Wednesday, July 17, 2013

Subsidy?


Recently, the politicians and the news have been awash with claims of a subsidy for flood risk provided by the National Flood Insurance Program (NFIP).  Similar sorts of claims have been and continue to be made about a subsidy for Florida hurricane risk.

But, how would you know a subsidy exists? What standard of comparison would you use? Is the existence of a subsidy dependent on perspective?

A classic measure of risk is average loss.  Traditionally in insurance this was called the pure premium- the sum of all losses over the number of years represented in the loss data. With the welcoming of catastrophe models, the pure premium became better known as the average annual loss (AAL).  The AAL is similar but different to the pure premium.  The AAL is calculated by multiplying the probability of a certain size loss times the loss, then adding all those up.  This is done for an entire model's event catalog.

Above is a graph comparing the estimated annual Florida hurricane loss by model type.  The first three estimates are pure premiums found using a commercial company catastrophe model for the all lines industry portfolio for Florida.  From left to right, the first two differ only by the inclusion of storm surge and run on a "stochastic" or "near term" catalog. The third is the company's FCHLPM approved model which means it has a "historic" catalog.  The final estimated is the AAL for normalized Florida historic event economic losses.  These were gathered from here.  Economic losses divided by two is a standard way to estimate insured losses.  One thing to note, all but the historic AAL includes estimates for demand surge.

In both 2011 and 2012 Citizens, alone, brought in about $2.2 billion in earned premium (written was similar).
 
There are, of course, many reasons not to rate and price insurance solely on the AAL or pure premium.  But, choosing one estimate of risk over another, particularly an estimate other than a historical average, represent hedges. There are tradeoffs in doing this. The table below shows each model's annual loss estimate compared to the normalized historic loss events. (There are some caveats for event loss versus loss year but this is fine for demonstration purposes).  Consider the annual loss estimate to be a prediction which will rarely if ever be spot on, but will come in too high or too low compared to the observed event.  The table demonstrates tradeoffs and compromise in the political process of ratemaking.
 

For example, using the pure premium from the Historic model, policyholders would be paying too much 68% of the time but too little 32% of time.  When policyholders are not paying enough to cover losses, insurers are burdened with the risk of running a deficit.  In comparison, using the Wind model, policyholders pay too little 13% of the time but too much 87% of the time.  This scenario sees insurers’ decreasing the probability of not having enough money for a loss and increasing profitable years, but it also increases the frequency that policyholders pay more than they needed.  Interestingly, the Wind +Surge model estimates a larger pure premium than wind alone, but with no change in the number of times the estimate comes up too high or too low.  It would seem that there is no added advantage, however, consider that the insurer is making a little bit more every time the estimate proves too big.  Given that policyholders do not want to pay more than they have to for their coverage, an 11-71 split will appear undesirable to purchasers of insurance.  Thus, the Approved FCHLPM model represents a compromise.

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