equilibrium in an ambiguity averse mean variance investors market abstract in a financial market composed of n risky assets and a riskless asset where short sales are allowed and mean variance investors can be ambiguity averse i e diffident about mean return estimates where confidence is represented using ellipsoidal uncertainty sets we derive a closed form portfolio rule based on a worst case max min criterion then in a market where all investors are ambiguity averse mean variance investors with access to given mean return and variance covariance estimates we investigate conditions regarding the existence of an equilibrium price system and give an explicit formula for the equilibrium prices in addition to the usual equilibrium properties that continue to hold in our case we show that the diffidence of investors in a homogeneously diffident with bounded diffidence mean variance investors market has a deflationary effect on equilibrium prices with respect to a pure mean variance investors market in equilibrium deflationary pressure on prices may also occur if one of the investors in an ambiguity neutral market with no initial short position decides to adopt an ambiguity averse attitude we also establish a capm like property that reduces to the classical capm in case all investors are ambiguity neutral

inefficient credit booms this paper studies the welfare properties of competitive equilibria in an economy with financial frictions hit by aggregate shocks in particular it shows that competitive financial contracts can result in excessive borrowing ex ante and excessive volatility ex post even though from a first best perspective the equilibrium always displays under borrowing from a second best point of view excessive borrowing can arise the inefficiency is due to the combination of limited commitment in financial contracts and the fact that asset prices are determined in a spot market this generates a pecuniary externality that is not internalized in private contracts the model provides a framework to evaluate preventive policies which can be used during a credit boom to reduce the expected costs of a financial crisis copyright 2008 wiley blackwell

capm and apt like models with risk measures abstract the paper deals with optimal portfolio choice problems when risk levels are given by coherent risk measures expectation bounded risk measures or general deviations both static and dynamic pricing models may be involved unbounded problems are characterized by new notions such as strong compatibility between prices and risks surprisingly the lack of bounded optimal risk and or return levels arises for important pricing models black and scholes and risk measures var cvar absolute deviation etc bounded problems present a market price of risk and generate a pair of benchmarks from these benchmarks we introduce apt and capm like analyses in the sense that the level of correlation between every available security and some economic factors explains the security expected return the risk level non correlated with these factors has no influence on any return despite the fact that we are dealing with risk functions beyond the standard deviation

anonymous markets and monetary trading abstract we study infinite horizon monetary economies characterized by trading frictions that originate from random pairwise meetings and commitment and enforcement limitations we prove that introducing occasional trade in centralized markets opens the door to an informal enforcement scheme that sustains a non monetary efficient allocation all is required is that trading partners be patient and their actions be observable we then present a matching environment in which trade may occur in large markets and yet agents trading paths cross at most once this allows the construction of models in which infinitely lived agents trade in competitive markets where money plays an essential role

asset price fluctuations without aggregate shocks we analyze the pricing of a productive asset in a class of dynamic exchange economies with heterogeneous infinitely lived agents and self enforcing intertemporal trades individual incomes fluctuate and are correlated preferences dividends and aggregate income are fixed almost all economies in this class have a unique stationary markovian equilibrium with fluctuations in asset prices as the set of unrationed households changes over time and states excess demand functions shift asset returns fluctuate and some households are shut out of asset markets examples suggest that the amplitude of these movements is negatively correlated with the productivity of the asset and with the penalty for default

investments holdup and the form of market contracts the authors analyze incomplete contracts to induce efficient investment with exogenous switching costs fixed price contracts are efficient generate some rigidity in prices are renegotiated intermittently by possibly small amounts and when inflation is positive generate asymmetric responses to shocks all consistent with evidence on prices and wages with two sided specific investments efficiency requires prices to have sufficient escalator clauses to avoid renegotiation as observed in many long term contracts a third case with one sided specific investments can generate take or pay contracts and explain why firms sometimes pay for specific investments that appear to benefit employees directly

a minimax portfolio selection strategy with equilibrium a new minimax model on optimal portfolio selection with uncertainty of both randomness and estimation in inputs is established and the corresponding optimal portfolio is derived analytically based on this result a sufficient condition for the existence and uniqueness of a nonnegative equilibrium price system under which the total demand and supply of each asset are equal is provided and an explicit formula for such a price system is obtained furthermore some properties of the equilibrium are discussed

banking a new monetarist approach we develop a model where i banks take deposits and make investments ii their liabilities facilitate third party transactions other models have i or ii not both although we argue they are intimately connected we show that they both emerge from limited commitment we describe an environment characterize desirable allocations and interpret the outcomes as banking arrangements banks are essential without them the set of feasible allocations is inferior as a technical contribution we characterize dynamically optimal credit allocations with frictions show they involve backloading and analyse how this interacts with banking we also confront the theory with economic history copyright 2013 oxford university press

stationary sunspot equilibria in a finance constrained economy abstract stationary sunspot equilibria are shown to exist in a production economy with infinite lived agents when it is not possible to borrow against future wage income equilibrium fluctuations exhibit persistence over time scales of the same order of magnitude as observed business cycles an active fiscal policy that stabilizes aggregate money expenditures can prevent such fluctuations

asset market equilibrium with short selling this paper presents simple conditions and a simple proof of the existence of equilibrium in asset markets where short selling is allowed and satiation is possible unlike standard non satiation assumptions the one used here is weak enough to be reasonable in the mean variance capital asset pricing model and in asset market models where investors maximize expected utility and where total returns to individual assets may be negative this paper analyses the existence of equilibrium in exchange economy models where choice sets may be unbounded below and satiation is likely there are two main examples of such models one is an asset market model where investors maximize expected utility and the total return to individual assets may be negative with positive probability the other is the mean variance capital asset pricing model capm where investors do not necessarily maximize expected utility but instead maximize a function of only the mean and variance of return to their portfolios in both of these models the investors choice sets will be unbounded if short selling is allowed to short sell a share of an asset means to borrow it and sell it promising to buy it back and return it to the lender at a later date formally short selling corresponds to holding a negative number of shares if unlimited short selling is allowed then there is no limit to how large negative numbers of shares can be held and therefore the choice sets are unbounded satiation can also occur both in the mean variance model and in the expected utility model unless there is a riskless asset in the expected utility model there may be satiation if the individual assets have negative returns with positive probability as the investor gets more and more shares the potential positive returns get larger and larger but so do the potential negative returns if the investor is very averse to large negative returns then he may eventually be satiated and not want any more shares in the mean variance model the expected return to an investor s portfolio increases as he holds more and more shares of the assets but so does the variance of return it may be that at some point the additional expected return gained from adding more shares to the portfolio is not sufficient to compensate for the increase in variance if so then there will be satiation satiation in the mean variance model iie analysed in nielsen 1987 1988 the expected utility model with short selling has been used in many specific analyses of portfolio selection and asset pricing to name but one connor 1984 studies arbitrage pricing in a general equilibrium model where there are no short sales restrictions the mean variance capm is of course very prominent in the finance literature because the

on the future of macroeconomics a new monetarist perspective this article argues that a pressing goal for macroeconomics is to incorporate financial considerations but we need models with solid microfoundations in particular the use of assets in facilitating exchange as well as different credit or other financial arrangements should be outcomes of not inputs to theories as a preview i suggest that mainstream macro does a good job explaining many phenomena and a financial crisis does not disprove such theory but understanding crises requires better incorporating factors related to money credit banking and liquidity the approach called new monetarist economics can help a lot in this regard

agency and optimal investment dynamics agency problems limit firms access to capital markets curbing investment firms and investors seek contractual ways to mitigate these problems what are the implications for investment we present a theory of a firm s investment dynamics in the presence of agency problems and optimal long term financial contracts we derive results relating firms investment decisions current and past cash flows firm size capital structure and dividends among the results optimal investment is increasing in current and past cash flow and optimal investment is positively serially correlated over time after controlling for investment opportunities these results hold for a range of agency problems jel g30 g31 g32 g35 d82 d86 d92 copyright 2007 oxford university press

bubbles and self enforcing debt we characterize equilibria with endogenous debt constraints for a general equilibrium economy with limited commitment in which the only consequence of default is losing the ability to borrow in future periods first we show that equilibrium debt limits must satisfy a simple condition that allows agents to exactly roll over existing debt period by period second we provide an equivalence result whereby the resulting set of equilibrium allocations with self enforcing private debt is equivalent to the allocations that are sustained with unbacked public debt or rational bubbles in contrast to the classic result by bulow and rogoff 1989a positive levels of debt are sustainable in our environment because the interest rate is sufficiently low to provide repayment incentives

on the sensitivity of mean variance efficient portfolios to changes in asset means some analytical and computational results tbis paper investigates the sensitivity of meanvariance mv efficientportfolios to changes in the means of individual assets when only a budget constraint is imposed on the investment problem the analytical results indicate that an mv efficient portfolio s weights mean and variance can be extremely sensitive to cbanges in asset means when nonnegativity constraints are also imposed on the problem the computational results confirm that a positively weigbted mv efficient portfolio s weigbts are extremely sensitive to cbanges in asset means but the portfolio s returns are not a surprisingly small increase in the mean of just one asset drives balf the securities from the portfolio yet the portfolio s expected return and standard deviation are virtually uncbanged this paper supersedes should investors hold well diversified portfolios financial support from the natural science and engineering research council of canada is gratefully acknowledged we also acknowledge the most capable assistance of ruth cornale simon ng jean marc potier and frederick shen the paper was presented at simon fraser university and the western finance association meetings in san diego we thank the participants especially stephen brown john herzog john heaney ray koopman and bruce lehmann and the editors jon ingersoll and chester spatt for

liquidity constrained markets versus debt constrained markets this paper compares two different models in a common environment the first model has liquidity constraints in that consumers save a single asset that they cannot sell short the second model has debt constraints in that consumers cannot borrow so much that they would want to default but is otherwise a standard complete markets model both models share the features that individuals are unable to completely insure against idiosyncratic shocks and that interest rates are lower than subjective discount rates in a stochastic environment the two models have quite different dynamic properties with the debt constrained model exhibiting simple stochastic steady states while the liquidity constrained model has greater persistence of shocks

capital asset pricing model capm with drawdown measure the notion of drawdown is central to active portfolio management conditional drawdown at risk cdar is defined as the average of a specified percentage of the largest drawdowns over an investment horizon and includes maximum and average drawdowns as particular cases the necessary optimality conditions for a portfolio optimization problem with cdar yield the capital asset pricing model capm stated in both single and multiple sample path settings the drawdown beta in the capm has a simple interpretation and is evaluated for hedge fund indices from the hfrx database in the single sample path setting drawdown alpha is introduced similarly to the alpha in the classical capm and is evaluated for the same hedge fund indices both drawdown beta and drawdown alpha are used to prioritize hedge fund strategies and to identify instruments for hedging against market drawdowns

equilibrium with investors using a diversity of deviation measures abstract it has been argued that investors who optimize their portfolios with attention paid only to mean and standard deviation will all end up choosing some multiple of a certain master fund portfolio justification for the capital asset pricing model of classical portfolio theory which relates individual assets to such a master fund has come from this direction in particular attempts have been made to provide solid mathematical support by showing that the imputed behavior of investors is a consequence of price equilibrium in a market in which assets are traded subject to budget constraints and optimization is carried out with respect to utility functions that depend only on mean and standard deviation in recent years reliance on standard deviation has come under increasing criticism because of inconsistencies in its effect on portfolio preferences one response has been to introduce generalized measures of deviation which lead to alternative master funds the market implications of such extensions of theory have hitherto been unclear but in this paper the existence of equilibrium is established in circumstances where nonstandard deviations are admitted equilibrium is guaranteed even when different investors use different measures of deviation and thereby end up with portfolios scaled from different master funds whether they employ the same measure or not they may impose caps on deviation which likewise may be different

equilibrium models displaying endogenous fluctuations and chaos abstract this paper surveys current developments in dynamic general equilibrium theory concerned with conditions under which endogenous fluctuations are possible existing contributions are divided into two classes the larger one consists of models with a unique perfect foresight equilibrium while the second includes models where equilibrium is indeterminate and the set of equilibria involving endogenous fluctuations includes sunspots equilibria while the two classes of models involve oscillations of different natures and with different policy implications we show that both are consistent with optimizing behavior and competitive equilibrium

money in search equilibrium in competitive equilibrium and in competitive search equilibrium we compare three market structures for monetary economies bargaining search equilibrium price taking competitive equilibrium and price posting competitive search equilibrium we also extend work on the microfoundations of money by allowing a general matching technology and entry we study how equilibrium and the effects of policy depend on market structure under bargaining trade and entry are both inefficient and inflation implies first order welfare losses under price taking the friedman rule solves the first inefficiency but not the second and inflation may actually improve welfare under posting the friedman rule yields the first best and inflation implies second order welfare losses

dynamic security design convergence to continuous time and asset pricing implications an entrepreneur with limited liability needs to finance an infinite horizon investment project an agency problem arises because she can divert operating cash flows before reporting them to the financiers we first study the optimal contract in discrete time this contract can be implemented by cash reserves debt and equity the latter is split between the financiers and the entrepreneur and pays dividends when retained earnings reach a threshold to provide appropriate incentives to the entrepreneur the firm is downsized when it runs short of cash we then study the continuous time limit of the model we prove the convergence of the discrete time value functions and optimal contracts our analysis yields rich implications for the dynamics of security prices stock prices follow a diusion reflected at the dividend barrier and absorbed at zero their volatility as well as the leverage ratio of the firm increase after bad performance stock prices and book tomarket ratios are in a non monotonic relationship a more severe agency problem entails lower price earning ratios and firm liquidity and higher default risk

moral hazard credit cycles with risk averse agents abstract we consider a simple overlapping generations model with risk averse financial agents subject to moral hazard efficient contracts for such financial intermediaries involve back loaded late career rewards compared to the analogous model with risk neutral agents risk aversion tends to reduce the growth of agents responsibilities over their careers this moderation of career growth rates can reduce the amplitude of the widest credit cycles but it also can cause small deviations from steady state to amplify over time in rational expectations equilibria we find equilibria in which fluctuations increase until the economy enters a boom bust cycle where no financial agents are hired in booms

liquidity and asset market dynamics this study analyzes economies with an essential role for liquid assets in the exchange process the model can generate multiple stationary equilibria across which asset prices market participation capitalization output and welfare are positively related it can also generate a variety of nonstationary equilibria even when fundamentals are deterministic and time invariant including periodic chaotic and stochastic sunspot equilibria with recurrent market crashes some equilibria have asset price trajectories that resemble bubbles growing and bursting endogenous private and public liquidity is also introduced sometimes it is efficient to provide enough liquid assets to satiate demand other times it is not

macroeconomic fluctuations and bargaining abstract i study the limit rule for bilateral bargaining when agents recognize that the aggregate economy and thus the match surplus follows a finite state poisson process the rule derived in this paper is of special importance for decentralized exchange economies with bargaining two simple applications are presented to illustrate this fact the first example is a model of wage bargaining and trade externalities i show that in such situations sophisticated bargaining tends to increase the volatility of the wage bill the second example is based on the kiyotaki wright model of money i explain how equilibrium prices depend in a fundamental way on the dynamic bargaining solution

money and credit with limited commitment and theft we study the interplay among imperfect memory limited commitment and theft in an environment that can support monetary exchange and credit imperfect memory makes money useful but it also permits theft to go undetected and therefore provides lucrative opportunities for thieves limited commitment constrains credit arrangements and the constraints tend to tighten with imperfect memory as this mitigates punishment for bad behavior in the credit market theft matters for optimal monetary policy but at the optimum theft will not be observed in the model the friedman rule is in general not optimal with theft and the optimal money growth rate tends to rise as the cost of theft falls

a model of moral hazard credit cycles this paper considers a simple model of credit cycles driven by moral hazard in financial intermediation financial agents or bankers must earn moral hazard rents but the cost of these rents can be efficiently spread over an agent s entire career by promising large late career rewards if the agent has a consistently successful record dynamic interactions among different generations of financial agents can create credit cycles with repeated booms and recessions in recessions a scarcity of trusted financial intermediaries limits investment and reduces employment under such conditions taxing workers to subsidize bankers may increase employment enough to make the workers better off

sensitivity analysis for mean variance portfolio problems this paper shows how to perform sensitivity analysis for mean variance mv portfolio problems using a general form of parametric quadratic programming the analysis allows an investor to examine how parametric changes in either the means or the right hand side of the constraints affect the composition mean and variance of the optimal portfolio the optimal portfolio and associated multipliers are piecewise linear functions of the changes in either the means or the right hand side of the constraints the parametric parts of the solution show the rates of substitution of securities in the optimal portfolio while the parametric parts of the multipliers show the rates at which constraints are either tightening or loosening furthermore the parametric parts of the solution and multipliers change in different intervals when constraints become active or inactive the optimal mv paths for sensitivity analyses are piecewise parabolic as in traditional mv analysis however the optimal paths may contain negatively sloping segments and are characterized by types of kinks i e points of nondifferentiability not found in mv analysis

bargaining and the value of money abstract search models of monetary exchange have typically relied on nash 1950 the bargaining problem econometrica 18 155 162 bargaining or strategic games that yield an equivalent outcome to determine the terms of trade by considering alternative axiomatic bargaining solutions in a search model with divisible money we show that the properties of the bargaining solutions do matter both qualitatively and quantitatively for questions of first degree importance in monetary economics such as i the efficiency of monetary equilibrium ii the optimality of the friedman rule and iii the welfare cost of inflation

sunspot equilibria rational bubbles in a model of money in the utility function abstract sunspot equilibria are constructed in brock s 1975 model of money in the utility function serial correlations of real balances and the nominal interest rate in these equilibria can be either positive or negative the example here suggests that local sunspots are more likely to exist when the agent s discount rate is small and that serial correlations in local sunspots when they exist are inversely related to the rate of money growth it is also shown that stationary sunspots may exist even when equilibrium cycles do not

a unified framework for monetary theory and policy analysis search theoretic models of monetary exchange are based on explicit descriptions of the frictions that make money essential however tractable versions of these models typically make strong assumptions that render them ill suited for monetary policy analysis we propose a new framework based on explicit micro foundations within which macro policy can be studied the framework is analytically tractable and easily quantifiable we calibrate the model to standard observations and use it to measure the cost of inflation we find that going from 10 percent to 0 percent inflation is worth between 3 and 5 percent of consumption much higher than previous estimates

equilibrium in capm without a riskless asset in the mean variance capm without a riskless asset the possibility of satiation sometimes leads to non existence of general equilibrium moreover because portfolio preferences are not necessarily monotone equilibrium asset prices when they exist may be negative or zero to demonstrate the possibility of non existence and to develop an intuitive understanding of when and why equilibrium does or does not exist this paper fully investigates the special case of utility functions linear in mean and variance and partially extends the results to the general case

endogenous credit cycles this paper studies models of credit with limited commitment and therefore endogenous debt limits there are multiple stationary equilibria plus nonstationary equilibria in which credit conditions change simply because of beliefs there can be equilibria in which debt limits display deterministic cyclic or chaotic dynamics as well as stochastic sunspot equilibria in which they fluctuate randomly even though fundamentals are deterministic and time invariant examples and applications are discussed we also consider different mechanisms for determining the terms of trade and compare the setup to other credit models in the literature

endogenous credit limits with small default costs we analyze an exchange economy of unsecured credit where borrowers have the option to declare bankruptcy in which case they are temporarily excluded from financial markets endogenous credit limits are imposed that are just tight enough to prevent default economies with temporary exclusion differ from their permanent exclusion counterparts in two important properties if households are extremely patient then the first best allocation is an equilibrium in the latter economies but not necessarily in the former in addition temporary exclusion permits multiple stationary equilibria with both complete and with incomplete consumption smoothing

bargaining in a non stationary environment we study an alternating offers bargaining model in which the set of possible utility pairs evolves through time in a non stationary but smooth manner in general there exists a multiplicity of subgame perfect equilibria however we show that in the limit as the time interval between two consecutive offers becomes arbitrarily small there exists a unique subgame perfect equilibrium furthermore we derive a powerful characterization of the unique limiting subgame perfect equilibrium payoffs we then explore the circumstances under which nash s bargaining solution implements this bargaining equilibrium finally we extend our results to the case when the players have time varying inside options 2003 elsevier science usa all rights reserved

sticky prices and costly credit we develop a theory of money and credit as competing payment instruments then put it to work in applications agents use cash and credit because the former latter is subject to the inflation tax transaction costs frictions that make the choice of payment method interesting also imply equilibrium price dispersion we derive closed form solutions for money demand and show how to simultaneously account for the price change facts cash credit shares in micro data and money interest correlations in macro data the effects of inflation on welfare price dispersion and markups are discussed as are nonstationary equilibria with dynamics in the price distribution

debt constrained asset markets we develop a theory of general equilibrium with endogenous debt limits in the form of individual rationality constraints similar to those in the dynamic consistency literature if an agent defaults on a contract he can be excluded from future contingent claims markets trading and can have his assets seized he cannot be excluded from spot markets trading however and he has some private endowments that cannot be seized all information is publicly held and common knowledge and there is a complete set of contingent claims markets since there is complete information an agent cannot enter into a contract in which he would have an incentive to default in some state in general there is only partial insurance variations in consumption may be imperfectly correlated across agents interest rates may be lower than they would be without constraints and equilibria may be pareto ranked

a dynamic equilibrium model of search bargaining and money abstract this paper considers dynamic equilibria in a model with random matching strategic bargaining and money equilibrium in the bargaining game is characterized in terms of a simple differential equation when we embed this characterization into the monetary economy the model can generate outcomes such as limit cycles that never arise if one imposes a myopic nash bargaining solution as has been done in the past journal of economic literature classification numbers c78 d83 e31

aid policies and growth in developing countries a new look at the empirics the relationship between foreign aid and economic growth has been the subject of much controversy a recent theme suggesting that aid promotes growth but only in a good policy environment has ratcheted up that debate in this paper we assess the importance of policy and aid in generating growth when the aid policy and growth relationship is nonlinear this allows us to examine the varying effects of aid and policy in different data segments which we do without imposing any particular structure on the underlying relationship we find that policy is an important determinant of growth we also find partial corroboration of the view that aid is growth enhancing in a good policy environment and some evidence of diminishing returns to aid these findings suggest that nonlinearities if not appropriately addressed fail to capture the detailed underlying dynamics and thereby mask some key features of the aid policy growth relationship

portfolio selection in the mean variance model a note a little recognized feature of the mean variance portfolio selection model is that induced preferences for asset holdings are not necessarily monotone more of an asset or portfolio is not necessarily better even if the asset or portfolio has positive expected return the model predicts that an investor typically wants only a limited number of shares of an asset and beyond that the increase in mean return from costlessly getting more of an asset is not sufficient to compensate for the increased risk this is reasonable if the model describes a market for contracts with unlimited liability where total returns may be negative e g they may be normally distributed it is unreasonable however if the model is used to describe a stock market with limited liability in that case it is desirable to impose conditions that ensure that there is no upper limit to how much of an asset or portfolio the investor wants the sharpest possible conditions are identified in section i since portfolio preferences are not monotone global satiation is possible again this is unrealistic when liability is limited satiation is bothersome also because it may lead to nonexistence of equilibrium in black s 4 capm without a riskless asset as demonstrated in nielsen 9 uniqueness of equilibrium in capm is investigated in nielsen 10 section i identifies the exact conditions under which global satiation does or does not occur the conditions compare the maximum ratio of mean to standard deviation of total return available from the assets with the investor s limiting degree of risk aversion as measured by the slope of his or her indifference curves at high levels of risk an optimal portfolio may or may not exist in the portfolio selection problem depending on the asymptotic slopes of the efficient frontier and the investor s indifference curves section ii identifies the exact conditions mean variance behavior can arise from expected utility maximization based on normal distributions in that case the conditions for nonsatiation and for existence of optimal portfolios can be stated in terms of the von neumannmorgenstern utility function section iii relates the relevant properties of the utility function for standard deviation and mean to properties of the von neumann morgenstern utility function