Academic journal article Review of Business

The Intuition and Methodology of Value at Risk

Academic journal article Review of Business

The Intuition and Methodology of Value at Risk

Article excerpt


Value at Risk (VaR) is the maximum dollar portfolio amount that can be lost in a given period of time with a specified level of confidence--usually 5%. VaR has become a valuable tool that financial managers can use to measure market risk. The three basic VaR methodologies are Historical, Parametric and Simulation VaRs. Each has advantages and limitations, as well as ease of application under varied circumstances. In theory, the three should generally give equal values and any differences in their computed values are attributable to modeling issues and violations of assumption. Trends in VaR should be noted and explained. More problematic than the actual number and/or differences in the number is the array of possible realizations during the "other 5% of the time." If the other 5% of the time is well behaved, then those realizations should be anticipated and easily dealt with. On the other hand, if the other 5% of the time is not well behaved, then those realizations could be catastrophic and could lead to the demise of the enterprise.


Risk, and how to measure it, are topics of great interest and increasing concern in the financial services industry these days. This comes as a consequence of macroeconomic turmoil and concomitant financial meltdowns in fixed income, mortgage and mortgage-backed securities over the past 12 months, as well as the spill-over into the equity markets, which has eroded personal and corporate balance sheets.

There are many sources of risk to an enterprise. Risk can be interest-rate related, exchange-rate related, political or geopolitical, weather risk, macroeconomic, model risk, accounting, fraud and malfeasance related, among others. Witness the financial crises the financial community has suffered postwar in general, but post 1970s in particular: oil price shocks (1973), Black Monday (Oct. 1987), the Mexican Peso crisis (1994), the Asian Crisis (1997), the Russian political crisis (1998), Long Term Capital Management (1998) the World Trade Center terrorist attack (2001) and others, all of which were the result of specific types of risk mentioned above. The importance of risk metrics increases with the size of the enterprises as well as increased risk associated with financial leverage and the use growth of derivative contracts.

Financial managers have seized on Value at Risk (VaR), a tool introduced in the 1980's, to monitor and manage market risk. VaR summarizes in one number the market risk of an enterprise--it is the maximum amount that an enterprise can lose in a given period of time with a given level of confidence. The purpose of VaR is to provide an analyst, an executive, a risk manager or a regulator with:

1. a guide as to the risk of market risk of an enterprise at any particular moment, as well as

2. the trends in the market risk of an entire enterprise over time.

VaR is a mathematical and statistical methodology with a number of assumptions--some quite restrictive and some less so. The accuracy of the VaR computation depends upon the degree to which the assumptions hold. If the assumptions do not hold, then the VaR will not be very accurate and the unknowing financial manager can be lulled into a false sense of security.

This paper discusses the intuition and methodology associated with several VaR metrics and identifies limitations and assumptions which underlie their accuracy. The broadcast and print media alike have wondered aloud how, given the level of expertise of so many large and sophisticated organizations, such large portfolio losses could have occurred where risk was presumably being adequately monitored. This paper helps identify reasons that could have happened and how, as the question has come to be framed, "so many smart people could get it wrong".

VaR--The Basic Goal

A discussion of Value at Risk (VaR) best begins with a definition reiterated from above:

  Value at Risk (VaR)--the greatest portfolio loss that could be
  sustained in any given period of time for a given level of confidence. … 
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