Value At Risk

Value At Risk - FINC 782: Energy Markets Portfolio Analysis...

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1 Value at Risk FINC 782: Energy Markets Portfolio Analysis AB Freeman School of Business, Tulane University, New Orleans, Spring 2007 Leslie McNew Email at Lmcnew@tulane.edu 865-5036
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2 Rationale for VAR Closed Form VAR Monte Carlo Simulation Estimations of VAR VaR in Energy Markets VaR in Kiodex Use of Stress Testing
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3 Basle Accord 1988 A group of the central bankers in the G- 10 agreed to set minimum capital requirements to guard against credit risk . 1995 initiatives allowed banks to use their own proprietary models. Many of the banks used VAR .
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4 Financial Disasters A rash of recent financial disasters has put the use of VAR in the spotlight, in the hopes that this indicator could help prevent financial collapse. Long-Term Capital Barings Bank Orange County
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5 What is Value at Risk? Summarizes the expected maximum loss (or worst case loss) over a target horizon within a single summary statistic (confidence interval, or standard deviation). I am 95% confident that this position (portfolio) will lose no more than $760 K in one day.
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6 What is Value at Risk? Value at Risk (VaR) measures the likelihood of losing more than Y dollars over some time horizon: “There is an X% chance l will have a mark-to-market loss of less than $Y over a Z day period” Firms use VaR to determine how much capital to hold against their derivative positions Essential for firms such as banks who are marking to market transactions on a daily basis VaR takes into account the correlations across assets and provides an integrated view of risk Z is typically 1, 3, 5, or 10 days X is typically 95% or 99%
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7 Closed Form VAR Determine probability distribution for the P&L of a portfolio. Closed form model assumes a Closed form model assumes a Normal Normal Distribution Distribution of P&L. of P&L.
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8 Standard Normal Distribution e x x f ] 2 [ 2 ) 2 ( 1 ) , ; ( σ μ - Π =
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9 Distribution is assumed: by taking the actual distribution of P&L. by estimating standard deviation and correlation of the P&L for every instrument in the portfolio. Closed Form VAR (sometimes called Variance/CoVariance VaR)
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10 Closed Form VAR With the Implicit assumption, P&L distributions are estimated by a variance/covariance variance/covariance matrix. P&L is a linear linear function of the matrix. This is the model used by a significant number of energy participants
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11 - = VAR dp p f ) ( % 95 Closed Form VAR Summarize the worst case loss within a certain confidence interval. Where p = P&L and f(p) is the density function of P&L.
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12 -VAR Closed Form VAR 0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016 -$500 -$473 -$446 -$419 -$392 -$365 -$338 -$311 -$284 -$257 -$230 -$203 -$176 -$149 -$122 -$95 -$68 -$41 -$14 $13 $40 $67 $94 $121 $148 $175 $202 $229 $256 $283 $310 $337 $364 $391 $418 $445 $472 $499 95%
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13 Closed Form VAR Higher confidence intervals will give higher VAR numbers. The Basle Committee recommends 99% for banking capital cushions.
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Value At Risk - FINC 782: Energy Markets Portfolio Analysis...

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