The Mathematics of Financial Modelingand Investment Management

23-RiskManagement Page 746 Wednesday, February 4, 2004 1:13 PM

746 The Mathematics of Financial Modeling and Investment Management

The basic idea of RiskMetrics is to represent the entire set of returns

and rates as a multivariate normal variable. In other words, RiskMetrics

is made up of a simple linear model with some robust estimation tech-

nique. JPMorgan provided daily the estimates of volatilities and correla-

tions essentially using empirical volatilities and correlations. Over the

years the initial model has been extended to cover more complex cases, in

particular derivative instruments. A suite of models for banks and asset

managers is commercialized by The RiskMetrics Group.

Multifactor models are often used to evaluate the market risk of

equity portfolios. Commercially available models such as Barra or APT

are now in use at many asset management firms to evaluate market risk.

However, if portfolios include derivative instruments, multifactor mod-

els must be completed with additional modeling tools able to capture

the behavior of these instruments.

Risk models are often based on the idea of creating a relatively small

number of scenarios, that is, paths of the key financial and economic

variables. The Toronto-based firm Algorithmics pioneered the use of sce-

nario-based risk management as a commercial software implementation.

Credit Risk

Credit risk models are inherently more complex than market risk mod-

els as the normal distribution is not a good approximation of default

distributions. A number of models have been proposed, in particular

CreditRiskMetrics from the RiskMetrics Group. This model is based on

an underlying process for ratings. Credit Suisse proposed an actuarial

credit risk model, Creditrisk+ that represents default distributions as a

mixture of Gaussians. Models of credit risk based on option theory have

been proposed by the firm KMV which is now part of Moody’s.

Kamakura Corporation has proposed models of credit risk based on the

work of Robert Jarrow. Credit risk models were covered in Chapter 22.

Operational Risk

Operational risk can be broadly defined as risk related to processes; it

generally falls under the responsibility of internal auditors or their

equivalents, but in a number of instances it is under the responsibility of

the risk manager. Determining its contribution to portfolio risk varies

from firm to firm. Some firms attribute to human error (e.g., changing

the benchmark and not informing) up to 75% of portfolio risk.

Large investment banks such as the former Bankers Trust and Credit

Suisse First Boston pioneered a quantitative approach to operational risk

several years ago, but the data problem is more severe in asset management