3. “Global Risk Management: Are We Missing the Point?” Richard Bookstaber, The Journal of
Portfolio Management (Institutional Investor, Spring 1997)
Purpose:
To test the candidate’s ability to define the three primary methods for calculating VAR and assess
the strengths and weaknesses of each method.
LOS: The candidate should be able to
“Value At Risk—New Approaches to Risk Management” (Session 18)
• define VAR;
• compare parametric, historical, and simulation approaches to VAR measurement;
• support and criticize VAR as a risk-measurement tool.
“Value at Risk for the Asset Manager” (Session 18)
• explain the calculation of VAR using the three primary methods;
• describe the strengths and weaknesses of each of the three methods;
• explain the practical applications of VAR for portfolio management.
“Global Risk Management: Are We Missing the Point?” (Session 18)
• comment on the implication of fat tails for risk managers;
• explain how nonlinearity can hide potential risk.
Guideline Answer:
A. Three methods of calculating value at risk (VAR), and their associated strengths and
weaknesses, are:
i. Variance/Covariance Method
Method: The Variance/Covariance Method, which is based on Modern Portfolio Theory and
assumes a normal distribution of returns, involves mapping security positions to a simple set
of instruments or exposures, each of which is affected by only one risk factor. Risk factors
are influences such as interest rates or exchange rates that drive the valuation of securities.
After mapping all positions to risk factors, the expected standard deviation of the portfolio is
calculated based on the historical variance/covariance relationships and weighting of the risk
factors. By utilizing the resulting distribution, the appropriate confidence interval, and the
total value of the portfolio, the portfolio’s VAR can be calculated.
Strengths: Based on the Modern Portfolio Theory, the calculation is relatively easy to
perform and the market data necessary to compute VAR are readily available to the
investment manager. This method does not require powerful computer systems to perform
the calculations, separate valuation models to price the assets or liabilities in the portfolio, or
the actual historical returns of portfolios. Only the values for correlation and volatility are
required.
Weaknesses: Volatilities and correlations are not necessarily stable over time, and the
Variance/Covariance method may assume that such is the case. To the extent that volatilities
and correlations break down (e.g., are not viable in times of market dislocation), the VAR
calculated using the Variance/Covariance approach may not produce accurate forecasts. The
Variance/Covariance VAR calculation may also become cumbersome as the number of risk
factors increases, which may increase the need for computational power in order to run the
calculation. Also, non-normal distributions and lack of serial independence need to be
accounted for using advanced statistical techniques. This method requires the mapping of
the portfolio to risk factors, which subjects the analysis to mismatching and therefore may
produce inaccurate risk characteristics. While non-linear risk can be approximated using the
option delta and gamma, portfolios best suited to this methodology have no optionality.
Finally, the results may not be comparable with other managers or portfolios, because the
assumptions or risk factors utilized may be different.
ii. Historical Simulation Method I
Method: The Historical Simulation Method uses historical market data to calculate the
market value of a portfolio for each day over a specified period of time (e.g., the last 100
trading days). The empirical distribution or ranking of market values resulting from the
portfolio’s calculated marked-to-market values is constructed. The VAR for a specified
confidence level (e.g., 95%) is then determined based upon this distribution.
Strengths: The Historical Simulation Method is easy to understand. It makes no assumptions
about whether returns are normally distributed or whether volatilities and correlations are
stable and does not require statistical estimates of standard deviations, variance/covariances,
and mean return.
Weaknesses: The use of a specified period of trading days of market data may not be
representative of future market movements. The VAR may be over or underestimated
depending upon market history. The investment manager may not be able to value all of the
positions in the portfolio or have access to reliable market data for the calculations. If an
institution has a large or complicated portfolio, it may be impossible or impractical to
maintain historical data on all of the instruments involved. Moreover, historical data do not
exist for many instruments, particularly those that are customized. This method requires the
use of valuation models, which may or may not be complex depending upon the nature of
positions. The method is inflexible, in that it does not allow the analyst to try different
values for volatilities and correlations to test the sensitivity of VAR to these assumptions. In
addition, the VAR is based upon the portfolio’s previous, rather than current, asset mix and
thus may not be representative of the future nor comparable to other managers or portfolios.
ii. Historical Simulation Method II
Method: The Historical Simulation Method entails “simulating” past portfolio returns by
using the returns of factors that influence the value of portfolio instruments. For example,
for a domestic bond, the primary risk factor is the level of domestic interest rates. Risk
factors are modeled based on the current portfolio composition to create simulated portfolio
returns. Then, an empirical frequency distribution is constructed by ranking the simulated
portfolio returns into percentiles; the VAR is determined at the chosen confidence level
given the portfolio’s current value.
Strengths: The Historical Simulation Method makes no explicit assumptions about the shape
of the distributions (e.g., whether or not returns are normally distributed) or whether
volatilities or correlations are stable. This method does not require separate valuation models
to price the assets or liabilities of the portfolio. Market data necessary to compute Historical
Simulation Method VAR should be readily available to the investment manager.
Weaknesses: The Historical Simulation Method is inflexible, in that it does not allow the
analyst to try different values for volatilities and correlations to test the sensitivity of VAR
to these assumptions. It requires the mapping of the portfolio to risk factors, which subjects
the analysis to mismatching and therefore may result in inaccurate risk characteristics. The
process may become cumbersome as the number of risk factors grows. The use of a
specified period of trading days of risk factor data may not be representative of future
market movements. VAR may be over or underestimated depending upon market history. In
addition, managers or portfolios often are not comparable, because the assumptions or risk
factors utilized may be different.
iii. Monte Carlo Simulation Method
Method: The Monte Carlo Simulation Method involves identifying a number of risk factors
that affect the portfolio and constructing a distribution for each risk factor. Using the
distributions, the method generates a large number of possible market scenarios (e.g.,
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