robust portfolio optimization with derivative insurance guarantees robust portfolio optimization aims to maximize the worst case portfolio return given that the asset returns are allowed to vary within a prescribed uncertainty set if the uncertainty set is not too large the resulting portfolio performs well under normal market conditions however its performance may substantially degrade in the presence of market crashes that is if the asset returns materialize far outside of the uncertainty set we propose a novel robust optimization model for designing portfolios that include european style options this model trades off weak and strong guarantees on the worst case portfolio return the weak guarantee applies as long as the asset returns are realized within the prescribed uncertainty set while the strong guarantee applies for all possible asset returns the resulting model constitutes a convex second order cone program which is amenable to efficient numerical solution procedures we evaluate the model using simulated and empirical backtests and analyze the impact of the insurance guarantees on the portfolio performance

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

portfolio optimization with tracking error constraints this article explores the risk and return relationship of active portfolios subject to a constraint on tracking error volatility tev which can also be interpreted in terms of value at risk such a constrained portfolio is the typical setup for active managers who are given the task of beating a benchmark the problem with this setup is that the portfolio manager pays no attention to total portfolio risk which results in seriously inefficient portfolios unless some additional constraints are imposed the development in this article shows that tev constrained portfolios are described by an ellipse on the traditional mean variance plane this finding yields a number of new insights because of the flat shape of this ellipse adding a constraint on total portfolio volatility can substantially improve the performance of the active portfolio in general plan sponsors should concentrate on controlling total portfolio risk

portfolio selection with uncertain exit time a robust cvar approach abstract in this paper we explore the portfolio selection problem involving an uncertain time of eventual exit to deal with this uncertainty the worst case cvar methodology is adopted in the case where no or only partial information on the exit time is available and the corresponding problems are integrated into linear programs which can be efficiently solved moreover we present a method for specifying the uncertain information on the distribution of the exit time associated with exogenous and endogenous incentives numerical experiments with real market data and monte carlo simulation show the usefulness of the proposed model

coalition proof trade and the friedman rule in the lagos wright model the lagos wright model a monetary model in which pairwise meetings alternate in time with a centralized meeting has been extensively analyzed but always using particular trading protocols here trading protocols are replaced by two alternative notions of implementability one that allows only individual defections and one that also allows cooperative defections in meetings it is shown that the first best allocation is implementable under the stricter notion without taxation if people are sufficiently patient and if people are free to skip the centralized meeting then lump sum taxation used to pay interest on money does not enlarge the set of implementable allocations

mean variance portfolio selection of cointegrated assets abstract this paper considers the continuous time mean variance portfolio selection problem in a financial market in which asset prices are cointegrated the asset price dynamics are then postulated as the diffusion limit of the corresponding discrete time error correction model of cointegrated time series the problem is completely solved in the sense that solutions of the continuous time portfolio policy and the efficient frontier are obtained as explicit and closed form formulas the analytical results are applied to pairs trading using cointegration techniques numerical examples show that identifying a cointegrated pair with a high mean reversion rate can generate significant statistical arbitrage profits once the current state of the economy sufficiently departs from the long term equilibrium we propose an index to simultaneously measure the departure level of a cointegrated pair from equilibrium and the mean reversion speed based on the mean variance paradigm an empirical example is given to illustrate the use of the theory in practice

the economic functions of private pensions an empirical analysis this paper presents an empirical analysis of the economic functions of defined benefit db pensions firms providing pensions choose between db and defined contribution formats the latter is essentially a tax preferred savings account the former may fill other roles determinants of firms choice of plan are estimated using plan sponsors reports to the internal revenue service firms that are larger are unionized employ mainly one sex invest in specific training and pay lower wages are more likely to provide db coverage these results suggest that the economic role of pensions is broader than mere provision of tax preferred savings accounts

robust portfolio selection using linear matrix inequalities abstract in this paper we consider the problem of robust optimal portfolio selection for tracking error when the expected returns of the risky and risk free assets as well as the covariance matrix of the risky assets are not exactly known we assume that these parameters belong to a convex polytope defined by some known elements which form the vertices of this polytope we consider two problems the first one is to find a portfolio of minimum worst case volatility of the tracking error with guaranteed fixed minimum target expected performance the second one is to find a portfolio of maximum worst case target expected performance with guaranteed fixed maximum volatility of the tracking error we show that these two problems are equivalent to solving linear matrix inequalities lmi optimization problems so that the powerful numerical packages nowadays available for this class of problems can be used a numerical example in the sao paulo stock exchange bovespa is presented

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

portfolio management with robustness in both prediction and decision a mixture model based learning approach abstract we develop in this paper a novel portfolio selection framework with a feature of double robustness in both return distribution modeling and portfolio optimization while predicting the future return distributions always represents the most compelling challenge in investment any underlying distribution can be always well approximated by utilizing a mixture distribution if we are able to ensure that the component list of a mixture distribution includes all possible distributions corresponding to the scenario analysis of potential market modes adopting a mixture distribution enables us to 1 reduce the problem of distribution prediction to a parameter estimation problem in which the mixture weights of a mixture distribution are estimated under a bayesian learning scheme and the corresponding credible regions of the mixture weights are obtained as well and 2 harmonize information from different channels such as historical data market implied information and investors subjective views we further formulate a robust mean cvar portfolio selection problem to deal with the inherent uncertainty in predicting the future return distributions by employing the duality theory we show that the robust portfolio selection problem via learning with a mixture model can be reformulated as a linear program or a second order cone program which can be effectively solved in polynomial time we present the results of simulation analyses and primary empirical tests to illustrate a significance of the proposed approach and demonstrate its pros and cons

search for a monetary propagation mechanism abstract this paper examines a monetary propagation mechanism in an economy where exchanges in goods and labor markets involve costly search it is shown that an increase in the money growth rate increases steady state employment and output when the money growth rate is low but reduces steady state employment and output when the money growth rate is already high the model produces persistent hump shaped responses in employment and output to money growth shocks even when the shocks have no persistence the model also generates desirable features in job vacancy sales inventory and the velocity of money all these features emerge here in an economy with perfectly flexible prices and wages journal of economic literatureclassification numbers e40 e30

risk uncertainty and option exercise many economic decisions can be described as an option exercise or optimal stopping problem under uncertainty motivated by experimental evidence such as the ellsberg paradox we follow knight 1921 and distinguish risk from uncertainty to capture this distinction we adopt the multiple priors utility model we show that the impact of ambiguity on the option exercise decision depends on the relative degrees of ambiguity about continuation payoffs and termination payoffs consequently ambiguity may accelerate or delay option exercise we apply our results to investment and exit problems and show that the myopic npv rule can be optimal for an agent having an extremely high degree of ambiguity aversion

active portfolio management with benchmarking adding a value at risk constraint abstract we examine the impact of adding a value at risk var constraint to the problem of an active manager who seeks to outperform a benchmark while minimizing tracking error variance tev by using the model of roll 1992 a mean variance analysis of tracking error journal of portfolio management 18 13 22 we obtain three main results first portfolios on the constrained mean tev boundary still exhibit three fund separation but the weights of the three funds when the constraint binds differ from those in roll s model second the constraint mitigates the problem that when an active manager seeks to outperform a benchmark using the mean tev model he or she selects an inefficient portfolio finally when short sales are disallowed the extent to which the constraint reduces the optimal portfolio s efficiency loss can still be notable but is smaller than when short sales are allowed

some results on the optimality and implementation of the friedman rule in the search theory of money abstract i characterize a large family of monetary policies that implement milton friedman s prescription of zero nominal interest rates in a monetary search economy with multiple assets and aggregate uncertainty this family of optimal policies is defined by two properties i the money supply must be arbitrarily close to zero for an infinite number of dates and ii asymptotically on average over the dates when fiat money plays an essential role the growth rate of the money supply must be at least as large as the rate of time preference

asset allocation in a downside risk framework 1991 asset allocation in a downside risk framework financial analysts journal vol 47 no 5 pp 28 40

index tracking model downside risk and non parametric kernel estimation abstract in this paper we propose an index tracking model with the conditional value at risk cvar constraint based on a non parametric kernel npk estimation framework in theory we demonstrate that the index tracking model with the cvar constraint is a convex optimization problem we then derive npk estimators for tracking errors and cvar and thereby construct the npk index tracking model monte carlo simulations show that the npk method outperforms the linear programming lp method in terms of estimation accuracy in addition the npk method can enhance computational efficiency when the sample size is large empirical tests show that the npk method can effectively control downside risk and obtain higher excess returns in both bearish and bullish market environments

the taylor rule and optimal monetary policy where it denotes the fed s operating target for the federal funds rate pt is the inflation rate measured by the gdp deflator yt is the log of real gdp and y t is the log of potential output identified empirically with a linear trend the rule has since been subject to considerable attention both as an account of actual policy in the united states and elsewhere and as a prescription for desirable policy taylor argues for the rule s normative significance both on the basis of simulations and on the ground that it describes u s policy in a period in which monetary policy is widely judged to have been unusually successful taylor 1999 suggesting that the rule is worth adopting as a principle of behavior here i wish to consider to what extent this prescription resembles the sort of policy that economic theory would recommend i consider the question in the context of a simple but widely used optimizing model of the monetary transmission mechanism which allows one to reach clear conclusions about economic welfare the model is highly stylized but incorporates important features of more realistic models and allows me to make several points that are of more general validity out of concern for the robustness of the conclusions reached the analysis here addresses only broad qualitative features of the taylor rule and attempts to identify features of a desirable policy rule that are likely to hold under a variety of model specifications

optimal mean variance portfolio selection using cauchy schwarz maximization fund managers highly prioritize selecting portfolios with a high sharpe ratio traditionally this task can be achieved by revising the objective function of the markowitz mean variance portfolio model and then resolving quadratic programming problems to obtain the maximum sharpe ratio portfolio this study presents a closed form solution for the optimal sharpe ratio portfolio by applying cauchy schwarz maximization and the concept of kuhn tucker conditions an empirical example is used to demonstrate the efficiency and effectiveness of the proposed algorithms moreover the proposed algorithms can also be used to obtain the optimal portfolio containing large numbers of securities which is not possible or at least is complicated via traditional quadratic programming approaches

monopolistic competition and the effects of aggregate demand how important is monopolistic competition to an understanding of the effects of aggregate demand on output we ask the question at three levels can monopolistic competition by itself explain why aggregate demand movements affect output can it together with other imperfections generate effects of aggregate demand in a way that perfect competition cannot if so can it give an accurate account of the response of the economy to aggregate demand movements the answers are no yes and yes

inflation and unemployment in the long run we study the long run relation between money measured by inflation or interest rates and unemployment we first document in the data a positive relation between these variables at low frequencies we then develop a framework where unemployment and money are both modeled using microfoundations based on search and bargaining theory providing a unified theory for analyzing labor and goods markets the calibrated model shows that money can account for a sizable fraction of trends in unemployment we argue it matters qualitativelynand quantitatively whether one uses monetary theory based on search and bargaining or an alternative ad hoc specification

confidence crashes and animal spirits this article is an attempt to reformulate what i take to be two key insights from keyness general theory keynes 1936 the first is that there is something profoundly different about the labour market from most other markets in the economy the second is that the beliefs of participants in the asset markets have an independent influence on economic activity in the language of modern dynamic general equilibrium theory we would say that there is a continuum of labour market equilibria and that beliefs about the value of the stock market select an equilibrium the general theory contains many ideas some of which are internally inconsistent and keynes did not try to reconcile his theory with walrasian economics that task was carried out by a group of interpreters including hansen 1936 and hicks 1937 the current dominant paradigm new keynesian economics originated with the third edition of samuelson s 1955 undergraduate textbook in which he introduced the idea of the neoclassical synthesis according to this doctrine the economy is keynesian in the short run but classical in the long run the short run is defined as the period over which not all prices have had time to adjust to their walrasian levels this article introduces a different interpretation of the key ideas from the general theory 1 although my work is inspired by keynesian economics this article is not about the history of thought i offer a way of formulating the idea that market economies are not inherently self stabilising without assuming that prices or wages are prevented from adjusting to their equilibrium levels by some kind of friction instead i claim that high persistent unemployment is a potentially permanent feature of a market economy in a steady state equilibrium

robust tracking error portfolio selection with worst case downside risk measures abstract this paper proposes downside risk measure models in portfolio selection that captures uncertainties both in distribution and in parameters the worst case distribution with given information on the mean value and the covariance matrix is used together with ellipsoidal and polytopic uncertainty sets to build up this type of downside risk model as an application of the models the tracking error portfolio selection problem is considered by lifting the vector variables to positive semidefinite matrix variables we obtain semidefinite programming formulations of the robust tracking portfolio models numerical results are presented in tracking sse50 of the shanghai stock exchange compared with the tracking error variance portfolio model and the equally weighted strategy the proposed models are more stable have better accumulated wealth and have much better sharpe ratio in the investment period for the majority of observed instances

worst case value at risk and robust portfolio optimization a conic programming approach classical formulations of the portfolio optimization problem such as mean variance or value at risk var approaches can result in a portfolio extremely sensitive to errors in the data such as mean and covariance matrix of the returns in this paper we propose a way to alleviate this problem in a tractable manner we assume that the distribution of returns is partially known in the sense that onlybounds on the mean and covariance matrix are available we define the worst case value at risk as the largest var attainable given the partial information on the returns distribution we consider the problem of computing and optimizing the worst case var and we show that these problems can be cast as semidefinite programs we extend our approach to various other partial information on the distribution including uncertainty in factor models support constraints and relative entropy information

small menu costs and large business cycles a macroeconomic model of monopoly i introduction the conflict between modern neoclassical and traditional keynesian theories of the business cycle centers upon the pricing mechanism in neoclassical models prices are fully flexible they represent the continuous optimization of economic agents and the continuous intersection of supply and demand in keynesian models prices are often assumed to be sticky they do not necessarily equilibrate all markets at all times one of the reasons for the resurgence of the equilibrium approach to macroeconomics has been the absence of a theoretical underpinning for this keynesian price stickiness this note shows that sticky prices can be both privately efficient and socially inefficient the business cycle results from the suboptimal adjustment of prices in response to a demand shock to the extent that policy can stabilize aggregate demand it can mitigate the social loss due to this suboptimal adjustment in some keynesian models prices are simply exogenously fixed 2 in others agents must set their prices in advance of the transaction date the act of altering a posted price is certainly costly these costs include such items as printing new catalogs and informing salesmen of the new price yet these menu costs are small and therefore generally perceived as providing only a weak foundation for these fixed price models however this inference is flawed small menu costs can cause large welfare losses the claim that price adjustment costs are small does not rebut the claim that they are central to understanding economic fluctuations

keynesian inefficiency and optimal policy a new monetarist approach a simple model of monetary labor search is constructed to study keynesian indeterminacy and optimal policy in the model economic agents have trouble splitting the surplus from exchange appropriately and we consider monetary and fiscal policies that correct this keynesian inefficiency a taylor rule neither implies determinacy nor does it support an efficient outcome an optimal policy yields an efficient and determinate allocation of resources but equilibrium policy actions wages and prices are indeterminate at the optimum

variance vs downside risk is there really that much difference abstract the popularity of downside risk among investors is growing and mean return downside risk portfolio selection models seem to oppress the familiar mean variance approach the reason for the success of the former models is that they separate return fluctuations into downside risk and upside potential this is especially relevant for asymmetrical return distributions for which mean variance models punish the upside potential in the same fashion as the downside risk the paper focuses on the differences and similarities between using variance or a downside risk measure both from a theoretical and an empirical point of view we first discuss the theoretical properties of different downside risk measures and the corresponding mean downside risk models against common beliefs we show that from the large family of downside risk measures only a few possess better theoretical properties within a return risk framework than the variance on the empirical side we analyze the differences between some us asset allocation portfolios based on variances and downside risk measures among other things we find that the downside risk approach tends to produce on average slightly higher bond allocations than the mean variance approach furthermore we take a closer look at estimation risk viz the effect of sampling error in expected returns and risk measures on portfolio composition on the basis of simulation analyses we find that there are marked differences in the degree of estimation accuracy which calls for further research

worst case value at risk of nonlinear portfolios portfolio optimization problems involving value at risk var are often computationally intractable and require complete information about the return distribution of the portfolio constituents which is rarely available in practice these difficulties are compounded when the portfolio contains derivatives we develop two tractable conservative approximations for the var of a derivative portfolio by evaluating the worst case var over all return distributions of the derivative underliers with given first and second order moments the derivative returns are modelled as convex piecewise linear or by using a delta gamma approximation as possibly nonconvex quadratic functions of the returns of the derivative underliers these models lead to new worst case polyhedral var wpvar and worst case quadratic var wqvar approximations respectively wpvar serves as a var approximation for portfolios containing long positions in european options expiring at the end of the investment horizon whereas wqvar is suitable for portfolios containing long and or short positions in european and or exotic options expiring beyond the investment horizon we prove that unlike var that may discourage diversification wpvar and wqvar are in fact coherent risk measures we also reveal connections to robust portfolio optimization this paper was accepted by dimitris bertsimas optimization

real business cycles and the animal spirits hypothesis abstract we calibrate a quantitative equilibrium macroeconomic model with an aggregate technology that is subject to increasing returns and show that this model may display fluctuations at business cycle frequencies even when there are no shocks to the fundamentals of the economy these fluctuations are due to the self fulfilling beliefs of investors which we call animal spirits we compare the impulse response functions predicted by our model and by two other more standard models with a four variable vector autoregression on u s data our animal spirits economy is the most successful of the three at matching broad features of the dynamic responses in the data journal of economic literature classification numbers e00 e3 e32

implications of rational inattention abstract a constraint that actions can depend on observations only through a communication channel with finite shannon capacity is shown to be able to play a role very similar to that of a signal extraction problem or an adjustment cost in standard control problems the resulting theory looks enough like familiar dynamic rational expectations theories to suggest that it might be useful and practical while the implications for policy are different enough to be interesting

a linear model for tracking error minimization abstract this article investigates four models for minimizing the tracking error between the returns of a portfolio and a benchmark due to linear performance fees of fund managers we can argue that linear deviations give a more accurate description of the investors risk attitude than squared deviations all models have in common that absolute deviations are minimized instead of squared deviations as is the case for traditional optimization models linear programs are formulated to derive explicit solutions the models are applied to a portfolio containing six national stock market indexes usa japan uk germany france switzerland and the tracking error with respect to the msci morgan stanley capital international index world stock market index is minimized the results are compared to those of a quadratic tracking error optimization technique the portfolio weights of the optimized portfolio and its risk return properties are different across the models which implies that optimization models should be targeted to the specific investment objective finally it is shown that linear tracking error optimization is equivalent to expected utility maximization and lower partial moment minimization