THE D. E. SHAW GROUP

MARKET INSIGHTS

February 2012
Vol. 4 No. 1

Two Reinsurance ParadigmsTh e r ein s u r ance indu s t ry has seen a major convergence between traditional players and newentrants seeking to profit from untapped opportunities. This installment of Market Insights examines two main
paradigms in reinsurance—diversification and risk aversion—and explains why our firm’s reinsurance investment
approach typically yields a riskier, more concentrated, but we also think ultimately more attractive, portfolio than
the strategies employed by many of our peers.
Before detailing that argument, we start with a quick overview of the reinsurance industry and its structure forthose less familiar with it.

CONFIDENTIAL

Two Reinsurance Paradigms
BackgroundL

ike individuals or firms, insurance companies must
protect themselves against losses they cannot sustain
themselves (or which the rating agencies responsible for
evaluating their creditworthiness essentially do not permit
them to take). As such, insurers are willing to pay a risk
premium to another party, the reinsurer, to take that excess
risk (i.e., pay the reinsurer for payouts in excess of the
expected losses projected for the particular risk covered).

The insurance industry is divided into two segments: lifeand property casualty. Property catastrophe is a major
sub-segment of property casualty and covers property
losses that may result from catastrophic events, with a focus
on natural catastrophes, such as hurricanes, earthquakes,
and the like. Many insurance companies focus on a specificgeographic region and would not be able to successfully
manage solely on their own balance sheet the losses associatedwith a large natural disaster on their home turf. Reinsurance
is thus an integral part of their risk mitigation process.
Here’s how it works. Consider a Florida-based homeownerinsurance company that insures 10,000 homes in Florida.
This insurer could typically handle on its own balance
sheet any property losses arising from fire, theft, and otherlocalized events. These losses can be predicted with a highdegree of accuracy and low degree of deviation from one
year to another, given the large number of independently
insured properties and reliable statistics on the occurrenceof these sorts of events. Thus, the insurer needs to maintain
only a relatively modest capital buffer to absorb any
deviations from such losses.
In contrast to these localized events, the Florida insurer’sbalance sheet would be unable to sustain losses arising froma large hurricane that destroys 1,000 homes in its portfolio.
Managing that risk would require the insurer to preserve asizable amount of capital on its balance sheet year after year,
even though losses of that magnitude would be infrequent.
Such a solution would be very inefficient from a cost ofcapital standpoint. Reinsurers—with their ability to diversify
risk—can unburden insurance companies of some of that
risk, allowing them to maintain a capital-efficient operation.
Those reinsurers can, in turn, also purchase reinsurance
protection, which is called “retrocessional” or “retro.”
Reinsurance contracts may take different forms. One typeis a facultative contract, in which the reinsurer assumes a
portion of a particular risk in the insurer’s portfolio (e.g., it

MARKET INSIGHTS

may share with the insurer the risk of a specific large estatein the insurer’s portfolio being wiped out by fire). A second
form of reinsurance is a quota share, in which the insurer
shares with a reinsurer on a pro rata basis the economics
of a part or its entire book of business. Third, and most
relevant to our business, reinsurance may be structured as
an “excess-of-loss” contract, which protects the insurer
against specific, pre-defined losses to its book. The following
sketch, typically used in the reinsurance industry to represent
such contracts, shows four layers of excess-of-loss coveragethat might be purchased by, for example, a Florida-based
insurance company.1[ Figure 1 ]FREQUENCY

POTENTIAL LOSSES

1 in 100 Years (1%)$350 mn

Layer D

1 in 25 Years (4%)$250 mn

Layer C

1 in 10 Years (10%)

Layer A

$150 mn

Layer B

1 in 5 Years (20%)$50 mnRetained by Insurer

1 The data shown in Figure 1 is stylized and not consistent with any real-world case.

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Two Reinsurance Paradigms
The right-hand numbers represent levels of potential losses
to the insurer prior to any reinsurance recoverable (losses“from the ground up” in industry jargon). The numbers on
the left represent the expected frequency of such losses (thiswould be called the “return period” in industry parlance).
An excess-of-loss contract may cover the insured against
aggregate losses during the risk period (typically one year)
arising from a series of events or, more commonly, against
losses arising from a single event. Assuming the latter, here’s
a breakdown of these layers: The bottom part of the tower is retained by the insurer,
which would absorb losses of up to $50 million arisingfrom any single event. This piece is somewhat similar to
the equity tranche of a securitized deal or the deductible
on a homeowner or automobile insurance policy.
 Protection on Layer A is provided by the Florida Hurricane
Catastrophe Fund (FHCF), a vehicle created by the
Florida Legislature to provide insurers with subsidized
protection and thereby reduce insurance costs for Florida
homeowners. In our hypothetical example, which only
roughly depicts how the FHCF functions, the FHCF would
cover 50% of losses between $50 and $250 million. For
example, if the insurer suffered losses of $100 million fromone event, then the FHCF would reimburse it for $25
million of its losses (i.e., 50% of the losses between $50
and $100 million).
 Layer B sits side-by-side with the bottom of Layer A andrepresents an exposure to 50% of losses between $50
and $150 million. Per the diagram’s frequency scale, theannual probability that this layer will begin to suffer losses(or “attach”) is about 20%,2 and the odds that it will
suffer a total loss (or “exhaust”) are 10%. The expected
loss3 of this layer would fall between those two numbers(typically, slightly below their average). A layer’s expected
loss is one of the salient factors that reinsurers consider
when pricing a deal, along with the standard deviationof that expected loss, the layer’s expected impact on thereinsurer’s total portfolio, and various other qualitativeand quantitative factors.

2 When analyzing any actual deal, a reinsurer would, among other things,
scrutinize the information provided by the insurer and generate its own estimateof the expected loss of each layer, which typically would be higher—sometimes
meaningfully higher—than that provided by the insurer.
3 For simplicity, all expected loss figures in this paper are examples and ignore thetime value of money and other factors that would have a marginal impact on thoseestimates in any actual deal.

MARKET INSIGHTS Similarly, Layer C exposes the reinsurer to 50% of theinsurer’s losses between $150 and $250 million. There’s a
10% annual probability that this layer would attach and a
4% annual probability it will exhaust. Its expected loss isroughly 7%.
 Layer D exposes the reinsurer to all of the losses between$250 and $350 million. There’s a 4% annual probability that
this layer will attach and a 1% probability it will exhaust, andits expected loss is in the neighborhood of 2.5%.
If the insurer purchased coverage for layers A, B, C, and D
and then experienced losses of over $350 million, it would
exhaust its reinsurance coverage altogether and be obligatedto pay all losses in excess of that amount. That would
typically mean insolvency for the insurer and its failure to
pay all insured policyholders, unless a government agency
opted to step in.

Hedge Funds in the Reinsurance Space
Hedge fund managers that have entered the reinsurance
market can be divided roughly into three groups. Some firms
employ a business model that combines hedge fund activities
within a reinsurance “wrapper” structure. In this model, ahedge fund manager raises capital for a rated reinsurance
entity that writes protection on relatively low-risk events andthen invests a large portion of its balance sheet in its hedge
fund strategies. Current notable players in this space include
Third Point LLC and Greenlight Capital Inc. This structure canprovide the hedge fund manager with a form of permanent
capital and may offer investors the added upside from thereinsurance strategy, a potentially profitable exit, and certain
structural and tax benefits. Investors in this kind of structure
are much more exposed to the fund manager’s investment
strategies and to capital markets than they are to reinsurance
risk per se. Although this is an interesting approach (andone our firm doesn’t pursue), this paper doesn’t evaluate its
relative merits.
Other hedge funds active in the space offer investors more
direct exposure to reinsurance risk and can be further divided
into those investing in a rated reinsurance vehicle (whether
or not managed internally) and those utilizing an unrated
vehicle. Managers of the latter type, ourselves included,
generally collateralize their obligations through trust
accounts set up for each contract. Although this structure
does not furnish the effective leverage available to a rated
entity (we’ll discuss the link between ratings and leverage
below), it offers other important advantages, including that it
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Two Reinsurance Paradigms
can be set up quickly and wound down if market conditions
are no longer attractive. (A rated entity would take several
years before it could wind down and return any excess funds
to its investors.)
Hedge fund firms seeking direct exposure to reinsurance
risk, whether through rated or unrated entities, tend to focus
their activities on property catastrophe risk, typically throughexcess-of-loss contracts, for several reasons.
First, most observers agree that catastrophe risk is by andlarge uncorrelated to other asset classes. In most cases,
earthquakes or severe aviation accidents don’t influence—and certainly aren’t caused by—capital markets, althougha given catastrophic event could have an impact on thosemarkets if it’s large enough.
Second, we believe that property catastrophe is a business inwhich one can expect, over the long run, to get paid a risk
premium that can sometimes be abnormally large because
the reinsurance market is inefficient and opaque: it has highbarriers to entry, its positions (reinsurance contracts) are
illiquid, information does not flow freely, and non-market
participants like regulators and rating agencies meaningfully
constrain the activities of market players.
Finally, property catastrophe is what the reinsurance industry
calls a “short-tail” business. In this context (and not as
meant in statistics or portfolio theory), short tail means thatthe duration of the risk period and the time between a loss
event and a payout on that loss are both relatively short (incontrast to liability or life insurance claims, for example). The
recognition of claims also happens relatively quickly after acovered event occurs. For example, a reinsurer usually willknow shortly after an earthquake whether it has exposure,even if the exact amount has yet to be determined. By
contrast, in a long-tail business, the events that give rise
to claims (for example, a malpractice liability) are notimmediately known to the insurer and may become known
only years later when a policyholder submits a claim or
following a court ruling or judgment. The short-tail natureof the property catastrophe business is especially attractive
to hedge fund managers that operate unrated entities andtherefore must collateralize their obligations until the levelof losses becomes clear. Minimizing that period and thereby
maximizing capital efficiency are essential for such managers.
By contrast, rated entities need to set aside smaller amounts
to ensure payment of future claims, and can more actively
invest this money, before any claims must be paid.

MARKET INSIGHTSWith this background in mind, let’s move on to the coreargument of this paper.

Two Reinsurance Paradigms

T

he reinsurance market is highly influenced by two
powerful paradigms: diversification and risk aversion.
Of course, diversification and risk aversion are related(diversification being a means of controlling risk), but webelieve that traditional reinsurers seek unnecessarily highlevels of diversification and are overly risk averse whenviewed from the standpoint of portfolio efficiency.
Before we explain what accounts for this, have a look at
the indicative pricing shown in Table 1 for different levels ofrisk and how they differ between deals that are consideredby the industry to be “non-diversifiers” (contracts exposed
solely or predominantly to U.S. wind, the world’s largest
reinsurance market) and “diversifiers” (contracts exposed
to European wind, Japanese wind or earthquake, and perils
in other regions of the world). The entire table is quoted inpercentage points of the limit sold by a deal. The expected
loss column shows different levels of risk. The price columns
show the premiums paid for the coverage (called “rateon line” by industry professionals), net of brokerage fees
(which typically are 5–15% of the premium). The figuresin the expected profit columns are simply the price minus
the expected loss. Thus, if a reinsurance deal provides $100
million of coverage to the insurer (like Layer D in Figure 1),
and its price is 9%, this means the insurer pays the reinsurer$9 million for the coverage. If the deal has Layer D’s 2.5%
expected loss (or $2.5 million), then the expected profit ofthe deal is $6.5 million.
[ Table 1 ]Expected
Loss 4

Non-Diversifiers(mostly U.S. wind)

Diversifiers

Price

Expected
ProfitPrice

Expected
Profit2%

7 – 12%

5 – 10%

1 – 6%-1 – 4%7%

15 – 22%

8 – 15%

6 – 14%-1 – 7%20%

32 – 42%

12 – 22%

18 – 30%-2 – 10%4 All figures in this table reflect what we believe to be typical pricing available in thereinsurance market as of December 2011. The expected loss figures shown representinternal estimates for select deals observed in the market. Those expected loss
estimates are more conservative—often significantly more conservative—than the
expected loss figures referenced by insurers and those generated by third-party risk
modeling software.

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Two Reinsurance Paradigms
Table 1 shows how the expected profit is lower for deals
with a lower expected loss and how the industry charges
less for deals with the same expected loss if they contributeto diversification. We argue that reinsurers sometimes
undercharge for deals that are less risky or that areconsidered diversifiers, and that two related but not purely
identical impulses, diversification and risk aversion, explain
why. Let’s explore those two urges in more detail.

Diversify, Diversify, Diversify
We noted previously that insurers seek to shift theirconcentrated risk to reinsurers in an effort to reduce theircapital requirements. Reinsurers can take that risk on a more
capital-efficient basis than insurers at least in part because of
their ability to reinsure a variety of insurance companies anddiversify their exposure to different catastrophic events.
The concept of insurance diversification was well understoodby the patrons of Edward Lloyd’s bustling London coffee
house in the late 17th century. London’s importance as a
trading center in that period had intensified demand forship and cargo insurance. Ship owners, highly exposedas they were to the risk of losing their prized vessels to
weather, piracy, pilot error, and other perils, came to Lloyd’s
coffee house seeking to offload that risk to investors. Thoseinvestors divided the risk of insuring one ship into multiple
pieces, enabling them to diversify their own portfolios byselling protection on portions of many ships. That’s how the
Lloyd’s organization—still probably the largest market forcatastrophic risk—got its start.
We’ll highlight three factors that may drive the demand fordiversification, sometimes beyond what we think might berational for risk management purposes.
Rating Agencies: Diversification plays a large role in theability of modern reinsurers to obtain a quality credit ratingfrom one or more of the major rating agencies, such as A.M.
Best Company and Standard & Poor’s. Rating agencies allow
reinsurers to write more business than their balance sheets
would otherwise permit because those agencies don’t requirethat the exposure to each contract be fully collateralized.
This not only serves the narrow interests of reinsurers, but
by effectively allowing them to leverage their capital, alsobroadly benefits the economy by allowing insurers andreinsurers to write more policies. For the insurance industry
as a whole, collateralizing every potential loss would not be
economical, let alone feasible. At the limit, if the entire world

were reinsured against loss, a duplicate world would be
required to ensure payment under all scenarios.
Under rating agency guidelines, rated carriers may write
business that substantially exceeds their amount of capital
as long as they remain diversified enough to absorb certain
losses that have reasonably low probabilities.5 For example,
rating agencies would rate reinsurers on their ability to avoid
insolvency from events that may occur once in 100 or 250
years (the so-called “probable maximum loss,” or PML).
As a result, rating agencies create incentives for reinsurers
to diversify, which, while rational, may lead reinsurers toovervalue diversification when evaluated solely from a
portfolio optimization framework.
Firms that operate fully collateralized, unrated entities are
not directly subject to such requirements. However, somemanagers obtain leverage by using a “fronting” structure inwhich a traditional, rated reinsurer assumes risk on behalfof the unrated entity for a fronting fee. If the collateralized
reinsurer’s book is sufficiently diversified, the fronting
company may allow the unrated entity, for additional fees,
to post collateral in an amount less than its total portfolio of
risk. This hybrid structure thus incentivizes the unrated entity
to pursue diversification, too.
Public Market Pressures: A majority of reinsurancecompanies are publicly traded and as such the subject ofcontinuous scrutiny by sell-side analysts. The executives ofthese reinsurers are expected to outperform their peers andbeat analyst estimates each quarter rather than over the
longer term. To achieve those objectives, they typically areheavily incentivized to avoid volatile results, increasing their
desire for a more diversified portfolio than might be the caseif the company were privately held. Similarly, privately held
reinsurers owned by hedge fund managers may be averse to
the optics of drawdowns and the attendant concerns of theirinvestors. Although this emphasis on reducing volatility may
be sound as a general principle of risk management, it canbe overplayed in any market, as we believe it often is in thereinsurance space.
Segmentation in the Reinsurance Industry: Reinsurers
typically divide their underwriting activities into various
segments, with each business line organized by geographic
region or type: U.S., international (non-U.S.), aviation,
marine, and so forth. This kind of segmentation is rational
5 In the interest of brevity, this paper has simplified many of the complexities
associated with the activities of and constraints imposed by rating agencies.

MARKET INSIGHTS

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Two Reinsurance Paradigms
and allows reinsurers to develop and build upon a repositoryof expertise that, over time, offers considerable advantages.
But segmentation may also incentivize an organization towrite different lines of business for reasons other than theeconomic attractiveness of any given deal. Each desk has aninterest in maintaining its share of the company’s business,possibly with less concern for the firm’s overall profitability.
Senior management may also have an interest in ensuring acontinual flow of business to all of its desks for more general
reasons, such as maintaining market share (and the firm’s
standing in industry league tables) or generating top-line
revenue. There are alternatives. For example, our reinsurancegroup isn’t divided into different segments, permitting us tooperate efficiently with a smaller team. We also tend to write
fewer, even if more customized, deals than traditional, rated
competitors, allowing us additional room to operate withsmaller staff, opportunistically devoting our attention only tothe segments of the market that we believe have the mostpotential upside.

Risk Aversion
Reinsurers tend to be very risk averse. Reinsurers shy awayfrom risk to a degree that we believe is suboptimal for them,which, again, creates attractive investment opportunities.
One often hears in reinsurance circles the refrain, “I didn’tlose a lot of money from X” (where X is some recent
catastrophic event). While losing money is never pleasant,many in the industry seem to focus more on losses avoided
than profits missed. A member of our reinsurance teamwith a long industry pedigree once said, “For 25 years I wastaught to avoid risk; when I joined D. E. Shaw, my focus
turned to evaluating whether I am being paid enough fortaking the risk.” Our view is that one should always assess
the risk taken against the reward for taking it, and we feelthe industry typically places too much emphasis on theformer and not enough on the latter. It’s interesting to notethat the commercially available risk-modeling tools mostwidely used by many in the reinsurance industry do notincorporate the premium received by reinsurers as a coreelement of the risk analysis. We thus don’t believe those
tools provide a sufficient basis for fully estimating therisk-reward tradeoff of a particular deal.
When reinsurers underwrite risk, they typically focus onless risky deals like the “higher layers” (Layers C and D) in
Figure 1. Those layers would be hit only if an unusually large
event occurred, which is a low-probability outcome. To use acapital markets analogy, reinsurers like to write “out-of-the-

MARKET INSIGHTS

money” put options. Why would reinsurers typically write
most of their business at such low levels of risk? We identify
three potential drivers of this risk aversion.
Rating Agencies: In addition to incentivizing diversification,
rating agencies play an important role in driving underwriters
away from risk. As already noted, rating firms often focus
on a reinsurer’s ability to absorb a 1-in-100-year (or 1-in250-year, or other rare frequency) event for each peril that it
underwrites. In general, deals that have a lower probabilityof getting hit (e.g., Layer D in Figure 1) tend to have a lesser
effect on such rating agency constraints than deals with ahigher probability. That is, for each dollar of limit sold bya reinsurer, underwriting such lower probability risk will
result in less of an increase in the cumulative 1-in-100-year
modeled loss than would a deal with a higher chance ofgetting hit (e.g., Layer B in Figure 1). This is partly because of
how reinsurance contracts interact with each other.
To demonstrate that point, consider the following example.
A reinsurer may write $100 million of coverage for one
insurer in Florida and another $100 million contract for an
insurer in Louisiana. If the reinsurer were to suffer losses, inmost cases it would be because it lost on either the Florida or
the Louisiana contract. But there would be a smaller but still
significant chance it would suffer losses on both contracts if,
say, a hurricane swept through Florida only to make landfall
again in Louisiana (as Hurricane Katrina did in 2005). Let’s
assume for simplicity that a third of all storms that hit either
Florida or Louisiana actually hit both, and that the expected
loss of each $100 million contract is 15%, a very aggressive
level of risk by industry standards. The probability thatboth contracts will be hit by the same event and cause thereinsurer a $200 million loss is thus 5% (a third of 15%),6
much higher than the 1% level around which the reinsurer isprobably optimizing its portfolio. As a result, when modelingthe two deals, this reinsurer would see a very big increase
in its cumulative 1-in-100-year modeled loss (close to the$200 million of limit it wrote). By contrast, if the reinsurer
were to write the same two deals but with a considerably
smaller expected loss of 2% for each, the probability of a$200 million loss from one event would be only 0.66%,
and the resultant increase in its cumulative 1-in-100-year
modeled loss would likely be a lot lower (probably aroundthe $100 million of limit it sold in each state). Thus, if thereinsurer wanted to write more business (in terms of its limit
6 To simplify this example, we are implicitly making certain assumptions that may
not apply in all cases.

February 2012 | Vol. 4 No. 1 | Page 6 of 12

Two Reinsurance Paradigmsof coverage) in both states, it’s incentivized to write less riskybusiness to reduce the probability of a simultaneous loss
in both states and hence to reduce the effect, if any, on its
1-in-100-year constraint.
As discussed earlier, although many fully collateralized
players in the reinsurance space operate unrated entities
and as such are not affected by the risk metrics employedby rating agencies, many of those players—and a growing
number, it seems—enter into leverage arrangements ofvarious sorts, which may entail constraints on their booksimilar to those imposed by rating agencies.
Agency Issues: Humans naturally attempt to avoid negative
outcomes and are averse to financial losses. Although thistendency can confound any investment activity, we believethat the structure of the reinsurance industry promotes
unusually strong risk aversion and gives rise to agency issues
between investors in and managers of reinsurance portfolios.
We believe that reinsurance, with its low correlation toother investment activities, can be unusually diversifying
for the average investor. A rational investor, who will likely
invest only a small portion of his total assets in reinsurance,
should probably seek more risk in the reinsurance portion ofhis portfolio than his reinsurance manager might rationallydesire. After all, the manager to whom that investor has
entrusted his capital, whether through a reinsurance hedge
fund or by investing in the stock of a reinsurance company,
has quite concentrated exposure to the sector.
Employees of traditional reinsurance companies and some fully
collateralized reinsurance players have a very concentrated
exposure to reinsurance risk. Those personnel depend on
the continued solvency of their company for their salary andyear-end bonus and may have invested a significant portionof their wealth in the firm. That structural risk exposure mayplace significant downward pressure on risk-taking. Moreover,
especially in traditional reinsurance companies, compensation
schemes may incentivize employees to take reduced risk
because they are compensated less for generating upside that
may come from taking properly priced risk than they are foravoiding losses altogether.
Although agency problems in a variety of investment
contexts typically result in managers taking excessive risk
at the potential expense of investors, too often, we believe,
reinsurers take too little risk and thereby deliver suboptimal
returns for investors.

MARKET INSIGHTS

Capital Markets Pressure: Finally, trading in public markets
may intensify risk aversion. As previously noted, publicly
traded reinsurers face market scrutiny regarding theirshort-term results, which may lead them to shy away fromrisk. Although a privately held company may not have thesame advantages in terms of accessing permanent capital,
it may have more latitude to take on levels of risk that moreclosely align it with the long-term interests of its investors.

When Are Diversification andRisk Avoidance Overpriced?

W

e have seen how many operators structure theirreinsurance businesses to take advantage ofleverage, access to capital markets, and the scale thatcomes with segmenting their operations. In isolation, eachof those attributes would seemingly enhance the efficientuse of capital. But when combined with the compensation
structures and certain agency issues that prevail in muchof the industry, those attributes have turned into a hardconstraint. As a result, we believe, the market for reinsurance
is actually inefficient.
Given the incentives and constraints outlined in the previous
section, most players have no choice but to diversify theirbooks and avoid risk. The mutually reinforcing goals ofdiversification and risk avoidance mean that many of those
active in the reinsurance market must compete heavily forwhat they perceive as “diversifiers”—contracts, often insmaller markets, that are critical for meeting rating agency
or fronting arrangement diversification requirements—and lower-risk deals. With an entire industry chasing
such deals, their pricing tends to fall to levels that are lessand less attractive. At the same time, to compensate forthe increasingly unattractive pricing on diversifiers, andsometimes low-risk deals, other segments of the reinsurance
space that have higher risk or generally don’t contribute todiversification—most noticeably, the U.S. wind segmentof the market—effectively make up for that reduced
profitability. One can see that dynamic as a way in which
the non-diversifying geographic zones and certain
higher-risk deals are subsidized by diversifiers and lower-risk
deals. In this section, we discuss general considerations inpricing diversification and risk avoidance. In the following
section, we briefly discuss a more flexible approach that may
avoid those pitfalls.
As shown in Table 1 on page 4 above, diversified risks
and low-probability risks offer much lower expectedFebruary 2012 | Vol. 4 No. 1 | Page 7 of 12

Two Reinsurance Paradigms
profit to the risk taker. Although adjusting pricing for thevalue of diversification and reduced risk is rational, whenshould diversification be considered “overvalued” andrisk avoidance “inefficient?” A full quantitative analysis,
including the specification and justification of various
subjective assumptions, is beyond the scope of this paper.
Instead, we’ll lay out a few considerations that we thinkshould be applied when evaluating the price of diversificationand the degree of investor risk aversion, and that we believe
are not always fully reflected in reinsurance pricing. We
should note at the outset that many of these considerations
are not specific to the reinsurance industry but apply to thepricing of risk generally.

Selling Risk at an Expected Loss
To begin with a stark example, if the price received by thereinsurer is lower than the expected loss, that’s clearly abad deal. On a probabilistic basis, any contract with thosefeatures is projected to lose money in the long run. It would
have been unnecessary to make this obvious point if we
didn’t sometimes see deals with that pricing, as Table 1
suggests. Why does that happen? First, it may be that thereinsurer selling the protection has a different view of therisk and may think it’s lower than other market participants,
including ourselves, estimate it to be. Second, while such adeal is projected to lose money in the long run, the reinsurer
writing that business may be incentivized to accept thatpricing given the relatively low probability that the deal willturn out to be a money-loser in the near term. Although acontract that pays 6% with an expected loss of 7%—andtherefore has an expected “profit” that is in fact an expected
loss of 1%—is a losing deal on a strictly probabilistic basis,
there’s still close to a 93% chance that the deal won’t resultin a payout this year, in which case the underwriter earns 6%
and may end up being considered a smart investor.

Factoring in Expenses
But even if a deal has a positive expected profit, as mostdeals do, assessing its expected profitability also requiresthat we factor in the costs incurred by investors to generate
the deal. For hedge funds in the reinsurance space, suchcosts include the fees paid to the fund manager. In the caseof traditional reinsurers, operating costs are not quoted
as fees but are accounted for as business expenses, which
typically are 15–20% of gross premiums (in contrast to
hedge fund performance fees which are typically stated on

profit, hence on a much smaller denominator).7 Thus a deal
done by a traditional reinsurer whose expected profit isn’t
at least 15–20% of the price will not yield investors any
profit. As Table 1 suggests, various diversifying deals don’t
meet that requirement.

Costs of Capital and Leverage
Thus far, we’ve mentioned only the bare minimum that we
believe is required for a deal to have any positive value forinvestors. But investors generally expect to make higher
returns on their reinsurance investment, particularly afterfactoring in its relative illiquidity and complexity. Of course,
the particular demands of investors vary considerably bydecision maker and market conditions, and the analysis
grows further complicated when we consider that areinsurance company must account for the cost of capitalof not one but many investors, each with a potentially very
different set of preferences and costs of capital.
In addition, for reinsurers that use leverage (through a ratingor fronting arrangement), and especially when such leverage
is non-recourse to investors (which is usually the case),
further analysis may be required. For example, one could
argue that if a rated reinsurer could write business in a region
that diversifies other risks in a way that doesn’t require it to
set aside any capital for the trade, then its cost of capitalfor the trade is essentially zero. A hypothetical example ofsuch a trade might be a Chilean earthquake deal with a
0.5% expected loss, a 1% price, and thus a 0.5% expected
profit (gross of expenses). For such a low-risk deal, some
rated carriers may not be required to set aside any capitalto support the trade. And because a rated entity typicallydoes not have recourse to investors beyond the capital they
invested in it, some might argue that as long as such a trade
yields a profit, however small, it benefits the underlying
investor. Although there may be some truth to that
assertion under certain circumstances, we believe caution is
warranted. In general, we are strong advocates of exercising
great care when using leverage,8 and this precept applies toreinsurance for at least the following reasons.
First, a 0.5% chance that a Chilean quake might happen
may not affect a company’s rating, but it still increases the
7 The reinsurance industry refers to the fraction of premiums earned that are eatenby expenses as the “expense ratio.” Most property catastrophe reinsurers have an
expense ratio higher than 15–20% because they include among their expenses thebrokerage fees they must pay. Here and in the rest of this paper (including in Table 1),
we have excluded brokerage fees from the figures presented.
8 We elaborate on the benefits and hazards of financing in “Lessons from theWoodshop,” Market Insights, Vol. 2 No. 1 (March 2010).

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Two Reinsurance Paradigms
company’s overall risk. Writing separate contracts on 20
uncorrelated perils, each with a 1% annualized probability,
may cap the maximum loss from one event at the size of thelargest contract, but doing so exposes the reinsurer’s total
portfolio to an approximately 18% annual probability thatany one of these perils will occur. As long as taking a riskof that magnitude is done intentionally, this may be a fineoutcome. However, we believe that too often reinsurers andtheir investors overlook the implications of that risk for theentire portfolio.
Second, when employing leverage, one should consider thecosts and risks associated with having that leverage revoked.
A rated reinsurer, for example, may have a balance sheetthat can absorb a loss from one large event, but it may still
end up with a loss that is large enough to cause a rating
downgrade unless it can raise more capital, which may provechallenging after such a loss. When that happens, a company
may lose much of its business—as counterparties would seek
to reinsure themselves with higher-rated companies—andmay enter a death spiral that, while not necessarily resulting
in insolvency, may force the business to wind down or besold at an unattractive price. Either way, this will have anegative impact on shareholder equity beyond the original
reinsurance loss itself.
Finally, we argue that one should maintain a healthy
skepticism about deals that “model well” for rating purposes.
After the 2008 global financial crisis, various commentators
suggested that certain financial products were engineered
to generate certain modeling results, principally fromthe standpoint of reducing the capital charge required
to keep them on the balance sheet. Although we’re notsuggesting that such engineering is actively taking place inthe reinsurance space, similar modeling limitations may leadmarket participants to take on risk that models well andso may look less risky than it really is. A purely hypothetical(and admittedly exaggerated) example demonstrating
this point might be a deal that protects against a storm
happening on a particular date that has a modeled expected
loss of 0% simply because the event set in the model doesn’t
include any storm on that particular date. Tolstoy long ago
recognized this when he wrote, “Happy reinsurance deals
are all alike (no loss), and every unhappy one (a loss) is
unhappy in its own way.”
In general, there are clear incentives and benefits forreinsurers having low-probability or out-of-the-money risks
that model well. But sometimes such analysis is based on

MARKET INSIGHTS

wishful thinking and guesswork; it’s harder to get one’s headaround the likelihood of an event estimated to occur roughly
once a century and that we haven’t recently experienced
than it is for an event that tends to happen every three to five
years and is therefore a lot more familiar. The methodologicaldifficulties associated with those once-a-century events may
expose investors to risk that is not well understood and forwhich they are not always well compensated.

Risk Profile
Beyond expenses, cost of capital, and leverage
considerations, a key determinant of whether a deal is
attractive to an investor is the investor’s own risk profile,including specific concerns or preferences about exposure
to particular perils or regions. In general, the more volatile adeal is, the more uncertain its risk, and the larger a deal is in
an investor’s portfolio, the more profit the investor should
demand to fund it.
As mentioned above, we would expect that most investors
will invest in reinsurance, if at all, on only a limited basis.
Given that property catastrophe risk is uncorrelated to manyother positions in their portfolio, we believe it’s rational inmost cases for them to seek to maximize the expected profit
over all deals in the asset class while being less concerned
about the overall risk of those deals. For these investors,
participation in deals that have lower risk and a lower
expected loss than other, riskier deals may be less efficientfor their total investment portfolio.9

An Alternative ApproachThe considerable discount offered by reinsurers fordiversifiers and low-risk deals has two important
implications. First, investors in many reinsurance deals may
not be adequately compensated, and second, reinsurersthat can tolerate a more concentrated portfolio may, fromtime to time, find highly profitable opportunities. Although
there are surely a lot of different ways to operate profitably
in the reinsurance space, here are some aspects of our firm
generally, and its reinsurance business in particular, that we
believe enhance our ability to prosper in that market.

 We conduct our reinsurance activity largely within theframework of our multi-strategy funds. As such, while thestrategy can be very meaningful in dollar terms, it’s still a
relatively small part of a larger, more diversified portfolioof, in aggregate, over a dozen distinct investment activities
9 We are implicitly applying various assumptions that may not hold true for all investors.

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Two Reinsurance Paradigms
apart from reinsurance. This strategy diversification
enables us to write reinsurance business on opportunistic,
risky, and concentrated deals, to the extent that market
pricing allow us to rationally do so—in other words, aslong as we’re being well compensated.
 We manage an unrated reinsurance entity and are notsubject to rating agency diversification requirements.
Furthermore, while we have historically employed certain
leverage facilities in our reinsurance strategy, we attempt
to be very careful with that leverage. In keeping withthat approach, we generally do not use leverage that istied to diversification requirements and therefore do not
face the diversification pressures that would normallyarise for hedge fund managers using a fronting structure
or other financing arrangements that require a highdegree of diversification.
 Operating an unrated, collateralized entity also helps us
manage reinsurance market cyclicality in general. Whenthe pricing environment is favorable, we’re able to quickly
increase our reinsurance exposure; when it’s not, we canquickly reduce the size of the strategy.
 Our firm is privately held and as such is not subject toearnings season pressures or analyst estimates, both ofwhich can increase risk aversion at the expense of superior
long-term risk-adjusted returns.

expected risk-adjusted return profile, while hopefully
benefiting from our flexible platform and mandate. In lightof the constraints discussed in this paper, we have typicallyfocused our reinsurance underwriting on less competitivemarkets offering more attractive pricing, which has
historically led us to riskier but better paying contracts on
non-diversifying perils. And because our reinsurance vehicle
isn’t rated, we can write bespoke contracts that are notbeholden to rating constraints, focusing instead purely on
the expected economics of such deals.

ConclusionWe have attempted to show in this paper thatstructural constraints and decision makerpreferences are critical drivers of inefficiency in thereinsurance market. The intense demand for diversifying
contracts and the general impulse to avoid risk tends to
skew pricing and creates the potential for profit for thoseable to deploy a more concentrated and risky portfolio ofreinsurance contracts. Our firm’s structure and preferences
may lead to a more optimal long-term reinsurance portfolio
if we are successful in rigorously evaluating the tradeoffs
between risk and reward.

 We believe our firm’s compensation structure helpsalign employee interests with those of our company
and our investors. A substantial amount of mostinvestment professionals’ annual compensation isawarded as deferred compensation that is deposited in
two multi-strategy funds with allocations to a range ofstrategies, including our reinsurance activities. This is incontrast to employees at many firms in the reinsurance
industry—both traditional players and hedge fundmanagers—whose exposure to their employer isdominated by their reinsurance business because that’s
their main or even sole activity. We believe the inherent
diversification of this multi-strategy approach may
help incentivize the personnel supporting ourreinsurance activities not to shy away from attractive,
but concentrated, reinsurance risk.
Of course, structural considerations in and of themselves
cannot substitute for rigorous analysis, sound judgment,
and careful execution. We work very hard to construct areinsurance portfolio with what we believe to be an optimal

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Two Reinsurance Paradigms
Risk Associated with D. E. Shaw Group Investment Products
Any investment in a product deploying the strategy outlined in this document should be regarded as highly speculative, is appropriate only for
sophisticated investors, and involves substantial risk that should be carefully considered before deciding whether to invest. Certain categories of risk
factors that may be considered applicable to an investment in a D. E. Shaw group product include: risks associated with investing generally (e.g., noassurance of investment return, competition, force majeure events, counterparty risk); risks associated with certain investment strategies and activities(e.g., limited diversification, concentration, correlation, complexity of quantitative strategies, reliance on third-party service and information providers);
risks associated with the structure of an investment product (e.g., ongoing offering of a product, lack of management control, limited liquidity); risks
associated with the D. E. Shaw group (e.g., limited resources, reliance on key personnel, reliance on technology); risks associated with reporting, valuation,accounting, and taxation (e.g., limited availability of information on investments); legal and regulatory risks; and potential conflicts of interest and related
party transactions (e.g., shared strategies, tools, and positions; conflicting positions, conflicting incentives, other business activities). For a discussionof certain risk factors applicable to D. E. Shaw group investment products, please review the risk factors outlined in the applicable Feeder’s offering
memorandum. It should be noted that there may be other risk factors applicable to an investment in a D. E. Shaw group product that are not identified
above or in an offering memorandum but that might still result in substantial or complete losses to investors. Prospective investors should consult theirown legal, investment, tax, and other advisers as to whether an investment with the D. E. Shaw group is appropriate for them.
Certain Risks Pertaining to Reinsurance Investments
Any product deploying the strategy described in this document is expected to make significant investments in assets, such as reinsurance contracts,
catastrophe bonds, and other reinsurance-related investments, that derive their value from the occurrence or non-occurrence of catastrophic or otherevents that are traditionally the subject of insurance. The success of the investment strategy described herein is largely dependent on the ability ofadvisers to the product to forecast the probability and risk of various perils and to price investments appropriately. However, the probabilities of theoccurrence and risk of catastrophic events, whether natural or man-made, are difficult to forecast accurately, and any such forecasts will require
subjective judgments. Moreover, even accurate forecasts do not prevent against the risk of an event subject to insurance. Should such an event occur,
such investments are subject to the risk of total loss or significant reduction of principal and/or income and could expose the product to liability that
substantially exceeds any premium or other consideration received. In addition, supply of reinsurance may fluctuate in response to various factors,
including the return on reinsurance-related investments, the frequency and severity of losses, and prevailing general economic and market conditions.
Increases in the supply of reinsurance could adversely affect the reinsurance industry generally, resulting in lower premium rates, increased difficulty
and cost to identify potential cedents, and less favorable policy terms and conditions, leading to losses by a product deploying the strategy describedherein. Climate change could create and/or increase physical and financial risks, such as an increase in sea levels, changes in weather conditions, and anincrease in extreme weather events, and could make it more difficult to predict the weather generally and related catastrophic events, which could resultin financial losses to insurers and reinsurers. Finally, evolving industry practices and changing legal, judicial, social, environmental, and other conditions
could have unexpected and unintended impacts on insurance claims and coverage. Such impacts may adversely affect a product deploying the strategy
described herein, including by extending coverage beyond the product’s underwriting intent or by increasing the number and/or size of claims.
THE VIEWS EXPRESSED IN THIS DOCUMENT ARE SOLELY THOSE OF THE D. E. SHAW GROUP AS OF THE DATE OF THIS DOCUMENT. THE
VIEWS EXPRESSED IN THIS DOCUMENT ARE SUBJECT TO CHANGE WITHOUT NOTICE, AND MAY NOT REFLECT THE CRITERIA EMPLOYED BYANY COMPANY IN THE D. E. SHAW GROUP TO EVALUATE INVESTMENTS OR INVESTMENT STRATEGIES. THIS DOCUMENT IS PROVIDED TO
YOU FOR INFORMATIONAL PURPOSES ONLY. THIS DOCUMENT DOES NOT AND IS NOT INTENDED TO CONSTITUTE INVESTMENT ADVICE,NOR DOES IT CONSTITUTE AN OFFER TO SELL OR PROVIDE OR A SOLICITATION OF AN OFFER TO BUY ANY SECURITY, INVESTMENT PRODUCT,OR SERVICE. THIS DOCUMENT DOES NOT TAKE INTO ACCOUNT ANY PARTICULAR INVESTOR’S INVESTMENT OBJECTIVES OR TOLERANCEFOR RISK. THE INFORMATION CONTAINED IN THIS DOCUMENT IS PRESENTED SOLELY WITH RESPECT TO THE DATE OF THE PREPARATION
OF THIS DOCUMENT, OR AS OF SUCH EARLIER DATE SPECIFIED IN THIS DOCUMENT, AND MAY BE CHANGED OR UPDATED AT ANY TIMEWITHOUT NOTICE TO ANY OF THE RECIPIENTS OF THIS DOCUMENT (WHETHER OR NOT SOME OTHER RECIPIENTS RECEIVE CHANGES ORUPDATES TO THE INFORMATION IN THIS DOCUMENT).
NO ASSURANCES CAN BE GIVEN THAT ANY AIMS, ASSUMPTIONS, EXPECTATIONS, AND/OR OBJECTIVES DESCRIBED IN THIS DOCUMENTWOULD BE REALIZED OR THAT THE INVESTMENT STRATEGIES DESCRIBED IN THIS DOCUMENT WOULD MEET THEIR OBJECTIVES. NONE OF
THE COMPANIES IN THE D. E. SHAW GROUP; NOR THEIR AFFILIATES; NOR ANY SHAREHOLDERS, PARTNERS, MEMBERS, MANAGERS, DIRECTORS,PRINCIPALS, PERSONNEL, TRUSTEES, OR AGENTS OF ANY OF THE FOREGOING SHALL BE LIABLE FOR ANY ERRORS (TO THE FULLEST EXTENTPERMITTED BY LAW AND IN THE ABSENCE OF WILLFUL MISCONDUCT) IN THE INFORMATION, BELIEFS, AND/OR OPINIONS INCLUDED IN THISDOCUMENT, OR FOR THE CONSEQUENCES OF RELYING ON SUCH INFORMATION, BELIEFS, AND/OR OPINIONS.
THIS DOCUMENT IS FOR INFORMATIONAL PURPOSES ONLY. IT DOES NOT CONVEY AN OFFER OF ANY TYPE AND IS NOT INTENDED TO BE,
AND SHOULD NOT BE CONSTRUED AS, AN OFFER TO SELL, OR THE SOLICITATION OF AN OFFER TO BUY, ANY INTEREST IN ANY FUND ENTITY,INVESTMENT, OR OTHER INVESTMENT VEHICLE. IF SUCH AN INVESTMENT OPPORTUNITY SHOULD BECOME AVAILABLE, AN OFFERINGMEMORANDUM OUTLINING SUCH INVESTMENT OPPORTUNITY WOULD BE PROVIDED TO YOU, AND THE INFORMATION IN THIS DOCUMENTWOULD BE QUALIFIED IN ITS ENTIRETY BY REFERENCE TO ALL OF THE INFORMATION IN THE OFFERING MEMORANDUM, INCLUDING WITHOUT
LIMITATION THE RISKS OUTLINED IN THIS DOCUMENT. NOTHING IN THIS DOCUMENT CONSTITUTES INVESTMENT ADVICE. AN INVESTMENT
IN ANY INVESTMENT VEHICLE EMPLOYING THE STRATEGIES OUTLINED IN THIS DOCUMENT, IF MADE AVAILABLE, SHOULD BE REGARDED AS
HIGHLY SPECULATIVE IN NATURE AND APPROPRIATE ONLY FOR SOPHISTICATED INVESTORS THAT CAN AFFORD A LOSS OF ALL OF THEIRINVESTMENT AND THAT ARE ABLE TO INVEST FOR AN INDEFINITE PERIOD. THE PURCHASE OF INTERESTS IN ANY SUCH INVESTMENT VEHICLEIS NOT INTENDED AS A COMPLETE INVESTMENT PROGRAM. IT SHOULD NOT BE ASSUMED THAT AN INVESTMENT IN ANY SUCH INVESTMENT

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Two Reinsurance Paradigms
VEHICLE WILL BE PROFITABLE OR THAT THE FUTURE PERFORMANCE OF ANY SUCH INVESTMENT VEHICLE WILL EQUAL OR APPROXIMATE THE
PAST PERFORMANCE OF SUCH INVESTMENT VEHICLE, OF ANY OTHER INVESTMENT VEHICLE IN THE D. E. SHAW GROUP OF COMPANIES, OR OF
ANY INVESTMENT STRATEGIES DEPLOYED IN SUCH INVESTMENT VEHICLES.
ANY MEASURE OF RISK IS INHERENTLY INCOMPLETE AND DOES NOT ACCOUNT FOR ALL RISKS OR EVEN ALL MATERIAL RISKS.
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THE INFORMATION PRESENTED IN THIS DOCUMENT MAY BE BASED, IN THE SOLE AND ABSOLUTE DISCRETION OF THE D. E. SHAW GROUP, UPON
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THIS DOCUMENT MAY CONTAIN CERTAIN INFORMATION THAT CONSTITUTES “FORWARD-LOOKING STATEMENTS,” WHICH CAN BE IDENTIFIEDBY THE USE OF FORWARD-LOOKING TERMINOLOGY SUCH AS “MAY,” “EXPECT,” “WILL,” “HOPE,” “FORECAST,” “INTEND,” “TARGET,”“BELIEVE,” AND/OR COMPARABLE TERMINOLOGY (OR THE NEGATIVES THEREOF). ACTUAL EVENTS, RESULTS, AND/OR PERFORMANCE
MAY DIFFER MATERIALLY FROM WHAT IS CONTEMPLATED IN SUCH FORWARD-LOOKING STATEMENTS. ANY SUCH FORWARD-LOOKING
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