Chapter 28A Multidimensional Framework for Risk Analysis

By Gifford Fong and Oldrich A. Vasicek

Financial Analysts Journal, 53 (4) (1997), 51–57.


The variety and complexity of portfolio holdings have given rise to the need for additional analyses for purposes of risk management. A framework for risk analysis includes three dimensions: sensitivity analysis, value at risk (VaR), and stress testing. This article describes each dimension and suggests a procedure for achieving a VaR measure. Once individual holdings are analyzed, attention can be directed to portfolio-level analyses and the types of output suitable for monitoring purposes. In combination, this framework can capture the important features of portfolio risk.


Risk control in asset management is the ability to manage the uncertainty associated with the investment process. Fundamental to risk control is risk measurement, which can be thought of as quantification of the characteristics of risk.

Early attempts at risk quantification dealt with investments in relatively simple security types. This approach included both fixed and known cash flows, as is the case for Treasury securities and equities described by lognormal return distributions. Risk was characterized by volatility of returns, measured by quantities such as variance, standard deviation, or mean absolute deviation (Markowitz 1952, 1959).

As the concept of risk measurement and risk control evolved over time, additional approaches were ...

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