How much will TWIA pay on losses?

How much will TWIA pay on losses? With the information about reinsurance discussed yesterday, we now have a pretty good sense of what the Texas Windstorm Insurance Association’s finances are going to look like this summer. This lets us build an interactive property insurance calculator for Texas. Yes, if there’s a special session, all of this could change, but unless there is a special session and the bill that emerges out of it passes by a two thirds vote of both Houses, it won’t take effect until deep into this hurricane season anyway. So, in the mean time, what I’m about to show should be quite useful. It’s an interactive property insurance calculator for Texas that lets you see how much your claim against TWIA might be worth.

If you install a CDF player, which you can get for free right here, you will have an interactive widget appear below that produces a pie chart showing the percent of claims that TWIA will be able to pay (green) and the percent that it will not (red).  You get to vary the size of the Catastrophe Reserve Trust Fund, the amount of Class 2 (or Class 2 alternative bonds) TWIA will sell, and, if all the Class 2 bonds are sold, the amount of Class 3 bonds that will sell.  You also get to choose the size of the loss TWIA will face. Or, if you want to watch a movie that shows how the percentages are affected by varying these parameters, click the little arrow in the top right of the widget. The output is an easy to read pie chart that shows how much TWIA will be able to pay.

[WolframCDF source=”” width=”600″ height=”515″ altimage=”” altimagewidth=”553″ altimageheight=”580″]

For those who don’t want to install a CDF player, here’s a snapshot showing some sample output.

An example of how much TWIA might pay: output from the interactive property insurance calculator for Texas

An example of how much TWIA might pay

An analysis of S.B. 1700 and H.B. 3622

Note: I’ve taken a second look at this bill and done a better job in analyzing it. Look here.

S.B. 1700 from Senator Larry Taylor of  Friendswood and its House cognate, H.B. 3622 from Representative Dennis Bonnen of Brazoria/Matagorda are the only bills among the major contenders in the legislature this session that addresses the short run problem with the Texas Windstorm Insurance Association.  And H.B. 3622 is set for a hearing in the Texas House Insurance Committee this April 30, 2013, at 2 p.m.  As with H.B. 2352 from Representative Todd Hunter and its cognate S.B. 1089 from Senator Juan “Chuy” Hinojosa, however, the Taylor/Bonnen bills prop up TWIA largely with money from people other than TWIA policyholders. In this instance, the entities that pay for much of the windstorm risk on the Texas coast are (1) Texas taxpayers via a reduction in otherwise owing premium tax revenue and (2) owners of insured homes, autos and other insured property (or liability insurance) throughout Texas via an assessment on insurers likely to be passed on in higher premiums. Here’s a legislative analysis.

The key to S.B. 1700 and H.B. 3622 is to make sure that no storm that causes less than about $1 billion in losses to TWIA needs to try to use post-event Class 1 Bonds to pay claims — a good idea considering that these bonds have been found to be unrateable and probably could not be issued in a large amount. Right now, it only takes a storm causing more than $180 million before TWIA will first look to Class 1 Bonds in order to pay claims. The padding between storms and the tenuous Class 1 Bonds is, at least for the 2013 hurricane season, not additional money from TWIA policyholders but instead an assessment on property and casualty insurers statewide. This assessment could be up to $800 million.

The bill softens the blow of this $800 million exposure in two ways.  First, up to $300 million of such an assessment could be credited against premium taxes the insurers would otherwise owe to Texas.  This crediting would take place in installments, however, lasting a minimum of 5 years.  Thus, in essence, Texas insurers are compelled to fork over up to $500 million and to front an interest-free $300 million loan to the state in order to pay clams.  (And even if they never pay, they will have to stockpile some reserves to address this contingent liability.) I have suggested elsewhere that it would insult the insurance industry to suggest that they will not find a way to get this money back. An obvious target will be Texas policyholders. Second, for each dollar the insurers pay at the lower attachment point (just above the end of the Catastrophe Reserve Trust Fund) they reduce the exposure they now have at a higher attachment point, one that lies above the top of the Class 2 Bonds or the Class 2 Alternative Bonds.  And the insurers no longer have to really pay fully for Class 3 assessments. Instead, up to $300 million, they just make an interest-free loan to the state that gets paid back over a minimum of 5 years via a reduction in otherwise owing premium taxes.

Here’s an interactive visualization of the effect of S.B. 1700. You’ll need to obtain and install the free CDF player to actually be interactive with this medium.

[WolframCDF source=”” CDFwidth=”560″ CDFheight=”800″ altimage=””]


So, if I had to guess at the realistic size of the TWIA stack today, I would say it was perhaps  $600 million: $180 million in CRTF, perhaps a sale of 25% of the amount authorized in Class 1 Bonds, and perhaps 25% of the amount authorized in Class 2 Alternative Bonds. If S.B. 1700 were to pass, the stack would grow to perhaps $1.5 million: $180 million in CRTF, $800 million in insurer assessments (some of which would just be an interest free loan), and, again, perhaps  sale of 25% of the amount authorized in Class 1 Bonds, and perhaps 25% of the amount authorized in Class 2 Alternative Bonds. Due to the bug in the existing statute — one that is not (yet) fixed in the Taylor bill — it’s my opinion that no Class 3 securities are likely to be issued. I also have doubts that useful reinsurance can currently be purchased by TWIA due to confusion about the appropriate attachment point.

A few additional comments.

1. I’d like to run analysis similar to that done on H.B. 2352 about how much of the expected risk of tropical cyclones is born by each group under S.B. 1700 and H.B. 3622. My suspicion is that a great deal will be borne by insureds statewide due to the low assessment attachment point. A great deal will be eaten by TWIA policyholders themselves in uninsured losses because, unless pieces of the statute are fixed, the realistic height of the stack is not the touted $4 billion but a number far lower than that.  In other words, S.B. 1700 and H.B. 3622, though they raise the height of the TWIA stack, still leaves a substantial risk of insolvency.

2. The bill has a provision I like: it prohibits TWIA from purchasing reinsurance with low attachment points.  This prohibition prevents TWIA from deciding to sacrifice policyholder interests in favor of insurance company interests.  How to trade these two interests off is a matter that should be resolved, as this bill does, by the legislature.

3. This bill does nothing to address major structural problems with TWIA.  These include:

  • low deductibles and no coinsurance that lead to problems of moral hazard
  • failure to warn TWIA policyholders about the risk of insolvency
  • continued subsidization by poor people throughout Texas of million dollar homes on the Texas coast
  • continued concentration of risk in a single entity that invariably leads to a difficult tradeoff between paying extremely high rates for reinsurance — and thereby preventing growth of an internal catastrophe reserve fund — or subjecting policyholders to a substantial risk of insolvency
  • fails to address the needless fragility of Class 3 Bonds. [This is not right, see my update]




A simulation of H.B. 2352 and S.B. 1089

H.B. 2352, a bill to reform the Texas Windstorm Insurance Association (TWIA) from Corpus Christi Representative Todd Hunter, is scheduled for hearing in the Insurance Committee of the Texas House this Tuesday afternoon at 2 p.m. I do not know yet if my teaching obligations will permit me to travel to Austin and testify, but if they do, here is about what I will say. It’s based on a Mathematica simulation of 100 sets of 100 years of storms and draws on work I’ve discussed here, herehere and here.

My name is Seth Chandler. I am a law professor at the University of Houston Law Center and author of the blog, which addresses the law and finance of catastrophic risk with a focus on Texas. The views expressed here are my own and do not necessarily reflect those of the University of Houston.

I have attempted to simulate the effects of H.B. 2352 and its companion bill S.B. 1089. The details of that simulation, including the source code, are available in the written submission made to the committee and available at Basically, I have run 100 100 year storm simulations using models calibrated to mimic those used by AIR and RMS, the two leading modeling companies on which TWIA has relied. Should members of the committee or staff have any questions on the technical details of the model or how variants of the law would affect the conclusons here, I am willing to try to assist.

Based on that research I find that over the initial 20 years of H.B. 2352 with a runoff, and assuming TWIA does not purchase reinsurance, TWIA policyholder premiums will cover about 68% of the losses suffered during that time period. The remaining losses will be paid 6% from replenishment of the catastrophe reserve fund, 8% from class A bonds, 5% from class B bonds, and 9% from class C bonds. Troublingly, 4% of the losses have no identified source of funding. If one assumes instead that TWIA purchases reinsurance at the top of the bonding stack in an amount equal to 1.4% of its direct exposure, as it has done in the past, TWIA policyholder premiums and reinsurance paid for by TWIA policyholder premiums cover a total of 61% of losses suffering during that time period. The remaining losses will be paid 8% from replenishment of the catastrophe reserve fund, 10% from class A bonds, 6% from Class B bonds, and 11% from class C bonds. The percent of losses that have no identified source of funding has decreased, but still rests at 3%. These numbers are, of necessity approximate, and they indeed vary based on a variety of assumptions that need to be made. I have not had the luxury of a large amount of time in which to refine the analysis. In general, however, I believe they accurately reflect the benefits and burdens of H.B. 2352 and S.B. 1089.

This simulation attempts to quantify the benefits and risks to TWIA policyholders created by H.B. 2352 as well as the burden it places on those not receiving direct benefit from TWIA policies. Personally, I do not like what occurs if H.B. 2352 were used to prop up a $72 billion TWIA. The concentration of correlated risk in that entity inevitably makes it an expensive proposition in which the organization either pays exorbitant prices to reinsurers or continues to run the risk of an inadequate stack of protection against larger storm. I believe there is much to the idea of significantly depopulating TWIA with an assigned risk plan or similar mechanism that decorrelates the risk by forced pooling with non-windstorm risk throughout Texas.

If, however, you want to persist with a large propped up TWIA but want to avoid otherwise inevitable biennial fights, it is crucial that the bonding limits contained in this bill with respect to Class A, B and C securities be stated not as absolute numbers, $1 billion, $900 million, $2.75 billion but, as you have wisely done in this bill with the CRTF, percentages of some measure of overall risk to the pool, perhaps direct exposure. Without this modification, the risk grows of storms overwhelming TWIA’s bonding capacity.

Finally, for reasons I have outlined elsewhere I persist in my view that wealthy people on the coast receive subsidized property insurance from poor people away from the coast. This bill continues that inequity although it masks the subsidization by terming what amounts to regional and statewide property taxes as premium surcharges or assessments on insurers. I would thus suggest that the bulking up of the CRTF that takes place in the early years of the HR 2352 plan be made less by non-TWIA policyholders on the coast and assessments on insurers, but more heavily by TWIA policyholders themselves, who will, notwithstanding the benefit that each part of Texas bestows on the other, be the primary beneficiaries of the CRTF protection.


I’m showing below a condensed version CDF on which this analysis depends.  You can get the full version here. If you don’t see anything substantive, you need to download the free CDF player so that you can interact within your browser with the model I have created.

[WolframCDF source=”” CDFwidth=”600″ CDFheight=”1600″ altimage=””]

Some further caveats and comments

  1. I am fully aware that this work done on short notice by an individual and not one certified as an actuary, though I do believe I have the skills to produce what I have done. As I have written elsewhere, the Texas legislature should seriously consider establishing an insurance think tank to help it with issues like this.
  2. The premiums in this model are static.  There is some possibility that as the size of the catastrophe reserve fund grows and TWIA is better able to handle storms without resort to post-event bonding, the premiums could decline.
  3. The basic problem with TWIA is that its risk is correlated.  If it were decorrelated, the premiums policyholders pay would likely be adequate to cover its losses and no cross subsidization would be needed.  The problem is that TWIA needs to build up its catastrophe reserve fund to the point where it is no longer dependent on the risks of post-event bonding or the expense of reinsurance.  Until it does this, a system that bundles up correlated risk is going to remain either really expensive or run a risk of insolvency.


An interactive hurricane damage model for Texas

For most people, hurricane modeling is kind of a black box. Various experts set forth figures on the distribution of losses or statistics derived from those distributions. You pretty much have to take their word on it. I think policy discussions are better when the data is more transparent. So, a few weeks ago I sent a public information request to the Texas Windstorm Insurance Association asking for the raw data that they used to model hurricane losses. TWIA cooperated and send back about 30 megabytes worth of data.

So, I’m now able to create an interactive tool that lets you model the losses suffered by the Texas Windstorm Insurance Association from tropical storms. To run the tool, you will need to get the free CDF plug in from Wolfram Research. Once you have the plugin, you can run any CDF file. CDF is basically like PDF except that it permits interaction.

[WolframCDF source=”” CDFwidth=”630″ CDFheight=”790″ altimage=””]

Once you have the tool, you can do many things.

You can use the landfall county control to choose a county in which the storm first makes landfall. Notice that some of the counties are outside Texas because storms may first make landfall in, say, Louisiana but then go on to go over Texas and do damage here.

You can restrict the storms under consideration to various strength levels. I’m not sure, honestly, how AIR classifies tropical storms that don’t make hurricane strength. Perhaps they list them as Category 1. Or perhaps — and this would result in an underestimate of damage — they don’t list them at all.
You can also limit yourself to major hurricanes (category 3 or higher) or non-major hurricanes (categories 1 and 2).

You then get some fine control over the method of binning used by the histogram. If you’re not an expert in this area, I’d leave these two controls alone. In the alternative, play with them and I think you will get a feel for what they do. Or you can check out documentation on the Mathematica Histogram command here.

You then decide whether you want the vertical scale to be logarithmic or not. If some of the bin heights are very small, this control helps you see them. If you don’t remember what a logarithm is, you might leave this control alone.

Finally, you choose what kind of a histogram you want to see. Common choices might be a Count or an Exceedance Curve (Survival Function).

The tool then produces the histogram you have requested and generates a number of useful statistics. Here’s a guide to the six rows of data.

Row 1: This is the mean loss from storms meeting your selection criteria.
Row 2: This is the mean annual losses from the types of storms you have selected. This number will be lower than the mean storm loss because Texas (and all of its subdivisions) average less than one storm per year. Many years there are no storms.
Row 3: This is the worst loss from 100 storms. Note again, this is NOT the mean loss in 100 years. Some years have no storms; occasionally some years feature multiple storms.
Row 4: The AIR method for generating storms can be well approximated by a Poisson distribution. Here, we find the member of the Poisson family that best fits the annual frequency data for the selected storms.
Row 5: The AIR method for generating storms can be decently approximated most of the time by a LogNormal distribution. Here, we find the member of the LogNormal family that best fits the loss data for the selected storms.
Row 6: I can create a new distribution that is the product of a draw from the Poisson distribution and the LogNormal distribution. I can then take 10,000 draws from this distribution and find the size of the annual loss that is higher than 99% of all the annual losses. This lets me approximate the 1 in 100 year loss. Notice that this number will move around a bit every time you tinker with the controls. That’s because it is using an approximation method based on random draws. Every time you change a control, new random draws occur. Still, it gives you a feel for that dreaded 1 in 100 year annual loss.

If people have additional features they want added to this tool, please let me know. I may be able to modify it or build a new tool with related capabilities.

An idea for future TWIA finance

Although they may thoroughly disagree on the direction in which reform should go, almost everyone agrees has come to agree with what I predicted in 2009:  TWIA finances are in serious need of reform.  This blog entry sketches out one direction in which TWIA might proceed.  The idea here is that TWIA should, in a steady state, have enough cash on hand in its catastrophe reserve fund to pay for insured losses and operating expenses, without having to borrow, with a high probability, say 99%.  Further TWIA should have borrowing capacity to address the rare situations (say 1% of years) in which its reserves would be inadequate. Those borrowings should be repaid by some percentage of TWIA policyholders, persons living on the coast, and Texans generally, perhaps collected through the proxy of insurers doing business in Texas.

Although people can quarrel about the precise parameters in this abstract statement of the goal, I have some hope that people could agree on the concept. Government-sponsored insurance companies that don’t have the right to draw on the government fisc, ought not to be relying heavily on post-event bonding as a way of paying claims; instead they need enough money in their piggy bank just as we require of their private insurer counterparts. But what if TWIA’s catastrophe reserve fund does not meet this lofty goal?  What then?  Especially given the magnitude of the current reserve shortfall and the current economy, matters can not be corrected overnight. There should, I say, be an adjustment period during which premiums are adjusted (either upwards or, at some hypothetical future time, downwards) such that, at the end of the adjustment period, things come into balance and the catastrophe reserve fund meets the goal.

How do we operationalize this idea? Here is the beginning of a statutory draft. I’ve put in dummy statute section numbers for ease of reference. Obviously, the real section numbers would have to be revised by legislative counsel. Also, we’re probably going to have to develop a more comprehensive process for 2210.355A(b)(1) and reconcile this provision with the alternative process currently set form in 2210.355A.


(a) Definitions

(1)  The “Exceedance Function for the catastrophe year” is a function that approximates the probability that insured lossses and operating expenses in the catastrophe year will exceed a specified dollar amount. Insured losses shall be computed on a net basis after consideration of any reinsurance or other sources of recovery.

(2) The term “Loss PDF” means the probability distribution function mathematically associated with the Exceedance Function.

(3) The term “Century Storm Reserve Adequacy” means having a catastrophe reserve fund at the start of each catastrophe year such that this fund would be able, without additional borrowing, to fully pay insured losses and operating expenses in the following catastrophe year with a 99% probability as computed using the Exceedance Function for the catastrophe year.

(4) The term “Reserve Adjustment Period” means ten years.


(1) The Association shall, prior to the start of each catastrophe year, use the best historical and scientific modeling evidence with considerations of standards in the business of catastrophe insurance, to determine the Exceedance Function and associated Loss PDF for the catastrophe year.”

(2) If, at any time, the Association finds that its catastrophe reserve fund at the start of a catastrophe year does not achieve Century Storm Reserve Adequacy,  the Association shall adjust the premiums to be charged in the following year either downwards of upwards as appropriate such that, were:

(A) such premiums to be charged for the Reserve Adjustment Period on the base of currently insured properties;

(B) insured losses and operating expenses of the Association to be for the Reserve Adjustment Period at the mean of the Loss PDF for the catastrophe year; and

(C) the Association were to earn on any reserve balances during the Reserve Adjustment Period the amount of interest for reasonably safe investments then available to the Association,

the catastrophe reserve fund at the end of Reserve Adjustment Period would achieve Century Storm Reserve Adequacy.

(c) By way of illustration, if the Exceedance Function takes on a value of 0.01 when the size of insured losses and operating expenses is a equal to 440 million dollars and the mean of the Loss PDF for the catastrophe year is equal to 223 million, the initial balance of the catastrophe reserve fund is 100 million dollars and the amount of interest for safe investments then available to the Association is equal to 2% compounded continuously, then the premiums charged for the following calendar year should be equal to $614,539,421.

And what happens, by the way, if a storm hits that exceeds the size of the catastrophe reserve fund?  Stay tuned.  I’ve got an idea there too.

How do we keep premiums low under this scheme?  Likewise, stay tuned.  Hint: think about coinsurance requirements and lower maximum policy limits.  Think about carrots to get the private insurance industry writing excess policies on the coast with ever lower attachment points.

  • Footnote for math nerds only. Anyone seeing the implicit differential equations in the model and the applications of control theory?
  • Footnote for Mathematica folks only. Here’s the program to compute the premium. Note the use of polymorphic functions.

p[\[Omega]_, \[Mu]_, q_, c_, r_, z_] :=
x /. First@
Solve[Quantile[\[Omega], q] ==
TimeValue[c, EffectiveInterest[r, 0], z] +
TimeValue[Annuity[x – \[Mu], z], EffectiveInterest[r, 0], z],
p[\[Omega]_, q_, c_, r_, z_] :=
With[{m = NExpectation[x, x \[Distributed] \[Omega]]},
p[\[Omega], \[Mu], q, c, r, z]]

  • Footnote for statutory drafters. Note the use of modular drafting such that one can change various parameters in the scheme (such as the 10 year adjustment period) without having to redraft the whole statute.

Why I blog on Texas Windstorms

I am blogging because Texas, and other coastal states, have set themselves up for disaster by engineering flimsy legal and financial regimes to address the risks of tropical cyclones.  I read accounts in the press or on the Internet that are based on incredible misinformation and wishful thinking that nature will not respect. I see many politicians in a cycle of untruths with their constituents that leave coastal residents and businesses at significant risk of a catastrophe. Selfishly, I know that I, a semi-coastal resident, will be asked, one way or another to help pick up the pieces in an expensive way if a major storm hits a densely populated part of the Texas Coast.

I am also blogging because, immodestly, I have considerable expertise in this area and can’t just submit every thought to the Houston Chronicle and hope that they publish it. As a law professor at the University of Houston Law Center with a deep interest in actuarial science and finance, I’ve studied the legal and financial operations of the Texas Windstorm Insurance Association for many years.

Finally, I guess I am blogging because I want to give some courage to people who want to look at the Texas insurance scene with an open mind.  I have seen one Texas political figure, Insurance Commissioner Eleanor Kitzman, vilified by many coastal politicians and residents for daring to tell the truth about the risks now being run.  That is just wrong.   We say we want politicians to tell us the truth.  But do we really?  So, my hope is to give useful information and analysis to people who dare to look without prejudice at Texas windstorm situation. 

I’ll be using several tools to present information.  WordPress supports text and pictures and all the usual stuff.  I’ll  use those modes of expression to the best of my ability. But it also supports interactive tools (CDF technology) that let you, the reader, really explore the situation and make up your own mind.  And, ultimately, I suspect that is how we will all learn best.

So, enjoy, read and think.