Catastrophe Insurance Options:
Are They Zero-Beta Assets?
Robert E. Hoyt* and Kathleen A. McCullough
Abstract: PCS Catastrophe Insurance Options were released in 1995 as a means of
providing property and casualty insurers with a method of hedging catastrophe
exposures. The options are based on the Property Claims Services Office (PCS) index
of catastrophe losses. Due to the fact that the underlying index is uncorrelated to
movements in the capital markets, it is believed that PCS Catastrophe Insurance
Options represent zero-beta assets. If this is true, then investment in catastrophe
options provides investors with a way to further diversify the current asset portfolios,
thereby improving portfolios’ reward-to-variability ratios. This study reviews actual
PCS Catastrophe Insurance Options performance to assess whether the hypothesis that
these contracts represent zero-beta assets is supported. In spite of relatively low
liquidity in this market thus far, our results do suggest that the actual contracts do
represent zero-beta assets.
INTRODUCTION
I
n 1992, the Chicago Board of Trade (CBOT) issued the first Catastrophe
Insurance futures and options contracts. In 1995, the contracts were
revised and a new series of options known as the PCS Catastrophe Insurance Options was released. PCS Catastrophe Insurance Options are
designed to provide insurers and reinsurers with an alternative, or supplement, to traditional reinsurance. The options allow parties to hedge their
catastrophic risk exposure through access to the capital markets. Aside
from the hedging benefits to insurers and reinsurers, the catastrophe
options also have the potential to act as zero-beta assets and, thus, provide
diversification benefits to a wide variety of investors.1
* Faculty of Risk Management and Insurance, Terry College of Business, University of Georgia, Athens, Georgia.
147
Journal of Insurance Issues, 1999, 22, 2, pp. 147–163.
Copyright © 1999 by the Western Risk and Insurance Association.
All rights reserved.
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HOYT AND M CCULLOUGH
The zero-beta characteristic was first promoted by the CBOT in its
User’s Guide for PCS Insurance Options (1995). This idea also has been
suggested in Canter et al. (1996) and O’Brien (1997). If these assets do have
zero-beta properties they can provide an effective way for investors to
improve the reward-to-variability ratio of their investment portfolios.
Several studies have considered aspects of the zero-beta characteristics
of catastrophe losses. For example, Froot et al. (1995) looked at the correlation of reinsurance contracts to the capital markets and the impact of these
contracts on portfolio returns. They found that not only was the loss
experience on a portfolio of reinsurance contracts uncorrelated to the
capital markets, but it outperformed certain classes of high-yield bonds.
Canter et al. (1996) confirmed that catastrophe experience was unrelated
to the market and hypothesized that investors could achieve positive
returns from selling PCS Catastrophe Insurance Options call spreads.
Although other studies have documented the zero-beta characteristics
of catastrophe losses generally (Froot et al., 1995; Canter et al., 1996) and
have discussed the expectation that the PCS Catastrophe Insurance
Options should trade as zero-beta assets (Canter et al., 1996), no study has
evaluated the actual trading behavior of the PCS contracts to determine
whether these contracts are actually exhibiting zero-beta characteristics in
the market. The main focus of our study is to evaluate whether the PCS
Catastrophe Insurance Options are actually trading as zero-beta assets.
One of the major problems affecting the growth of the PCS Catastrophe
Insurance Options market has been the difficulty in attracting investors to
this market. Although theoretically the contracts, whose underlying index
historically has been uncorrelated with other investments, should trade as
zero-beta assets, the low level of trading volume and the dramatic upswing
in catastrophe losses over the past 10 years make the nature of their actual
performance less clear. This relatively low level of liquidity is one of the
major motivations for studying the actual behavior of these contracts in the
market. If the contracts were actively traded and very liquid, then there is
little doubt that they would trade as zero-beta assets. However, we seek to
assess whether the contracts are actually trading as zero-beta assets, in spite
of these market imperfections.
If our results demonstrate that the current contract performance has
been consistent with zero-beta behavior, then investors who have been
sitting on the sidelines to this point might be more likely to enter this
market. This would add liquidity to an illiquid market and increase the
likelihood that what theoretically should be true about these derivatives
will actually be true in the market.
The paper is organized as follows. First, we provide a brief background
on the PCS Catastrophe Insurance Options. Second, we analyze catastro-
CATASTROPHE INSURANCE OPTIONS
149
phe losses in general, with special attention focused on their relation to the
capital markets. Third, given the exposure of reinsurers to catastrophe risk,
we examine the viability of investing in reinsurance stocks as a means of
obtaining portfolio diversification from catastrophe risk. Fourth, in order
to assess the extent to which the PCS Catastrophe Insurance Options are
behaving as zero-beta assets, we examine the relation between PCS Catastrophe Insurance Options returns and capital markets returns over the
period from September 1995 to March 1997. We conclude the paper with a
summary of our findings and the implications for investors, hedgers, and
the PCS Catastrophe Insurance Options.
AN OVERVIEW OF
CATASTROPHE INSURANCE OPTIONS
In 1992, the first series of catastrophe insurance futures and options
contracts was issued. The contracts were linked to the Insurance Services
Offices (ISO) catastrophe index.2 The contracts were not widely traded. One
of the principal problems with the first generation of contracts was the use
of the ISO indices. Not only was it difficult for insurers and reinsurers to
estimate the correlation of their own loss experience with the loss experience underlying the indices, but the contracts were based on only three
regional indices and a national index. The lack of historical data coupled
with the broad geographic areas covered by each index made it difficult to
effectively hedge catastrophe exposures, especially for specific regions of
the country.
In response to the difficulties with the original contracts, the CBOT
issued a second series of contracts in September of 1995. These contracts
corrected many of the problems associated with the first issue. For example,
the contracts are now based on an index created with data from the
Property Claims Services Office (PCS). The data supporting the PCS index
are available since 1949, providing insurers with a reasonable time series
to determine the correlation of their loss experience with the catastrophe
experience of the index. Secondly, the contracts now offered are based on
nine indices. These comprise a national index and eastern, western, midwestern, northeastern, southeastern, Texas, California, and Florida indices.
The addition of new indices tied to more specific regions reduces basis risk,
which allows insurers and reinsurers to create better hedges (Harrington
et al., 1997). It should be noted that futures contracts are no longer available.
Put options are occasionally traded, but most of the activity comes from
the trading of call spreads. PCS Catastrophe Insurance Options typically
are quoted on the basis of a premium for a given call spread. This premium
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HOYT AND M CCULLOUGH
Table 1. Trading Volume for PCS
Catastrophe Insurance Optionsa
Volume
September 1995
October 1995
November 1995
December 1995
1995 Total
40
256
706
62
January 1996
February 1996
March 1996
First Quarter Total
734
700
338
a
1064
1772
April 1996
May 1996
June 1996
Second Quarter Total
430
722
1584
July 1996
August 1996
September 1996
Third Quarter Total
1490
270
4208
October 1996
November 1996
December 1996
Fourth Quarter Total
1496
656
2060
January 1997
February 1997
March 1–13 1997
First Quarter Total (through 3/13/97)
574
1251
627
Total Trading Volume
Totals
2736
5968
4212
2452
18204
Data provided by the Chicago Board of Trade.
can then be converted to a rate-on-line to provide the purchaser and seller
a better gage of the potential profitability of the transaction.3
While these contracts have been more actively traded than the original
series of options and futures, the market is still relatively small. Table 1
provides a summary of trading activity for the period from September 1995
to March 1997.
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CATASTROPHE INSURANCE OPTIONS
Table 2. Summary of Trading Volume For PCS
Catastrophe Insurance Options
Most Frequently Traded PCS Catastrophe Insurance Options
Region
Spread
Date
Year
Number of
Days Traded
Volume
Midwestern
10/20
Jun
97
17
1004
Eastern
40/60
Sep
96
13
1230
Northeastern
40/60
Sep
96
13
167
Eastern
20/30
Mar
96
12
618
Western
80/100
Annual
96
10
876
National
25/40
March
97
9
371
National
80/100
Annual
97
8
197
National
120/140
Annual
97
7
267
National
200/250
Dec
96
6
650
National
200/250
Sep
96
6
650
Western
80/100
Annual
97
6
53
California
80/100
Annual
97
5
27
Eastern
50/70
Sep
96
5
35
Eastern
80/100
Sep
96
5
42
Midwest
10/20
Jun
96
5
51
Summary of Less Frequently Traded Call Spreads
Days of Trading
Number of Call Spreads
4
5
3
6
2
17
1
29
The volume of contracts traded has increased since the first issues.
While the total volume of contracts traded has increased, the number of
each individual call spread traded has remained relatively low. Table 2
provides a detailed account of the most actively traded call spreads.
In a survey conducted on perceptions of the use of catastrophe options
as an alternative to reinsurance, Bouzouita and Young (1998) found that
property and casualty insurance company managers felt that lack of market
liquidity was the greatest obstacle to entering the catastrophe options
market. Studies on the original contracts noted that the illiquidity of the
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HOYT AND M CCULLOUGH
market would introduce elements of price risk (D’Arcy and France, 1992).
This price risk could lead to correlation between these contracts and market
indices, even though the nature of the underlying catastrophe index would
suggest a lack of correlation (a zero-beta relation). In an analysis of the
current contracts, Canter et al. (1996) note that price risk is still an issue.3
In order to alleviate this problem, a market for the other side of the options
must be developed. Previous studies (D’Arcy and France, 1992; Hoyt and
Williams, 1995; Jaffee and Russell, 1997; McCullough, 1995) have raised the
issue that for liquidity to increase, there must be many buyers and sellers
of the contracts. While insurers clearly stand to lose from higher catastrophe losses, those authors have commented that there is no obvious group
that benefits from the occurrence of catastrophes. Canter et al. (1996)
suggest that reinsurance companies that wish to reposition their exposures
by selling contracts in one layer and purchasing contracts in another layer
may provide one source of sellers in the market. D’Arcy and France (1992)
suggest that lumber companies also may provide a market for the sellers’
side of the contracts. However, as Boose and Graham (1994) note, the
correlation between the lack of catastrophes and financial losses for many
of these firms is low. This coupled with the fact that many of these firms
do not have a large diversified exposure base implies that this group of
potential investors is unlikely to provide the number of participants necessary to create a liquid market of sellers for catastrophe options.
Another potential market includes investors wishing to exploit the
zero-beta attribute of the PCS Catastrophe Insurance Options to diversify
the risk of their overall portfolio. Modern portfolio theory suggests that as
the number of assets in a portfolio increases, the portfolio variance will
decrease and approach the average covariance of the portfolio (Copeland
and Weston, 1992). PCS Catastrophe Insurance Options may provide an
important method of diversification, since the price of the option is tied to
an index that historically has been uncorrelated with the stock and bond
markets. In terms of the theory described above, the covariance of the
catastrophe index with the market is hypothesized to be zero. Purchasing
options based on the catastrophe index would provide investors with an
opportunity to lower the risk of their portfolios through capturing the
diversification benefits of an asset that has a return that is expected to be
uncorrelated with movements in the market. Investors are able to reduce
the overall covariance, or risk, of the portfolio by adding an asset that has
a zero covariance with the existing portfolio.
In order to set the stage for our evaluation of the zero-beta aspect of
the PCS Catastrophe Insurance Options, we first consider whether the
pattern of catastrophe losses making up the underlying index for these
153
CATASTROPHE INSURANCE OPTIONS
Table 3. Correlation Analysis of Historical Catastrophe
Losses and the Financial Markets 1970–1995
Adjusted Catastrophe Lossesa
1970–1995
(p-values)
1970–1988
(p-values)
1989–1995
(p-values)
S&P 500
.0401
(.6873)
.0445
(.7046)
.0526
(.7906)
3 Month
T-Bill
–.0675
(.4978)
–.0937
(.4241)
–.2974
(.1244)
6 Month
T-Bill
–.0769
(.4400)
–.0932
(.4264)
–.2916
(.1321)
Aaa
–.0436
(.6619)
–.0074
(.9495)
–.1427
(.4688)
Baa
–.0862
(.3864)
–.0262
(.8232)
–.2580
(.1841)
a
All catastrophe losses adjusted to 1995 dollars. Correlations are Pearson correlation
coefficients. Results were qualitatively unaffected using Spearman correlation
coefficients.
options contracts exhibits zero-beta characteristics. This analysis is conducted in the next section of the paper.
CORRELATION OF CATASTROPHE LOSSES
TO THE STOCK AND BOND MARKET
Previous studies such as Canter et al. (1996) and the CBOT (1995) have
reported that catastrophe loss experience is uncorrelated with changes in
the financial markets. We examined the relation between quarterly catastrophe loss experience from 1970 to 1995 with the experience of the stock
and bond markets for that period. As seen in Table 3, the correlation
between catastrophe losses and changes in the financial markets is not
significant at the 10% level.
Given the dramatic upswing in catastrophe losses over the past 10
years, we compute correlations for the full period and for two sub-periods.
Even after adjusting for inflation, seven of the ten worst catastrophe years
have occurred since 1989. Since at least part of the reason for this upswing
in catastrophe losses is related to the significant growth in property values
exposed to catastrophes, we evaluate the recent catastrophe series separately to verify that the expected zero-beta characteristic of catastrophe
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HOYT AND M CCULLOUGH
Fig. 1. Relation between catastrophe losses and capital markets.
losses has persisted during the period of our study. No statistically significant relation was found in any of the periods. This can be seen graphically
in Figure 1, which depicts the relation between capital market returns and
the percentage change in the catastrophe index.
Whether viewed graphically or statistically, the lack of correlation
between the capital markets and the catastrophe index provides the basis
for the argument that securities with returns based on the level of a
catastrophe index should be uncorrelated with movements in the capital
markets.
If these movements can be captured in an asset, the overall covariance
of a diversified portfolio can be reduced, as the covariance between the
portion of assets invested in catastrophe-based assets and the remaining
assets in the portfolio will be zero. The issue then becomes, what is the most
effective way to capture the movements in the catastrophe index? An
investor cannot purchase units of the PCS Indices directly; thus the investor
must find a financial instrument that captures these movements in its
returns. The following sections examine two choices, the purchase of
reinsurance stocks and the purchase of PCS Catastrophe Insurance
Options.5
REINSURANCE STOCKS AS A MEANS OF
CAPTURING CATASTROPHE RISK
The CBOT has marketed PCS Catastrophe Insurance Options primarily as a means to create synthetic reinsurance—that is, as a way to transfer
a layer of catastrophe risk away from an insurance company. The purchase
CATASTROPHE INSURANCE OPTIONS
155
of a call spread is similar to the purchase of a layer of excess-of-loss
reinsurance.6
The similarities to reinsurance may lead to the expectation that the
proposed diversification benefits of investing in a portfolio of PCS Catastrophe Insurance Options can be achieved through the purchase of stock
in a reinsurance company. The loss experience of both a reinsurance
contract and a catastrophe option are tied to similar sets of exposures.
Further, Froot et al. (1995) documented the zero-beta characteristics of
portfolios of losses on reinsurance contracts. However, analysis of the betas
of a selection of reinsurance companies shows that the same diversification
benefits are not achievable.
A primary reason for this difference lies in the fact that while a
reinsurance company may have underwriting loss patterns similar to the
patterns reflected in the catastrophe options portfolio, a reinsurer’s profits
are heavily influenced by returns on its investment portfolios. Industry
averages of professional reinsurers show that in 1996, net underwriting
income was –$917,732,000 while ne t in vestmen t in come was
$3,906,210,000. The net investment income represented 92.8 percent of the
net income for professional reinsurers in 1996 (Best’s Aggregates and Averages, 1997). The relation between overall market performance and the value
of reinsurers’ stock prices can be seen in the reinsurance company betas
listed in Table 4. Canter et al. (1996) present similar numbers for reinsurer
betas, but do not comment on the factors that contribute to this correlation
with the market.
Many of the betas are close to one, indicating a high correlation with
financial market returns. The high correlation with the market indicates
that investment in reinsurance stocks would not provide the reduction in
the covariance that could be achieved with an asset having a return more
closely tied to the catastrophe index.
CATASTROPHE INSURANCE OPTIONS AS A MEANS
OF CAPTURING CATASTROPHE RISK
PCS Catastrophe Insurance Options provide a method of securitizing
the catastrophe risk described earlier. By investing in a portfolio of PCS
Catastrophe Insurance Options, an investor may be able to achieve the
desired diversification benefits.
The settlement values of the PCS Catastrophe Insurance Options are
based on the catastrophe records for that period. The anticipated settlement
value should be reflected in the price of the contract. From a seller ’s
perspective, the seller of the call spread would wish to price the spread to
reflect the probability that the option will be exercised (i.e., the catastrophe
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HOYT AND M CCULLOUGH
Table 4. Potential for Portfolio Diversification
with Reinsurance Stocks
Company
Betasa
Everest Re
1.39
General Re
1.21
IPC Holdings
NAC Re
Parnterre Holdings
.89
1.03
.51
Transatlantic Holdings
.85
Vesta Insurance Group
1.87
a
Betas collected from O’Neil Data Base, September 26, 1997 edition.
index for that period will reach the prescribed level). The pricing from this
perspective can be viewed in the same manner with which a purchaser of
a bond gages the default risk of the bond (Canter et al., 1996). Since the PCS
index, upon which these prices are developed, is not correlated with the
stock market or the bond market, then it is anticipated that the price
movements of the options will be uncorrelated with the market as well.
However, what remains untested is whether the available PCS Catastrophe
Insurance Options are actually behaving as zero-beta assets in the market.
It is the assessment of the behavior of the actual contracts available to
investors that is the focus of this study. If the PCS Catastrophe Insurance
Options already are behaving as zero-beta assets, then sorely needed
investors could be attracted into this market, producing liquidity that
would certainly reinforce the zero-beta qualities of this security.
Creation of a Portfolio of PCS
Catastrophe Insurance Options
In the 1992 version of the Catastrophe Options Contracts, Boose and
Graham (1994) describe the risk facing investors. In their discussion, they
note that due to the Pareto distribution underlying the loss exposure of the
contracts, participants entering the market for a short time period are likely
to experience high variability in returns. Another issue that makes catastrophe options unique from other options contracts is the impact the
seasonal nature of weather-related catastrophes has on the pricing and
trading patterns of the contracts. Many of the contracts are designed to
hedge specific weather-related risks such as ice storms or hurricanes.
During seasons in which the region is not exposed to the catastrophe risk,
CATASTROPHE INSURANCE OPTIONS
157
the contracts tied to the region may experience little or no movement in
price as well as minimal trading volume, since the underlying exposure is
stagnant and the contract is unlikely to settle in the money. The variation
in trading volume combined with the lack of normality in the distribution
of catastrophe losses requires that investors adopt a careful strategy when
using catastrophe options as a means of portfolio diversification.
One of the benefits of the PCS Catastrophe Insurance Options over the
previous catastrophe options offered by the CBOT is the flexibility the
options provide. Not only are there nine indices, but most of the contracts
can be traded on a quarterly basis. Additionally, the options can be traded
on a small cap or large cap basis. The small cap options track losses ranging
from $0 to $20 billion, while the large cap options track losses from $20
billion to $50 billion. In addition to these features, the contracts can be
traded at a variety of strike prices. This flexibility allows the purchasers of
the call spreads to create hedges to meet the specific needs of their firms.
It also creates an opportunity for the sellers of the contracts to diversify
their portfolio of catastrophe exposure. By selling call spreads tied to a
variety of indices over different periods, the seller is able to diversify the
risk of the option settling in-the-money while still achieving the benefits of
holding the securities. By selling contracts for different periods and different geographic regions, an investor can reduce the exposure to a given
catastrophe loss in the same way insurance companies reduce their exposure by insuring risks in a geographically dispersed area.
In order to address some potential problems encountered in the actual
market for PCS Catastrophe Insurance Options and to simulate an
approach that would be feasible for potential investors, we conduct our
analysis on portfolios of options instead of on individual contracts. The
creation of portfolios of catastrophe options is beneficial for two reasons.
First, it allows traders the ability to examine the results of a diversified
portfolio of catastrophe insurance options. Second, it provides increased
liquidity in an otherwise illiquid market. As illustrated in Table 2, many of
the options were traded on fewer than five days in the total life of the
option. Other options traded on up to 17 days of their life. The creation of
the portfolio allows for a better indication of how the price movements in
the overall pool of contracts are related to the market during the sample
period. It should be noted that while the portfolio provides some element
of liquidity in this rather thinly traded market, the overall trading is still
thin and price changes may not be reflected immediately in the prices of
the options. Additionally, the price movements also may be exaggerated.
In spite of this, the creation of portfolios, as described in the next section,
increases our sample size to over 300 in the largest portfolio and increases
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HOYT AND M CCULLOUGH
the days with trading activity as much as tenfold. Trading occurred on an
average of 20 to 25 percent of the days in each of our portfolios.
Methods of Portfolio Creation
Three approaches are used to create the options portfolios. Each of the
three approaches is described below. Data for PCS Catastrophe Insurance
Options traded in the period between September 1995 and March 1997 are
available.7 For each of these three approaches, results are estimated for the
full sample period and for two sub-periods. The two sub-periods, April
1996 to March 1997 and August 1996 to March 1997, are used to control for
the possible impact on the results of infrequent trading between September
1995 and March 1996.
Portfolio one is created as follows. All of the options traded are
included in the portfolio. On the first day in which an option is traded, the
option is added to the portfolio at its closing price for that day. The option
is then included in the portfolio until the end of its development period or
the end of the sample period. An exception to this occurs when the
catastrophe loss level for the loss period of the contract does not reach the
strike price of the contract. In this case, the CBOT drastically reduces the
price of the contract to indicate that there is little probability the option will
be exercised. When the price reduction occurs, the contract is removed
from the portfolio and the returns are based on the prices prior to its
removal. The returns are calculated on the basis of an equally-weighted
portfolio. That is, only one contract of each traded option is included in the
portfolio. Since the CBOT only marks price changes after a trade, it is
assumed that the prices of the options are stationary between trades. In
summary, portfolio one is based on the individual prices of the call options
and on one contract of each traded option being included in the portfolio,
regardless of trading volume.
A potential weakness of this method of portfolio creation stems from
the way in which the prices are marked by the CBOT. Rather than price
each half of the call spread, a trader wishing to buy or sell a call spread
makes an offer on the difference in value between the two option contracts.
This difference is known as the premium for the call spread. Once the trade
is complete, the CBOT then prices the two individual option contracts in
relation to the call spread. While it is possible to purchase individual call
options for the PCS Catastrophe Insurance Options, it is not a common
practice. A vast majority of the trading is based on call spreads. As mentioned above, the price for the call spread is developed according to the
probability that the seller of the spread will have to pay the purchaser of
the spread in the event catastrophe levels for the period reach the strike
price of the options. The premium charged accounts for the maximum
CATASTROPHE INSURANCE OPTIONS
159
amount that the seller of the spread may have to pay (i.e., how wide the
spread is). In essence, the seller of the options is being compensated for the
risk he or she is bearing up front. Once an appropriate premium level is
developed for a given spread, the prices of the individual options are
created to account for the desired difference in price. This is different from
other call spreads in which the prices for the individual options are created
first, and then the premium for the spread is developed on the basis of the
difference in price.
To account for this unique method of pricing, two additional portfolios
are created. Portfolio two is based on the changes in the premiums for the
vertical call spreads rather than on the price of the individual call options as
used in portfolio one. Including all of the call spreads in the portfolio would
have the result of biasing the results of the correlation with the market
toward zero, as many of the spreads were traded only once or twice in their
existence. In an effort to reduce this potential bias, only those spreads that
were traded five or more times were included in the portfolio. This set of
options accounts for 55.7 percent of the number of trading days and 72.1
percent of the trading volume for the period. A call spread is included in the
portfolio from the time it is first bought or sold in the market until the end
of its loss development period. As with the portfolio one, it is assumed that
prices do not change between trades. Thus, portfolio two is constructed on
the basis of the quoted premium for all call spreads traded five or more times
during their existence. One contract of each of the selected call spreads is
included in the portfolio. The results for this method of portfolio creation are
reported for the full time period and the two sub-periods.
Portfolio three is constructed in a manner similar to portfolio two. The
major difference is the measure of pricing. While returns on portfolio two
are based on the premium of the call spreads, portfolio three reflects returns
based on the rate-on-line of the call spreads. Rate-on-line combines the
premium and the size of the call spread. One contract of each of the call
spreads trading more than five times in the full time period are included
in the portfolio. Results are calculated for the full time period and the two
sub-periods.
Results
We compute betas using the standard market model, which rests on
the theory of the capital asset pricing model (see Copeland and Weston,
1992, for discussion of the CAPM). We use returns on the S&P 500 stock
index as our measure of market returns in this model. For the reasons
discussed in the previous section, we estimate the betas for three different
time periods and three different portfolios. Table 5 provides a summary of
the results calculated in this analysis.
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HOYT AND M CCULLOUGH
Table 5. Betas of the Catastrophe Options Portfolios Created
Portfolio 1a
(p-values)
Portfolio 2b
(p-values)
Portfolio 3c
(p-values)
Full Period
9/1/95–4/1/97
n = 379
–.0379
(.8560)
–.0960
(.8548)
–.1320
(.8078)
Sub-period 1
4/1/96–4/1/97
n = 233
.0625
(.5054)
–.2123
(.6243)
–.2282
(.6346)
Sub-period 2
8/1/96–4/1/97
n = 167
.0771
(.5357)
–.3421
(.5386)
–.3597
(.5701)
n = observations in
market model
a
Portfolio constructed using the price changes in the individual call options.
Portfolio constructed using the changes in the rate on line for the call spreads over the
period.
c
Portfolio constructed using the changes in premiums for the given call spreads.
b
Regardless of the time period or the method of portfolio construction
used, the results indicate that the returns on the PCS Catastrophe Insurance
Options actually traded are not statistically significantly related to the
returns in the market. Hence, our results suggest that the contracts already
are exhibiting behavior that is consistent with zero-beta assets.
As discussed above, the market for PCS Catastrophe Insurance
Options has not been very active. Our evidence that the contracts are
exhibiting zero-beta characteristics already could serve to attract additional
investors to this market. As the market liquidity increases, the pricing of
the call spreads should move closer to a value reflective of the risk being
assumed by the seller of the spread. That is, as more investors begin to use
these options for purposes other than the creation of synthetic reinsurance,
the price structure should begin to reflect a more accurate cost of risk. The
removal of this price risk may alter our numerical results. However, as the
price risk is removed, it is likely that the asset prices will more closely reflect
the movements in the PCS catastrophe index, which has been and is
expected to be uncorrelated with the market.
CONCLUSIONS
The results of this study support the hypothesis that PCS Catastrophe
Insurance Options behave as zero-beta assets. Their pricing is based upon
the anticipated movements in the PCS Catastrophe Index. The results
CATASTROPHE INSURANCE OPTIONS
161
confirm that the catastrophe index is historically uncorrelated with movements in the capital markets. Even with the low trading volume of PCS
Catastrophe Insurance Options, the current price movements do appear to
be uncorrelated with the overall movements in the market over the period
of our study.
The significance of our study is twofold. First, it provides evidence in
support of the CBOT’s claim that PCS Catastrophe Insurance Options are
zero-beta contracts. Second, it suggests that potential investors could use
these contracts as a means to efficiently diversify their portfolios. The low
correlation of the prices of catastrophe options and the movements in the
capital markets allows for a decrease in the overall risk of a well-diversified
portfolio. This reduction in risk is due to the decrease in the total covariance
of the portfolio from the addition of the uncorrelated returns of the catastrophe options. This overall reduction in risk, coupled with a potential
positive return from the investment in a portfolio of PCS Catastrophe
Insurance Options, would increase the reward-to-variability ratio of an
investor’s portfolio by a greater amount than many traditional assets. Thus,
the zero-beta attribute provides a benefit to the speculative investor as well
as to the hedger (insurers and reinsurers).
A logical extension in the market of our portfolio construction
approach would be the creation of investment funds based on pools of PCS
Catastrophe Insurance Options. These funds would generate a wider
market for investors wishing to benefit from the zero-beta characteristic of
the contracts. As investors enter the market for diversification reasons, the
overall liquidity of the market will increase, removing one of the major
concerns of insurers wishing to hedge their catastrophe exposure with the
purchase of PCS Catastrophe Insurance Options. Since the speculative
investors should be indifferent to buying or selling the options, this will
create a market for the short side (or sellers) of the options, which has been
very thin.
While the market for catastrophe options promises to provide an outlet
for investors wishing to seek diversification, other potential zero-beta
products such as catastrophe bonds are being developed. This new generation of financial instruments based on catastrophe risk provides both an
alternative to traditional catastrophe financing instruments such as reinsurance and a new outlet for investors wishing to better diversify their
existing investment portfolios.
NOTES
Zero-beta assets are assets having returns that are uncorrelated with the capital market. The
potential benefits of zero-beta assets to investors are discussed on pp. 151–152.
1
162
2
HOYT AND M CCULLOUGH
See Hoyt and Williams (1995) for a more complete discussion of these contracts.
3
The rate-on-line is defined to be the premium paid divided by the gross amount of risk
transferred.
4
Canter et al. (1996) provide a discussion of the impact of a net hedger imbalance, or a situation
in which there are more hedgers willing to buy than investors willing to sell. In some cases the
additional risk premium created by this imbalance may be up to nine percent.
5
Other methods of securitization of catastrophe risk are being explored in the market. These
include such instruments as Cat bonds, contingent surplus notes, and CatEPuts.
6
Under an excess-of-loss reinsurance treaty, the reinsurer agrees to be liable for all losses exceeding a certain amount on a given class of business during a specific period (Trieschmann
and Gustavson, 1998).
7
The pricing information used is based on the historical trading history from the CBOT.
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