Value at Risk and Historical Simulation Essay

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Q1
Backtesting of VaR models plays a crucial role in portfolio management. Capital serves as a cushion to absorb part of the effect of adverse economic development. Market risk is quantified using the concept of value at risk. It is important for portfolio managers to compute VaR. Backtesting is one of general process of checking whether a model is adequate. Backtesting of VaR model can make sure the VaR model to accurately compute the market risk exposure.

VaR measures the maximum loss in value of a portfolio over a predetermined time period for a given confidence interval. There are three methods to calculate the VaR, which are variance-covariance approach, historical simulation and Monte Carlo simulation. Variance-covariance approach is a parametric method. It is based on the assumption that changes in market parameters and portfolio value are normally distributed. Historical simulation is a non-parametric method and probably the easiest approach to implement. It is simply to use only historical market data in calculation of VaR for the current portfolio. However, the market conditions are not necessary to normally distribute. And forecast future asset prices using historical market data does not necessarily reflect the market environment in the future. VaR methods may not work for accurately computing the market risk exposure.

In order to verify that the results acquired from VaR calculations are consistent and reliable, the models should always be backtested. Backtesting is a procedure where actual profits and losses are compared to projected VaR estimates. If the VaR estimates are not accurate, the models should be reexamined for incorrect assumptions, wrong parameters or inaccurate modeling. For example, if daily VaR estimates are computed at 99% confidence for one year (252 trading days), it is expected to occur on 2-3 VaR violations during this period. If the frequency of VaR violations under backtesting is more than three times, the VaR estimates are not accurate and the model should be correct.

Backtesting & Regulation
The 1988 Basle accord have amended to accommodate the increased importance of market risk. One of the innovative features of the Amendment is that capital requirement are based on banks’ internal risk management models. Banks are allowed to use their own ,purpose-tailored models to compute the capital required rather than use the uniform supervisory approach. Moral hazard problem is the major drawback of the proposed internal model approach. Banks are likely to underreport their market risk under different conditions in order to increase the profit opportunity set. Supervisors have to make sure that banks use an adequate model to meet the regulatory capital requirement. Backtesting procedure is introduced to control this moral hazard problem and keep the financial system stable.

Backtesting of VaR model is a useful measure to monitor the internal model of banks. The backtesting procedure will result in increased capital requirement if the bank underreports their market risk. The bank will have strong incentive to develop good internal model under penalty scheme. The bank should revise its risk management model when number of VaR violations exception is larger than 4 after backtesting.

Q2

The backtesting of the VaR model is under normality and historical simulation, which is 10-day VAR model with 99% confidence level over 253 trading days in 1997. It is expected to occur on 2-3 VaR violations during this period.

There are two VaR violations in the backtesting of the
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