# Portfolio Risk Analysis

By Gregory Connor; Lisa Goldberg et al. | Go to book overview

Key Notation

This section gives some of the key notation that we use throughout the text. It is not a comprehensive list; it covers only the most commonly used symbols in the book. We use bold font for vectors and matrices and regular font for real values; so for example r is an individual asset or portfolio return and r is a vector of asset returns.

 0n×k an n × k matrix of zeros 1n an n-vector of ones arg max in an optimization problem this denotes the value of the choice variable that gives a maximum of the objective function B the n × k matrix of the assets' exposures to the factors C the n × n matrix of return covariances Cf the k × k matrix of factor return covariances Cε the n × n matrix of asset-specific return covariances cum(·) the cumulative distribution function of an asset or portfolio return; hence cum(a) =Pr(r ≤ a) cumloss(·) the cumulative distribution function of an asset or portfolio loss; cumloss(a) = Pr(–r ≤ a) den(·) the density function of an asset or portfolio return Diag[a1…, an] an n × n diagonal matrix with elements a1,…, an along the diagonal E[·] the expectation operator for a random variable E*[·] the expectation operator for a random variable under the risk-neutral probability measure (see chapter 1 for a discussion ES(1 – α) the expected shortfall of an asset or portfolio, with confidence level 1 – α (see chapter 1 for a description

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