Quantitative Risk Management

Notes for McNeil, A.J., Frey, R. & Embrechts, P. “Quantitative Risk Management: Concepts, Techniques, and Tools”, Princeton University Press, 2005, Chapter 1.

Risk is most often understood as a hazard, a chance of bad consequences, etc., or something that is primarily a downside event.  An initial definition might be ‘an action or event that may adversely affect an organization’s ability to achieve its objectives or execute its strategies’.  This does not capture all the essence of risk, however.

Risk is strongly related to uncertainty and therefore to randomness, another term that has defied a very firm universal definition for centuries until Kolmogorov’s axiomatic definition (1933). Kolomogorov’s probabilistic model is a triplet (Ω,F,P), where Ω is a state, F is the set of events, of which P is a member, and P(A) is the probability of event A occurring.

FINANCIAL RISK

In the context of finance and insurance, the most common types of risk include:

• Market risk – the risk of a change in the value of a financial position due to change in its underlying components.
• Credit risk – the risk of not receiving promised repayments.
• Operational risk – risk of losses resulting from inadequate or failed internal processes, people, systems, and external events.

Liquidity risk is the risk stemming from the marketability of an investment, that it cannot be sold in time to prevent a loss or achieve a gain.
The only viable way to achieve successes in financial risk management is through a holistic approach, taking all types of risks and their interactions into account.

Risk measurement. Measuring the risk of a portfolio of X holdings with w weightings requires a distribution function Fx(x) = P(X <= x).

Basel II defines operational risk a the risk of losses resulting from inadequate or failed internal processes, people and systems or from external events.

THE REGULATORY FRAMEWORK OF BASEL II

Basel II released in 2004. Focuses on more risk-sensitive minimum capital requirements for banking organizations, by laying out principles, enhancing transparency in financial reporting

3-Pillar Concept. In Pillar 1, banks are required to quantify their minimum capital charge (regulatory capital) in line with their economic loss potential. There is a capital charge for credit, market, and operational risk. There was no consideration for operational risk in Basel I. Pillar 2 focuses on ensuring there is a well-functioning corporate governance with appropriate checks and balances.  Pillar 3 is about ensuring appropriate public disclosure of risk measures.

Market Risk Capital Charge. Banks are allowed use internal VaR (Value at Risk) models.  Example: A 10-day VaR at 99% for $20 million means there is a 1% probability for the bank to lose at least $20 million by the end of the 10-day period.

Credit Risk. Under Basel I and Basel II, credit risk is assessed as the sum of risk-weighted assets. The risk weight is reflects the credit worthiness of the counterparty.  In Basel I, creditworthiness was crude and allowed only 3 categories: governments, regulated banks, and other.  Hence risk-weighting for all corporate borrowers are the same, independent of their actual creditworthiness.  In Basel II banks can choose to use standardised approaches or more advanced internal-ratings-based approaches.  The new standardised approaches provide substantially more classifications than the old Basel I.

The premise under Basel II is that while individual banks will reduce their credit risk capital charge through internal credit models, the overall size of regulatory capital will remain unchanged.  All agree that operational risk is important, but there is disagreement and uncertainty about how to quantify this risk.

Cooke ratio says that capital should be at least 8% of the risk-weighted assets of a company.

Criticism of Basel II:

• Cost of setting up a compliant risk management system is substantial
• ‘Risk management herding’ could take place.  This is the phenomenon where organizations simply follow the same rules and behave the way during crisis, exacerbating the situation. 
• Overconfidence may come about due to regulation.

Some have raised the notion that regulatory risk management actually makes organisations even more risky.

SOLVENCY 2

Solvency 2 is a review of the capital adequacy of the European insurance industry.  Basel II is aimed to reinforce the soundness and stability of the international banking system.   Solvency 2 is aimed to protect policyholders against isolated bankruptcy of their insurance company.  Basel II addresses systematic risk, Solvency 2 does not (and is not intended to).

Solvency I was very basic and focused on solvency margins. It was not risk based.

Decision on solvency is based on a 2-tier approach. The first level is a target capital, based on risk-sensitive, market-consistent valuation.  Breaching the first level triggers regulatory intervention. The second level is the minimum capital, computed with the old Solvency I rules.

WHY MANAGE FINANCIAL RISK?

Different stakeholders have different interests as to an institutions investment in quantitative risk management.  A balance between the interests have to be sought. Stakeholders can include customers, shareholders, regulators, board of directors, politicians, etc. SOCIETAL VIEW

Modern society depends on the smooth and reliable functioning of the global financial system. There is  a danger of systemic risk.  Modern models attemp to spread out the risk to those most willing and presumably able, to accept the risk. Derivatives are instruments that help to enhance the stability of this system. Challenges of Quantitative Risk Management

It is the large, extreme, unexpected events that form one of the challenges for QRM.  Modelling the expected and normal outcomes may have the advantage of simplifying things but risk understating the risks.

Concentration of risks is about exposure to what was thought to be diversified risks, but which happened to experience simultaneous falls or rises.  It is a case where many things go wrong at the same time.

If a portfolio is too expansive, multivariate models for all risk factors may not be feasible.  QRM needs to be simplified to use broad brush strokes, concentrating on the key features only. This is a problem in scalability of QRM.

Successful QRM requires integration with many disciplines. Understanding QRM requires integrating techniques from various disciplines, such as mathematical finance, statistics, financial economics, and actuarial mathematics.

QRM FOR THE FUTURE

QRM has had an overall positive impact in the insurance and banking industry. Other industries (e.g., car manufacturing) have similar practices albeit called differently (e.g., total quality control).

QRM techniques have been adopted in the transport and energy industries, among others. Electrical power is traded on energy exchanges, derivative contracts are used to hedge price increases. There is debate on how much of Basel II can be transferred to the energy industry.

A new area of application is establishments of markets for environmental emission allowances.  The Chicago Climate Futures Exchange offers futures contracts on sulphur dioxide emissions.

Alternative risk transfer is the transfer of risks between industries.