: The market risk of a portfolio refers to the possibility of financial loss due to the joint movement of systematic economic variables such as interest and exchange rates. Quantifying market risk is important to regulators in assessing solvency and to risk managers in allocating scarce capital. Moreover, market risk is often the central risk faced by financial institutions. The standard method for measuring market risk places a conservative, one-sided confidence interval on portfolio losses for short forecast horizons. This bound on losses is often called capital-at-risk or value-at-risk (VAR), for obvious reasons. Calculating the VAR or any similar risk metric requires a probability distribution of changes in portfolio value. In most risk management models, this distribution is derived by placing assumptions on (1) how the portfolio function is approximated, and (2) how the state variables are modeled. Using this framework, we first review four methods for measuring market risk. We t...

This paper examines the systematic relationship between correlation mis-estimation and the corresponding Value-at-Risk (VaR) mis-calculation. To this end, first a semi-parametric approach, and then a parametric approach is developed. Both approaches are based on a simulation setup. Various linear and non-linear portfolios are considered, as well as variance-covariance and Monte-Carlo simulation methods are employed. We find that the VaR error increases significantly as the correlation error increases, particularly in the case of well-diversified linear portfolios. In the case of option portfolios, this effect is more pronounced for short-maturity, in-the-money options. The use of MC simulation to calculate VaR magnifies the correlation bias effect. Our results have important implications for measuring market risk accurately.

This working paper is being distributed to solicit comments, recollections and anecdotes from regulators and market participants who worked with VaR or related risk measures prior to 1993. Please forward any comments directly to the author. Topics of particular interest are: • early implementations of VaR or VaR-like measures in trading environments during the 1970’s or 1980’s; • the extent to which industry practice (existing risk measures used in trading environments) influenced the SEC’s Uniform Net Capital Rule, the SFA’s 1992 capital rule and Europe’s Capital Adequacy Directive; • early use (especially during the 1980’s) of names such as “value-at-risk”, “capital-at-risk ” and “dollars-at-risk”—which name arose first? • papers published prior to 1993 that mention or describe VaR measures.

This paper proposes an analytical form of CoVaR, which is compatible with the existing VaR and stress-test based risk management framework, adding value by capturing systemic risk of a portfolio. Analytical CoVaR is a computationally inexpensive risk tool used to screen systemic risk. It is reasonably accurate and also has desired statistical properties hence is suitable for use by investment companies, brokerage …rms, mutual funds and any business that evaluates risk. Empirical backtest results show that historical analytical CoVaR exceedances pass both Failure Frequency Test and Conditional Test. The paper also presents a theoretical frameworks within which to investigate how analytical CoVaR captures systemic risk when asset and market returns are serially independent and when they are serially correlated. Analytical CoES is presented as an extension to capture loss beyond CoVaR.