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Unformatted text preview: 1 VALUE AT RISK (VAR) What is the most I can lose on this investment? This is a question that almost every investor who has invested or is considering investing in a risky asset asks at some point in time. Value at Risk tries to provide an answer, at least within a reasonable bound. In fact, it is misleading to consider Value at Risk, or VaR as it is widely known, to be an alternative to risk adjusted value and probabilistic approaches. After all, it borrows liberally from both. However, the wide use of VaR as a tool for risk assessment, especially in financial service firms, and the extensive literature that has developed around it, push us to dedicate this chapter to its examination. We begin the chapter with a general description of VaR and the view of risk that underlies its measurement, and examine the history of its development and applications. We then consider the various estimation issues and questions that have come up in the context of measuring VAR and how analysts and researchers have tried to deal with them. Next, we evaluate variations that have been developed on the common measure, in some cases to deal with different types of risk and in other cases, as a response to the limitations of VaR. In the final section, we evaluate how VaR fits into and contrasts with the other risk assessment measures we developed in the last two chapters. What is Value at Risk? In its most general form, the Value at Risk measures the potential loss in value of a risky asset or portfolio over a defined period for a given confidence interval. Thus, if the VaR on an asset is $ 100 million at a one-week, 95% confidence level, there is a only a 5% chance that the value of the asset will drop more than $ 100 million over any given week. In its adapted form, the measure is sometimes defined more narrowly as the possible loss in value from normal market risk as opposed to all risk, requiring that we draw distinctions between normal and abnormal risk as well as between market and non- market risk. While Value at Risk can be used by any entity to measure its risk exposure, it is used most often by commercial and investment banks to capture the potential loss in value of their traded portfolios from adverse market movements over a specified period; 2 this can then be compared to their available capital and cash reserves to ensure that the losses can be covered without putting the firms at risk. Taking a closer look at Value at Risk, there are clearly key aspects that mirror our discussion of simulations in the last chapter: 1. To estimate the probability of the loss, with a confidence interval, we need to define the probability distributions of individual risks, the correlation across these risks and the effect of such risks on value. In fact, simulations are widely used to measure the VaR for asset portfolio....
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This note was uploaded on 12/01/2011 for the course FINANCE 350 taught by Professor Aswath during the Summer '10 term at NYU.
- Summer '10