MFIN514.3.1 - Value-at-Risk (VaR) For risk management...

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Value-at-Risk (VaR) For risk management purposes, it might be useful to estimate how much money your portfolio might lose over a given time span and a certain confidence level . VAR is defined as VAR (holding period; 1 – α) where 1 – α is your confidence interval. If VAR (30-day; 95%) = $10,000 then in 95 out of 100 months the change in the value of your portfolio will be less than $10,000. Note that this tells you nothing about the magnitude of potential losses in extreme cases. Use expected shortfall rather than VAR for such cases.
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Graphically Change in the value of the portfolio -V $0 The most difficult part is to understand the nature of risks that your portfolio is exposed to and figuring out its expected loss distribution.
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How to calculate VAR in EXCEL? . to al proportion is VaR horizon, time the of regardless that shows formula The ). assumption good a always (not d distribute normally is portfolio your of value in the changes that is formula this behind assumption The EXCEL) in function (NORMSINV on distributi normal cumulative inverse the is (.) horizon, time over the change portfolio the of deviation standard the is level, confidence the is X where ) ( 1 1 σ N N X VaR - - =
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How to choose the time horizon The time horizon can differ from a few hours for an active trading desk to one month for a pension fund. How to compute T-day VaR using 1-day VAR? (1) T-day σ = 1-day σ x √T (2) VaR = σ x N -1 (X) From (1) and (2) it’s easy to show that T-day VAR = 1-day VAR x √T We assume that the value of the portfolio on successive days have independent identical normal distributions with mean zero (i.e., no autocorrelation)
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The role of autocorrelation If daily changes in portfolio values are first-order autocorrelated
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This note was uploaded on 07/19/2010 for the course FIN 853 taught by Professor Longchen during the Fall '06 term at Michigan State University.

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MFIN514.3.1 - Value-at-Risk (VaR) For risk management...

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