Risk Management and Insurance
Kenneth A. Froot*
* Froot is a Research Associate in the NBER's Programs on International
Finance and Macroeconomics, International Trade and Investment, Asset
Pricing, Corporate Finance, and Monetary Economics. He is Director of
Research at the Graduate School of Business at Harvard University.
My research over the past several years has focused on two topics:
corporate risk management, with a special emphasis on the insurance sector,
and the portfolio flows of international investors. In this article, I first discuss the
work on risk management, explaining why the insurance industry provides a
wonderful set of experiments for testing some ideas about the subject. I then turn
to my work on international portfolio flows.
Financial risk management is probably the central activity of financial
intermediaries, including banks and insurance companies. Intermediaries take
risks by investing their capital in illiquid and information-intensive financial
activities. It is these imperfections in financial markets that allow intermediaries to
make profits. But the imperfections are not merely a source of profit -- they also
create costs. That is, intermediaries must finance themselves by issuing claims
that are at least partially illiquid and information-intensive. This suggests that
exogenous shocks to intermediaries' financial capital should have implications for
the pricing and availability of the instruments in which they invest.
How do financing imperfections influence financial policies, such as risk
management, capital budgeting, and capital structure? For example, suppose
that a financial firm becomes concerned about the feasibility or cost of raising
equity capital, or that its costs of carrying a given amount of capital rise. The
marginal value of the firm's internal funds will have increased. As a result, that
firm will wish to reduce risks to its capital in order to conserve on internal funds.
The first thing the firm can do is to hedge out any and all "market risks" --
for example, risks that can be hedged without friction in the capital markets.
These hedges have zero net present value from the market's perspective, since
they are done at fair prices. However, they create additional firm value because
they allow the firm to use less capital and to raise needed capital less often.(1)
Having hedged all frictionless market risk, can the firm further reduce its
risk? Yes, the firm can alter its capital budgeting policy by raising internal hurdle
rates. At first blush, an increase in hurdle rates would seem to do little to
conserve on internal funds. After all, industrial firms are more likely to reduce
new investment than they are assets in place, so higher hurdle rates would not
reduce risk quickly. In this regard, however, financial firms are special. Financial
firms have larger and more liquid balance sheets. Higher hurdle rates would
encourage a reduction in risk exposures.
However, it would not be optimal for a financial firm to raise all its hurdle
rates by the same amount. Investments that co-vary positively with fluctuations in
overall firm capital should receive higher hurdle rates. However, investments that
co-vary negatively with internal capital should see their hurdle rates decline. In a
recent paper, Jeremy C. Stein and I model these internal hurdle rates. We show
that, in the presence of financing imperfections, optimal hurdle rates should
include an additional factor driven by co-variance with internal capital. For
internal pricing, the price of capital at risk is measured by a risk-aversion term
that reflects the shadow value of internal funds, whereas the quantity of capital at
risk is measured by a given investment's covariance with the rest of the firm's
If financial imperfections are present, then negative shocks to financial-firm capital should be associated with increases in hurdle rates and more
aggressive hedging. Unfortunately, it is difficult to provide unambiguous empirical
evidence that an intermediary's capital position matters for pricing. That is
because classical hurdle rates are not directly observable, and changes in
intermediary capital are often endogenous. Consider the often-cited correlation
between bank capital and bank lending, for example. One could argue that such
a correlation emerges because losses reduce capital, causing banks to raise
hurdle rates and cut back on lending. But it is difficult to rule out the alternative
interpretation: that a decline in lending opportunities causes the decline in lending
and the increase in observed lending rates. Under this interpretation, there is no
need for a change in bank hurdle rates.
To determine which of these explanations is correct, one would need to
observe either hurdle rates or losses that are unrelated to changes in investment
opportunities. These conditions come close to being met in one area of the
insurance markets -- catastrophe (cat) insurance. Insurers purchase catastrophe
re-insurance against natural disasters (such as hurricane, earthquake, freezing
weather conditions, and the like) to offset losses triggered by such events on the
policies they write. Such events stress insurer capital, since the trigger claims
against many policies at once. Re-insurance treaties are traded contracts that
permit insurers to pay a premium to hedge out portions of the cat risk embedded
in their policies.
Can the market for catastrophe risk help one understand whether financial
imperfections are present? Most important is the transparency in cat-risk hurdle
rates. In an essay published a few years ago, I constructed the returns from
bearing cat risk exposures over a 20-year period using historical cat re-insurance
contracts. I argued that historical cat losses as well as returns on catastrophe re-insurance appear uncorrelated with returns on other major asset classes.(3) This
suggests that the classical hurdle rate for cat risk is the risk-free rate, which is
readily observable. The implication is that cat re-insurance premiums should
equal cat re-insurance expected losses. While we cannot observe expected
losses directly, they can be estimated indirectly using models produced by
independent catastrophe modeling firms, of which there are several. While these
models are no doubt imperfect, they provide objective, scientific estimates of
expected contract losses. Thus it is possible to construct a crude, but presumably
unbiased, estimate of the cat risk embedded in each cat contract.
Data on cat re-insurance contracts since 1970 suggest that, first, re-insurance
premiums have on average exceeded expected contract losses. To reach this
conclusion, Paul O'Connell and I model the event-loss distributions from five
different natural perils across five U.S. regions. We then use the exposure
patterns of U.S. insurers to develop estimates of the cat risk imbedded in the re-insurance treaties purchased by these insurers. We find that average premiums
exceed expected losses by a multiple of four or five. That is, premiums have
historically been four or five times expected losses, a shockingly large
differential. Even allowing for considerable measurement error in the models of
actuarial risk, this suggests that cat premiums are far too high to be successfully
explained by classical hurdle rates.(4)
In the same paper, we also demonstrate that after a cat event, cat re-insurance premiums increase strongly while the quantity of cat re-insurance
purchased by insurers falls. These simultaneous movements in price and
quantity are important in identifying the role of supply-versus-demand shocks.
Prices could increase after a cat event because capital is depleted and re-insurers raise hurdle rates (that is, supply of re-insurance contracts when capital
is depleted). Alternatively, premiums could increase because there is a surge in
insurance and re-insurance demand following a cat event (that is, demand for re-insurance increases when there is an event). The change in quantity purchased
is decisive in separating these two explanations: in the former, quantity
decreases, whereas in the latter quantity rises. Our finding that the quantity of re-insurance purchased falls subsequent to an event suggests that a reduction in
the supply of re-insurance is more important than any increase in demand for
explaining premium levels and changes.
Next, we estimate re-insurance supply and demand curves explicitly in order to
examine a critical prediction of the financial imperfection models: that
intermediary hurdle rates reflect the co-variance of a particular cat risk with the
intermediary's preexisting portfolio. We find that re-insurers do indeed increase
their hurdle rate for those cat risks that are positively correlated with their
preexisting portfolios. In other words, the supply of re-insurance for a particular
cat risk falls as the risk is more highly correlated with U.S. nationwide cat risks.
This is a direct contradiction of the classical hurdle rate approach, and is
consistent with the Froot and Stein model of financial intermediaries described
Some of these conclusions require us to assume that cat events do not trigger
updates in the perceived (and modeled) probability of such events going forward.
This assumption may not hold up however. The distribution of cat risk perceived
by market participants may shift when events occur. This could lead event losses
to be correlated with premium increases and for correlated risks to (potentially)
command even higher premiums. To address this "probability updating"
hypothesis, O'Connell and I examine how the re-insurance premiums on one
type of peril change when a different peril occurs. For example, we look at how
the premiums for southeastern U.S. hurricane risks change when an earthquake
occurs in the western United States. We assume that earthquake losses do not
help us understand how well Florida construction will hold up in high winds, even
though an earthquake may teach us something about the vulnerability of
California construction to ground motion. The data demonstrate strongly that an
event loss from a particular peril increases subsequent re-insurance premiums
for that peril, but also for all other perils. Probability updating cannot explain this
result. Instead, it is consistent with the financial imperfections story, which
predicts that re-insurer losses lead to higher charges for re-insurer risk
A final pervasive fact about the cat-risk market is how little cat-risk transfer
occurs. U.S. households and businesses are underinsured in general, and
businesses in particular have relatively little cat-risk protection. Insurers who
accumulate cat exposures by writing individual insurance policies purchase only
a small amount of re-insurance, given the size of their exposures. In a well-functioning capital market, a much larger fraction of cat exposures would be
hedged. Inefficiency is suggested when a Long Island regional home insurer
asks its policyholders to bear some of the risk that a large hurricane will strike
Long Island, precisely the risk policyholders are trying to avoid.
While the financial imperfections theory explains these facts, a number of other
explanations are also helpful, including 1) monopoly power on the part of re-insurers; 2) tax and agency inefficiencies in the organizational form that re-insurance takes; 3) the high frictional costs of re-insurance (attributable to the
illiquidity of contracts and the ways in which they are transferred); 4) the
presence of adverse selection and moral hazard, which tend to degrade the
quality of the cat-risk market; 5) regulation of insurance rates by state insurance
commissioners, which influence insurers' willingness to purchase re-insurance; 6)
ex post reimbursements for cat losses from the government and industry pools,
which distort incentives to purchase re-insurance; and 7) behavioral factors that
may dampen demand for re-insurance, and particularly so for large event losses.
In a recent essay, I examine the financial imperfections explanation in addition to
these other explanations of the low levels of risk transfer.(6) I conclude that
financial imperfections are the single most robust explanation (although
combinations of these other factors are very important). I also argue that recent
and future developments in this market are going to be critical to finding the right
These recent developments are telling indeed. In the past few years, cat re-insurance contracts have been securitized for the first time (that is, sold into the
capital market as securities rather than absorbed by re-insurers as re-insurance
treaties). It is interesting to track the impact that these transactions have had. I
detail the most important landmark cat securitization in a case focusing on the
issue's pricing and its implications for risk management.(7) This 1997 transaction
involved the sale of a large fraction of a major insurer's cat exposure to the
capital market. The premiums received by investors were very large (but in line
with historical results): the premium over the risk-free rate was approximately
seven or eight times expected losses.
However, some of these generous premiums have been transitory. Even though
relatively little cat risk has been securitized to date, premiums have declined
precipitously. For example, in 1998, the same major-insurer cat exposure was
sold in an almost identical securitization. Here investors received approximately
five or six times expected loss. In 1999, the same exposure is expected to reach
the market once again in a similar security. But this time indications are that it will
fetch only about four times the expected loss.(8)
These developments suggest that, first, securitization permits additional risk-bearing capacity to be supplied by investors. Re-insurers are no longer the only
suppliers of capital. Second, the potentially lower cost of this new source of
capital allows premiums to be bid down. Even though securitizations account for
a small fraction of cat-risk transfer, they have made the market contestable.
Third, new pressures for re-insurers to reduce their costs of capital and improve
the efficiency with which they use capital will keep them competitive. But
considerable reform in the way re-insurers source funds will occur.(9)
Finally, the insurance and re-insurance industries are beginning to adjust to
changes in capital-raising capabilities, in risk-management techniques, and in
information technology. This will ultimately lead to considerable change in the
organization of these industries, in the types of insurance policies and risk-management devices available to individuals and firms, and in the way these
policies are distributed. Howard Kunreuther and I have started a project at the
NBER devoted to understanding both the supply and demand sides of these
changes. We held our first project meeting in February 1999, and the papers
given at that meeting are posted on the NBER web site.
1. For a model of corporate risk management along these lines, see K. A. Froot,
D. Scharfstein, and J. C. Stein, "Risk Management: Coordinating Corporate
Investment and Financing Decisions," NBER Working Paper No. 4084, May
1992; revised in Journal of Finance, 48 (December 1993), pp.1629-58.
2. See K. A. Froot and J. C. Stein, "Risk Management, Capital Budgeting, and
Capital Structure Policy for Financial Institutions: An Integrated Approach,"
Journal of Financial Economics, 47 (January 1998), pp. 55-82. (Revised from
NBER Working Paper No. 5403, January 1996.)
3. See K. A. Froot, B. Murphy, A. Stern, and S. Usher, "The Emerging Asset
Class: Insurance Risk," Special Report from Guy Carpenter and Company, Inc.,
July 1995. Reprinted in Viewpoint, 24, no. 3 (Summer 1995), pp.19-28.
4. K. A. Froot and P. G. O'Connell, "On the Pricing of Intermediated Risks: Theory
and Application to Catastrophe Reinsurance," NBER Working Paper No. 6011,
5. See K. A. Froot, and P. G. O'Connell, "The Pricing of US Catastrophe
Reinsurance," NBER Working Paper No. 6043, May 1997, in The Financing of
Catastrophe Risk, K. A. Froot, ed. Chicago: University of Chicago Press, 1999.
6. "The Limited Financing of Catastrophe Risk: An Overview," NBER Working
Paper No. 6025, April 1997; Introductory essay in The Financing of Catastrophe
Risk, K. A. Froot, ed. Chicago: University of Chicago Press, 1999.
7. See K. A. Froot and M. Seasholes, "USAA: Catastrophe Risk Financing," Case
no. N9-298-007, Harvard Business School, Boston, 1998.
8. The evolution of these transactions is traced out in K. A. Froot, "The Market for
Catastrophe Risk: A Clinical Examination," Harvard Business School and Journal
of Financial Economics joint conference on clinical studies, July 1999,
forthcoming. See also K. A. Froot, "The Evolving Market for Catastrophe Risk,"
Harvard University; published as a Marsh McLennan Securities and Guy
Carpenter & Co. White Paper, September 1998.
9. These issues are discussed in greater detail in the papers cited in footnote 8.