# Brandeis FIN 285a - Computer Simulations and Risk Assessment Section 4.2 (25 pages)

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## Computer Simulations and Risk Assessment Section 4.2

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- Pages:
- 25
- School:
- Brandeis University
- Course:
- Fin 285a - Financial Economics

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Fin285a Computer Simulations and Risk Assessment Section 4 2 VaR Issues Dan elson 4 4 Overview Just a quantile Violates technical risk properties Can VaR be manipulated Fall 2014 LeBaron Fin285a 4 2 2 23 Just a quantile Violates technical risk properties Can VaR be manipulated Just a quantile Fall 2014 LeBaron Fin285a 4 2 3 23 VaR is just a quantile VaR marks quantile point on the distribution Does not tell you about left tail beyond VaR Might ignore a lot of risk Might be sensitive to probability level Fall 2014 LeBaron Fin285a 4 2 4 23 VaR ignores left tail 10000 9000 Frequency out of 100 000 8000 7000 6000 5000 4000 3000 2000 0 1 1000 0 Fall 2014 LeBaron 2 1 5 1 0 5 Profit loss 0 0 5 1 Fin285a 4 2 5 23 VaR Paradox Danielson page 80 Two portfolios X straight equity position Y is hedged with a put option which puts a floor on the losses Ignore the cost of this option Also assume the floor is below the VaR p quantile cutoff Result VaR is the same in both cases but risk is quite different see next figure See Danielson page 80 for another example Fall 2014 LeBaron Fin285a 4 2 6 23 VaR quantile confusion 4 x 10 4 3 2 1 83 6 0 60 80 100 120 140 100 120 140 4 x 10 4 3 2 1 0 Fall 2014 LeBaron 83 6 60 80 Fin285a 4 2 7 23 Just a quantile Violates technical risk properties Can VaR be manipulated Violates technical risk properties Fall 2014 LeBaron Fin285a 4 2 8 23 Properties of a coherent risk measure Let h X be a quantitative measure of risk 1 Monotonic Xi Yi h X h Y 2 Homogeneous h cX ch X 3 Translation invariance h X c h X c 4 Subadditivity h X Y h X h Y Fall 2014 LeBaron Fin285a 4 2 9 23 Quick info bonds and VaR Bond 1 year maturity Principal Interest No 100 5 default pays 105 Price 100 Default probability 0 0125 If there is a default bond returns 0 100 uniform recovery Fall 2014 LeBaron Fin285a 4 2 10 23 Quick info bonds and VaR 4 2 x 10 1 0 0 20 40 60 80 100 20 40 60 Recovery value 80 100 4 PDF 2 x 10 1 0 0 100 1 25 10 4 0 0125 Fall 2014 LeBaron 80 1 25 10 4 0 01

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