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@@ -48,3 +48,4 @@ simulated[[:space:]]trades/draft/main.pdf filter=lfs diff=lfs merge=lfs -text
 simulated[[:space:]]trades/simplified/main.pdf filter=lfs diff=lfs merge=lfs -text
 total[[:space:]]setups[[:space:]]count/main.pdf filter=lfs diff=lfs merge=lfs -text
 leverage[[:space:]]and[[:space:]]margin/main.pdf filter=lfs diff=lfs merge=lfs -text
+composite[[:space:]]ranking[[:space:]]via[[:space:]]mae[[:space:]]metrics/main.pdf filter=lfs diff=lfs merge=lfs -text

composite ranking via mae metrics/main.pdf

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+version https://git-lfs.github.com/spec/v1
+oid sha256:3ed594cbb9fb6dc5bbb5a9a47d836ec40e5fdbb567d2938bcc9c6e3cf1e064ad
+size 111797

composite ranking via mae metrics/main.tex

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+\documentclass[11pt]{article}
+\usepackage[margin=1in]{geometry}
+\usepackage{amsmath,amssymb}
+\setlength{\parindent}{0pt}
+\setlength{\parskip}{0.5\baselineskip}
+
+\title{Compact Ranking via MAE Metrics}
+\author{algorembrant}
+\date{\today}
+
+\begin{document}
+\maketitle
+
+\section{Setup \& Notation}
+Let SETUP \(s \in \{1,\dots,S\}\) denote a parameter set. 
+For trade \(i \in \{1,\dots,I\}\) within \(s\), let \(m_{s,i} > -1\) be the max-adverse-excursion (MAE) ratio.
+
+\section{Metrics}
+Arithmetic and geometric means of \(m\):
+\begin{align}
+    \mu_s &= \frac{1}{I}\sum_{i=1}^{I} m_{s,i}, &
+    \varphi_s &= \left[\prod_{i=1}^{I}(1+m_{s,i})\right]^{1/I} - 1
+\end{align}
+Volatility drag (\(\nu_s\)) and cumulative excursion (\(\upsilon_s\)):
+\begin{equation}
+    \nu_s = \mu_s - \varphi_s, \qquad
+    \upsilon_s = \sum_{i=1}^{I} m_{s,i}
+\end{equation}
+
+\section{Composite Ranking (Rank 1)}
+Normalize across all SETUPs \(k \in \{1,\dots,S\}\):
+\begin{align}
+    \tilde{\upsilon}_s &= \frac{\upsilon_s - \min_k \upsilon_k}{\max_k \upsilon_k - \min_k \upsilon_k}, &
+    \tilde{\nu}_s &= \frac{\nu_s - \min_k \nu_k}{\max_k \nu_k - \min_k \nu_k}
+\end{align}
+Define the scalar:
+\begin{equation}
+    \lambda_s = \tilde{\upsilon}_s + \tilde{\nu}_s
+\end{equation}
+The single highest rank (Rank 1) is awarded exclusively to:
+\begin{equation}
+    s^* = \arg\min_{s} \lambda_s \quad \implies \quad \text{Rank}(s^*) = 1
+\end{equation}
+as \(s^*\) best approximates the simultaneous minimization of \(\upsilon_s\) and \(\nu_s\). Sorting by \(\lambda_s\) provides the hierarchy, but only \(s^*\) is selected as the top performer.
+
+\end{document}