Practical Problems with Building Fixed-Income VAR Models

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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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### Practical Problems with Building Fixed-Income VAR Models

Rick KlotzManaging Director Global Head of Market Risk ManagementGreenwich NatWest

Value At Risk: Definition

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

Visualizing VAR: An Example

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.

VAR and Capital Requirements For Banks

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]

Back-Testing A VAR Model
• Calculate 1-Day 95% VAR for a (changing) portfolio each day for some substantial period of time (e.g., 100 Days)
• Compare the P/L on the succeeding trading day with the previous close of business day’s VAR
• Count the number of times the loss exceeds the VAR
The Need For VAR Model Accuracy
• If the VAR is systematically “too low”, the model is underestimating the risk and you tend to have too many occasions where the loss in the portfolio exceeds the VAR. This can lead to an increase in the “multiplier” for the capital calculation.
• If the VAR is systematically “too high”, the model is over estimating the risk and your regulatory capital charge will be too high
• Estimate the change in the value of the portfolio P, as a function of the change in the value of risk factors , . . ., (e.g., , may be the change in 1-year U.S. interest rates, may be the change in 2-year U.S. interest rates, etc.).

Example:

Building A VAR Model: Basic Methodologies

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 .

Building A VAR Model: Basic Methodologies

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

Building A VAR Model: Basic Methodologies

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.

General Challenges for VAR Models
• Obtaining Good Historical Data
• Finding a “complete” set of risk factors - fixed income VAR models generally miss bond specific information (e.g., issuer specific risk)
• How to weight historical data to accurately determine a 1-day VAR.
Poor Data

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

Missing Data

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)

Asynchronous Data

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
Finding a Complete Set of Risk Factors
• Fixed Income VAR models generally miss bond (even market) specific information