Risk Sharing And Financial Stability

The literature states that under certain conditions,risk sharing allocation is Pareto efficient,i.e.,there is no other allocations that dominate risk sharing.The welfare implication behind it is that we should share and diversify risk.However,after the 2008 financial crisis in the United States,growing number of researchers believe that systemic risk can be raised by excessive risk sharing and it contributed greatly to the occurrence of financial crisis.The interconnections between financial institutions formed by risk sharing became a channel for risk transmission and improved the overall risk of the financial system during the financial crisis.In this way,risk sharing is not always desirable for society,which is not supported by most of the traditional welfare theories.Therefore,we refine the tranditional Pareto criterion and propose the systemic Pareto criterion whereby betting systemic dominates risk sharingThe traditional welfare economics supports risk sharing because it does not take systemic risks into account.The Pareto criterion is an important notion for making welfare judgments,which tells us what should not be done.In other words,for two alternatives f and g,if all individuals(weakly)prefer f,then choosing g over f should not be supported by society.Suppose we use subjective expected utility to represent personal preferences,then the statement amounts to that if everyone’s expected utility of f is greater than or equal to g,the social planner should not replace f with g.This provides a method to aggregate personal preferences into social preference.Therefore,we only need to consider personal preferences,and neglect the aggregate concepts like systemic riskThe latest research on the Pareto standard shows that the traditional Pareto standard only considers personal preferences,which results in the judgments that do not accord with our intuitions.For example,when people have heterogeneous beliefs,that is,different subjective beliefs about the occurrence of an event,the ex ante optimal results for everyone are not preferred by them ex post.In other words,considering only personal preferences cannot reflect the true preferences of society.Studies have refined or expanded the traditional Pareto standard,such as limiting the scope of application of the Pareto criterion,so that the modified Pareto standard can be used to aggregate personal preferences to truly reflect social preferences,which requires considering things other than personal preferences.These additional things are generally not explicitly stated in the literature,but are implicitly related to risk sharing and risk diversification.Disregarding personal preferences,the literature suggests that an increase in personal risk is not good for society,so that the social planner have a reason to violate personal preferences in pursuit of greater welfare for societyAnother strand of the literature argues that there is a trade-off between individual risk and systemic risk.While one goes down,the other will increase.This challenges the standard Pareto literature.According to their reasoning,society should violate personal preferences in pursuit of lower personal risks,which is beneficial to society in their eyes,but lower personal risks is related to lower financial stability,which is obviously harmful to society.We believe that the contradiction is caused by that the existing literature does not consider the trade off between systemic risk and personal risk,but simply believes that reducing individual risk is beneficial to society.To solve this problem,based on the traditional Pareto standard,this paper takes financial stability into consideration and proposes a systemic Pareto criterion to make the judgment truly reflect social preferences.The systemic Pareto criterion does not consider personal risk because society is more concerned with systemic risks than individual risks,and individual risks are already included in their preferences.Since social planners have considered individual preferences,we do not need to consider the individual risk separatelyOverall,from the perspective of theoretical research,the efficiency of risk sharing is problematic.The systemic Pareto standard proposed in this paper unifying the contradicting literatures:the Pareto efficiency criteria and systemic risk research.From a practical view,although risk sharing is not always beneficial to society,financial institutions are encouraged to form links with each other by holding assets or debts.As a result,enhancing the homogeneity of financial institutions will undermine financial stability and even trigger a financial crisis.The research in this paper offers a microscopic basis to maintain financial stability and implementing financial supervision.The systematic Pareto criterion not only fills gaps in existing research,but also provide a micro-foundation for maintaining financial stability.The introduction is roughly divided into two parts.In the first part,we introduce the theoretical and practical background of this article in detail,as well as the contribution and innovation of this article.Specifically,the systemic Pareto criterion considers heterogeneous beliefs,information shocks,and systemic risks jointly.As far as we know,this paper is the first study to embed these three factors into framework of the Pareto criterion.In the second part,we conduct a literature review.Due to the complexity of the literature involved in this paper,we organize it in sections.We(1)review the definition and application scope of the traditional Pareto standard;(2)introduce the difficulties encountered by the traditional Pareto,that is,the inconsistency between the ex ante and ex post judgements,and the inconsistency between theory and reality.We focus the latter inconsistency;(3)introduce the reasons for the emergence of heterogeneous beliefs and their impact on financial market pricing;(4)review studies on financial stability,including the definition of systemic risk,how to measure systemic risk,the internal mechanism of financial stability,and the relationship between systemic risk and individual riskIn chapter 1,we use the example of "King’s the dilemma" to elicit the problems studied in this paper.In the King’s Dilemma,we use the good king to represent the social planner,the two princes to represent the group with heterogeneous beliefs,the bad king to represent unpredictable nature,and the bad king’s madness as an information shock.We compare the performance of risk sharing and betting,when they are impacted by information shock.It is found that compared to risk sharing,under betting allocation,everyone’s expected utility drops less,which implies that the degree of market panic is smaller and the financial market is more stable.In Chapter 2,we formally present the systematic Pareto standard.First,we review the existing Pareto criteria:non-betting and belief neutral Pareto criteria.Some of these problems,such as the incompleteness of belief neutral Pareto criterion,have made them inapplicable to some cases as the King’s Dilemma example.Agents are "quasi-rational" in that they are the maximizers of subjective expected utility,but not updating their beliefs by the Bayesian theorem.They show optimistic bias of "persistent belief." We formally define persistent beliefs based on the notion of Reverse Bayesian which implies when a new state appears,individuals assign new states positive beliefs by reducing the beliefs on existing states.The reduced proportion of individual beliefs on good states is smaller than that on bad states.The so-called "good state" and "bad state" are relative concepts.An individual has greater wealth when state s1 is realized than when state s2 is realized.We refer to s1 as a good state and s2 as a bad state.In addition,we define systemic risk as the decrease in expected utility of decision makers under the information shock.The greater the decrease in expected utility,the greater the systematic risk.The economic intuition mainly comes from financial panic.We believe that the more stable the financial system is,the more difficult it is to experience financial panic when it encounters the negative information shock,and the micro-foundation of panic is the reduction of personal expected utility.Therefore,the lower the expected reduction in utility,the smaller the systemic risk and the more stable the financial system.In addition,we compare this definition with systematic risk in the literatureThe systemic Pareto criterion can be roughly expressed as:f systemic dominates g is equivalent to(1)everyone prefers f to g;(2)f contains less systemic risk than g Condition(1)indicates that the criterion is a refinement of the traditional Pareto criterion,and our criterion considers individual preferences that involves attitude towards individual risks Condition(2)is the novel contribution of this paper,which includes systemic risk in the paradigm of the Pareto criterion.We then apply the criterion to full insurance and betting distribution.Full insurance allocation is a special case of risk-sharing allocation,which means that agents are indifferent to the realizations of states.We prove an important proposition in this paper:given that all individuals have persistent beliefs,betting dominates full insurance This is exactly the opposite of the conclusion of the existing welfare analysis.They believe that everyone’s assets under full insurance are risk free,which should be desirable for society However,when full insurance affected by information shock,the expected utilities will drop greatly,which indicates that it is more likely to cause panic and weaken market stability Finally,we compared systemic Pareto standards with existing Pareto standards from three perspectives:tautology,paternalism,and robustnessChapter 3 abandons Savage’s subjective expected utility framework and uses Choquet expected utility to represent personal preference instead.One of the great advantages of this change is that we no longer need the assumption of persistent belief to limit the way in which individuals update their beliefs.This is because in the framework of Choquet’s expected utility,individual’s belief in the possibility of an event is called capacity which is not additive Furthermore,capacity is assumed to be convex,which implies that the individual is ambiguity averse.The sum of the capacity of the exclusive states is less than 1,so including a state with a low probability does not need to reduce the beliefs of the existing states.In this way,by changing the representation of preferences,we drop one assumption and make the model more concise.In fact,we just change the way personal preferences are represented and the content of the systematic Pareto criterion is the same as before.We reanalyze the King’s Dilemma with the systemic Pareto criterion.Now individuals are ambiguity averse and they assign the greatest possible weights to the bad states and the smallest possible weights to the good states.When the disturbing state occurs,the utilities are the lowest,and the weight assigned to it by the individual is certain:1 minus the capacity of other states.This clarifies the way of belief s updating process,the utilities before and after the information shock,and the change in utilitiesFinally,we use the systemic Pareto criterion under Choquet’s expected utility framework to reprove the conclusion of this paper that betting dominates full insurance.In this way,we demonstrate that whether the decision makers are optimistic in that they have persistent belief,or pessimistic in that they admit Choquet’s expected utility,our conclusions are valid.The common part of those setups is that agents are required to treat different results differently For example,the scaled reduction of beliefs for good states is smaller,and the capacity assigned to good states is relatively small;the scaled reduction of beliefs for bad states is larger,and the capacity assigned to bad states is relatively greater.Although under subjective expected utility framework,agents are more convinced to the occurring of good states,under Choquet expects utility framework,individuals tend to think bad states will occur.The different attitude towards good and bad states is enough to ensure the validity of our conclusion.In Chapter 4,we extend the benchmark model under the case-based decision theory.The case-based decision theory is different from the decision theory under uncertainty introduced earlier and it no longer describes the possibility of an event with probability.The intuition of the theory is very simple:"People expect similar causes to result in similar results",so decision makers should make decisions based on cases,that is,their previous experience,under uncertainty.Ranking of an alternative depends on its past performance in a similar environment.If the current environment is more similar to the environment appeared in the past,and a certain alternative has performed better in the past environment,then in the current environment it is higher ranked.First,we briefly introduce the background and application scope of case-based decision theory through examples.Probabilistic method requires a clear description of the state space.Agents are required to list every possible state and every possible result,which is a difficult task in some cases.We formally introduce the case-based decision theory,compare it with the subjective expectation theory,and introduce the learning process to describe the changes in personal beliefs under information shock.Finally,we applied this decision theory to reanalyze King’s Dilemma and draw a consistent conclusion under certain reasonable conditionsChapter 5 extends the benchmark model under the mean-variance framework.The purpose of this expansion is to extend the full insurance to the general risk-sharing allocation,and directly compare different allocations through the social planner’s mean-variance utility,thereby avoiding the trouble of introducing information shocks.The variance in the mean-variance utility directly represents the systemic risk of the financial network.Therefore,it is not necessary to measure the stability of the financial system by comparing the expected utility loss before and after the information shock,which further simplifies the model.We first introduce the traditional mean-variance model and its connection with the expected utility model.Existing literature indicates that the two methods are equivalent when the asset returns involved are in the same position-scale family.The King’s Dilemma is more complicated because the beliefs of decision makers are different,so the traditional mean-variance analysis is not applicable.We also introduce the latest research results of mean-variance analysis under heterogeneous beliefs.It should be noted that although we relax the restrictions on the form of risk sharing,it limits the beliefs behind risk sharing.We find that risk sharing caused by homogenous belief involves greater systemic risk.Because the homogeneous beliefs assumption is a sufficient and unnecessary condition for risk sharing,social planners can start with the beliefs behind allocations,encourage greater divergence in beliefs,and interfere with the formation of risk sharing.This shows from another perspective that betting based on heterogeneous beliefs is beneficial to society and is consistent with the main purpose of the paperIn Chapter 6,we use the regret theory to extend the benchmark model.Chapters 2,3,and 4 measure the stability of the financial system by comparing the reduction in expected utilities before and after a given information shock.In other words,fixing the magnitude of a given information shock and compare the magnitude of the response.Now we fix the magnitude of the response,that is,the decision maker will regret the previous choice,and infer the required magnitude of the information shock,that is,the change in the prior beliefs.First,we briefly introduce the theory of regret.Next,we revisit the King’s Dilemma under the theory of regret,and find that under the betting,a greater impact is needed to cause decision makers to regret their choices,while under sharing risks,the less belief change is needed to cause regretChapter 7 forsakes the previous analysis paradigm.From the perspective of price volatility in general equilibrium,it shows that betting based on heterogeneous beliefs can reduce price fluctuations.Specifically,the equilibrium price under betting under react to the arrived information.And when the dispersing degree between individuals’ beliefs is larger,the underreaction becomes more significant.First,we introduce some anomalies documented in finance,such as short-term momentum and long-term reversals,which can be explained by the underreaction of prices to public information.We then build a binary event asset pricing model in which traders hold limited endowments.There is an underreaction to information under the setup.We believe that when the shock is negative,this underreaction is good for society because it alleviates market panic.Comparing risk sharing under homogeneous beliefs and betting under heterogeneous beliefs,we find that the latter underreaction is more significant.In other words,betting can withstand the impact of negative information and maintain price and market stabilityIn Chapter 8,we enrich examples related to systemic Pareto standards.We present the example of "tossing a coin”as a supplement to the"King’s Dilemma" and compare the two examples.The example is added to make the content easier to understand.More importantly,we list empirical facts related to the conclusions of this article,which confirm the harm caused by risk sharing to society.These facts include the 2008 U.S.financial crisis,and the The Financial Crisis Inquiry Report" specifically investigated the causes of this crisis.The correlation risks,common shocks,financial shocks,and panics involved in this article appear in the reasons summarized in the report.For example,we use "bad kings going crazy" or coins landing on edges" to represent common shocks,which shows that the research in this article is close to realityIn Chapter 9,we attempt to confirm the previous analysis and main conclusions from an empirical perspective.First,we distinguish between several notions in this article,such as risk sharing,financial institutions’ interconnectedness,financial institution homogeneity,and systemic risk.Here we emphasize that our purpose is the correlation between risk sharing,or financial Institutional homogeneity,and with stock market volatility.We mainly use the principal component analysis to measure the degree of risk sharing in China’s financial network,and find that the degree of risk sharing is negative correlated with the performance of the stock market.This counter-cyclicity can help us to prevent stock disasters.In addition,we also verify the predictive power of this indicator across institutions.As a result,it is found that for each institution,the higher the degree of risk sharing with the whole system,the higher capitalization loss ratio in the distress timesOverall,from both theoretical and empirical perspectives,this paper argues that under certain conditions,risk sharing can disrupt financial stability by compromising financial stability.Therefore,encouraging the formation of heterogeneous beliefs and betting,such as the introduction of short selling mechanisms,would enhance the stability and resilience of financial markets to negative information.