Value at Risk

MGT 4850

Spring 2008

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

• 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

• 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:

B6 B7

CALCULATING THE QUANTILES p.211-212

Inverse of the lognormal cumulative distribution function

p.213

VaR for 3 asset problem p. 215

p.216