“GLOBAL RISK MANAGEMENT

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.,