1. Value at Risk (VaR) is a measure of the maximum likely loss over a target period at a given confidence level. It provides a common measure to assess and aggregate market risk across different products in a portfolio. 2. Calculating VaR involves determining exposures to various risk factors from positions, as well as the historical variance and covariance of returns for those risk factors. Common methods to calculate VaR include historical simulation, variance-covariance, and Monte Carlo simulation. 3. While VaR provides a useful measure of risk, it has limitations as it only provides information about losses up to the confidence level and does not indicate how large losses could be in extreme events. Therefore, stress testing is also needed to

1. Introduction to
Value at Risk
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Toshifumi Kuga CEO of TOSHI STATS SDN. BHD
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2. Needs for Value at Risk
• How much market risk is the company taking?
• Is the list of company s positions by products good enough to
capture risk profile?
• Maximum potential loss with likelihood is needed
• Market risk can be defined based on probability
• Definition of Value at Risk (VaR) : The maximum likely loss over
some target period
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3. Advantage of Value at Risk
• Common consistent measure of risk
• VaR enable us aggregate the risks of sub-positions into firm wide
portfolio
• Consideration on Interdependence and correlations among risk
factors
• VaR is probabilistic
• VaR is expressed as lost money
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4. Three key questions for VaR
1. Holding period
• How can we set time horizon?
• Depend on the liquidity of markets
• Depend on the investment horizon
• Depend on regulations
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5. Three key questions for VaR
2. Confidence interval
• How can we say 99% ?
• What assumption is used?
3. Observation period for data
• Why is it important to understand VaR?
• Are market events included in observation period?
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6. Two key components of VaR
1. Exposures
• Exposures come from each product/inventory in the
company
• Exposures are captured based on risk factors such as
interest rates, stock price and foreign currencies
• Exposures are calculated by front office system (with
pricing models) and fed to VaR system
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7. Two key components of VaR
2. Variance/Covariance on returns
• Created based on market movement/trends in the past
• Historical time series data of markets during observation
period is used
• If observation periods are different, Variance/Covariance on
returns are also different even though kind of exposures are
same in the portfolio
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8. Exposures in detail
• Where does market risk come from?
• Example: if Japanese investors have US equities, what risk
factors do they have?
• Answer : two risk factors 1. US stocks 2. JPY/USD rate
• Exposure: Sensitivities to risk factors which the products in
the position/inventory have
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9. Exposures in detail
• Examples of Exposures
• Exposure of Equity
• Exposure of Fixed Income
• Exposure of Foreign currencies
• Delta,Gamma and Vega are often used for derivative products
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10. Variance-Covariance approach
• Normal distribution is usually assumed for risk factors movement
• Volatilities
• Definition : the annualized standard deviation of return
• Historical Volatilities : Assumed that volatility is constant
• Covariance/Correlation
• It defines inter-dependence among risk factors movement
• Noted : Volatility and Covariance/Correlation tends to change over time in reality
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11. Calculation method for VaR
• Historical method
• No statistical assumption used about distribution of risk factors
movement
• Variance-Covariance method
• Normal distribution is usually assumed
• Monte Carlo Simulation
• Normal distribution is usually assumed
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12. Advantage of Historical method
• No need for assumptions about probability distributions of
risk factors movement
• Good to capture of tail risk, which rarely happens
• Easier to implement VaR model than other methods because
it is simple
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13. Limitaions of VaR
• Is VaR a perfect KRI to monitor risk of portfolios?
• What will happen beyond the confidence level?
• VaR tells us the most we can lose if tail events do not occur (Ex. the most
we can lose over 99% of time)
• VaR itself gives us no indication of how much the loss might be if tail
events occur
• Stress tests are needed to capture the risk which can not be identified by
VaR
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14. Back Testing
• Comparison between the estimated VaR and the actual
results of P/L of a portfolio
• A relative large number of extreme observations indicates
that our risk measures are probably too low
• Back Testing are required by regulators in many countries.
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15. Thanks for your attentions
!
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• CEO : Toshifumi Kuga, Certified financial services auditor
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