Tuesday, June 5, 2012

Pricing the probability of a rare event


This article appeared in The Edge in April 2012
By Jasvin Josen
In the previous article, I mentioned the convenience of utilising cat bonds to distribute catastrophic risk out of the insurance industry. The market for cat bonds however has not taken off very satisfactorily and I cited some research that attempted to understand investors’ reluctance to invest in this product. In a nutshell, investors find high loss and highly improbable events, very unsettling.
In this article, I describe the expected loss and some basic thoughts in pricing the probability of a rare event.


Underlying behavioural economics
The catastrophic market has quite a different underlying behavioural profile compared to financial markets: Financial markets are affected by human sentiment, which at times could be irrational. Crowd dynamics are important. But in the catastrophic market, hurricanes and earthquakes do not exhibit crowd behaviour. There is a true underlying risk that one must comprehend.

Understanding Expected Losses
Chart 1 shows a typical probability statistic for catastrophic risk. The probability for trivial losses is much higher compared to the probability for excessive losses close to the “tail”.

Chart 1 – Expected Losses from Catastrophes
Source: The Garnaut Climate Change Review, Australia

Pricing the tail risk
When hurricane insurance premiums skyrocket after a big storm, then settles back down, this is a sign that the market is not assuring investors. The tail risk is not priced well enough.
Chart 1 shows that the tail is also getting “fatter” and “longer” i.e. rare events are getting more frequent and more severe. The present market essentially have to deal with two contradicting issues; pricing the tail correctly and at the same time, appreciate that more loss is accumulating in the tail.

Michael Lewis, in his article called “the Nature’s Casino” [The New York Times, Aug 2007] talked about a hedge fund manager, John Seo, who justified why traders should not be charging excessively for catastrophic protection.

Say an investor wanted to buy $1 billion of insurance for a year against a once-in-100-years stock-market crash. The expected loss would be 1 in 100, 1 percent of $1 billion: $10 million. The insurance would cost $40 million to $50 million because the market tended to charge four or five times the expected loss.

The hedge fund manager had a request from a client. It operated factories in Japan and California, both near fault lines. It could handle one of the two being shut down by an earthquake, but not both at the same time. The client wanted a price for an option that would pay the company $10 million if both Japan and California suffered earthquakes in the same year.

The manager could have simply called an insurance company and buy $10 million in coverage for the Japanese quake and then another $10 million in coverage for the California quake; the going rate was $2 million for each policy. He then could have lazily charged $4million to the client for this option.
But he had a better solution. He bought just enough Japanese earthquake insurance that would make a payout of $2m in case of a disaster. If a disaster also strikes in California, he could use the first payout of $2m as the premium for the Californian policy and receive a payout of $10m to pay the client. His revised cost was now down to a mere $400,000. Anything above that was pure profit.

If we take this one level further…

The quakes being insured against were once-a-decade events. But since each earthquake had a 1-in-10 chance of happening in a year, the chances that both of them would occur were far more remote: 1 in 100 (10 percent of 10 percent). Basically here, we are pricing a tail event.
Thus the hunches of Wall Street practitioners were not quite right previously. The expected loss of the more ordinary risk of a single earthquake was $1 million (a 10 percent chance of a $10 million loss). The expected loss of the remote combined risk was only $100,000 (a 1 percent chance of a $10 million loss).
According to Lewis, the hedge fund manager’s math served two purposes: “to describe this universal rule about the pricing of risk and to persuade investors that there was a deeper, hidden logic to investing in catastrophe”.

Models have blind spots
The above-expected losses rely heavily on the fundamentals of catastrophe modelling. The models failed to predict the New Orleans disaster even though they were equipped with an imaginary 100,000-year history of hurricanes.
Recently, there has been an effort to create and circulate open multi-hazard cat risk modelling tools, according to Alliance for Global Open Risk Analysis (AGORA).

As disasters get more frequent…
Agencies like S&P and Moody’s that rated the insurance companies rely on the catastrophic models to evaluate their exposure. When the scientists increases the likelihood of catastrophic storms, the rating agencies will demand that the insurance companies raise more capital to cover their suddenly more probable losses.
For example, if the probability of hurricanes now have doubled compared to before 2000, an insurance company that lost $40 billion in the Hurricane Katrina, now has to raise $82 billion from their shareholders just to keep their investment-grade rating. This could explain why some insurance companies have sneaked out of giving protection on these tragedies. The action of the European Directive, Solvency II to encourage mitigation of this risk via securitisation could very well be passed to dampen the unhealthy reaction of insurance companies.

What about Asia?
Asia is equally exposed and has had experienced major losses from catastrophic events in recent years. In 2011, 70 percent of total catastrophe events were associated with events outside of the U.S.[http://www.gccapitalideas.com]
Other than Japan, there is a lack of insurance penetration across the rest of Asia. Reports show that countries such as China, Indonesia, the Philippines, Malaysia, Thailand and Vietnam have very low levels of insurance, typically around 15%. This means reinsurance levels are low too.
As countries develop and their economies and industry grow, there will be a natural need to transfer risk. The disparity between the significant exposure to catastrophe and low insurance levels will need to correct itself.

Conclusion
As natural disasters start looming across the planet more than ever before, there will be a major drive to share the risk in the wider financial market through securitisations. Cat bonds and other weather derivatives may soon become more widespread in the market, initiated by the regulators or the market players themselves. 

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