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Unformatted text preview: II. Tools and Applications of Market Risk Management A. Basic Concepts in Measuring Risk Version: January 3, 2011 Unit II.A p. 2 of 58 The Concept of ValueatRisk o ValueatRisk: the minimum loss that will be incurred x% of the time o Sometimes defined as the maximum loss 1 – x% of the time (but be careful) o Example: 1day, 5%, $1 million n The probability is 5% that the firm will lose at least $1 million in one day n The probability is 95% that the firm will do no worse than lose $1 million in one day Version: January 3, 2011 Unit II.A p. 3 of 58 The Concept of ValueatRisk (cont.) o Note that it is not the most one can lose . The most one can lose is everything! o How VaR can be misinterpreted: On May 5, 2004 The Wall Street Journal (p. A1) gave the following statement about Goldman Sachs. Goldman’s last quarterly results indicated that the average sum it could lose on any given day grew to $71 million, up from just $28 million in the fourth quarter of 2000. Goldman’s quarterly report shows a VAR for the three months ending February 2004 of $71 million on p. 59. Version: January 3, 2011 Unit II.A p. 4 of 58 The Concept of ValueatRisk (cont.) o How VaR can be misinterpreted (cont.) On p. 58, Goldman correctly defines VAR as follows: ValueatRisk (VaR) is the potential loss in value of Goldman Sachs’ trading positions due to adverse market movements over a defined time horizon with a specified confidence level. For the VaR numbers reported below, a oneday time horizon and 95% confidence level were used. This means that there is a 1 in 20 chance that daily trading net revenues will fall below the expected daily trading revenues by an amount at least as large as the reported level. Thus, shortfalls from expected trading net revenues on a single trading day greater than the reported VaR would be expected to occur, on average, about once a month. Shortfalls on a single day can exceed reported VaR by significant amounts. Shortfalls can also accumulate over a longer time horizon such as a number of consecutive trading days. Version: January 3, 2011 Unit II.A p. 5 of 58 The Concept of ValueatRisk (cont.) o Calculating VaR n First identify a source of risk n The Analytic Method o Assumes normal distribution % VAR = Expected return – (Standard Deviation)*(risk adjustment) where the “risk adjustment” is 1.65 for a 5% VAR and 2.33 for 1% VAR. The calculated number here is the return that falls exactly in the x% tail. This number is then multiplied by the portfolio value to obtain the VAR. Version: January 3, 2011 Unit II.A p. 6 of 58 The Concept of ValueatRisk (cont.) o Calculating VaR (cont.) n The Analytic Method (cont.) 5% of the area in this tail is to the left of 1.651.65 Suppose the return on the portfolio is represented by the variable r, with expected value of E(r) and standard deviation of σr. We observe a return of r. The return expressed as a standard normal is r r  E(r) ....
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 Fall '11
 DonChance
 Variance, Value at risk, Cont

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