-xs text-slate-400 mb-1">Panel Model Specification with VIX Controls:</p>
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<BlockMath math="R_{ptj} = \\beta_0 + \\beta_{\\text{drift}} \\text{Pre}_t + \\beta_{\\text{impact}} \\text{Post}_t + \\beta_{\\text{VIX}} VIX_{tj} + u_j + e_{ptj}" />
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<p className="text-[10px] text-slate-500 mt-2 font-mono leading-relaxed">
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where:
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<br />
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- <InlineMath math="t \\in [-30, +30]" /> is the relative day offset from event date <InlineMath math="T_j" />.
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<br />
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- <InlineMath math="\\text{Pre}_t = \\mathbb{I}(t < 0)" /> and <InlineMath math="\\text{Post}_t = \\mathbb{I}(t > 0)" /> are relative phase indicators.
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<br />
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- <InlineMath math="VIX_{tj}" /> is the background market-wide volatility covariate.
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<br />
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- <InlineMath math="u_j \\sim N(0, \\sigma_u^2)" /> is the random group intercept (event instance shock).
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<br />
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- <InlineMath math="e_{ptj} \\sim N(0, \\sigma_e^2)" /> is the residual error.
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</p>
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</div>
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</div>
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</div>
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{/* Section C: Kelly Criterion & Fractional Betting Sizing */}
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<div className="space-y-3">
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<h4 className="text-xs font-bold text-teal-400 uppercase tracking-wider font-mono flex items-center gap-1.5">
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<ShieldAlert className="w-3.5 h-3.5" /> C. Kelly Criterion & Fractional Betting Sizing
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</h4>
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<p className="text-xs leading-relaxed text-slate-400">
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The Kelly Criterion optimizes allocation sizing to maximize the expected value of the logarithm of wealth, balancing capital preservation with growth:
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</p>
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<div className="bg-slate-950/40 p-4 rounded-xl border border-slate-800/60 my-2 space-y-4">
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<div>
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<p className="text-xs text-slate-400 mb-1">Theoretical Kelly Fraction (<InlineMath math="f^*" />) Equation:</p>
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<BlockMath math="f^* = \\frac{p \\cdot b - (1 - p)}{b}" />
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<p className="text-[10px] text-slate-500 mt-2 font-mono leading-relaxed">
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where:
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<br />
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- <InlineMath math="p" /> is the probability of a positive outcome (rebound or trade success).
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<br />
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- <InlineMath math="b" /> is the payout odds ratio (average win size divided by average loss size).
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</p>
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</div>
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<div className="border-t border-slate-850 pt-3">
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<p className="text-xs text-slate-400 mb-1">Fractional Kelly (Half-Kelly) Safety Buffer:</p>
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<BlockMath math="f_{\\text{applied}} = \\max\\left(0, 0.5 \\times f^*\\right)" />
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<p className="text-xs text-slate-400 leading-relaxed mt-2">
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To mitigate estimation variance and protect against catastrophic drawdown due to model error or fat-tailed market returns, the cockpit clips the suggested sizing to a **Half-Kelly** multiplier ($0.5$).
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</p>
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</div>
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</div>
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</div>
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</div>
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</div>
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</div>
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);
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}
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