Japan that the financial market crisis has had a devastating effect on the economy. Elsewhere there does not seem to be a strong connection between crises in financial markets and the risk to the real economy. Thus the main sufferers are the investors. For example, in 1998 the Long Term Capital Management (LTCM) company, whose shareholders included some of the most successful Wall Street traders and most respected Nobel Prize winners, had debts of the order of $100 billion and extraordinarily highly leveraged positions amounting to approximately $1 trillion. Unfortunately, their mathematical models (which had been beating the markets consistently for a number of years) could not cope with the totally unexpected Russian debt crisis and did not prevent them from huge illiquid exposures in other markets. The US Federal Reserve bailed them out at a cost of $3.5 billion. But most of the losses were borne by LTCMs shareholders and investors.

During the last decade many banks and securities houses have also experienced very large losses. These have often been attributed to fraud, bad management or poor advice, and it is hoped that the institutions concerned will not repeat the same mistakes. But the scale of these individual losses should be put into perspective, when it is considered that the value of large multinational corporations could change by similar amounts in the course of a normal days trading on the stock market.

The forces behind the measurement and control of financial risk are, therefore, extremely strong. There are internal forces to gain the optimal return on capital (where capital is risk-based) and to ensure the survival of a firm as a whole. There are external forces that are driven by competition, by the enormous growth in the risk management industry and by the increased volatility of financial markets, with new products that enable participants to increase leverage to very high levels. And there are regulatory forces to promote fair competition between firms, protect the solvency of financial institutions, and control systemic risk.

The scale of these individual losses should be put into perspective, when it is considered that the value of large multinational corporations could change by similar amounts in the course of a normal days trading on the stock market

9.1.1 The 1988 Basel Accord and the 1996 Amendment

Three main tools are available to regulators for the measurement and control of financial risk: minimum risk capital requirements; inspections and reporting requirements; and public disclosure and market discipline. This section concerns only the first of these three pillars of regulation, the minimum risk capital requirements that are imposed by the regulatory body. The discussion focuses on the Basel Accord of 1988 and its 1996 Amendment which, though only formally adopted by the G10 countries, have had an enormous international influence.

The 1988 Basel Accord linked minimum capital standards to credit risk, and this was extended to market risks in the 1996 Amendment. The basic principle

of the 1996 Amendment is to measure regulatory capital by a minimum solvency condition, the Cooke ratio. This is the ratio of eligible capital to risk-weighted assets, where eligible capital is the sum of tier 1 (core capital), tier 2 (complementary capital) and tier 3 (sub-supplementary capital), and risk-weighted assets are the sum of a credit risk capital requirement (CRR) and a market risk capital requirement (MRR).

Regulators currently favour placing transactions in the banking book, where securities attract a CRR

Credit risk requirements apply to all positions except the equity and debt positions in a trading book, foreign exchange and commodities. At the time of writing the CRR is simply calculated as a percentage of the nominal (for on-balance-sheet positions) or a credit equivalent amount (for off-balance-sheet positions).3 Regulators currently favour placing transactions in the banking book, where securities attract a CRR (the banking book CRR is very broadly defined to compensate for the lack of MRR). In particular, the current method used to calculate the CRR provides little incentive to diversify a portfolio or to employ other risk mitigation techniques. However, the Basel 2 Accord that is currently under discussion will define new rules for calculating the CRR, for implementation by G10 banks in 2005.

The MRR applies to all on- and off-balance-sheet positions in a trading book. It is necessary to mark positions to market, which is easily done in liquid markets where bid and offer prices are readily available. Otherwise it is acceptable to mark the portfolio to a model price, where the value of a transaction is derived from the value of liquid instruments, or to make a liquidity adjustment that is based on an assessment of the bid-offer spread.

The standardized approach is to sum the MRRs of positions in four different categories or building blocks: equities, interest rates, foreign exchange and gold, and commodities. In each block the total MRR is the sum of general and specific risk requirements that are percentages of the net and gross exposures, respectively; these percentages depend on the building block.4 The minimum solvency ratio that has been set in the 1988 Accord is 8%. That is, the eligible (tier 1, tier 2 and tier 3) capital of a firm must be at least 8% of the sum of the MRR and CRR. In this way the regulator protects the solvency of a firm by tying its total risk exposure to its capital base.

9.1.2 Internal Models for Calculating Market Risk Capital Requirements

The 1996 Amendment outlined an alternative approach to measuring the MRR, which is to use an internal model to determine the total loss to a firm when netted over all positions in its trading book (§9.1.2). Internal models for measuring the MRR must determine the maximum loss over 10 trading days at

3This percentage is determined by the type of counterparty.

4 For example, in equities the general MRR is 8% of net exposure and the specific MRR is often 8% of gross exposure.

a 99% confidence level. They are subject to some strong qualitative and quantitative requirements. Qualitative requirements include the existence of an independent risk management function for audit and control, a rigorous and comprehensive stress testing program on the positions of the firm, and on the IT and control side the MRR model must be fully integrated with other systems. Quantitative requirements include frequent estimation of model parameters, separate assessment for the risks of linear and non-linear portfolios, rigorous model validation techniques, the use of a minimum number of risk factors and a minimum length of historic data period.

Although these models can be based entirely on scenario analysis (§9.6), many firm assess their MRR using a VaR model. VaR has been defined as the loss (stated with a specified probability) from adverse market movements over a fixed time horizon, assuming the portfolio is not managed during this time. So VaR is measured as a lower percentile of a distribution for theoretical profit and loss that arises from possible movements of the market risk factors over a fixed risk horizon. To see this, first note that the loss (or profit) for a portfolio that is left unmanaged over a risk horizon of h days is

= +ft ~ Pf

In other words, AhP, is the forward-looking A-day theoretical (or unrealized) P&L, that is, the P&L obtained by simply marking the portfolio to market today and then leaving it unchanged and marking it to market again at the risk horizon. We do not know exactly how the underlying risk factors are going to move over the next h days, but we do have some idea. For example, we might expect that historical volatilities and correlations would remain much the same. The possibilities for movements in risk factors can be summarized in a (multivariate) distribution, and this in turn will generate a distribution of AhP„ as each set of possible values for the risk factors at the risk horizon are entered into the pricing models for the portfolio, weighted by their joint probabilities.

The significance level of VaR, that is, the probability that is associated with a VaR measurement, corresponds to the frequency with which a given level of loss is expected to occur. Thus a 5% 1-day VaR corresponds to a loss level that one expects to exceed, in normal market circumstances, one day in 20. And a 1% 1-day VaR is the loss level that might be seen one day in 100.5 Now the definition of VaR above can be rephrased as follows: the 100a% h-day VaR is that number x such that the probability of losing x, or more, over the next h days equals 100a%-in mathematical terms,

the 100a% A-day VaR is that number x such that Prob(AAP, < -x) = a.

Sometimes we use the notation VaRa h to emphasize the dependency of the VaR measurement on the two parameters a, the significance level, and /?. the holding period. Thus,

These are also called the 95% and 99% VaR measures, but no confusion should arise.