Julien Tattevin, Consultant

Within the large family of bank risks, catastrophic risk is usually considered an operational risk, likely to affect bank business by damaging it physically. A financial institution can also be exposed in a more indirect way, through numerous intermediary connections to the economic system, of which certain sectors are particularly prone to extreme events. The risk is often ignored by banks because of its traditional affiliation with the insurance industry.

Still, the existence of a residual risk has gained ground in bank thinking over the last several years, as catastrophic natural events have become more frequent – among which the violent earthquakes that devastated Haiti and Chili and the windstorm Xynthia that hit the French coast, all of these in only the first part of this year. If the causal relationship with climate change has sometimes been contested, the increase in the density of human activities and in the interdependence among them is sufficient to justify acknowledgment of rising frequency, and leads one to believe that future losses may continue to grow.

The present article offers an analytical and management approach to this risk in the extreme case of a credit portfolio whose borrowers are subject to the same unforeseen event. Our approach is based on a structural understanding of the process by which catastrophic effects spread to such a portfolio. A purely statistical approach does not seem appropriate to the problem, given the few data available and the excessive dependence of results on the specifics of the assets considered.

Risk identification
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Take a loan portfolio having as its counterparty a group of businesses located in an at-risk region and assume that a natural disaster occurs. The most immediate consequence is the partial destruction of the businesses and the cost generated from necessary repairs and replacements. 

These losses are however only the tip of the iceberg: the most significant damage for a business is the disruption to its business activity. The disruption may be both long-term and intense when a region has been devastated by an extreme event. 

Indeed, the normal operating cycle of a business depends on:

> Its capacity to buy the inputs necessary for production and to maintain production using these inputs;
> The capacity of its environment to produce and deliver these inputs;
> The business’s ability to deliver its product to consumers;
> The existence of sufficient demand for the product.

Each of these points may be affected by a natural disaster and impact the bottom line of the firms considered over the entire time it takes for the local economy to recover. 

In short, we have identified two types of losses for each firm: material and operating. Still, these losses do not in themselves seem likely to spread since one would expect them to be completely absorbed by companies’ insurance coverage. In reality, choosing an insurance contract depends on the cost of coverage, on the businessperson’s perception of his exposure and his risk aversion. A poor assessment of potential damages, an erroneous rating, or excessively risky behavior can leave room not covered by insurance. 

In order to select the most appropriate contract and, therefore, reduce residual risk to the utmost, the business should be able to respond to the following questions:

> What types of event (hurricane, earthquake, flood, etc.) should I cover?
> What types of damages (material, operating losses)?
> Up to what amount?
> For how long?

We should emphasize one source of residual risk: the period of time between the occurrence of a disaster and insurance reimbursement is often quite long. If the business does not have sufficient cash on hand or is unable to refinance, it may become illiquid and be forced to declare bankruptcy. In any case, insurance payments don’t instantaneously put the business, its suppliers, and its clients back to where they were before the disaster.

The vector for the spread of these residual losses is therefore the structure of the business balance sheet: as soon as its capital can no longer absorb the losses – or as soon as it lacks liquidity – its creditors start taking a hit in turn, from the standpoint of the protection furnished by the terms and conditions of the debt.

In order to adopt the strategy most appropriate to its situation, the bank holding such a portfolio must be able to quantify the risk to which it is exposed. To that end, in what follows we present a methodology based on the process described above.

Risk quantification
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Methodology

Our methodology is based on a classic breakdown of risk as a function of an unforeseen event and the vulnerability of a system.

An unforeseen event is an event that modifies the state of a system or its environment and is assumed to be independent of this state. Anticipating a natural disaster is almost impossible beyond a very limited window of time. The unforeseen event is thus often described by way of a distribution of probabilities or by way of scenarios that are considered relevant.

The vulnerability of a system expresses the sensitivity of a specific property of the system to an unforeseen event. This formalizes the idea that a similar shock does not necessarily lead to the same damages in two different systems. Determining vulnerability requires detailed knowledge of the system under study – its different components, its environment and their interactions – knowledge gained during the inventory phase. From there, the process by which the unforeseen event spreads to the property under study can be applied.
 

The unforeseen event

An unforeseen event is represented by the geographic distribution of the intensity of physical damage caused, that is, the graph Γ of the function that at a point x in region X combines the percentage yЄY of destruction of physical structures caused by the unforeseen event:

The description of the unforeseen event greatly depends on the nature of the disaster: a tornado is characterized by variables such as maximum sustained wind speed, the trajectory of its center and radius; an earthquake by its magnitude, the location of its epicenter and hypocenter; a tidal wave by the mechanical energy released, its period, its wavelength, the speed of its development, height, etc.

A necessary step therefore entails transforming physical characteristics into a value that can be used in our problem.

Inventory

The purpose of the inventory is to describe, for a system and its environment, everything that seems necessary in order to understand how the system is affected by the unforeseen event under consideration.

In our example, the system is the credit portfolio held by the bank and each title therefore represents an item in it. The description of these items plays out on several levels: beyond the financial attributes of each of the titles (maturity, cash flows, seniority, etc.), they are described according to the business counterparties, the latter in turn described by their location, their balance sheet structure, their insurance coverage, and their production process.

In the present context, the system environment is essentially made up of the economic environment of these businesses. We have represented it according to the production of the sectors that make it up, which allows us to simply model the interactions between the latter by basing ourselves on a regional input/output model. This method is also invaluable for taking account of the resilience of a local economy, as S Hallegatte expertly showed in his article on assessing the economic cost of hurricane Katrina.

Vulnerability

Like risk, vulnerability is a notion that only makes sense once we have specified the unforeseen event likely to cause a major disruption and the property to be protected, which is, in our case, the value of the portfolio.

If we note Π and Π₀, respectively, the current values of the portfolio after the occurrence or non-occurrence of the unforeseen event Γ – putting aside all the other sources of risk to the portfolio – it is clear that the vulnerability of the portfolio is non-existent if, on the one hand, Π = Π₀, and, on the other hand, that it is an increasing function of Π₀ – Π. The function that gives the loss percentage of the portfolio caused by the unforeseen event offers a good example:

We calculate the function by applying the process described above: the balance sheet of each company is reduced due to the destruction of physical assets, their production is affected along with that of different sectors of the local economy, imposing limits on the number of units produced per time interval and taking into account the consequences of these limits in terms of supply and demand, difficulties in input delivery, etc. We then verify that each business is able to satisfy its financial commitments by studying its liquidity and solvency, after accounting for the compensation the subscribed insurance is supposed to pay out in order to deduct the portfolio losses over the period.

We thus repeat the steps, period after period, revaluating each time the Γ variable, considering that the damages caused by the unforeseen event diminish as the physical damage is repaired, until the region recovers to “normal” conditions.

Starting from this υ function and the determination, whether only probable or not, of the unforeseen event Γ, it is possible to have an estimate of the potential losses to the portfolio and, therefore, to develop a strategy for managing this risk.

Risk management
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As soon as a bank has identified its exposure to a risk, it can take measures to reduce it, to contain or transfer it by acting on those parameters of the portfolio it has available.

Among the relevant items enumerated in order to assess portfolio vulnerability, everything touching on the intrinsic operations of businesses and their local economic environment remains exterior to bank’s field of action. The most obvious variables on which it might take action are the very structure of its portfolio and the characteristics of the assets that make it up. It may also be possible to negotiate with providers in order to modify the insurance coverage so that it is the most appropriate to their situation.

Risk reduction

Adapting the contract

In the case where examining the portfolio brings out items in loan terms and conditions that increase its vulnerability, the bank may act on these by renegotiating the contracts with the businesses concerned. Specifically, one could expect significant improvements by integrating, in particular, guarantee clauses of a parent company or the collateral deposit.

Adapting insurance coverage

The insurance coverage to which businesses subscribe may reveal costly flaws should a disaster occur. Vulnerability analysis of the portfolio will bring these to light. They can then also be brought to the attention of the subscribers and prompt them to reconsider their coverage. The creditor can specifically ask them to buy credit insurance if this isn’t already in place.

Containing balance sheet risk

Risk premium

Should it decide to remain exposed to catastrophic risk, whether or not it has taken reduction measures, the bank should nonetheless make sure that the premium paid under the contract is reevaluated in order to account for the new items brought to light through risk analysis.

Portfolio optimization

The portfolio that is to be optimized has a particular characteristic: the very close correlation of its assets with a natural disaster, which arises because of their close geographic proximity. It follows that an effective strategy may require diversifying the portfolio by adding non-correlated or even correlated assets, which is made possible when the bank exposes itself to businesses for which the occurrence of a disaster is unlikely, or even advantageous. This is particularly the case in construction, in the affected region, which always experiences strong demand following such an event.

Risk transfer

Disaster derivatives

In 1995, the Chicago Board of Trade issued disaster options which function according to the following principle: the buyer of the option pays a premium to the seller, who pays him in exchange a certain amount of money when an index measuring the entirety of the losses to the insurance sector exceeds a threshold fixed beforehand. However, these products were dropped in 1999, because the volume on the exchanges was too low and entailed a major liquidity risk.

The scale of damage caused by hurricane Katrina in 2005 renewed interest in natural disaster derivatives. Indeed, the damage, calculated at 79 billion dollars, has given rise to uncertainty regarding the insurance markets capacity to absorb the risk alone; to this uncertainty should be added the desire among investors and manufacturers to effectively cover the volatility tied to their assets’ exposure to “CatNat.” Moreover, this class of assets interests investors in hedge funds as an alternative management instrument uncorrelated to the market.

The last several years have seen the development of hurricane derivate contracts:

> The Chicago Mercantile Exchange (CME) annually issues options and futures for hurricanes hitting the Gulf Coast, indexed on the CHITM index (cf. focus);
> In 2009 Eurex launched standardized futures contracts on insurance losses for different regions in the US;
> The same year, Weather Risk Solutions created Hurricane Risk Landfall Options (HuRLOs) whose underlying is the occurrence of a hurricane that makes landfall in that particular region of the US.

These products don’t all present the same features and the choice of one of them will depend on the specific needs brought to light via portfolio analysis.

The reemergence of hurricane derivative contracts is part of a growing transfer movement to insurance risk financial markets on the part of insurers and reinsurers over the last twenty years through the issuance of products like disaster bonds or cat bonds.

The trend springs from the inability of the insurance market to handle alone the increasingly substantial losses provoked by extreme events. Should this trend continue, one might imagine the creation of a climate and disaster market that would include a larger number of at-risk regions and a larger variety of unforeseen events.

The closer ties between finance and insurance seems to reflect another concern that has come out of the current financial crisis, that of taking better account of complex structural connections that unite finance to the economy and which the theory of financial markets has tended to neglect for the last forty years. The inability of quantitative models to foresee events considered rare but, in hindsight, obvious is a reflection of this. This is why economic fundamentals have to be reintroduced into research programs in quantitative finance •

FOCUS
 

THE CME HURICCANE INDEXTM (CHITM)

The CME Huriccane IndexTM (CHITM) is an index measuring the potential damage caused by a hurricane. It responds to an obvious need to overcome the insufficiency of the current Saffir-Simpson scale. Indeed, the latter provides a granular classification (from 1 to 5) of hurricanes defined uniquely according to wind speed. CHITM, on the other hand, provides a continuous measure defined by wind speed and hurricane radius.

CME contracts are distinguished according to three parameters:
1. The type of contract,
2. The calculation method of the underlying index,
3. The region concerned.

We thus find futures, options, and binary options, split into three large families:
1. Named Storm Contracts which deal with the CHITM of an individual hurricane;
2. Seasonal Aggregate Contracts whose underlying is the cumulative CHITM of hurricanes studied over a year;
3. Seasonal Maximum Contracts, indexed according to the maximum CHITM observed for the season.

Finally, the contract concerns the CHITM considered during hurricane landfall in a specific zone on the Gulf Coast or, in the case of the Cat-In-A-Box zone, the CHITM observed during the occurrence of a hurricane in this area.

Title : Zones covered by CME hurricane contracts

Source : “Parametric Hurricane Contracts. The Carvill Hurricane Index and the Chicago Mercantile Exchange” published by Carvill Reinsurance Company