Tax Costs of Equity Capital and Social Welfare Implications for Catastrophe Insurance
Reserves*
June 12th, 2007
Abstract
We examine the use of catastrophe loss reserves in a stylized one-period model of
insurance where insurers use equity capital and premiums to set up tax-deductible
reserves for future catastrophes. The tax cost of equity capital, which accounts for a
large part of insurance premiums, could essentially be removed through catastrophe
reserves. Taking account of the potential changes in consumer behavior due to the
institution of catastrophe reserves, we discover large social welfare gains are possible
under certain circumstances. Specifically, the net social welfare gain due solely from
the Florida market is estimated to be in the range of $58.5 million to $81.5 million.
The benefits, however, depend on the actuarial assumptions underlying the expected
loss distribution.
Martin F. Grace
James S. Kemper Professor of Risk
Management
Department of Risk Management
& Insurance
PO Box 4036
Georgia State University
Atlanta, GA 30302-4036
JEL Classification:
Keywords:
Andreas Milidonis
Lecturer in Finance
Accounting & Finance Division
Manchester Business School
The University of Manchester
Crawford House
Booth Street East
Manchester, M13 9PL
C15, C16, D61, G13, G18, G22, G28, H20, H25, H71
Catastrophe Financing, Insurance Pricing, Taxes.
Corresponding Author:
Andreas Milidonis
Lecturer in Finance
Accounting & Finance Division
Manchester Business School
The University of Manchester
Crawford House, Booth Street East
Manchester, M13 9PL
Telephone Number:
+44 (0)161 275 0432
Fax Number:
+44 (0)161 275 4023
Email:
Andreas.Milidonis@mbs.ac.uk
*
We would like to thank Sam Cox for suggestions on actuarial methodology and Richard Derrig, Richard
Phillips and Tyler Leverty for comments and assistance on an earlier version of the paper. We would also
like to further acknowledge the prompt and valuable help of Mr. Edward N. Trevelyan of the U.S. Census
Bureau. All errors or omissions, however, are the authors’ responsibility. Comments are welcome, but
please do not cite without permission.
-1-
Tax Costs of Equity Capital and Social Welfare Implications for Catastrophe Insurance
Reserves
1. Introduction
Over the past decade we witnessed more intense hurricanes in the North Atlantic basin.
The 2005 hurricane season broke records in terms of both human and financial cost. Hurricane
Katrina which struck Louisiana, Mississippi and Alabama was responsible for approximately
1,300 hundred deaths and insured damages of about $35 billion dollars. It is now ranked third on
the list of deadliest and first on the list of costliest hurricanes to hit the US (Blake, Rappaport,
Jarrell and Landsea, 2005). Wilma, another 2005 hurricane, reached a record pressure of 822
millibars. A growing literature exists among oceanologists and weather researchers which
documents and attempts to explain the variation in trends in hurricane activity. Webster et. al.
(2005) find evidence of an increasing trend in hurricane frequency and intensity in the North
Atlantic basin over the last decade. On another note, hurricanes have become potentially more
destructive compared to the 1970s (Emanuel, 2005). More recent climatology research
(Goldenberg, Landsea, Mestas-Nunez & Gray, 2001) predicts that the era of increased hurricane
activity the Caribbean and US that began in 1995 will continue for the next few decades.
The increase in the frequency and severity of catastrophic losses has forced the propertyliability insurance market to innovate new ways to deal with the changing market, such as the
introduction of catastrophe bonds and the continued refinement and implementation of
catastrophe simulation models using detailed trends in climatology. Policymakers have also
proposed public programs designed to provide protection to insurers for the most extreme losses.
One proposal is the establishment of tax-deferred pre-event catastrophe reserves. The proposal
would allow private insurers and re-insurers to set up reserves that could be assessed only in the
event of a catastrophe (Davidson, 1996). Pre-event tax deductible catastrophe loss reserves would
-2-
allow insurers to supply homeowners’ insurance at lower prices as the tax savings would be
passed onto consumers.1
Alternatives to the tax-deferred proposal exist include establishing a National Disaster
Insurance Corporation which would act as a disaster insurance company for the states2, a
government reinsurance program like the Terrorism Risk Insurance Act of 20023 and state
insurance funds like the Florida Hurricane Catastrophe Fund4 (Grace and Klein, 2002). Reserves
of this nature have already been instituted in Europe, Japan and Puerto Rico (GAO 2005). Thus
U.S. insurers and reinsurers are at a competitive disadvantage internationally.
According to the financial pricing literature for insurance, price depends on the present
value of expected future losses, the cost of equity capital and the insolvency put reflecting each
company’s financial position and obligation to meet future claims (Phillips, Cummins and Allen,
1998). The cost of equity capital becomes a major part of the price of insurance especially when
contracts cover losses occurring from extreme events, such as Hurricane Andrew in 1992 and
Hurricane Katrina in 2005. To the extent that tax free reserves will allow a lower cost of
insurance is the prime rational behind the establishment of public windstorm and catastrophe
funds.
Private insurers collect equity capital from the market to build reserves so as to minimize
the probability of insolvency from future catastrophic losses. In a competitive environment where
economic profits are zero, property-casualty insurers cannot absorb the cost arising from equity
capital. The cost, therefore, must be passed onto consumers for insurers to remain solvent.
1
The current proposal was introduced in the House of Representatives on January 4, 2007 and is entitled
the “Policyholder Disaster Protection Act of 2007”, H.R. 164 (110 Congress, 2007).
2
See e.g. H.R. 3728 (105 Congress, 1998).
3
H.R. 3210 (107 Congress, 2002) P.L 107-297.
4
Florida Statutes § 215.555. The purpose of the fund created in 1993 is to permit the tax-free accumulation
of hurricane reserves. Thus, it is a public entity with the ability to set up tax free reserves. The major
difference between such a public entity and a private one is that the public entity can issue bonds to fund
deficits or it may tax or “assess” future insurance premiums to reduce its deficits. In contrast, a private firm
will spread the risk rather than place it on the citizens of the state. The public catastrophe funds could also
spread the risk by purchasing reinsurance, but they do not seem to be inclined to do so as reinsurance is a
certain current expense while a future catastrophe deficit is an uncertain claim on the future taxpayers.
-3-
Consequently, homeowners are called to pay more than the actuarial fair value of an insurance
contract since they have to absorb part of the total cost of equity capital.
The cost of equity capital, as a percentage of the present value of expected claim costs,
ranges from 11% to more than 1000% for large layers of insurance (Harrington and Niehaus
(HN), (2003)) making some types of insurance unaffordable5. In addition, insurers have to
charge “high” risk premiums over the actuarial fair value of the underlying risk to provide for
potentially large losses. Consumers on the other hand find such prices unaffordable and decide to
stay un-insured against catastrophes. As a result, the Federal Government is called to release
disaster relief funds to cover the alleged social welfare gap that arises from losses suffered by
under-insured or uninsured homeowners.
Tax-deferred pre-event catastrophe reserves may provide a partial long term solution to
this problem by reducing the tax related costs of equity capital. The argument is that companies
will be able to put reserves aside and will not have to pay taxes unless a certain number of years
go by without a triggering event.6 As homeowners’ markets are reasonably competitive, insurers
will pass their tax savings onto consumers, prices will decrease as the cost of equity capital will
decrease (Cummins and Weiss, 1991). Further, as the price elasticity for the demand for the
catastrophic and non-catastrophic components of homeowners insurance in Florida is negative,
any decrease in the price of insurance will be followed by an increase in the quantity demanded
(Grace, Klein and Kleindorfer, 2004).
As more consumers will be insured (or less under-
insured) the potential call on the government treasury will be reduced.
Our paper is the first attempt to price the tax-deferred proposal and provide estimates of
its social welfare effects. To determine the economic efficacy of tax deferred catastrophe reserves
5
Harrington and Niehaus (2003) assume that the two main financing resources for the insurance company
are equity capital and premiums collected from policyholders. We follow the same assumption in our
analysis.
6
The recent proposed legislation suggests a twenty-year time frame under which companies can
accumulate funds tax-free. If at the end of this period no catastrophe occurs that depletes the reserves they
have to release parts of those funds as taxable revenue. Funds from such reserves will be used only if losses
exceed a pre-determined loss based proportionally on the risk that each company undertakes.
-4-
we first estimate the aggregate loss distribution for insured catastrophic losses for the state of
Florida, using a dataset of historical catastrophe losses since 1949 from Property Claims Services,
Inc. (PCS). We also estimate the distribution by using the most recent recorded losses (19902004) to account for the recent increasing trend in the frequency and severity of hurricanes.
We refine the estimates of the loss event tails using Extreme Value Theory. Next, using
the two estimated aggregate loss distributions and HN’s model over different layers of
homeowners insurance against catastrophic damages, we estimate the portion of the price of
homeowners’ insurance that is then attributable to federal income taxes.
Using the estimates of the price elasticity of homeowners’ demand from the literature in
conjunction with our cost of capital estimates, we then calculate the expected percentage increase
in the quantity of homeowners’ catastrophe insurance demanded in Florida.
Assuming a
horizontal supply curve, where all savings from the proposal are passed onto the consumer, we
then estimate the loss in federal tax revenue and the social welfare gain from pre-event taxdeferred catastrophe reserves for Florida consumers. Finally, we calculate the federal assistance
funds released to uninsured homeowners’ losses in Florida resulting from catastrophes and
compare them with projected social welfare gains from the tax-deferred proposal.
The rest of the paper is organized as follows. Section 2 discusses the model and its
implications. Section 3 describes the data and the actuarial methodology used to estimate the
aggregate loss distributions. Section 4 states our economic assumptions and discusses the
economic implications of enacting the tax-deferred loss reserve proposal. Section 5 estimates the
social welfare effects and section 6 concludes.
2. Model
The price of insurance (or the premiums paid by the insured) consists of three parts: the
present value of expected losses, the cost of equity capital and a loading that companies in good
financial standing charge because they can provide more security to the consumer that their
claims will be paid out (Cummins, 1990; Phillips, Cummins and Allen, 1998; Myers and Cohn
-5-
1987). The establishment of tax-deferred catastrophe reserves is a proposal that aims at
decreasing the cost of equity capital. This is done by deferring taxes (on investment income from
earned premiums and equity capital) payable to the federal government.
To derive an estimate of the cost of capital as a percentage of the price of insurance we
use the Harrington and Niehaus (2003) (HN) model. In their one period model, HN solve two
simultaneous equations to estimate the premium (P) and capital (K) levels that insurers need to
maintain to stay in business in the event of a catastrophe:

K 1  r    1 f L  dL 
0
  P 1 r  Kr
  P  K 1 r 

3
  P 1 r  Kr
  2 f L dL 
 
 
 L  K  P 1  r     f L  dL
 K  P 1 r 
 



 L    f L  dL  f L  dL
 f L  dL

 
1

  K  P 1  r  f L  dL

 
  

 L    f L  dL  f L  dL

2

The first equation (equation 1: capital market constraint) equates the accumulated value of equity
capital based on the market’s required rate of return (left hand side) with the expected payoff
function determined by the distribution of aggregate catastrophic losses, the corporate tax
structure and the company’s payoff function. The second equation (equation 2: insolvency
constraint) assigns a constraint in which the exogenous insolvency probability has to be equal to
the ratio of expected unpaid claims divided by total expected insured losses.
The values for P and K are obtained for several contracts and market conditions by
solving the capital market and insolvency equations simultaneously. The parameters of the model
are varied successively (explained in greater detail below). Using the values of P and K, the cost
of capital component of the price of insurance can then be calculated. The basic scenario
calculates the premium (P) that an insurer has to charge and the amount of equity capital (K) it
will need in order to offer a contract for a layer of insurance (  ) over an attachment point (  )
against catastrophic losses (L). The distribution f L represents the density function of aggregate
-6-
catastrophic losses.7 We aggregate losses to the industry level, thus the model assumes that there
exists only one insurance (reinsurance) company that offers insurance (reinsurance) contracts at
competitive prices (P).
The capital market constraint (equation 1) integrates the insurer’s payoff function (right
hand side) over the three integral limits and sets it equal to the capital at the end of the period
which is accumulated at the market required rate of return (r).8 i denotes the insurer’s payoff
for each of the three integrals which varies according to losses, L, that are expected to occur. At
the end of the period interest on equity capital at the market’s required rate of return, K*(r), is
returned to equity holders and furthermore any profits (

i
) of the insurance company are
i
released to its shareholders. Profits are made if the balance of revenues (premiums and
investment return on premium and capital) after deducting expected claims (a function of f L )
is positive. Expected claims are calculated by evaluating the distribution of annual aggregate loss
claims, f L , over the entire range of losses that insurance contracts cover.
The important implication of the HN model is that the insurer pays corporate taxes on its
underwriting revenue, P1  r  , and investment income, K r  , when taxable earnings are
positive. The cost of equity capital component of the insurance price depends on the amount of
taxes the firm pays on K when taxable earnings are positive. In the case that taxable earnings are
depleted, the company receives a tax-reimbursement equal to b * provided it remains solvent9.
If the company becomes insolvent, it still has indemnity obligations to policyholders but it has no
7
The distribution of aggregate catastrophic losses is estimated in detail by Milidonis and Grace (2006).
Harrington and Niehaus (2003) provide detailed explanations and diagrams regarding the corporate tax
structure and company payoff functions used in equations 1 and 2. In short, since the corporate tax structure
is not linear due to tax shields given to companies when they make a loss, the payoff function of the
company is also non-linear. In addition the payoff function depends on which funds are used first to pay off
claims. According to the model investment income from premiums and equity capital is used first while
actual reserves from equity capital are used second.
9
To account for the time taken to collect on the tax shields, “ b ” takes values between 0 and 1. A value of 1
indicates that the insurer will receive all tax shields at the end of the year, while values less than 1 means
that it will take a few years for tax shields to be received and they are therefore discounted.
8
-7-
tax shields. The non-linear corporate tax schedule makes the insurer’s payoff structure non-linear
and as a result the firm has different payoffs over different ranges of losses.
Figure 1 shows the structure of the proposed contract. The insurer offers coverage for a
layer of insurance,  , over an attachment point  . Since losses (claims) are stochastic, they can
fall anywhere along the x-axis of Figure 1. In the first case, if losses fall below the attachment
point  the firm does not pay any losses to policyholders and at the end of the year it pays out
profits to shareholders equal to the sum of all premiums collected, the investment return on
premiums minus corporate taxes on premiums and investment income. All equity capital (in
addition to the investment income on capital, minus corporate taxes) is also returned to the
market. 1 is calculated by subtracting taxes from insurer’s taxable revenues.
When losses fall above the attachment point but below the layer of insurance,  , and the
maximum taxable revenues, P1  r   Kr , then the insurance company has payoff  2 . In this
case, losses paid out are those in excess of  only. Taxes are only paid on the taxable revenues
remaining after settling claims. Therefore  2 would be the amount of taxable revenues
remaining after losses and taxes are paid out.
The next possible range of losses would be again between  and    but in excess of
maximum taxable revenue and below the maximum losses that the insurer can pay,
  P  K * 1  r  .10 The insurer will pay losses in excess of  (as before), but as it is forced to
draw on capital to make the loss payments, no corporate taxes will be paid, as there a loss in
capital. Instead a tax shield will be provided by the government. We follow HN’s notation and
use b to denote the value of tax shields.11 Tax shields will be paid only on the amount of capital
The sum of premiums, capital and investment income of the insurer is equal to 1   *  , which is equal
to the probability of staying solvent times total promised claims.
11
To account for the time taken to collect on the tax shields, “ b ” takes values between 0 and 1. A value of
1 indicates that the insurer will receive all tax shields at the end of the year, while values less than 1 means
that it will take a few years for tax shields to be received and they are therefore discounted.
10
-8-
that the insurer will have to use to cover losses. Therefore, there will be no amount left (  3 =0) to
be given to shareholders at the end of the period. Finally,  4 will be zero since losses will be in
excess of    and the insurer will be insolvent as premiums, capital and investment income
will fall short of the total promised claims (  ).
The second equation (equation 2) addresses the solvency issue of the insurer, a necessary
condition for the insurer to meet the capital market constraint. The left hand side of the
insolvency constraint represents the probability of insolvency (  ), while the right hand side
represents the ratio of expected unpaid claims divided by the total expected promised claims.
Expected unpaid claims (numerator of left hand side) are a function of the aggregate loss density
function, the order of claim payment, the required market return and the level of the attachment
point, while the total expected claims represent the loss exposure of the insurer as those are stated
by the contract terms. The insolvency probability is an exogenous variable.
Given that equations 1 and 2 are solved simultaneously to obtain values for P and K, we
now turn to the methodology used to estimate the aggregate loss distribution for insured
catastrophic losses in Florida, f L  . Milidonis and Grace (2006) use maximum likelihood
estimation to model the frequency and severity of the catastrophic loss distribution for Florida.
Then they simulate 25,000 annual aggregate losses and finally they provide two estimates for the
annual aggregate loss distribution: a conservative approach based on the historical data from
1949-2004 and a more aggressive approach that accounts for the more frequent and severe trends
experienced from 1990-2004. We choose the estimate based on the most recent data as the high
frequency and severity trend is expected to continue.
3. Data
Our dataset is obtained from Property Claim Services (PCS) and contains historical
catastrophic losses that have taken place in Florida since 1949. PCS collects data from a network
of agents and other sources throughout the US about losses resulting from disasters in the US
-9-
since 1949. A disaster is categorized as a catastrophe if it exceeded $1 million before 1983, $5
million from 1983 to 2004 and $25 million after 2004.12 Figure 2 shows the catastrophe
frequency trend since 1949. From 1949 to 2004, 125 catastrophes were recorded by PCS for the
state of Florida. On the other hand, if we look at the data after 1990, it is obvious that there have
been events in every year with the most common frequency being two events per year and
interestingly enough, one year having seven events.
There were significant changes in the value of the underlying property insured under
homeowners’ insurance contracts over the 56-year span (1949-2004). In order to account for
changes in the insured property value and economic inflation, we constructed a Housing Value
index (HVI) for the state of Florida in order to make all loss amounts since 1949 equivalent to
2004 dollar values. For the HVI we have gathered the value of specified13 owner-occupied
housing as reported by the U.S. Census Bureau (reported in ten year intervals back to 195014) and
normalized housing values against the 2004 housing values to get annual accumulation factors for
all years since 1949.15
Figure 3 plots the loss amounts of the 125 catastrophes that took place in Florida in
chronological order. Hurricane Andrew surpasses all other losses. In fact, the second largest
event was Hurricane Charley in 2004, which was about three times smaller in insured damages
than Andrew ($7.4B vs. $22.3B). In 2004, Florida experienced 4 hurricanes with estimated total
insured losses of $19 billion. Table 1(i) and (ii) summarize all recorded losses since 1949 and
1990 respectively. As we have already mentioned the most recent data (1990-2004) includes
12
The thresholds used in the data pertain to the total losses incurred from one event. In our case we focus
our analysis only on the state of Florida (due to limitations in price elasticity estimates of homeowners
insurance in Florida only). Therefore, in isolating costs from catastrophes that only involve Florida, there
are data points that are below the thresholds specified by PCS.
13
Represents single family units on less than 10 acres without a business or medical office on the property.
14
Specified owner occupied housing value was the only value reported consistently back to 1950 in
contrast to the Owner-occupied housing value (includes specified owner-occupied value) which was not
reported for 1970.
15
The HVI was used to multiply losses that took place in 1949 by a factor of 19.44, in 1950 by 18.28 e.t.c.
These factors were determined by dividing the value of specified-owner occupied housing for each year by
the value estimated for year 2004. Linear interpolation was used to get housing values for the years
between the 10-year periods lapsing between census reports.
- 10 -
more frequent and severe catastrophes, which are mainly a result of wind damage from increased
hurricane activity. Both data sets are very much skewed to the right with the mean of the entire
dataset ($428 million, Table 1(i)) being about 21 times the median ($20 million, Table 1(i)). In a
similar fashion the more recent catastrophes show a similar pattern with the mean ($834 million,
Table 1(ii)) being about 31 times the median ($27 million, Table 1(ii)). The difference between
the mean and the median of loss amount is attributed to the 28 hurricanes that have taken place
over the years with an average loss amount of $1.755 billion (10 hurricanes since 1990 with a
mean value of $4.579 million), while wind losses make up most of the remaining observations.
In Table 2 we provide estimates of simulated results for the two versions of the aggregate
loss distribution (1949-2004 (conservative) and 1990-2004 (aggressive) respectively), (Milidonis
and Grace, 2006). To show the differences between the two distributions we show right-tail
probabilities of exceeding certain thresholds. For example, under the conservative estimate, we
expect that about 32% of the time there will be no insured catastrophic losses while this
percentage is expected to be less than 2% for the more aggressive estimate. In the same fashion,
the probability of having a year with losses approximately equal or greater than the insured losses
suffered from Hurricane Andrew is 0.30% under the conservative estimate and 8.23% under the
aggressive estimate. Finally, surpassing the $100B threshold would be an almost negligible case
(0.03%) under the conservative approach while on aggressive side (4%) it would likely worry
some insurance executives.
4. Results
a. Base Case and The Effect of Tax-deferral on Price
We evaluate the HN model for many different scenarios in an attempt to measure the
possible market reactions to the tax deductible pre-event catastrophe loss reserve proposal. The
results could equally apply to two cases: either the Florida market can be captured by only one
insurance company that provides insurance to homeowners, or there is only one reinsurance
company that provides coverage to all insurance companies in Florida. The theoretical
- 11 -
justification for our assumption is that it is Pareto optimal for each insurer to hold a proportion of
the “market portfolio” of insurance contracts whereby each insurer pays a portion of total industry
losses (Borch, 1962). Therefore the industry behaves as a single firm which pays 100% of the
losses up to the point that net premiums and equity capital run out.
In Table 3 we set the background for our analysis. Following the notation in equations 1
and 2, we pick an attachment point  (column 1) and a layer of insurance  (column 2). We
exogenously assign values for the probability of insolvency  (column 3), the corporate tax rate
 (column 4), the value of tax shields b 16 (column 5) and the risk-free rate (or required-rate of
return) r (column 6). For Table 3  ,  , b and r are kept constant, while  and  are varied.
We start from a contract that covers the first $500 million, and then recalculate the model for each
successive $500 million layer. In order to examine the effect that extreme losses would have on
contracts with large exposures we have designed four contracts (last four rows) in a way that the
insurance company covers a larger layer of exposure with no deductible. By solving equations 1
and 2 simultaneously we then calculate the amount of premium P the insurance company has to
collect from policyholders (column 8) and the amount of equity capital K it needs from the
market (column 9). In column 7 we calculate the present value of expected claim costs (PVECC)
which is equal to the total promised claims17 times the probability of remaining solvent 1    .
Since tax costs are the only loading on the PVECC (administrative expenses are not
included in the model), the difference between P and PVECC is the cost of capital as a function
of taxes payable on equity capital. This mark-up from PVECC to P is shown in column 10 and
represents the minimum amount above the PVECC that insurers charge in order to accept the risk.
The tax-deferred catastrophe reserve proposal aims at postponing this tax liability and thus
diminishing the tax impact on the pricing formula. More specifically, the proposal requires the
16
The tax shields represent the reduction in the value of tax returns the company would receive by carrying
forward to future years operating losses (if this was a multi-year model). If the company becomes
insolvent, there is no value to tax shields (b=0).
17
The denominator of equation 2.
- 12 -
establishment of reserves which will be used only in the case of a catastrophe. Thus, insurers will
be able to grow these reserves tax-free for up to a period of say 20 or 30 years and only if a
catastrophe does not strike over this period will the insurance companies pay taxes to the federal
government. It is interesting to note that the probability of not having a catastrophe in Florida in a
twenty year period is effectively zero for the fitted frequency distributions18 (Milidonis and
Grace, 2006). This implies that the federal income tax liability will be zero for the insurance
industry for Florida. Any benefit to the government, then must come from reduced calls for
disaster relief.
In order to capture the effect of taxes on the mark-up of insurance prices, we re-estimate
the model by assuming that the federal tax rate (and consequently the tax shield) is zero. The
results are reported in columns 11 through 14. The difference in the mark-up from removing
taxes from the model is reported in column 15. Overall we observe a decrease that ranges from
8.7% to 43.8% for the largest catastrophe exposure we examine (covers the first 100 billion
dollars in losses). This change in mark-up (43.8%19) is used in section 5 to estimate the expected
changes in the quantity of insurance demanded and the resulting social welfare effects.
b. Discussion
In a world of certainty and no-insolvency, the insurer will choose premiums and raise
capital to pay-off all claims. This would be possible in our case if the insolvency constraint was
set to zero. Further, this would imply insurers would have to collect enough equity capital to
cover all potential contract losses above earned premiums. However, if the insolvency probability
(  ) is greater than zero it would imply that premiums (P) and capital (K) would only cover up to
(100-  )% of potential contract losses. For example when the insolvency constraint is set at 4%.,
it means that the insurance company has collected enough P and K at the beginning of the period
such that by the end of the period when claims are due, the sum of premiums, capital and
18
19
In particular, 0.339720 and 0.019620 for the conservative and aggressive estimates, respectively.
From table 2 we see that there is only a 4% probability that losses will be higher than 100 billion dollars.
- 13 -
investment income will be enough for the company to have a 96% probability of meeting total
promised claims.
As we see in Tables 3 and 4, P, K and the investment income fall short of the contract’s
loss exposure when added together. This is because the probability of default is not zero. When
the insolvency probability is set to zero then the insurance company can meet all claims at the end
of the year with certainty20. The highly skewed catastrophic loss distribution also contributes to
the fact that numbers in the two tables do not seem to add up. In the next two tables we do a
sensitivity analysis of our results for one contract, to see how the values of P and K change when
we vary the exogenously given variables.
Taxes are part of the cost of capital that insurers include in premiums. By removing taxes
from the equation, we eliminate taxation of earned premiums and investment income. We
measure the effect of tax-deferral by the percentage change in the mark-up with and without
taxes. The expected decrease in price decrease is reported in column 15.
The next point of interest relates to the values of P and K relative to the level of
attachment point and layer of insurance. For successive layers of $500 million we observe, as
expected, a decrease in PVECC and an increase in K. A layer of coverage over a part of the
distribution where there is less density will give a lower PVECC. This forces the company to
collect more equity capital, ceteris paribus. Even though premiums (P) fall in absolute terms the
price (mark-up) of insurance increases because there are greater tax costs from equity capital to
set up sufficient reserves for the loss exposure. In order to get a better idea of what insuring the
whole market would look like (last 3 rows of Table 3) we calculate P and K in a similar way. We
assume a competitive insurance market and thereby that these tax costs are passed onto the
consumer. As a result, consumers are expected to pay any mark-up on the actuarial value of a
We verified this by running the model with  = 0.00% for the layer covering the first $500 million with
no deductible (row 1 of Table 3) and got P=293.77 and K=177.92. Therefore at the end of the year the
company will have (293.77+177.92)*1.06 = $500. Therefore P and K accumulated with interest add up to
the total layer of insurance offered if the probability of default is zero.
20
- 14 -
catastrophic insurance policy (Column 10). The increases in price multiply rapidly as exposure
increases -- since the required reserves are now more heavily weighted on capital, implying a
higher tax cost.
Table 4 shows how changes in the exogenously given factors of the model (interest rate,
tax and tax-shield rate and insolvency constraint) affect the price of insurance, by examining a
contract which covers a layer of $1 billion dollars in excess $1 billion. Decreasing the probability
of default for the company implies that PVECC, P, K and the mark-up in the price of insurance
increase, which is consistent with a higher rated company (0.02%) needing more capital and
therefore charging higher premiums than a lower rated company (4%). This follows from the
literature of the insolvency put of an insurance company which emerges from the financial
pricing of insurance literature (see e.g., Phillips, Cummins and Allen, 1998). When removing
taxes from the equation we observe a decrease in mark-up which is again attributed to tax costs.
Increasing the corporate tax rate increases the overall tax costs without changing PVECC. The
company now collects a higher portion of required reserves from premiums since it becomes
more expensive to collect equity capital from the market. Varying the value of unused tax shield
does not affect the results much, mainly because we are looking at a large insurance layer ($1
billion). The value of tax costs decreases only slightly through the relative size of P, K and markup for the three different tax shields examined.
Interest rates (required market rate of return) constitute the last exogenous factor in the
model. As interest rates increase we observe a decrease in PVECC as we discount future expected
claims by a higher interest rate. A decrease in P and K is observed as higher interest rates help
accumulate reserves faster. We include high interest rates (last column: 20%) in order to
approximate the compounding effect of interest if a few years pass by without a catastrophe. If no
catastrophes take place, a higher interest rate could give an indication of the accumulated effect of
interest on premiums and reserves over the years with no catastrophes. Similarly, a large
probability of default (1%) could be interpreted as the multi-year probability of default of a
- 15 -
company with a relatively good credit rating (0.2%). Even though the tax structure would become
more complicated over multiple years, the probability of surviving a year with no catastrophes
hitting Florida is very small.
5. The Effects of Tax-Deferral on Quantity Demanded and Social Welfare
In this section we estimate and explain changes in the quantity of homeowners’ insurance
demanded from a potential decrease in the price of homeowners’ insurance21. Given these
changes and assuming perfectly competitive and frictionless markets, we then estimate the social
welfare effects from the proposal. Finally we summarize the amount of federal disaster assistance
given out in the state of Florida over the past twenty years and attempt to link any costs or
benefits to the current proposal.
To measure the social welfare implications of tax-deferred catastrophe reserves we use
data from the Federal Disaster Assistance funds released from 1983-2001 to compare the
projected social welfare benefits of the tax-deferred proposal with the money spent by the Federal
government to remedy the losses of uninsured homeowners. This dataset includes grant outlays
and obligations to the state of Florida, local governments and other individual recipients. The data
are carefully parsed to isolate the part of disaster assistance dollars given to uninsured
homeowners since there were frequent changes in program codes over the years and much of the
money was spent in other tasks like cleaning debris and fixing public transportation and utilities.
Our approach only accounts for the added savings in future catastrophes from the increased
quantity of individuals able to afford catastrophic home insurance, which gives us an accurate
estimate of the amount of Federal assistance dollars used for our analysis.22 All details on the
21
GKK (2004) provide estimates of the price elasticity of demand for homeowners insurance by using
changes in the mark-up of insurance as indicators of change in the price of insurance. Since we are using
their estimates in this section of the paper we will also use their terminology. By changes in price of
insurance we refer to changes in the mark-up of insurance prices.
22
As in the case of catastrophes, all amounts were multiplied by the HVI factors in order to bring
everything to 2004 US dollars. We only include funds released up to 2001 since there is usually a time-lag
between when a disaster hits and when the entire disaster funds pertaining to a catastrophe are released.
The data set was obtained from the Census Bureau website.
- 16 -
programs that we used in our analysis as well as the money given out for each program for the
period 1983-2001 are summarized in Table 6.
We use the price elasticity, indicated loss costs (ILC) and price estimates from Grace,
Klein and Kleindorfer (GKK 2004) to estimate the expected increase in quantity of insurance
demanded. In particular, we estimate expected increases in the quantity of insurance demanded at
different risk zones. To make the analysis tractable, we assume that the Florida homeowners’
insurance market is competitive with frictionless transactions and zero economic profits to the
insurers, thus any savings from the proposal will accrue to consumers. Furthermore, we exclude
any dynamic pricing effects and “force” the insurer to collect all required equity capital at the
beginning of the year. Finally in estimating the tax burden, we assume that no catastrophes take
place over the one-time period. However, in case they do occur, insurers are not liable to pay
taxes, but consumers pay prices that reflect the tax cost of capital and accumulated premiums.
In areas where catastrophic risk is low (25th percentile of catastrophic related modeled
Indicated Loss Costs23; ILC-CAT) the price elasticity of demand is about -0.95 (Table 5).
Similarly for moderate (50th percentile of ILC-CAT) and high (75% percentile of ILC-CAT) risk
zones the respective price elasticity estimates are -0.71 and -1.668. In a perfect market, one would
expect low-risk consumers to have a less elastic demand for insurance than higher risk. However,
the Florida market is heavily regulated and we suspect that cross-subsidization between the risk
groups contributes to the non-linear relationship between price elasticity estimates.
According to their estimates, GKK report that the catastrophic ILC for low, moderate and
high risk zones are $84.85, $229.38 and $623.98 respectively. These amounts represent the
portion of homeowners’ insurance attributable to catastrophic coverage and can be interpreted in
a similar way to the PVECC we use in the model above. Specifically, homeowners in a low risk
23
GKK (2004) had data from the Insurance Services Office which provided indicated (or expected) loss
costs for catastrophic and non-catastrophic costs. The non-catastrophic component was based on historical
actuarial data while the catastrophic component also used here, was based upon the results of a catastrophe
model.
- 17 -
zone would have expected catastrophe related insurance claims equal to $84.85. Similarly the
price (mark-up) they would pay would be 1.38, 1.6 and 1.79 for low, moderate and high risk
zones, respectively24.
With the range of expected price decreases in hand, prices charged and quantities of
insurance demanded at different risk zones, we now calculate social welfare effects from using
tax deferred reserves (Table 5). Assuming a competitive market, the flat supply curve intersects
the downward sloping demand curve as shown in figure 4. Considering the current environment,
where taxes are included in the price of insurance, the consumer pays PTAX to buy the ILC for her
house depending in its location risk zone. The quantity of insurance bought is denoted by QTAX
and represents the number of insured houses in each risk zone. From U.S. census data we found
that about 28.33% of all housing units in Florida eligible to be covered by the specific
homeowners’ insurance policy examined are not mortgaged and, thus are potentially uninsured.
We make the assumption that all houses with no outstanding mortgage are uninsured due to the
price of insurance. If the proposed legislation is enacted, then any projected increase in the
quantity of insurance demanded would be coming from this pool of uninsured housing units.
In Figure 4 we show our result graphically. We observe that the price of insurance after
taxes are removed drops to PNO-TAX and the corresponding quantity demanded rises to QNO-TAX. The
difference between PTAX and PNO-TAX is potentially tax-deferrable revenue in the event there is no
catastrophe. Area “A” denotes consumer surplus, area “B” the federal tax revenue and area “C”
for the deadweight cost of the tax.
If the proposal is approved, then consumer surplus will
amount to areas “A+B+C”, resulting into a social welfare gain for consumers. Producer surplus is
zero under both scenarios since we assume a flat supply curve. Finally, the amount by which
prices decrease and quantities increase depends on each risk zone’s price elasticity of demand and
the distribution used to evaluate each model.
24
These estimates are obtained by looking at the 25th, 50th and 75th percentiles of the mark-up distribution
as estimated by Grace, Klein and Kleindorfer (2004).
- 18 -
In order to estimate the change in quantity demanded we assume that all homeowners
who can afford catastrophe insurance insure the total expected catastrophic damage (ILC-CAT) to
their house for one year. Thus any increase in quantity demanded will be reflected through an
increase in the number of housing units covered. From the U.S. Census Bureau we find that there
are 4,174,840 houses in Florida eligible to be covered under the policies analyzed by GKK.
About 69% of these houses are classified as low risk based on their ILC, 28% as moderate and
about 3% as high risk. The estimated increase in quantity demanded ranges from 31% to 73%.
We further assume that the percentage of insured housing units in Florida is equal to the
percentage of those units that have a mortgage (71.67%; U.S. Census, 2000). In order to estimate
the number of additional homeowners which may now be able to afford insurance due to the tax
deferred catastrophe reserve, we apply the expected increase in quantity demanded to the number
of houses with a mortgage. We calculate the mark-up after removing taxes by assuming a
decrease in price by 43.81%25. From our estimation we find that almost all homeowners in
Florida would be willing to purchase catastrophe coverage (4,104,387 out of 4,174,840 houses).26
According to our model the amount of money previously collected by the federal
government as tax revenue when no catastrophes would take place (area B in Figure 4), now
becomes consumer surplus. Additionally, the deadweight cost due to taxation (area C in Figure 4)
also becomes consumer surplus. Therefore the net social welfare gain to consumers in Florida
from passing the proposal would be an amount equal to $58.5 million, while the respective
consumer surplus to Florida homeowners would be $386.9 million. It is important to emphasize
that these gains in consumer surplus and the resulting social welfare gain assume that the
25
We know that the mark-up from GKK is 2.38 for the high risk zone. This includes tax and other
(administrative, e.t.c.) costs. From our estimation, mark-up with tax cost is 1.4381 which drops to 1.0 when
the tax cost is removed. Therefore the respective mark-up in the GKK scenario should be (2.38*1.0)/1.4381
for the high risk zone.
26
Given our results we could work backwards to find the optimal tax rate decrease to insurers that would
generate such a price decrease to consumers that the all remaining uninsured houses in Florida could now
be insured. However, our results provide ballpark estimates of the social welfare effects of this proposal
with numerous other assumptions.
- 19 -
company begins operation at the beginning of one year. At that point the company collects
premium, raises capital and offers catastrophe insurance. The insurer does not have to pay taxes,
which is also the case without the proposal in place when a catastrophe takes that wipes out the
insurer’s taxable revenue.
Finally, to estimate the net benefit to the federal government from implementing the tax
deferred catastrophe reserve we have gathered data on disaster assistance dollars given out by the
Federal government for damages suffered by uninsured homeowners to the state of Florida. Since
taxes on insurance reserves are revenue to the Federal government, allowing tax-deferred preevent catastrophe reserves to be established will either defer or decrease federal tax receipts. On
the other hand, a decrease in the price of homeowners’ insurance and, hence, an increase in the
quantity of insurance purchased reduces the Federal government’s disaster assistance obligations.
In table 6 we summarize all the programs that were used to estimate the annual amounts
of federal disaster assistance from 1983-200127. These amounts are updated to 2001 US dollars
using the housing value index discussed earlier. We aggregate all federal disaster assistance
dollars and the cost of catastrophes over the examination period to account for the time delay in
releasing federal disaster assistance funds and are use of a one-period model to estimate the cost
of catastrophes and the position of insurance companies. In the last columns of Table 6 we
calculate ratios of the cumulative Federal disaster assistance amount released in all years since
1983 to the respective estimated cost from the catastrophes that took place up to that point in
time.28 More specifically, if we look at year 1995, the value of this ratio would be equal to the
amount of Federal disaster assistance funds released from 1983-1995, divided by the estimated
cost of catastrophes from 1983-1995 (inclusive). We find that over the eighteen year period we
examine the ratio of disaster assistance to uninsured damages to the total insured catastrophe
damages is about 16% (95% confidence interval: 12.75% - 20.8%).
27
Program descriptions and name changes are tracked in Appendix A.
In the last column we estimate the ratio including the federal disaster assistance released one year past
the time of the last catastrophe.
28
- 20 -
An alternative and comparable measure to the cumulative ratio above would be the ratio
of the total ILC to uninsured homes divided by total ILC of insured homes. We use the last four
rows in Table 5 to show what the expected damages on uninsured housing units are today versus
what they will be after the proposal is put in place (with and without taxes respectively). The ratio
for today (with taxes) is 39.5%29 while if the tax deferred catastrophe reserve is permitted this
ratio falls to 2.8%. We can use these ratios to conclude that passing the proposal will provide
insurance for almost all homeowners who are currently uninsured (Total Uninsured Housing
Value = $16,160,427 out of a total of $593,231,243). Comparing the decrease in these ratios to
the ratio of disaster assistance paid towards uninsured homeowners to the total insured
catastrophe losses, we can deduce that passing the proposal could be a large relief to the federal
disaster assistance budget.
In absolute terms this would mean that under the aggressive loss distribution about $152
million of uninsured housing value will have the potential to be insured. If this housing value is
insured this would imply that the amount of disaster assistance funds that would have to be
released to uninsured homeowners would be minimal (16% of $16,160,427)30.
The social welfare effects from passing the tax-deferred catastrophe loss reserve proposal
would equal the sum of the current tax revenue (area B; Figure 4) and deadweight cost (area C).
Area B is calculated by multiplying the expected decrease in price (PNO-TAX – PTAX) with the
number of houses (QTAX) under each risk level (similarly area C). We estimate the total social
welfare gain to be $58.5 million under the 1990-2004 loss distribution31.
6. Discussion and Conclusions:
a. Discussion
29
39.5% = $168,062,411 / $425,168,832 (Table 5)
Under the 1949-2004 scenario all uninsured housing value could be potentially insured (Milidonis and
Grace, 2006).
31
$81.5 million under the 1949-2004 loss distribution.
30
- 21 -
The first restriction of this model is that data is generated based on simulated
distributions which do not account for the maximum loss that could occur based on the total
property value in Florida. In other words, even if a hurricane hits Florida which is twenty times as
powerful as Hurricane Andrew and destroys all property standing above sea level in Florida, this
does not mean these losses will be proportional to the projected hurricane strength or a simulated
loss, but will be bounded by the total property value that exists in Florida.
The second discussion point refers to the economic interpretation of the results. The
economic assumptions that accompany the results are that the market is competitive in the sense
of zero economic profit, and any projected savings from tax deferrals are passed entirely to the
consumers. Our results are derived from a one-period model that only allows collection of
premium and equity capital for a large catastrophe over one period. Therefore any estimates of
potential decrease in the price of insurance are based on the assumption that the company is in
business for only one year, after which any profits are distributed to shareholders. A more
realistic but definitely more complicated model would account for a multi-year accumulation of
reserves, during which years loss events could trigger release of reserve funds or in the case of no
triggering event, the company would have to be taxed on any investment and capital income.
Finally the probability of insolvency of the company would probably not be stable over a multiyear period, but would fluctuate depending on loss occurrence.
b. Conclusions
The tax cost of equity capital for insurance companies is high for risks with long tails,
such as the catastrophe risk for homeowners’ insurance policies. The current situation forces
insurance companies to pass the tax cost of equity capital to policyholders thus increasing
insurance prices. The institution of tax-deductible pre-event catastrophe loss reserves will allow
insurance companies to diversify catastrophe risk over time without the burden of annual
taxation. This is because insurers will be able to grow catastrophe reserves tax free for a specified
period, after which they will be liable to pay taxes if their reserves are not used for catastrophe
- 22 -
losses. The potential removal of the tax cost of equity capital is expected to lead to lower
insurance prices, less uninsured homeowners and therefore less federal disaster assistance to
uninsured homeowners. In this paper we estimate the tax cost of equity capital for catastrophe
insurance in Florida, the expected decrease in insurance premiums and the associated social
welfare benefit from the implied increase in quantity of catastrophe insurance demanded.
In order to account for the increasing trend in the frequency and intensity of hurricanes
over the last ten years (that is expected to continue over the next few decades) we provide an
aggressive estimate of catastrophic losses (based on data from 1990-2004) to obtain competitive
prices for the market based on a two-equation simultaneous model of a capital market and an
insolvency constraint. Calculations based on this model and a series of underlying economic
assumptions allow decomposition of the price of catastrophic insurance into a part equal to the
present value of expected claim costs and the equity capital charge which is mostly a function of
the non-linear corporate tax structure. By making the strong assumption that all savings that
insurance companies will realize from the establishment of tax-deferred catastrophe loss reserves
will be passed to consumers, then using estimates of the price elasticity of demand for
catastrophic insurance from a paper by Grace, Klein and Kleindorfer (2004), we estimate a
projected increase in coverage of about 31-73%. Given these caveats, our simulation model
suggests that the introduction of the catastrophic reserve would allow for prices to be lowered by
about 41% so that all uninsured would have the incentive to purchase coverage.
Using estimated increases in the quantity of catastrophe insurance demanded, we then
provide dollar estimates of the changes in consumer surplus and social welfare gains resulting
from passing the tax-deferred proposal. We find the gain to be in the range of $58.5 million to
$81.5 million depending on the underlying actuarial assumptions.
Finally, we compare the government’s stake in allowing the establishment of tax-deferred
pre-event catastrophe loss reserves by looking at federal disaster assistance funds released to
uninsured homeowners and the projected savings in disaster assistance from this proposal. Given
- 23 -
our assumptions we find that the government may save significantly on disaster assistance funds
to approximately 16% of expected future damages, while at the same time not necessarily
forgoing tax revenues since taxes may not be paid by insurers over the next decades if the
increasing catastrophic trend of hurricanes continues to decrease their taxable income.
- 24 -
References
Blake, E.S., E.N. Rappaport, D.J. Jarell and C.W. Landsea, 2005, The Deadliest, Costliest,
and Most Intense Tropical Cyclones from 1851 to 2004. Retrieved December 29th,
2005 from the National Oceanic and Atmospheric Administration Website:
http://www.aoml.noaa.gov/hrd/Landsea/dcmifinal2.pdf
Borch, K., 1962, Equilibrium in a Reinsurance Market, Econometrica, 30 (3): 424-444.
Crosbie, P. and J. Bohn, 2003, Modelling Default Risk, Moody’s KMV technical document.
Cummins, J.D. 1990, Multi-Period Discounted Cash Flow Ratemaking Models, Journal of
Risk and Insurance, 47: 79-109.
Cummins J.D. and M.A. Weiss, 1991, Structure, Conduct, and Performance In PropertyLiability Insurance, Financial Condition and Regulation of Insurance Companies
(Boston: Federal Reserve Bank of Boston).
Davidson, J. R., 1996, Tax-deductible Pre-event Catastrophe Reserves. Journal of Insurance
Regulation, 15 (2): 175-190.
Emanuel, K., 2005, Increasing Destructiveness of Tropical Cyclones Over the Past 30
Years, Nature, 436 (4): 686-688.
Goldenberg, S.B., C.W. Landsea, A.M. Mestas-Nunez and W.M. Gray, 2001, The Recent
Increase in Atlantic Hurricane Activity: Causes and Implications. Science, 293
(5529): 474 - 479.
Grace, M.F. and R.W. Klein, 2002, Natural Disasters and the Supply of Home Insurance.
Retrieved February 3, 2006 from the Social Science Research Network Website:
http://ssrn.com/abstract=816924
Grace, M.F. and R.E. Klein, and P.R. Kleindorfer, 2004, Homeowners Insurance With
Bundled Catastrophe Coverage. The Journal of Risk and Insurance, 71: 351379.
Harrington, S. and G. Niehaus, 2003, Capital, Corporate Income Taxes, and Catastrophe
Insurance, Journal of Financial Intermediation 12: 365-389.
Milidonis, A. and M.F. Grace, 2006, Tax-deductible Pre-event Catastrophe Loss Reserves:
The case of Florida, Retrieved February 28th, 2007 from the Social Science Research
Network Website: http://ssrn.com/abstract=893154
Myers S.C. and R. Cohn, 1987, Fair Rate of Return in Property-Liability Insurance (Norwell,
MA: Kluwer Academic Publishers).
Phillips, R. D., J. D. Cummins, and F. Allen, 1998, Financial Price of Insurance in the
Multiple Line Insurance Company, Journal of Risk and Insurance 65: 597-636.
United States Government Accountability Office, Catastrophe Risk: U.S. and European
Approaches to Insure Natural Catastrophe and Terrorism Risks, Report GAO 05-199,
(Washington, DC, GAO).
Webster, P.J., P.J. Holland, J.A. Curry and H.R. Chang, 2005, Changes in Tropical Cyclone
Number, Duration, and Intensity in a Warming Environment, Science, 309: 1844-1846.
- 25 -
Appendix A
Federal Disaster Assistance Amount spent from 1983-2001: CFDA Program Codes included
The most recent (2004) Catalog of Federal Domestic Assistance (CFDA) was used to
track program codes back to the date programs were established and the changes in codes that
have taken place ever since.
Two main programs were aggregated together to estimate the amount of Federal money
spent on disaster assistance in the state of Florida. The first program, (14.701) started in 1973,
changed in 1980 (83.300), 1982 (83.516) and in 1997. The second program (59.002) started in
1970 and was consolidated in 1989 (59.008). All changes are tracked below:
83.300 Disaster Assistance (1980B)
Transferred from 14.701 (1980B)
Number changed to 83.516 (1982B)
83.537 Community Disaster Loans
Incorporated from 83.516 (1997U)
Transferred to 97.030 (2003B)
83.538 Cora Brown Fund
Incorporated from 83.516 (1997U)
Transferred to 97.031 (2003B)
83.539 Crisis Counseling
Incorporated from 83.516 (1997U)
Transferred to 97.032 (2003B)
83.540 Disaster Legal Services
Incorporated from 83.516 (1997U)
Transferred to 97.033 (2003B)
83.541 Disaster Unemployment Assistance
Incorporated from 83.516 (1997U)
Transferred to 97.034 (2003B)
83.542 Fire Suppression Assistance
Incorporated from 83.516 (1997U)
Transferred to 83.55 (2002B)
83.543 Individual and Family Grants
Incorporated from 83.516 (1997U)
Transferred to 97.035 (2003B)
83.544 Public Assistance Grants
Incorporated from 83.516 (1997U)
Transferred to 97.036 (2003B)
83.545 Disaster Housing Program
Incorporated from 83.516 (1997U)
Transferred to 97.037 (2003B)
83.548 Hazard Mitigation Grant
Incorporated from 83.516 (1997U)
Transferred to 97.039 (2003B)
59.002 Economic Injury Disaster Loans
(1970B)
Reinstated (1984B)
Consolidated into 59.008 (1989B)
Reinstated (1989U)
59.008 Disaster Loans (1967B)
Physical Disaster Loans (1970B)
Consolidated from 59.002 (1989B)
- 26 -
Table 1(i)
Descriptive Statistics: Florida Property Catastrophes (1949-2004)
Standard
Catastrophe Count
Mean
Deviation
Median
Kurtosis
Skewness
Minimum
Maximum
Brush fires
2
39,279,511
41,862,809
39,279,511
-
-
9,678,035
68,880,988
Hurricanes
28
1,755,301,407
4,568,428,604
203,167,540
19
4
601,407
23,160,673,653
Tornadoes
9
42,629,985
41,883,154
26,670,679
1
1
5,691,685
130,908,748
Wind
84
44,366,875
138,777,044
13,845,632
35
6
1,086,950
920,962,197
Other
2
94,861,714
121,006,492
94,861,714
-
-
9,297,202
180,426,225
125
428,217,673
2,251,675,582
20,203,199
86
9
601,407
23,160,673,653
TOTAL
SOURCE: Property Claims Services
NOTE: Losses were adjusted to 2004 exposure and price levels using the Housing Value Index (HVI). For the HVI we have gathered the value of
specified owner-occupied housing as reported by the U.S. Census Bureau (reported in ten year intervals back to 1950) and normalized housing
values against the 2004 housing values to get annual accumulation factors for all years since 1949.
- 27 -
Table 1(ii)
Descriptive Statistics: Florida Property Catastrophes (1990-2004)
Standard
Catastrophe Count
Mean
Deviation
Median
Kurtosis
Skewness
Minimum
Maximum
Brush fires
-
-
-
-
-
-
Hurricanes
10
4,579,136,901
6,982,381,467
2,490,809,849
7
2
Tornadoes
8
41,135,009
44,517,528
24,068,510
1
2
5,691,685
130,908,748
Wind
41
75,505,579
194,284,196
19,343,693
16
4
1,676,360
920,962,197
Other
-
-
-
-
-
-
-
-
59
834,172,505
3,240,859,911
26,670,679
40
6
TOTAL
-
-
60,491,284 23,160,673,653
1,676,360 23,160,673,653
SOURCE: Property Claims Services
NOTE: Losses were adjusted to 2004 exposure and price levels using the Housing Value Index (HVI). For the HVI we have gathered the value of
specified owner-occupied housing as reported by the U.S. Census Bureau (reported in ten year intervals back to 1950) and normalized housing
values against the 2004 housing values to get annual accumulation factors for all years since 1949.
- 28 -
Table 2:
Characteristics of the Estimated Florida Annual Aggregate Loss Distributions*
Descriptive Statistics
Estimated Distribution
based on 1949-2004 data
Estimated Distribution
based on 1990-2004 data
Probability of loss = $ 0.00 billion
32.18%
1.90%
Probability of loss > $ 0.25 billion
19.56%
55.95%
Probability of loss > $ 0.5 billion
11.61%
42.73%
Probability of loss > $ 1 billion
6.33%
31.81%
Probability of loss > $ 2 billion
3.22%
23.39%
Probability of loss > $ 5 billion
1.26%
15.47%
Probability of loss > $ 10 billion
0.62%
11.29%
Probability of loss > $ 20 billion
0.30%
8.23%
Probability of loss > $ 50 billion
0.12%
5.42%
Probability of loss > $100 billion
0.06%
3.99%
Probability of loss > $200 billion
0.03%
2.91%
*Results from Milidonis and Grace (2006).
- 29 -
Table 3: Estimated Decrease in the Price (Mark-Up) of Homeowners' Catastrophic Insurance for Florida.
Results are evaluated using an aggregate loss distribution derived from historical data on insured losses from Florida catastrophes covering period 1990-2004*
Exogenous Parameters
(1)
Attach.
Point
(2)
Alpha
+ layer


(3)
(4)
Insolvency Tax
constraint Rate


Calculations With Taxes (column 4)
(5)
(6)
(7)
Value Interest Present Value
of
Rate
of Expected
unused
Claim Costs
tax
(b)
(r)
(PVECC)
(8)
Premium
(9)
Capital
(P)
(K)
(10)
Markup
Calculations Without Taxes
(11)
Present Value
of Expected
Claim Costs
(PVECC)
(12)
(13)
Premium Capital
(P)
(14)
Markup
(15)
Change
in Price
(Markup)
Price
(K)
-
500
4.00% 25%
0.5
6.00%
274
298
148
0.09
274
274
171
-
-8.70%
500
1,000
4.00% 25%
0.5
6.00%
165
196
254
0.19
165
165
285
-
-18.96%
1,000
1,500
4.00% 25%
0.5
6.00%
131
162
290
0.23
131
131
320
-
-23.21%
1,500
2,000
4.00% 25%
0.5
6.00%
113
142
310
0.26
113
113
339
-
-25.89%
2,000
10,000
4.00% 25%
0.5
6.00%
1,095
1,430
5,717
0.31
1,095
1,095
6,052
-
-30.65%
-
10,000
4.00% 25%
0.5
6.00%
1,777
2,175
6,603
0.22
1,777
1,777
7,002
-
-22.39%
-
50,000
4.00% 25%
0.5
6.00%
4,408
5,906
37,873
0.34
4,408
4,408
39,371
-
-33.98%
- 100,000
4.00% 25%
0.5
6.00%
6,486
9,328
79,463
0.44
6,486
6,486
82,305
-
-43.81%
*Milidonis and Grace (2006)
- 30 -
Table 4: Sensitivity Analysis of Estimated Decrease in the Price (Mark-Up) of Catastrophic Homeowners Insurance for Florida.
Results are evaluated using an aggregate loss distribution derived from historical data on insured losses from Florida catastrophes covering period 1990-2004*
(1)
Attach.
Point
Exogenous Parameters
(2)
(3)
(4)
(5)
Alpha Insolvency Tax Value
+ layer constraint Rate
of
unused
tax



1,000
2,000
4.00%
1,000
2,000
1.00%
1,000
2,000
0.20%
1,000
2,000
0.02%
1,000
2,000
4.00%
1,000
2,000
4.00%
1,000
2,000
4.00%
1,000
2,000
4.00%
1,000
2,000
4.00%
1,000
2,000
4.00%
1,000
2,000
4.00%
1,000
2,000
4.00%
1,000
2,000
4.00%
1,000
2,000
4.00%
1,000
2,000
4.00%
*Milidonis and Grace (2006)

0.25
0.25
0.25
0.25
0.15
0.25
0.35
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
(b)
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
1.00
0.50
0.50
0.50
0.50
0.50
(6)
Interest
Rate
(r)
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.08
0.10
0.12
0.15
Calculations With Taxes (column 4)
(7)
(8)
(10)
(9)
Present
Premium Capital MarkValue of
up
Expected
Claim Costs
(PVECC)
244
251
253
254
244
244
244
244
244
244
244
239
235
231
225
(P)
301
311
313
314
276
301
332
303
301
300
301
298
295
292
287
(K)
599
622
628
629
625
599
568
597
599
600
599
585
573
560
543
0.24
0.24
0.24
0.24
0.13
0.24
0.36
0.24
0.24
0.23
0.24
0.25
0.26
0.26
0.28
Calculations Without Taxes
(11)
(12)
(13)
(14)
Present
Premium Capital MarkValue of
up
Expected
Claim Costs
(PVECC)
244
251
253
254
244
244
244
244
244
244
244
239
235
231
225
(P)
244
251
253
254
244
244
244
244
244
244
244
239
235
231
225
(K)
656
681
688
689
656
656
656
656
656
656
656
644
632
621
605
-
(15)
Change
in Price
(Markup)

-23.62%
-23.65%
-23.66%
-23.66%
-13.07%
-23.62%
-36.15%
-24.29%
-23.62%
-22.95%
-23.62%
-24.59%
-25.51%
-26.39%
-27.65%
- 31 -
Table 5
Social Welfare Effects from the Tax Deferred Loss Reserve Proposal using 1990-2004 Distribution
Moderate :
High :
Percentile (riskiness level)
Low : 25th
50th
75th
TOTAL
Price elasticity
-0.95
-0.71
-1.668
ILC $
84.85
229.38
623.98
Price (Mark-up)
1.38
1.6
1.79
House allocation per Risk Percentile
69%
28%
3%
100%
PTAX ($)
Housing units in Florida
QTAX
= Houses Insured with PTAX
Estimated Price
Estimated Quantity
Price (Mark-up) - No Taxes
201.94
2,877,376
2,062,215
-43.81%
41.62%
0.6550
596.39
1,167,019
836,403
-43.81%
31.11%
0.8079
1,740.90
130,445
93,490
-43.81%
73.08%
0.9401
PNO-TAX ($)
QNO-TAX = Houses Insured with PNO-TAX
Area B = Possible Tax Revenue ($)
Area C = Possible Social Welfare Gain ($)
140.42
2,877,376
126,866,510
25,074,147
414.71
1,096,566
151,959,688
23,633,607
1,210.56
130,445
4,104,387
49,581,982 328,408,180
9,799,481 58,507,234
Total Uninsured Housing Value (with taxes)
Total Uninsured Housing Value (without taxes)
Total Insured Housing Value (with taxes)
Total Insured Housing Value (without taxes)
69,166,379
174,978,975
244,145,354
75,836,809
16,160,427
191,854,009
251,530,391
23,059,224 168,062,411
- 16,160,427
58,335,847 425,168,832
81,395,071 577,070,816
4,174,840
2,992,108
Numbers in italics have been obtained from Grace, Klein and Kleindorfer (2004)
Assumptions made:
1. Market is competitive and Company is breaking even.
2. Dynamic pricing effects are excluded.
3. We force the insurer to take the capital it will need for the contract at the beginning of the year.
4. Tax revenue assumes there are no catastrophe losses.
5. The percentage of insured houses before passing the tax-deferred loss reserve proposal is assumed to be
71.67%, which is equal to the percentage of houses covered by mortgage.
- 32 -
Table 6
Federal Dollars spent in Disaster Assistance and Respective Insured Losses from Catastrophes (1983-2001)
Disaster
Cumulative
Cumulative
CFDA Amounts $
Assistance
DA
CAT Cost
Ratio
Ratio
Year
59.002*
59.008*
83.516*
83.543* 83.548*
(DA) ($)
(2004 $US)
(2004 $US)
DA/CAT** DA(t+1)/CAT**
1983
0
22,400
101,789
0
0
124,189
277,771
115,188,822
0.24%
32.17%
1984 3,744,200 13,723,700
0
0
0
17,467,900
37,055,752
4,242,725
31.26%
61.18%
1985 5,087,000 11,905,200
859,779
0
0
17,851,979
36,013,805
449,525,517
12.89%
26.48%
1986 3,419,900 24,433,450 12,484,662
0
0
40,338,012
77,572,900
0
26.53%
26.98%
1987
437,900
491,700
623,767
0
0
1,553,367
2,853,857
0
27.03%
27.29%
1988
0
391,100
622,017
0
0
1,013,117
1,781,751
79,140,698
24.00%
25.45%
1989
824,400
5,054,400
-132,221
0
0
5,746,579
9,692,150
33,731,893
24.24%
25.86%
1990 2,776,700
2,575,005
1,660,000
0
0
7,011,705
11,360,253
9,721,105
25.54%
25.72%
1991
701,500
556,900
-263,644
0
0
994,756
1,545,470
88,556,152
22.84%
82.78%
1992 4,922,400 108,060,200 200,549,586
0
0
313,532,186
467,885,159 23,485,871,488
2.66%
9.28%
1993 82,993,000 556,740,800 479,234,082
0
0 1,118,967,882 1,606,441,618
904,456,898
8.95%
9.82%
1994 12,181,900 29,117,480 117,440,528
0
0
158,739,908
219,558,424
163,209,708
9.76%
10.43%
1995 15,490,600 42,613,300 70,250,699
0
0
128,354,599
171,266,931 2,395,115,906
9.53%
10.79%
1996 11,866,301 91,933,500 166,148,087
0
0
269,947,888
347,921,469
96,663,509
10.75%
11.01%
1997 1,944,200 20,444,500 35,321,490
0
0
57,710,190
71,927,976
149,563,832
10.95%
12.17%
1998
0 67,795,561 214,717,755
0 13,475
282,526,791
340,895,367
609,330,393
11.91%
13.17%
1999
0 100,078,500 207,505,708 20,000
0
307,604,208
359,676,680
259,581,049
13.05%
14.20%
2000
0 53,296,100 240,520,580
0
0
293,816,680
333,250,241
178,638,302
14.12%
16.22%
2001
0 73,322,300 482,653,067
0
0
555,975,367
611,679,028
132,022,905
16.15%
Sources: US Census Bureau; Property Casualty Services (PCS)
Some amounts show a negative sign as they are decreased from prior year projections
* CDFA program Codes are given as those explained in Appendix A
** For example the 1995 % is calculated by dividing the sum of DA from 1983 to 1995 and divided by the respective amount of catastrophe (CAT) cost.
- 33 -
- 34 -
19
49
19
51
19
53
19
55
19
57
19
59
19
61
19
63
19
65
19
67
19
69
19
71
19
73
19
75
19
77
19
79
19
81
19
83
19
85
19
87
19
89
19
91
19
93
19
95
19
97
19
99
20
01
20
03
Number of Events
10
Figure 2: Annual Frequency of Florida Catastrophic Events
(1949-2004)
8
6
4
2
0
- 35 -
3
20/08/200
1
9
20/08/200
20/08/199
7
20/08/199
5
20/08/199
3
20/08/199
1
20/08/199
9
7
20/08/198
20/08/198
5
3
20/08/198
20/08/198
1
9
20/08/198
20/08/197
7
20/08/197
5
20/08/197
3
20/08/197
1
20/08/197
9
7
20/08/196
20/08/196
5
3
20/08/196
20/08/196
1
9
20/08/196
20/08/195
7
20/08/195
5
20/08/195
3
20/08/195
1
20/08/195
9
20/08/194
LOSS ($MILLION)
25,000
Figure 3: Individual Florida Catastrophic Loss Events
(1949-2004)
20,000
15,000
10,000
5,000
0
- 36 -
- 37 -