Value at Risk
MGT 4850
Spring 2009
University of Lethbridge
Who can use VaR?
• Financial Institutions – not to expose
themselves to expensive failure (Barings,
Daiwa, Société Générale, Amaranth
Advisors LLC)
• Regulators – Basel Committee
• Nonfinancial corporations (cash flow at risk)
• Asset Managers - funds
Steps in Constructing VaR
•
•
•
•
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Current portfolio value
Measure the variability per year
Set time horizon
Set the confidence interval
Report the worst loss
Definition
• The worst expected loss under normal
market conditions over a specific time
interval at a given confidence level.
– Confidence level
– Time period
• Example – daily VaR equal to $1mil at 1%
(i.e. only one chance in 100 that a daily
loss bigger than 1 mil occurs under normal
market conditions)
Portfolio example - 394
• Value $100mil;mean return 20%; std 30%
Probability of 20 mil loss (9.12%)
PDF
• The probability density function of the
normal distribution is a Gaussian
function
• density function of the "standard" normal
distribution:
Probability density vs.
Cumulative
PDF and CDF
CALCULATING THE QUANTILES p.211-212
B6 B7
Continuous compounding
• Exponential function ex
• Natural logarithm - ln(x)
• Mean value of a portfolio in 1 year:
– ln(int. value) + (mean ret.+σ2/2)T
Now we need “loginv” function for the cutoff
point
Inverse of the lognormal
cumulative distribution function
p.213
VaR for 3 asset problem p. 215
p.216