Notation Reference

Contents

Notation Reference#

This document contains the LaTeX notation definitions used throughout the course materials.

Usage Notes#

The LaTeX commands defined in this document are automatically compiled into the global MathJax configuration and are available in all discussion notebooks. Exercise and solution notebooks have local copies automatically injected from the global config for standalone use.

Chapter 1: Risk and Return Metrics#

Symbol	Definition	Description
\(\E\)	`E`	Matter what period
\(\Nassets\)	`K`	Mathematical notation
\(\Ntime\)	`N`	Period of time
\(\covest\)	`\hat{\boldsymbol{\Sigma}}`	Mathematical notation
\(\covmat\)	`\boldsymbol{\Sigma}`	Mathematical notation
\(\meanest\)	`\hat{\mu}`	the vector of sample averages:
\(\meanestvec\)	`\hat{\boldsymbol{\mu}}`	Mathematical notation
\(\muvec\)	`\boldsymbol{\mu}`	Mathematical notation
\(\onevecNt\)	`\boldsymbol{1}_{\Ntime\times 1}`	the vector of ones
\(\rmat\)	`\boldsymbol{R}`	the matrix of sample returns
\(\rvec\)	`\boldsymbol{r}`	Interest rate

Chapter 1: Optimizing Risk and Return#

Symbol	Definition	Description
\(\Nsec\)	`K`	Mean variance optimization
\(\avg\)	`\text{avg}`	Avg
\(\covmat\)	`\boldsymbol{\Sigma}`	Mathematical notation
\(\mux\)	`\tilde{\mu}`	Mathematical notation
\(\muxvec\)	`\boldsymbol{\mux}`	Mathematical notation
\(\quant\)	`q`	Is the value
\(\rVaRqtau\)	`r^{\VaR_{q,\tau}}`	Is the value
\(\rf\)	`r_f`	Interest rate
\(\rx\)	`\tilde{r}`	Against several factor
\(\sigx\)	`\tilde{\sigma}`	Mathematical notation
\(\tan\)	`\text{tan}`	Tan
\(\wt\)	`w`	Mathematical notation
\(\wtvec\)	`\boldsymbol{\wt}`	Mathematical notation
\(\zscore\)	`\texttt{z}`	the value (z-score) of the standard normal cdf associated with quantile

Chapter 3: Value-at-Risk#

Symbol	Definition	Description
\(\CVaR\)	`\text{CVaR}`	Cvar
\(\E\)	`E`	Matter what period
\(\Nt\)	`N`	Mathematical notation
\(\Ntime\)	`N`	Period of time
\(\Pr\)	`\mathbb{P}`	Is the value
\(\VaR\)	`\text{VaR}`	Normal distribution
\(\VaRqtau\)	`\VaR_{q,\tau}`	Mathematical notation
\(\cdf\)	`\Phi`	the (unspecified) cdf of returns, and is its inverse
\(\cdfz\)	`\cdf_{\zscore}`	the standard normal cdf, then
\(\loss\)	`L`	Mathematical notation
\(\pdf\)	`\phi`	the pdf of the standard normal
\(\pdfz\)	`\pdf_{\zscore}`	the pdf of the standard normal
\(\pnl\)	`\Gamma`	Profit and loss (P&L)
\(\pnlCVaRqtau\)	`\pnl^{\CVaR_{q,\tau}}`	Mathematical notation
\(\pnlVaRqtau\)	`\pnl^{\VaR_{q,\tau}}`	Is the value
\(\port\)	`\Pi`	Is the value
\(\quant\)	`q`	Is the value
\(\rCVaRqtau\)	`r^{\CVaR_{q,\tau}}`	Interest rate
\(\rVaRqtau\)	`r^{\VaR_{q,\tau}}`	Is the value
\(\rlog\)	`\texttt{r}`	Interest rate
\(\zscore\)	`\texttt{z}`	the value (z-score) of the standard normal cdf associated with quantile

Chapter 3: Coherent Risk Measures#

Symbol	Definition	Description
\(\riskmeasure\)	`\varrho`	Risk measure

Chapter 5: Managing Tail Risk#

Symbol	Definition	Description
\(\text{CVaR\)	`\newcommand{CVaR}{\text{CVaR}`	Cvar

Chapter 7: Forecasting#

Symbol	Definition	Description
\(\E\)	`E`	Matter what period
\(\rx\)	`\tilde{r}`	Against several factor

E.2.1 Replicating Regressions#

Symbol	Definition	Description
\(\hyg\)	`\text{hyg}`	Fitted regression value
\(\spy\)	`\text{spy}`	Fitted regression value
\(\targ\)	`EEM`	Mathematical notation

Total notation entries: 45 Organized across 7 chapters