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Chapter 28: Value at Risk (VaR)
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Value at risk (VaR)
Measures the worst expected loss
Under normal market conditions or stressed conditions
Over a specified time interval
At a specific confidence level
“VaR answers the question: how much can I lose with x% probability over a pre-set horizon?” (JP Morgan, RiskMetrics—Technical Document)
Simple example
Portfolio value: $100 million
Return distribution: mean = 20%, sigma = 30%
What is the probability of losing more than $20 million by year-end?
To answer the question (probability of ending up with less than $80), you have to all the probabilities below the red line on the y-axis.
This means we need to look at the Cumulative Normal distribution.
Cell B6: Cumulative Normal Distribution
Initial investment 100
Probability that
portfolio worth less
than cutoff
9.12%<-- =NORMDIST(B5,(1+B2)*B4,B4*B3,TRUE)
Portfolio value
Data table header: =NORMDIST(B5,(1+B2)*B4,B4*B3,FALSE)
PROBABILITY OF YEAR-END PORTFOLIO VALUE
0.0000.0020.0040.0060.0080.0100.0120.014020406080100120140160180200220240End-of-Year Portfolio Value
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