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.

0kan n × k matrix of zeros
1nan n-vector of ones
arg maxin an optimization problem this denotes the value of the choice variable that gives a maximum of the objective function
Bthe n × k matrix of the assets' exposures to the factors
Cthe n × n matrix of return covariances
Cfthe k × k matrix of factor return covariances
Cεthe n × n matrix of asset-specific return covariances
cum(·)the cumulative distribution function of an asset or portfolio return; hence cum(a) =Pr(ra)
cumloss(·)the cumulative distribution function of an asset or portfolio loss; cumloss(a) = Pr(–ra)
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

-xix-

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