Market Risk Measurement in Context

by Eben Maré, Associate Professor, Department of Mathematics and Applied Mathematics,

Traditionally, market risk is defined as the risk of losses in on- and off-balance sheet exposures as a result of market movements. The market events surrounding the 2008-credit crisis force us to have a deeper understanding of market risk and its effects on our enterprise. The aim of this short article is to present the market risk process and to present its (frequently misunderstood) measurement metrics.

Risk management process

Figure 1 illustrates the market risk management process.

Firstly, risk identification looks at the sources of market risk in our business. This entails understanding our income statement and balance sheet and the source of any changes to these. As part of this process we need to consider carefully how we value any financial instruments directly or indirectly. Direct valuation would pertain to holdings in shares and physical assets, for example, whereas indirect valuation would pertain to embedded derivatives.

Monitoring and control of exposures ensures that identified and measured risks conform to the stated risk appetite of the organization.

The second step relates to measurement metrics. This entails quantifying our exposure to moves in the market, i.e., what is the monetary effect of a move in the underlying on our business? We provide a detailed discussion of typical metrics, namely, Value-at-Risk and Stress Testing, in the next section.

Monitoring and control of exposures ensures that identified and measured risks conform to the stated risk appetite of the organization. Attaching a metric to identified risks means that we have a sense of the economic damage that could be caused as a result of that risk. We would therefore impose a limit on the risk to ensure adequate control. We would monitor actual exposure against the limit periodically (typically on a daily basis). Exposures above our limits would be reported to senior management and a process would be enacted to ensure the exposures are reduced to within the agreed levels.

The last step of the process is highly important but frequently neglected. How do we test whether our market risk management metrics and controls are working? We need to substantiate our metrics and back-test these to the actual statements of profit and loss on a periodic basis to ensure that we have not overlooked any sources of risk, no matter how small they might seem. [[[PAGE]]]

Risk measurement

A frequently used measure of risk in a portfolio is the so-called Value-at-Risk (VaR) metric. VaR is broadly defined as the loss (stated within a specific probability) from adverse market movements over a fixed time horizon (assuming no management action).

Let us illustrate the VaR concept with an example. Suppose we hold a R1bn investment in the FTSE/JSE TOP40 index. We revalue the position using historical moves based on weekly closing data from the start of 1999 to present. A graph detailing the profit/(losses) is shown in Figure 2 – the VaR of the portfolio, denoted by the dotted red line, amounts to R59.2m with 95% confidence, i.e., estimated on this historical basis we are 95% certain that the maximum loss of the portfolio would be R59.2 on a weekly basis.

Stress testing is especially important after long periods of benign economic and financial conditions.

There are several methods that we can use to estimate VaR. We illustrated the use of the so-called historical simulation method in our example. Also frequently used is the Variance-Covariance approach (initially described and applied in the J.P. Morgan Risk Metrics approach). We could also use Monte Carlo simulation to estimate the VaR – this entails an assumption of future asset price movements to generate potential profit/(loss) scenarios.

VaR is a risk measurement tool but it is not a universal panacea. VaR has the benefit of capturing risk inherent to our business as a single number but unfortunately, as a result of assumptions or methodology, fails to provide the full extent of losses  which could hit our business in bad times.

Any risk measurement process therefore needs to be augmented with a set of tools that would describe the effect of disastrous market events on our business. We call these stress tests.

Stress tests are designed to evaluate the effect of unusual events on our business. It could entail simulating shocks that we suspect are more likely to occur than suggested by history, simulating shocks which have never occurred, examining the effect of structural breaks which could occur in the future.

There are three principal methods used to create scenarios for stress testing, namely historical stress testing, predefined scenarios and mechanical search tests.

Historical stress testing uses market upsets that have already occurred. Examples include the 2008 credit crisis, the 1987 stock market collapse, the European exchange rate mechanism breakdown in 1992 and so forth. In historical scenario analysis the price changes that occurred during the specified events would be applied to current market prices to create a set of new prices against which the portfolio would be revalued.

Scenario analysis works on the same basis as historical stress testing although the scenarios used are hypothetical. Scenarios could assume an extreme event or a shock to a specific risk factor using a user  specified amount. Alternatively one could also consider an external factor shock (using a macro-economic series or any index) and estimate specific risk factor returns based on the shock.

Mechanical search tests would specify shocks to arbitrary factors and revalue the portfolio using these. The main aim here is to search for exposures without specific recourse to history or judgement.[[[PAGE]]]

Stress testing is especially important after long periods of benign economic and financial conditions. During these the fading memory of negative conditions easily leads to complacency and under-pricing of risk. Stress testing is also a key risk measurement tool to be used during periods of expansion when new product innovation leads to complexity that should be evaluated without data.

It should be clear from this description that stress testing provides useful information about a firm’s exposures that VaR methods typically will not provide. This information is essential for the risk management process but also useful in capital planning, strategic planning, hedging and other major decisions taken by the firm.

Care should be taken with stress testing given that it is subjective by design. This creates some problems for risk managers who need to choose which set of risk exposures to ‘believe’. It is therefore important to ensure that stress tests are designed to be plausible and to ensure that the whole firm understands the relevance of specific tests in the total risk measurement process.

Recent lessons

The events of 2008 have highlighted certain shortcomings within traditional market risk measurement approaches. We highlight some of these problems below.

• Stress testing should form part of the internal risk management debate and results should be challenged at all levels of the organization.

• Risk measurement should take account of liquidity effects such as the speed at which positions could be liquidated or hedged.

• We need to understand that historical relationships could break down completely.

• Stress tests need to incorporate the behavior of complex structured products under stressed liquidity conditions.

• Stress tests need to take account of basis risk in relation to hedging strategies. An example would be the interest rate swap curve versus the government bond curve. Frequently stress tests would work on the basis of a parallel move in interest rates but ignore the difference between these curves and resulting corporate bond curves, the results would neglect basis risk which could amount to significant losses.

• Contingent risks and funding liquidity risks need to be understood and form part of any stress measurement exercise.

• We need to take a longer-term view into account in stress models as well. As an example the U.S. market lost 86% of its value during the depression years although the maximum loss in any one day was limited to approximately 10%.

Conclusion

In this short article we have attempted to explain typical market risk measures and place these in context of the total market risk management process. Market risk management is a process. This process depends on the measurement and identification of risks. Measurement and management of risk is frequently understood to be the same thing which it clearly is not. The 2008 credit crisis has taught us that we need to understand the complex interactions between different risks in our businesses better; reliance on one specific number or measure is not enough!