Transcript Value at risk (VaR) - Loyola Marymount University

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Measures the potential loss in value of a risky
asset or portfolio over a defined period for a
given confidence interval
For example:
◦ If the VaR on an asset is $100,000 at a one-week,
95% confidence level, then there is only a 5% chance
that the value of the asset will drop more than
$100,000 over any given week
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Focus is on downside risk and potential
losses
Most often used by commercial and
investment banks to capture the potential
loss in value of their traded portfolios from
adverse market movements
The VaR can be compared to available capital
& cash reserves to ensure that the losses can
be covered without putting firms at risk
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Variance-Covariance Method
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Historical Simulation
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Monte Carlo Simulation
◦ Using an assumed distribution for the asset return (e.g.
normally distributed), estimated mean, variances &
covariance, compute the associated probability for the
VaR
◦ Use sorted time series data to identify the percentile
value associated with the desired VaR
◦ Specify probability distributions & correlations for
relevant market risk factors and build a simulation
model that describes the relationship between the
market risk factors and the asset return. After
performing iterations, identify the return that produces
the desired percentile for the VaR.
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Returns may not be distributed as assumed. Thus
there could be more outliers than expected and
the actual VaR could be much higher than the
computed VaR
Variance-Covariance matrix is based on historical
data, which is a collection of estimates that might
have large standard errors
Variance-Covariance matrices can change over
time when the fundamentals that drive these
numbers change over time (e.g. oil prices)