5_VaR_I - VALUE AT RISK (VAR) I Brief history Definition of...

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VALUE AT RISK (VAR) I J. Wei, Department of Management, U of T 1 MGTD78 Brief history Definition of VaR Stats review Coherent risk measures Definition of expected shortfall Choice of parameters for VaR Choice of parameters for VaR: calculation issues Back testing and stress testing
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BRIEF HISTORY OF VAR J. Wei, Department of Management, U of T 2 MGTD78 J.P. Morgan Chairman, Dennis Weatherstone - tired of long, complicated reports - demanded something simpler, focusing on the total exposure over the next 24 hours - by 1990 accomplished 4:15 report 1993, VaR established as an important risk measure 1994, J.P. Morgan made publicly available a simplified version of their own system: RiskMetrics Many commercial softwares developed subsequently BIS Amendment based on VaR in 1996 and implemented in 1998 RiskMetrics spun off as a separate company, developed CreditMetrics in 1997 and CorporateMetrics in 1999 VaR became a universally accepted risk measure, and centerpiece of Basel II
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DEFINITION OF VAR J. Wei, Department of Management, U of T 3 MGTD78 Definition: We are X% certain that we will not lose more than V dollars in the next N days. The variable V is the value at risk (VaR). Example: for a bank with $600 billion assets, we are 99% certain that in the next 10 days, we will not lose more than $12 billion. The VaR is $12 billion in this case. Two parameters: time horizon (N days) and confidence level (X%) - a longer horizon leads to a higher VaR - a higher confidence level leads to a higher VaR VaR is the loss corresponding to the (100 – X)th percentile of the distribution of the change in the portfolio value over the next N days.
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STATS REVIEW J. Wei, Department of Management, U of T 4 MGTD78 Standard normal distribution: mean μ = 0, standard deviation σ = 1. 1 -2 -3 -1 2 3 95% confidence x = -1.645 99% confidence x = -2.326 0 Normal distribution: mean μ , standard deviation σ . - 95% confidence level, x = μ - 1.645 σ - 99% confidence level, x = μ - 2.326 σ
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STATS REVIEW J. Wei, Department of Management, U of T 5 MGTD78 Example: A normal distribution with = 12.5 and = 2.5. Then at the μ σ 95% confidence level, the lower tail cut-off is – 1.645 = 12.5 – 1.645(2.5) = 8.3875. μ σ Similarly, at the 99% confidence level, the lower tail cut-off is – 2.326 = 12.5 – 2.326(2.5) = 6.6850. μ σ The higher the confidence level, the farther away the cut-off point is. Another way of describing: + we are 95% certain that the variable will not go down by more than 12.5 – 8.3875 = 4.1125; + we are 99% certain that the variable will not go down by more than 12.5 – 6.6850 = 5.8150. the higher the confidence level, the bigger the maximum loss. This is basically VaR.
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NATURE OF VAR J. Wei, Department of Management, U of T 6 MGTD78 loss gain (100 – X)% 0 For simplicity: work with mean of 0 and standard deviation of 1. for specific situation, scale by standard deviation
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5_VaR_I - VALUE AT RISK (VAR) I Brief history Definition of...

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