Insurance: Ambiguity aversion (part II)

Recap
>> Ambiguity describes situation where events do not have obvious probabilities
>> An ambiguity averse decision maker doesn’t like having imprecise beliefs about the true odds.
>> The simplest model of ambiguity averse behaviour is the Maxmin Expected Utility (MEU) model, where a decision maker has a set of probability distributions he/she considers reasonable, and when comparing alternative courses of action is as pessimistic as possible when deciding upon the probability distribution to use in a particular situation.

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Introduction
In the first part of this series, I introduced the idea of ambiguity aversion, a generalisation of actuarial prudence under parameter or model uncertainty. In this article I’ll briefly mention some of the many areas which can be illuminated by thinking explicitly about ambiguity aversion in financial markets. The first two sections were the focus of my SA0 dissertation.

Livelihood index insurance
It’s all very well developing abstract theories of how financial institutions behave but does the observation that financial firms or individuals act as though they were averse to ambiguity add any insight into how real financial markets behave? Robert Shiller has spent a decade or more being confused by the lack of certain financial markets that are described by classical financial economics but not observed in real life. His answer to these missing markets was to try to set some of them up, and to date this seems to have been a commercial failure. I argue that the absence of some of the markets can be explained by ambiguity aversion of financial institutions and individuals.

One of Shiller’s hypothetical products was livelihood insurance for an aspiring scientist who has committed to acquire a specialised education in a specific field. If the field is successful the scientist will prosper but, if not, the scientist will suffer, perhaps finding it impossible to switch occupations. Direct income insurance is impossible for standard moral hazard reasons: the scientist may work less hard if lifetime salary is guaranteed. Shiller instead suggests an index insurance contract which would take in premiums if incomes in the field are higher than some contractual level and provide a payout if incomes in the field are lower than this level. The insurance contract is essentially a financial swap, swapping the index of average income in the field for a risk-free income stream. The scientist could pass a substantial amount of lifetime career income risk to the capital markets without any moral hazard problems (barring grand moral hazard where the individual is able to alter the index). Were such a product available, an aspiring scientist would gladly enter into the contract to transfer some lifetime career risk through the capital markets to investors the world over.

Shiller thinks that this product should be offered by commercial insurance companies. I think that this product could never be commercially viable under any current regulatory framework; regulators would implicitly require prices to include substantial prudence margins and the high prices would choke demand. Moreover the scientist may prefer to bear well-understood individual career risk, rather than swapping some of it for poorly-understood aggregate career risk; preferring risky uncertainty to ambiguous uncertainty.

Rainfall insurance
Academic economists interested in the developing world estimate that at any given moment in time around a third of all dollar-a-day poverty is due to temporary, rather than permanent, hardship. This is true despite the observation that the vulnerable poor go to great lengths to protect themselves from shocks by sharing uncertainty with family and friends, and by not taking up high expected income activities where there is significant downside risk. This behaviour reduces overall expected future quality of life and even then only provides partial insurance; in particular, people are usually not protected against really big shocks or shocks that hit a whole family, village, or region.

Imperfections in formal insurance markets can be a matter of life and death in a developing country context. For example, if financial contracts had ensured that the economic fortunes of Ethiopian farmers had risen and fallen with the economic fortunes of the world there would have been no horrific famines in 1984-5; there was then no overall shortage of food in the world. By smoothing outcomes, the widespread availability of cheap formal insurance could lift about 300 million people out of dollar-a-day poverty. Why doesn’t it?

Agricultural risk is substantial for the rural poor and shocks tend to affect whole communities at a time, so cannot be pooled by local informal institutions. By offering a link to wider risk pools, formal crop insurance has the potential to dramatically improve the lives of the rural poor. Unfortunately, attempts to provide commercially viable crop insurance in the developing world have been dismal failures because of acute moral hazard and adverse selection.

To sidestep these problems, the World Bank has recently been trialling rainfall insurance products where insurance payouts are a function of recorded rainfall. Farmers cannot change the weather, and statistical techniques applied to historic data offer pretty good predictions, so the potential for moral hazard or adverse selection is minimal. However, rainfall insurance does not appear to be selling as easily as anticipated. In addition to the obvious point that rainfall insurance doesn’t protect against other agricultural risks and therefore might be less desirable than full crop insurance, I believe ambiguity aversion of insurers and farmers is playing a role.

Despite having a good understanding of rainfall risk, actuarial prudence increases insurance prices above best estimate. Moreover, farmers may have a good understanding of the agricultural uncertainty they face but may not understand the payoffs from the insurance product well, particularly if the relevant rainfall station is far away. They may prefer to keep the uncertainty they understand (their rainfall risk) instead of swapping some of it for uncertainty they don’t understand (payoffs from the insurance product), even if their beliefs about the payoffs from the insurance product are right ‘on average’.

Ambiguity aversion has two effects in this instance: increasing the price at which an insurer will sell and decreasing the price at which a farmer will buy. By driving a wedge between buyers and sellers, ambiguity aversion constrains trade, even in simple products like rainfall insurance.

Credit ratings should be two-dimensional
Credit ratings are supposed to categorise securities based on the likelihood of default. However, do rating agencies really base credit ratings on their best estimate default probability or do they penalise ambiguity, giving lower ratings to uncertainty they don’t understand?

This ambiguity aversion in credit ratings might make commercial sense, as rating agencies are more likely to be blamed when a poorly understood security unexpectedly defaults than the same situation for a well understood security. However, if credit ratings drive asset prices then ambiguity aversion in ratings is bad for anyone trying to pass on ambiguous uncertainty to capital markets; their securities are being arbitrarily discounted due to the ambiguity aversion of rating agencies. Could this be part of the explanation for the slow growth of cat bond markets (see footnote)?

Investors may well be averse to ambiguity, but it is unlikely that they will be exactly as averse to ambiguity as credit rating agencies. If rating agencies could separately provide information on risk and ambiguity, rather than lumping the two together, investors could make up their own minds about how to price ambiguity and ambiguous securities may be easier to pass to capital markets.

Asset market volatility
Elementary reasoning suggests that an investor should be rewarded in expected value terms for taking on market risk: why else would anyone take on market risk? However, this argument becomes a little weaker if the market participants with deep pockets are averse to ambiguity, holding bid prices that are strictly lower than offer prices. At any moment in time these investors would ensure that market prices stay within some range they consider reasonable. The precise market price within this range would however be determined by supply and demand of other investors driven by more mundane concerns, such as liquidity and statements of investment principles. Asset price volatility would be much higher than can be explained by fundamentals, as appears to be the case in practice.

Classical financial theories, such as the Capital Asset Pricing Model (CAPM), assume that all market participants are expected utility maximisers, holding bid prices exactly equal to offer prices. To my mind this is a poor assumption as active market participants with deep pockets do seem to hold bid prices that are quite a bit lower than offer prices. If the big players are indeed ambiguity averse the lessons would be that investors should buy and hold market risk for long periods so as to spread out the volatility within the big players’ bid-offer spread, and that timing can be important.

Mutuality
Until recently insurance companies in most developed countries have been mutuals where, in addition to receiving claim payouts, policyholders share in the profits of the company. There is a sense that mutuals should prosper when regulation forces insurers to price prudently, as though they were averse to ambiguity, and insurance companies hold ambiguous beliefs about the risks to be insured.

Consider an insurance company selling insurance products to a large number of policyholders. Regulation forces all insurance companies to price prudently under ambiguity, charging more than the best estimate cost as a precaution against getting the odds wrong. If the insurance portfolio behaves as expected the company will make a profit on the policies sold. Indeed, even if the insurance company is somewhat unlucky the company will still make a small profit, due to the prudent pricing.

Under prudential regulation, competition on price alone cannot reduce the insurance company’s expected profit to zero. However, by pricing prudently but then allowing policyholders a share in the performance of the insurance company’s total risk portfolio, policies can be offered that are better value for the policyholder while maintaining a low probability of insurer insolvency.

Mutuality may have gone out of vogue in developed insurance markets, where actuaries have a good understanding of the odds, but should still have a place in lines of business where the odds are less well known, such as those in developing countries.

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Footnote
A catastrophe (cat) bond is a high-yield debt instrument designed to pass catastrophic insurance risks from insurers and reinsurers to capital markets.

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Further reading
>> You can read Daniel Clarke’s full SA0 dissertation by searching for “Daniel Clarke” on the profession’s website or directly at www.actuaries.org.uk/files/pdf/library/ClarkeDaniel_
AmbiguityAversionandInsurance_20070914.pdf

>> Robert Shiller wrote about macro markets in The New Financial Order, 2003. Reports of commercial failure include ‘New ETFs Struggle to Gain Footing’ in the Wall Street Journal, January 2008

>> For a non-technical introduction to finance for the poor, see Yunus’s Nobel Lecture at http://nobelprize.org/nobel_prizes/peace/laureates/2006/  

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Daniel Clarke is currently a doctoral candidate in economics and part time lecturer in actuarial science at Oxford University. His first article on ambiguity aversion can be found in the April 2008 edition of The Actuary or at http://www.the-actuary.org.uk/757470