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×kan 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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Portfolio Risk Analysis
Table of contents

Table of contents

  • Title Page iii
  • Contents vii
  • Acknowledgments xi
  • Introduction xiii
  • Key Notation xix
  • 1: Measures of Risk and Return 1
  • 2: Unstructured Covariance Matrices 36
  • 3: Industry and Country Risk 61
  • 4: Statistical Factor Analysis 79
  • 5: The Macroeconomy and Portfolio Risk 101
  • 6: Security Characteristics and Pervasive Risk Factors 117
  • 7: Measuring and Hedging Foreign Exchange Risk 134
  • 8: Integrated Risk Models 155
  • 9: Dynamic Volatilities and Correlations 167
  • 10: Portfolio Return Distributions 191
  • 11: Credit Risk 212
  • 12: Transaction Costs and Liquidity Risk 241
  • 13: Alternative Asset Classes 271
  • 14: Performance Measurement 299
  • 15: Conclusion 319
  • References 323
  • Index 345
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