10,000) that are consistent with expected volatilities and correlations. While each scenario is
different, the total simulations will aggregate to the overall statistical parameters chosen at
the outset. The portfolio positions are revalued under each scenario resulting in distributions
of market value changes. VAR is derived from the distribution produced by the Monte Carlo
simulation analysis and the portfolio value.
Strengths: The Monte Carlo approach makes no set assumptions about linearity, normality,
or position relationships. It is a powerful approach, in that it is not constrained by
assumptions about asset returns and generates many more scenarios than the Historical
Simulation method.
Weaknesses: The Monte Carlo approach requires considerable computer power. The greater
the number of risk characteristics in the portfolio, the greater the number of scenarios
required. It requires sophisticated mathematical modeling and its results are only as good as
the underlying assumptions. In addition, managers or portfolios often are not comparable,
because the assumptions or risk factors utilized may be different.
B. The two consultants may obtain dramatically different VAR results for several reasons; the
consultants may have:
• used different past time periods over which the simulations were run.
• used different models, including different assumptions about pricing, distributions, and risk
factors in the simulations.
• used different distributions to drive the simulation process. Normal distributions, lognormal
distributions, t-distributions, or actual historical distributions could be used to produce the
simulations, each resulting in different VARs.
• used different statistical parameters to drive the simulation process. Different empirical
inputs—means, variances, and correlations—can have dramatic consequences, including
markedly different VARs, for the simulation results.
• used different “risk factors” to model the portfolio. For example, if one consultant used the
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