Notation Reference

Symbols used in this book, grouped by the chapter that introduces them. The last column names the pages where each one appears.

Risk and Return

Symbol	Description	Used in
\(\avg\)	Average	Optimizing Risk and Return
\(\covest\)	Estimated covariance matrix	Risk and Return Metrics
\(\covmat\)	Covariance matrix of returns	MV of S&P500; Optimizing Risk and Return; Risk and Return Metrics
\(\E\)	Expectation	Risk and Return Metrics
\(\meanest\)	Estimated mean return	Risk and Return Metrics
\(\meanestvec\)	Estimated mean vector	Risk and Return Metrics
\(\mutarg\)	Target mean return of the portfolio	Harvard’s Endowment
\(\muvec\)	Mean return vector	Risk and Return Metrics
\(\mux\)	Mean excess return	Harvard’s Endowment; Optimizing Risk and Return
\(\muxvec\)	Mean excess return vector	Optimizing Risk and Return
\(\Nassets\)	Number of assets	Risk and Return Metrics
\(\Nsec\)	Number of securities	MV of S&P500; Optimizing Risk and Return
\(\Ntime\)	Number of time periods	Risk and Return Metrics
\(\onevecNt\)	Vector of ones	Risk and Return Metrics
\(\quant\)	Quantile level	Optimizing Risk and Return
\(\rf\)	Risk-free rate	Optimizing Risk and Return
\(\rmat\)	Return matrix - assets by time	Risk and Return Metrics
\(\rVaRqtau\)	Return at VaR for quantile q over horizon τ	Optimizing Risk and Return
\(\rvec\)	Return vector	Risk and Return Metrics
\(\rx\)	Excess return	Optimizing Risk and Return
\(\sigx\)	Volatility of excess returns	Optimizing Risk and Return
\(\tan\)	Tangency portfolio	Optimizing Risk and Return
\(\wEW\)	Equally weighted portfolio	Harvard’s Endowment
\(\wREG\)	Regularized portfolio weights	Harvard’s Endowment
\(\wRP\)	Risk parity portfolio	Harvard’s Endowment
\(\wt\)	Portfolio weight	Optimizing Risk and Return
\(\wtan\)	Tangency portfolio	Harvard’s Endowment
\(\wtvec\)	Weight vector	Optimizing Risk and Return
\(\zscore\)	Z-score - a standardized value	Optimizing Risk and Return

Linear Factor Decomposition

Symbol	Description	Used in
\(\hfri\)	HFRI - the hedge fund research index	ProShares Replication
\(\hyg\)	HYG - the high-yield corporate bond ETF	Replicating Regressions
\(\merr\)		ProShares Replication
\(\spy\)	SPY - the S&P 500 ETF	Replicating Regressions
\(\targ\)	EEM - the emerging markets ETF, the regression target	Replicating Regressions

Dynamics

Symbol	Description	Used in
\(\cdf\)	Standard normal CDF	Value-at-Risk
\(\cdfz\)	Standard normal CDF evaluated at a z-score	Value-at-Risk
\(\CVaR\)	Conditional Value at Risk - the mean loss beyond VaR	Comparing VaR Estimates
\(\E\)	Expectation	Comparing VaR Estimates; Value-at-Risk
\(\loss\)	Loss	Value-at-Risk
\(\pdfz\)	Standard normal density at a z-score	Value-at-Risk
\(\pnl\)	Profit and loss	Value-at-Risk
\(\pnlCVaRqtau\)	P&L in the CVaR tail for quantile q over horizon τ	Value-at-Risk
\(\pnlVaRqtau\)	P&L at VaR for quantile q over horizon τ	Value-at-Risk
\(\port\)	Portfolio value	Value-at-Risk
\(\Pr\)	Probability	Barnstable and Long-Run Risk; Value-at-Risk
\(\quant\)	Quantile level	Value-at-Risk
\(\rCVaRqtau\)	Return in the CVaR tail for quantile q over horizon τ	Value-at-Risk
\(\riskmeasure\)	Risk measure, generically	Coherent Risk Measures
\(\rlog\)	Log return	Value-at-Risk
\(\rVaRqtau\)	Return at VaR for quantile q over horizon τ	Value-at-Risk
\(\VaR\)	Value at Risk	Value-at-Risk
\(\VaRqtau\)	Value at Risk at quantile q over horizon τ	Value-at-Risk
\(\zscore\)	Z-score - a standardized value	Value-at-Risk

The CAPM

Symbol	Description	Used in
\(\covmat\)	Covariance matrix of returns	Fundamental Theorem of Asset Pricing
\(\E\)	Expectation	Fundamental Theorem of Asset Pricing
\(\muvec\)	Mean return vector	Fundamental Theorem of Asset Pricing
\(\mux\)	Mean excess return	Fundamental Theorem of Asset Pricing
\(\muxvec\)	Mean excess return vector	Fundamental Theorem of Asset Pricing
\(\rf\)	Risk-free rate	Fundamental Theorem of Asset Pricing
\(\rx\)	Excess return	Fundamental Theorem of Asset Pricing
\(\tan\)	Tangency portfolio	Fundamental Theorem of Asset Pricing
\(\wt\)	Portfolio weight	Fundamental Theorem of Asset Pricing

Forecasting Returns

Symbol	Description	Used in
\(\E\)	Expectation	Forecasting
\(\rx\)	Excess return	Forecasting

Projects

Symbol	Description	Used in
\(\Pr\)	Probability	Contextual Alertness