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@@ -39,3 +39,5 @@ Using[[:space:]]My[[:space:]]Flesh[[:space:]]to[[:space:]]Make[[:space:]]TeX-wri
 variance[[:space:]]and[[:space:]]standard[[:space:]]deviation/image.png filter=lfs diff=lfs merge=lfs -text
 variance[[:space:]]and[[:space:]]standard[[:space:]]deviation/main.pdf filter=lfs diff=lfs merge=lfs -text
 volatility[[:space:]]drag/volatility[[:space:]]drag.png filter=lfs diff=lfs merge=lfs -text
+volatility[[:space:]]drag/volatility[[:space:]]drag[[:space:]]more.png filter=lfs diff=lfs merge=lfs -text
+volatility[[:space:]]drag/volatility[[:space:]]drag.pdf filter=lfs diff=lfs merge=lfs -text

volatility drag/volatility drag.pdf

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+version https://git-lfs.github.com/spec/v1
+oid sha256:4d975c84dfe6e3d74a4f4f25117292e7e9ca18d25e0b72869bb7ade32978183a
+size 113713

volatility drag/volatility drag.tex

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+
+\documentclass[11pt]{article}
+\usepackage[margin=0.5in]{geometry}
+
+% Core packages
+\usepackage{amsmath,amssymb}
+\usepackage{xcolor}
+\usepackage{tikz-cd}
+\usepackage{multicol}
+
+\newcommand{\colortext}[2]{\textcolor{#1}{#2}}
+
+% Paragraphs
+\setlength{\parindent}{0pt}
+\setlength{\parskip}{1\baselineskip}
+
+
+\author{algorembrant}\date{\today}
+
+\begin{document}
+\maketitle
+
+\section{Variance and Standard Deviation}
+
+\begin{align}
+    \sigma &= \sqrt{\underbrace{\frac{1}{T}\sum_{t=1}^{T}\left(x_t-\underbrace{\frac{1}{T}\sum_{t=1}^Tx_t}_{\mu = \text{average}}\right)^2}_{\sigma^2=\text{variance}}}, \quad \text{standard deviation (population); use }\frac{1}{T-1}\sum_{t=1}^T(\dots)^2 \text{ for sample variance} \\
+    \sigma &= \sqrt{\underbrace{\frac{1}{T}\sum_{t=1}^{T}\left(\textcolor{red}{r}_t-\underbrace{\frac{1}{T}\sum_{t=1}^T\textcolor{red}{r}_t}_{\mu = \text{average}}\right)^2}_{\sigma^2=\text{variance}}}, \quad \text{volatility, where } r \text{ is return}
+\end{align}
+
+\section{Volatility Drag}
+
+\begin{align}
+    v &= \underbrace{\frac{1}{T}\sum_{t=1}^T\textcolor{red}{r}_t}_{\mu} - \underbrace{\underbrace{\left(\prod_{t=1}^T 1+\textcolor{red}{r}_t\right)^{\frac{1}{T}}}_{g_{\text{factor}}} - 1}_{g}, \quad \text{volatility drag, no } \sigma^2 \text{ nor } \sigma \text{ involved} \\
+    v &\approx \underbrace{\frac{1}{T}\sum_{t=1}^T\textcolor{red}{r}_t}_{\mu} - \underbrace{\underbrace{\exp \left(\log(1+\mu)-\frac{1}{2}\cdot \frac{1}{(1+\mu)^2} \cdot \sigma^2\right)}_{g_{\text{factor}{\approx}}}-1}_{g_{\approx}}, \quad \text{volatility drag, uses approximated } g
+\end{align}
+where $\mu$ is arithmetic mean, and $g$ is geometric mean.
+
+
+
+\end{document}