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Practical Problems with Building Fixed-Income VAR Models. Rick Klotz Managing Director Global Head of Market Risk Management Greenwich NatWest. Value At Risk: Definition.
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Rick KlotzManaging Director Global Head of Market Risk ManagementGreenwich NatWest
The value at risk (VAR) of a portfolio is the loss in value in the portfolio that can be expected over a given period of time (e.g., 1-Day) with a probability not exceeding a given number (e.g., 5%).
Probability (Portfolio Loss < - VAR) = K
K = Given Probability
A one day VAR of $10mm using a probability of 5% means that there is a 5% chance that the portfolio could lose more than $10mm in the next trading day.
Regulatory Capital = Market Risk Capital + Specific Risk Capital + Counterparty Risk Capital
Market Risk Capital = Max [Ave. of 10-Day 99% VAR x Multiplier, yesterday’s 10-Day 99% VAR]
1) Variance/Covariance Method - Use historical variances and covariances of risk factors, , to estimate how large 1.645 (for 5%) is for the distribution of .
2) Historical Simulation Method - Take an historical period, say the last 501 trading days, and calculate
Order from highest to lowest and take the 475th as the VAR
3) Monte Carlo Simulation Method - Simulate a set of 500 (for example) by choosing for risk factors ( can be historical or implied from options, are usually historical). Order the from highest to lowest and take the 475th as the VAR.
Even actively traded markets can have “noisy” historical data
Less actively traded markets can pose a significant challenge to finding clean historical data
Historical data can be misleading if a market is maturing over that period
It may be difficult to find historical data in relatively new (e.g., U.K. Asset Backeds) or inactive markets (e.g., inverse I.O.s)
The data for risk factors that are traded against each other (e.g., Mortgages and Treasuries, Futures and Cash Securities, etc.) must reflect simultaneous closes.Obtaining Good Historical Data