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

portfolio resampling review and critique a well understood fact of asset allocation is that the traditional portfolio optimization algorithm is too powerful for the quality of the inputs recently a new concept called resampled efficiency has been introduced into the asset management world to deal with estimation error the objective of this article is to describe this new technology put it into the context of established procedures and point to some peculiarities of the approach even though portfolio resampling is a thoughtful heuristic some features make it difficult to interpret by the inexperienced portfolio resampling review and critique a comment

static mean variance analysis with uncertain time horizon we generalize markowitz analysis to the situations involving an uncertain exit time our approach preserves the form of the original problem in that an investor minimizes portfolio variance for a given level of the expected return however inputs are now given by the generalized expressions for mean and variance covariance matrix involving moments of the random exit time in addition to the conditional moments of asset returns although efficient frontiers in the generalized and the standard markowitz case may coincide under certain conditions we demonstrate that by means of an example in general that is not true in particular portfolios efficient in the standard markowitz sense can be inefficient in the generalized sense and vice versa as a result an investor facing an uncertain time horizon and investing as if her time of exit is certain would in general make suboptimal portfolio allocation decisions numerical simulations show that a significant efficiency loss can be induced by an improper use of standard mean variance analysis when time horizon is uncertain

a general mean variance approximation to expected utility for short holding periods the mean variance model is precisely consistent with the expected utility hypothesis only in the special cases of normally distributed security returns or quadratic utility functions there is little evidence however that security returns follow normal distributions see 13 for references and quadratic preferences can be shown to generate implausible results exhibiting increasing absolute risk aversion in the pratt ll arrow 1 2 sense and displaying negative marginal utility after some finite wealth level in addition hakansson 4 has shown that single period mean variance efficient portfolios can have disastrous consequences over time even when return distributions are stationary such criticisms of the mean variance approach within the von neumann morgenstern framework have prompted several writers to suggest that investors maximize the expected value of utility functions with more realistic properties while others have criticized the single period focus of the model one popular alternative utility function is the logarithmic function which exhibits decreasing absolute risk aversion and conveniently leads to myopic decision processes through time i e investors treat each period as if it were the last basing investment decisions on that period s wealth and return distributions only 8 4 other utility functions with constant relative risk aversion such as the power function also imply myopic decision rules within a multiperiod setting

a two person dynamic equilibrium under ambiguity this paper describes a pure exchange continuous time economy with two heterogeneous agents and complete markets a novel feature of the economy is that agents perceive some security returns as ambiguous in the sense often attributed to frank knight the equilibrium is described completely in closed form after identifying agents as countries the model is applied to address the consumption home bias and equity home bias puzzles 2002 elsevier science b v all rights reserved jel classi cation d81 g11 g12 g15

a test of the linear rational expectations equilibrium inventory model in the eec abstract in this paper i test an extension of the familiar holt modigliani muth and simon 1960 inventory model using annual data from the eec countries the two step two stage least squares estimation technique of cumby et al 1983 is used the model is tested using the generalized variance bounds test developed by kollintzas 1988 and the variance bounds test of west 1986 in the majority of the cases the empirical evidence gives support to the traditional inventory model when allowing for stochastic cost shocks and stock out avoidance motives

dynamic asset allocation with event risk major events often trigger abrupt changes in stock prices and volatility we study the implications of jumps in prices and volatility on investment strategies using the event risk framework of duffie pan and singleton 2000 we provide analytical solutions to the optimal portfolio problem event risk dramatically affects the optimal strategy an investor facing event risk is less willing to take leveraged or short positions the investor acts as if some portion of his wealth may become illiquid and the optimal strategy blends both dynamic and buy and hold strategies jumps in prices and volatility both have important effects

investor sentiment and the financial crisis a sentiment based portfolio theory perspective the article proposes a portfolio model subjected to a constraint that captures the investor s goal with maximum estimation of expected return that is affected by investor sentiment and we give a solution of the portfolio model by exploring the geometric features furthermore we discuss the relationship between investor sentiment and the financial crisis by analysing the optimal allocation the results show that when investor sentiment is low enough the investor should reject the investment this condition leads the depression financial market to prevail then the financial crisis erupts when investor sentiment is modest the financial crisis is difficult to erupt unless the decline of investor sentiment is quick and deep but there is a special status that the financial crisis is caused by other factors rather than by investor sentiment and only improving investor sentiment cannot move away from the financial crisis

innovations and issues in monetary policy panel discussion martin feldstein 1 chairman alan greenspan s remarks today give us an opportunity to understand his thinking about monetary policy and about the federal reserve s actions during the past 15 years it was a period of substantial accomplishment that no doubt reflects in considerable measure the views of the chairman himself the fed s primary goal price stability has been achieved with inflation down from 4 percent at the end of the 1980 s to about 1 5 percent now the 2 percentage point difference between the interest rate on conventional treasury bonds and on inflation indexed bonds tips shows that financial markets expect inflation will remain at about 2 percent for at least the next decade

classical and variance bounds tests of the production smoothing hypothesis in this paper we test the controversial production smoothing role of inventories by applying both classical econometric techniques and variance bounds tests we use seasonally unadjusted data measured in physical units for five industries the model used is a version of the familiar holt et al 1960 inventory model we also use the data on one industry disaggregated at the district level to investigate potential bias which may arise from aggregation overall the empirical evidence suggests production smoothing in the great majority of the industries examined

learning and control in a changing economic environment abstract in this paper we investigate optimal bayesian learning and control with lagged dependent variables and time varying unknown parameters we assess both the performance of alternative decision rules as in the computationally oriented dual control literature as well as the dynamics of learning and convergence of beliefs as in the more theoretically oriented bayesian learning literature our numerical results indicate that the optimal decision rule involves a noticeable degree of experimentation for moderate to large levels of uncertainty in most situations though the optimal rule will remain less activist than a certainty equivalent rule and induce gradualism exceptions occur when the process to be controlled is near the deterministic steady state in this situation we find that the decision maker will repeatedly undertake costly experiments the extent of optimal experimentation is lower if the unknown parameter is perceived to vary over time in contrast to the fixed parameter case however parameter uncertainty is continually renewed and the incentive to experiment never ceases

an alternative test of the capital asset pricing model reply in our 1980 paper we tested the joint hypothesis that prices are determined by the mean variance mv capital asset pricing model capm and that beliefs are stationary by focusing on the invariance law of prices we avoided the questionable practice of estimating ex ante expectations with ex post returns moreover we circumvented the need to identify the true market portfolio and hence avoided the ambiguity noted by richard roll 1977 in the traditional security market line sml tests of the same joint hypothesis however stuart turnbull and ralph winter t w and richard sweeney point to a further inconsistency in the joint hypothesis that they believe can be removed by relaxing the stationarity assumption this new concern is fundamental in that it applies to all empirical tests which assume stationarity of the return distribution whether they are simply tests of the capm or tests employing the capm the concern would apply a fortiori to tests that assume stationary betas as well both comments also suggest that the ad hoc addition of a random error term to our invariance law equation and the subsequent statistical tests of it are unnecessary we first address these two criticisms and then address some further criticisms raised separately by t w and sweeney

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

multivariate stochastic volatility via wishart processes financial models for asset and derivatives pricing risk management portfolio optimization and asset allocation rely on volatility forecasts time varying volatility models such as generalized autoregressive conditional heteroscedasticity and stochastic volatility svol have been successful in improving forecasts over constant volatility models we develop a new multivariate svol framework for modeling financial data that assumes covariance matrices stochastically varying through a wishart process in our formulation scalar variances naturally extend to covariance matrices rather than to vectors of variances as in traditional svol models model fitting is performed using markov chain monte carlo simulation from the posterior distribution because of the model s complexity an efficiently designed gibbs sampler is described that produces inferences with a manageable amount of computation our approach is illustrated on a multivariate time series of monthly industry portfolio returns a test of the ec

tail risk and robust portfolio decisions this paper formulates a portfolio choice problem in a multiasset incomplete market characterized by ambiguous jumps and arbitrary tail assumptions we derive the optimal portfolio in closed form th

normality solvency and portfolio choice this paper examines whether investors with power utility functions choose mean vari ance mv efficient portfolios when returns are approximately normally distributed and there is borrowing or lending at a riskless interest rate the results show that the unlevered portfolios of power utility investors plot very closely to the mv efficient frontier how ever there are marked differences in the mix of risky assets regardless of whether the portfolios are highly concentrated or widely diversified such differences allow power investors to remain solvent even when they lever their optimal portfolios to a greater ex tent than less risk averse mv investors who risk bankruptcy it is concluded that the investment policies of power utility and mv investors with similar risk aversion measures are not as similar as is commonly believed this is particularly true for high power inves tors unless explicit solvency constraints are imposed on the mv problem and for low power investors when quadratic utility approximations are made to the power utility func tions these differences in the investment policies of power utility and mv investors lead us to question the widely accepted assertion that the assumptions of homogeneous beliefs normality a riskless asset and risk averse investors imply the simple mv capm where all investors including power utility investors hold combinations ofthe market portfolio and the riskless asset

the mean variance optimization puzzle security portfolios and food portfolios the markowitz mean variance optimization framework presents a puzzle although it is the standard model of portfolio construction investors rarely use it and when used it is constrained so much that portfolios reflect the constraints more than the optimization why do investors dislike unadulterated optimized mean variance portfolios the typical answer focuses on biases introduced by estimation errors more important is the fact that investors goals are quite different from mean variance optimization people care about more than cost and nutrition when they construct their diets they also care about palatability similarly investors care about more than expected returns and variance as they construct their securities portfolios they also care about the investment equivalent of palatability we use an analogy between security portfolios and food portfolios to explore the nature of the gap between intuitively appealing portfolios and mean variance optimized portfolios

bond ladders and optimal portfolios we analyze complex bond portfolios within the framework of a dynamic general equilibrium asset pricing model equilibrium bond portfolios are nonsensical and imply a trading volume that vastly exceeds observed trading volume on financial markets instead portfolios that combine bond ladders with a market portfolio of equity assets are nearly optimal investment strategies the welfare loss of these simple investment strategies when compared to the equilibrium portfolio converges to zero as the length of the bond ladder increases this article therefore provides a rationale for naming bond ladders as a popular bond investment strategy

robust consumption and portfolio policies when asset prices can jump abstract we study the consumption portfolio allocation problem in continuous time when asset prices follow levy processes and the investor is concerned about potential model misspecification we derive optimal consumption and portfolio policies that are robust to uncertainty about the hard to estimate drift rate jump intensity and jump size parameters we also provide a semi closed form formula for the detection error probability and compare various portfolio holding strategies including robust and non robust policies our quantitative analysis shows that ignoring uncertainty leads to significant wealth loss for the investor

a note on portfolio selection with restrictions on leverage abstract this note focuses on a mean variance asset allocation framework having restrictions on leverage namely where investors are constrained either to hold funds in a risk free asset i e to lend or to hold debt i e to borrow it is shown that the optimal portfolio in a constrained leverage situation will not have the same composition as the optimal portfolio in an unconstrained situation we give formal justification for the intuitive notion that the more debt an investor is constrained to hold the more the investor should tilt the remaining investments towards a portfolio of less risky assets conversely the greater the proportion an investor is constrained to hold in a risk free asset the more the investor should tilt remaining investment towards a portfolio of more risky assets

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

uncertainty shocks asset supply and pricing over the business cycle this article estimates a business cycle model with endogenous financial asset supply and ambiguity averse investors firms shareholders choose not only production and investment but also capital structure and payout policy subject to financial frictions an increase in uncertainty about profits lowers stock prices and leads firms to substitute away from debt as well as reduce shareholder payout this mechanism parsimoniously accounts for the postwar comovement in investment stock prices leverage and payout at both business cycle and medium term cycle frequencies ambiguity aversion permits a markov switching var representation of the model while preserving the effect of uncertainty shocks on the time variation in the equity premium

decomposing the determinants of trade deficits turkey in the 1970s abstract persistent trade deficits in developing countries have followed the increases in crude oil prices of the 1970s this paper examines through econometric estimation and shock decomposition analysis this persistence for the turkish economy results highlight the primary role played in trade deficit creation by government tariff and exchange rate policies also of interest is the measured responsiveness of the private economy to price incentives offered both by changing international conditions and government policy the turkish economy provides an empirical example of contractionary devaluation the importance of devaluation cum liberalization for deficit reduction and economic growth is established

intermediate inputs and international trade an analysis of the real and monetary aspects of a change in the price of oil abstract this paper studies the effects of a change in the price of a traded intermediate input on the real and monetary sectors of a fully employed small open economy the real side of the model examines the relationship between the pricee of the input and relative factor and commodity prices the pattern of trade and the levels of production in various industries the monetary side focuses on the dynamics of the nominal exchange rate and the stock of traded assets with particular emphasis on the role of changes in real income and asset values that result from this disturbance

evaluating the impact of inequality constraints and parameter uncertainty on optimal portfolio choice we present new analytical results for the impact of portfolio weight constraints on an investor s optimal portfolio when parameter uncertainty is taken into account while it is well known that parameter uncertainty and imposing weight constraints results in reduced certainty equivalent returns in the general case there are no analytical results in a special case commonly used in the funds management literature we derive analytical expression for the certainty equivalent loss that does not depend on the risk aversion parameter we illustrate our theoretical results using hedge fund data from the perspective of a fund of fund manager our contribution is to formalize the framework to investigate this problem as well as providing tractable analytical solutions that can be implemented using either simulated or asset manager returns

time diversification and estimation risk the recommendation that investors with long investment horizons tilt their portfolios toward stocks is commonplace we used a nonparametric bootstrap approach to investigate whether in a mean variance efficient portfolio the weights for u s stocks and u s t bills vary in a systematic manner with investment horizon this approach allowed us to analyze the impact of estimation risk on the optimal weights of stocks and fixed income securities the results show that an investor can gain from time diversification the weights for stocks in an efficient portfolio were significantly larger for long investment horizons than a one year horizon

an examination of resampled portfolio efficiency we examined the out of sample performance of using resampled portfolio efficiency an approach proposed in 1998 in international asset allocation strategies for the period january 1983 to may 2000 for most models we used to estimate expected returns using strategies based on resampled portfolio efficiency provided some benefits in terms of improved sharpe ratios and abnormal returns over using traditional mean variance strategies we found little evidence however that active mean variance strategies or resampled efficiency strategies would have generated significantly positive abnormal returns for the time period we considered

some empirical evidence on the production level and production cost smoothing models of inventory investment the production smoothing model of inventories has long been the basic paradigm within which empirical research on inventories has been conducted the basic hypothesis embedded in this model is that inventories of finished goods serve primarily to smooth production levels in the face of fluctuating demand and convex cost functions however once we allow for shocks to technology and the costs of producing output firms will also use inventories to shift production from periods in which production costs are relatively high to periods in which production costs are relatively low in this sense inventories can serve to smooth production costs rather production levels in this paper we examine the empirical plausibility of the production level and production cost smoothing models of inventories our basic strategy is to derive and contrast a set of unconditional moment restrictions implied by these models in a way that minimizes the role of auxiliary assumptions regarding market structure and industry demand we find overwhelming evidence against the production level smoothing model and very little evidence against the production cost smoothing mode1 we conclude that the variance of production exceeds the variance of sales in most manufacturing industries because the production cost smoothing role of inventories is quantitatively more important than the production level smoothing role of inventories this abstract was borrowed from another version of this item

bayesian estimation of the global minimum variance portfolio in this paper we consider the estimation of the weights of optimal portfolios from the bayesian point of view under the assumption that the conditional distribution of the logarithmic returns is normal using the standard priors for the mean vector and the covariance matrix we derive the posterior distributions for the weights of the global minimum variance portfolio moreover we reparameterize the model to allow informative andnon informative priors directly for the weights of the global minimum variance portfolio the posterior distributions of the portfolio weights are derived in explicit form for almost all models the models are compared by using the coverage probabilities of credible intervals in an empirical study we analyze the posterior densities of the weights of an international portfolio

large scale minimum variance portfolio allocation using double regularization abstract estimation of time varying covariances is a crucial input in minimum variance mv portfolio allocations rolling window based sample estimates are widely used for this purpose but they usually suffer from two major issues when applied to a moderately large number of assets the curse of dimensionality and temporal instability here we propose a double regularized estimator for a high dimensional covariance matrix in which we impose both a temporal and cross sectional sparsity regularization on the sample based estimates to simultaneously mitigate these two issues we investigate the performance of our proposed covariance estimator for mv portfolio construction using monte carlo experiments and empirical examples we find that the resulting mv portfolio strikes a good balance between risk and turnover reduction and produces more accurate equivalent returns after transaction costs are taken into account when compared to four other mv strategies

markowitz with regret abstract providing a framework to integrate regret as an additional decision criterion in markowitz s model of portfolio selection we propose two different views on regret an investor might feel regret with respect to the ex post best alternative either in terms of return or in terms of preference value under both views regret can be captured by adjusting the vector of expected returns or alternatively by adjusting the return covariance matrix retaining the tractability of the markowitz model the regret model however has very different implications for how asset characteristics affect optimal portfolios while the impact of the skewness of an asset is strengthened the impact of the variance shrinks moreover we show for a variety of real portfolios that the effects of regret on optimal portfolio weights and the ex ante return distribution are large

portfolio optimization under a minimax rule this paper provides a new portfolio selection rule the objective is to minimize the maximum individual risk and we use an l function as the risk measure we provide an explicit analytical solution for the model and are thus able to plot the entire efficient frontier our selection rule is very conservative one of the features of the solution is that it does not explicitly involve the covariance of the asset returns

the optimal investment and current account response to oil price shocks under putty clay technology abstract the motivation for this paper is the discrepancy between actual ca responses to oil price shocks and the prediction derived from simple intertemporal optimizing models these models indicate a decline in investment and a ca improvement as the optimal response in this paper we introduce putty clay technology into a two period optimizing model and show that that leads to an increase in gross investments and a ca deterioration as an optimal response to large oil price shocks by net importers of oil successful adapters to the 1973 1974 oil price shocks korea taiwan indeed followed such a policy

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

risk forecasting models and optimal portfolio selection this study analyses from an investor s perspective the performance of several risk forecasting models in obtaining optimal portfolios the plausibility of the homoscedastic hypothesis implied in the classical markowitz model is dicussed and more general models which take into account assymetry and time varying risk are analysed specifically it studies whether arch type based models obtain portfolios whose risk adjusted returns exceed those of the classical markowitz model the same analysis is performed with models based on the lower partial moment lpm which take into account the assymetry in the distribution of returns the results suggest that none of the models achieve a clearly superior average performance it is also found that models based on semivariance perform as well as those based on the variance but not better than even if the evaluation criterion is based on the reward to semivariance ratio when attention turns to the analysis of worst case performance the results are clearly differ

bayesian economist bayesian agents i an alternative approach to optimal learning we generalize the results on bayesian learning based on the martingale convergence theorem to the sequential framework we show that the variability in the sequential framework is sufficient under mild conditions to circumvent the incomplete learning results that characterize the optimal learning literature we then give an alternative approach whereby the economist is bayesian with a prior on the space of agent priors we illustrate the usefulness of our approach by applying it to two popular economic examples a monopolist who does not know the demand curve he faces and the stochastic single sector growth model with an unknown production function

model misspecification and underdiversification in this paper we study intertemporal portfolio choice when an investor accounts explicitly for model misspecification we develop a framework that allows for ambiguity about not just the joint distribution of returns for all stocks in the portfolio but also for different levels of ambiguity for the marginal distribution of returns for any subset of these stocks we find that when the overall ambiguity about the joint distribution of returns is high then small differences in ambiguity for the marginal return distribution will result in a portfolio that is significantly underdiversified relative to the standard mean variance portfolio

calibration of agricultural risk programming models abstract positive mathematical programming pmp is one of the most commonly used methods for calibrating activity programming models in this article we consider pmp as a calibration method for risk programming models with a mean variance e v specification we argue that the restrictive theoretical assumptions employed by typical linear e v models limit their applicability in analyzing the effects of decoupled payments on agricultural production decisions furthermore the requirement for eliciting a risk aversion coefficient renders such models incompatible with the pmp method for this reason we propose a nonlinear e v specification and develop a pmp based procedure for its calibration which does not aim at introducing further nonlinearities in the objective function but at recovering the true distribution of wealth that will allow the final model to reproduce base year observations we also examine how our approach relates to the recent pmp developments on calibration against elasticity priors and we show how such priors can be used for the calibration of the nonlinear e v model

reputation and time consistency recent work has shown that reputational arguments based on trigger strategies can sometimes be used to deal with the problem of time inconsistency in government policy this idea was exploited by robert barro and david gordon 1983 in a model of inflation and by v v chari and patrick kehoe 1988 in a model of capital taxation here it is shown that reputational arguments of this sort are widely applicable 2 a general policy model is developed based on an economy that is stationary over time contains identical households and has no endogenous state variables it is shown in general that the infinite horizon version of this model has equilibria in trigger strategies that yield outcomes strictly better than those attainable as equilibria in the one period model

there is no silver bullet the value of diversification in planning invasive species surveillance abstract in this study we demonstrate how the notion of diversification can be used in broad scale resource allocation for surveillance of invasive species we consider the problem of short term surveillance for an invasive species in a geographical environment we find the optimal allocation of surveillance resources among multiple geographical subdivisions via application of a classical portfolio framework which allocates investments among multiple financial asset types with uncertain returns in a portfolio that maximizes the performance and by meeting the desired diversification targets protects against errors in estimating the portfolio s performance we illustrate the approach with a case study that applies a spatial transmission model to assess the risk of spread of the emerald ash borer eab a significant pest in north america with infested firewood that may be carried by visitors to campground facilities in central canada adding the diversification objective yields an expected survey performance that is comparable with undiversified optimal allocation but more importantly makes the geographical distribution of survey priorities less subject to possible errors in the spread rate estimates overall diversification of pest surveillance can be viewed as a viable short term strategy for hedging against uncertainty in expert and model based assessments of pest invasion risk

60 years of portfolio optimization practical challenges and current trends abstract the concepts of portfolio optimization and diversification have been instrumental in the development and understanding of financial markets and financial decision making in light of the 60 year anniversary of harry markowitz s paper portfolio selection we review some of the approaches developed to address the challenges encountered when using portfolio optimization in practice including the inclusion of transaction costs portfolio management constraints and the sensitivity to the estimates of expected returns and covariances in addition we selectively highlight some of the new trends and developments in the area such as diversification methods risk parity portfolios the mixing of different sources of alpha and practical multi period portfolio optimization

do constraints improve portfolio performance the discrete time dynamic investment model using only historical data in various asset allocation settings often produces significant abnormal returns however the model does not choose the diversified portfolios that theory suggests it should therefore in this paper we compare the investment policies and returns of the model with and without constraints on the mix of risky assets the constraints lead to appreciably more diversification and less realized risk but only at the cost of less realized return visual comparisons of compound return standard deviation plots and statistical comparisons of jensen s alpha suggest that the reduction in return is not worth the reduction in risk for more risk averse investors ex post utility and certainty equivalent returns suggest that it is the results however illustrate the problems associated with using ex post utility to measure performance 2000 elsevier science b v all rights reserved

asset allocation with correlation a composite trade off abstract we assess the ability of minimum variance portfolio allocation strategies accounting for time varying correlation between assets to provide performance benefits relative to an equally weighted portfolio prior to transaction costs correlation based strategies emphatically outperform the equally weighted benchmark this finding is strongest for short horizon correlation forecasts and attributed to dynamic correlation as opposed to variance forecasts thus estimation error is not found to be the primary obstacle to successful portfolio optimization rather frequent rebalancing and associated transaction costs pose a significant challenge limiting portfolio turnover through short selling restrictions and greater rebalancing error tolerance results in regular outperformance of the correlation based strategies even for large transaction costs taken together these findings provide evidence of a trade off between optimal portfolio performance forecasting horizon rebalancing frequency and transaction costs

strategic asset allocation in a continuous time var model abstract this paper derives an approximate solution to a continuous time intertemporal portfolio and consumption choice problem the problem is the continuous time equivalent of the discrete time problem studied by campbell and viceira q j econ 114 1999 433 in which the expected excess return on a risky asset follows an ar 1 process while the riskless interest rate is constant the paper also shows how to obtain continuous time parameters that are consistent with discrete time econometric estimates the continuous time solution is the limit of that of campbell and viceira and has the property that conservative long term investors have a large positive intertemporal hedging demand for stocks

portfolio selection under distributional uncertainty a relative robust cvar approach robust optimization one of the most popular topics in the field of optimization and control since the late 1990s deals with an optimization problem involving uncertain parameters in this paper we consider the relative robust conditional value at risk portfolio selection problem where the underlying probability distribution of portfolio return is only known to belong to a certain set our approach not only takes into account the worst case scenarios of the uncertain distribution but also pays attention to the best possible decision with respect to each realization of the distribution we also illustrate how to construct a robust portfolio with multiple experts priors by solving a sequence of linear programs or a second order cone program

the benefits of differential variance based constraints in portfolio optimization abstract the main problem of portfolio optimization is parameter estimation error various methods have been suggested to mitigate this problem among which are shrinkage resampling bayesian updating naive diversification and imposing constraints on the portfolio weights this study suggests two substantial extensions of the constrained optimization approach the variance based constraints vbc and the global variance based constraints gvbc methods by the vbc method the constraint imposed on the weight of a given stock is inversely proportional to its standard deviation the higher a stock s sample standard deviation the higher the potential estimation error of its parameters and therefore the tighter the constraint imposed on its weight gvbc employs a similar idea but instead of imposing a sharp boundary constraint on each stock a quadratic cost is assigned to deviations from the naive 1 n weight and a single global constraint is imposed on the total cost of all deviations comparing ten optimization methods we find that the two new suggested methods typically yield the best performance as measured by the sharpe ratio gvbc ranks first these results are obtained for two different datasets and are also robust to the number of assets under consideration

inflation ambiguity and the term structure of u s government bonds abstract variations in trend inflation are the main driver for variations in the nominal yield curve according to empirical data investors observe a set of empirical models that could all have generated the time series for trend inflation this set has been large and volatile during the 1970s and early 1980s and small during the 1990s i show that log utility together with knightian uncertainty about trend inflation can explain the term premium in u s treasury bonds the equilibrium has two inflation premiums an inflation risk premium and a knightian inflation ambiguity premium

systemic risk and international portfolio choice returns on international equities are characterized by jumps moreover these jumps tend to occur at the same time across countries leading to systemic risk we capture these stylized facts using a multivariate system ofjump diffusion processes where the arrival of jumps is simultaneous across assets we then determine an investor s optimal portfolio for this model of returns systemic risk has two effects one it reduces the gains from diversification and two it penalizes investors for holding levered positions we find that the loss resulting from diminished diversification is small while that from holding very highly levered positions is large returns on international equities are characterized by jumps 1 moreover these jumps tend to occur at the same time across countries implying that conditional correlations between international equity returns tend to be higher in periods of high market volatility or following large downside moves 2 our objective in

how many stocks make a diversified portfolio we show that a well diversified portfolio of randomly chosen stocks must include at least 30 stocks for a borrowing investor and 40 stocks for a lending investor this contradicts the widely accepted notion that the benefits of diversification are virtually exhausted when a portfolio contains approximately 10 stocks we also contrast our result with the levels of diversification found in studies of individuals portfolios

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

general uncertainty in portfolio selection a case based decision approach abstract often a portfolio investor can hardly imagine all states of nature relevant to his investment problem causing general uncertainty concerning an asset allocation model we quantify general uncertainty as the weakness of an investor s belief in a conventional portfolio procedure then we develop the case based decision making approach for determining the optimal belief degree the economic effect of the proposed case based methodology is investigated in the empirical study the empirical results suggest two successful patterns of case based decisions that could be linked to the issue of market efficiency moreover our case based modeling reflects some behavioral phenomena observed on financial markets

impossible frontiers a key result of the capital asset pricing model capm is that the market portfolio the portfolio of all assets in which each asset s weight is proportional to its total market capitalization lies on the mean variance efficient frontier the set of portfolios having mean variance characteristics that cannot be improved upon therefore the capm cannot be consistent with efficient frontiers for which every frontier portfolio has at least one negative weight or short position we call such efficient frontiers impossible and show that impossible frontiers are difficult to avoid in particular as the number of assets n grows we prove that the probability that a generically chosen frontier is impossible tends to one at a geometric rate in fact for one natural class of distributions nearly one eighth of all assets on a frontier is expected to have negative weights for every portfolio on the frontier we also show that the expected minimum amount of short selling across frontier portfolios grows linearly with n and even when short sales are constrained to some finite level an impossible frontier remains impossible using daily and monthly u s stock returns we document the impossibility of efficient frontiers in the data

a note on robustness in merton s model of intertemporal consumption and portfolio choice abstract the paper presents a robust version of a simple two assets merton 1969 review of economics and statistics 51 247 57 model where the optimal choices and the implied shadow market prices of risk for a representative robust decision maker rdm can be easily described with the exception of the log utility case precautionary behaviour is induced in the optimal consumption investment rules through a substitution of investment in risky assets with both current consumption and riskless saving for the log utility case precautionary behaviour arises only through a substitution between risky and riskless assets on the financial side the decomposition of the market price of risk in a standard consumption based component and a further price for model uncertainty risk which is positively related to the robustness parameter is independent of the underlying risk aversion parameter

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

the sampling error in estimates of mean variance efficient portfolio weights this paper presents an exact finite sample statistical procedure for testing hypotheses about the weights of mean variance efficient portfolios the estimation and inference procedures on efficient portfolio weights are performed in the same way as for the coefficients in an ols regression ols t and f statistics can be used for tests on efficient weights and when returns are multivariate normal these statistics have exact t and f distributions in a finite sample using 20 years of data on 11 country stock indexes we find that the sampling error in estimates of the weights of a global efficient portfolio is large

learning and asset prices under ambiguous information we propose a new modeling framework to study the asset pricing implications of learning under ambiguity aversion in a continuous time partial information lucas economy we characterize analytically equilibrium equity returns and make the following observations first learning under ambiguity aversion implies an equilibrium discount for ambiguity if and only if relative risk aversion is below one or equivalently the elasticity of intertemporal substitution eis is above one in this case ambiguity aversion increases conditional equity premia and volatilities second equilibrium interest rates are lower irrespective of risk aversion third no time invariant relation between excess returns and conditional variances exists therefore estimated relations between excess returns and equity conditional variances are highly time varying and have an indeterminate sign fourth estimates of the eis based on standard euler equations for equity returns are strongly downward biased in a setting of learning and ambiguity aversion therefore an eis well above one can be consistent with estimates of eis well below one fifth ambiguity does not resolve asymptotically finally using realistic model parameters we show that a low risk aversion and a moderate amount of ambiguity are consistent with the equity premium the low interest rate and the excess volatility puzzles

keynes meets markowitz the trade off between familiarity and diversification we develop a model of portfolio choice to nest the views of keynes who advocates concentration in a few familiar assets and markowitz who advocates diversification we use the concepts of ambiguity and ambiguity aversion to formalize the idea of an investor s familiarity toward assets the model shows that for any given level of expected returns the optimal portfolio depends on two quantities relative ambiguity across assets and the standard deviation of the expected return estimate for each asset if both quantities are low then the optimal portfolio consists of a mix of familiar and unfamiliar assets moreover an increase in correlation between assets causes an investor to increase concentration in familiar assets flight to familiarity alternatively if both quantities are high then the optimal portfolio contains only the familiar asset s as keynes would have advocated in the extreme case in which both quantities are very high no risky asset is held nonparticipation this paper was accepted by brad barber teck ho and terrance odean special issue editors

robustness and u s monetary policy experimentation we study how a concern for robustness modifies a policy maker s incentive to experiment a policy maker has a prior over two submodels of inflationunemployment dynamics one submodel implies an exploitable trade off the other does not bayes law gives the policy maker an incentive to experiment the policy maker fears that both submodels and his prior probability distribution over them are misspecified we compute decision rules that are robust to misspecifications of each submodel and of the prior distribution over submodels we compare robust rules to ones that cogley colacito and sargent 2007 computed assuming that the models and the prior distribution are correctly specified we explain how the policy maker s desires to protect against misspecifications of the submodels on the one hand and misspecifications of the prior over them on the other have different effects on the decision rule

a generalized variance bounds test with an application to the holt et al inventory model abstract this paper derives a variance bounds test for a broad class of linear rational expectations equilibrium models according to this test if observed data accord with the model then a weighted sum of autocovariances of the covariance stationary components of the endogenous state variables should be nonnegative the new test reinterprets west s 1986 variance bounds test and extends its applicability by not excluding unobservable exogenous state variables nonstationary exogenous and endogenous state variables and nonzero initial values for the endogenous state variables the new test is computed together with west s test for the holt et al inventory model using nondurable industry data while west s test almost always rejects the model the latter almost always passes the new test this and other evidence provide strong support for the importance of supply shocks in explaining aggregate inventory behavior via the holt et al model

optimal hedging with a subjective view an empirical bayesian approach the standard optimal hedging model has been the preferred theoretical model of normative hedging behavior in empirical applications the model is often implemented with the parameter certainty equivalent pce procedure however the pce procedure completely ignores parameter estimation risk and subjective views we develop an empirical bayesian optimal hedging model that not only effectively accommodates parameter estimation risk but also provides hedgers with a theoretically intuitive yet quantitatively rigorous framework to blend their subjective views and a marketwide or firmwide consensus in determining optimal hedging positions ratios

an analytic derivation of admissible efficient frontier with borrowing the admissible efficient portfolio selection problem for risky assets has been discussed by zhang and nie in this paper the admissible efficient portfolio model is proposed under the assumption that there exists the borrowing money or a risk free asset case the admissible efficient frontiers are developed by the spreads of expected return and risk from admissible errors the analytic forms of the admissible efficient frontiers when short sales are not allowed on all risky assets are derived from two cases the borrowing with an upper bound constraint or without an upper bound constraint the influence on the admissible efficient frontier is explained under the different interest rates of the borrowing the differences between the results with the borrowing and the results without the borrowing is revealed by a real numerical example

robust growth optimal portfolios the growth optimal portfolio is designed to have maximum expected log return over the next rebalancing period thus it can be computed with relative ease by solving a static optimization problem the growth optimal portfolio has sparked fascination among finance professionals and researchers because it can be shown to outperform any other portfolio with probability 1 in the long run in the short run however it is notoriously volatile moreover its computation requires precise knowledge of the asset return distribution which is not directly observable but must be inferred from sparse data by using methods from distributionally robust optimization we design fixed mix strategies that offer similar performance guarantees as the growth optimal portfolio but for a finite investment horizon and for a whole family of distributions that share the same first and second order moments we demonstrate that the resulting robust growth optimal portfolios can be computed efficiently by solving a tractable conic

eliciting von neumann morgenstern utilities when probabilities are distorted or unknown this paper proposes a new method the gamble tradeoff method for eliciting utilities in decision under risk or uncertainty the elicitation of utilities to be used in the expected utility criterion turns out to be possible even if probabilities are ambiguous or unknown a disadvantage of the tradeoff method is that a few more questions usually must be asked to clients also the lotteries that are needed are somewhat more complex than in the certainty equivalent method or in the probability equivalent method the major advantage of the tradeoff method is its robustness against probability distortions and misconceptions which constitute a major cause of violations of expected utility and generate inconsistencies in utility elicitation thus the tradeoff method retains full validity under prospect theory rank dependent utility and the combination of the two i e cumulative prospect theory the tradeoff method is tested for monetary outcomes and for outcomes describing life duration we find higher risk aversion for life duration but the tradeoff method elicits similar curvature of utility apparently the higher risk aversion for life duration is due to more pronounced deviations from expected utility

capital asset pricing compatible with observed market value weights we show that the set of expected return vectors for which an observed portfolio is mean variance mv efficient is a two parameter family we identify ten ways to specify the time series behavior of the two parameters the result highlights a number of inconsistencies involved in mv modelling for each of the cases it permits the inference of the time series of expected return vectors as well as all the other capital asset pticing model capm variables compatible with a known covariance matrix and the observed time series of market value weights the empirical work shows that there are substantial case to case differences in the time series of mean vectors and many of them are quite different from the constant mean vector envisioned in tests of

the efficient use of conditioning information in portfolios we study the properties of unconditional minimum variance portfolios in the presence of conditioning information such portfolios attain the smallest variance for a given mean among all possible portfolios formed using the conditioning information we provide explicit solutions for n risky assets either with or without a riskless asset our solutions provide insights into portfolio management problems and issues in conditional asset pricing

volatility of aggregate volatility and hedge fund returns abstract this paper investigates empirically whether uncertainty about equity market volatility can explain hedge fund performance both in the cross section and over time we measure uncertainty via volatility of aggregate volatility vov and construct an investable version through returns on lookback straddles on the chicago board options exchange cboe volatility index vix we find that vov exposure is a significant determinant of hedge fund returns after controlling for fund characteristics we find a robust and significant negative risk premium for vov exposure in the cross section of hedge fund returns we corroborate our results using statistical and parameterized proxies of vov over a longer sample period

improving diversification opportunities for socially responsible investors socially responsible investment sri has grown enormously and has expanded globally in recent years it allows sri investors to reduce their portfolio risk assumptions through international diversification in this context the aim of this paper is twofold i to examine price and volatility linkages among the most representative sri indexes for north america europe and asia pacific employing a multivariate approach and ii to provide the out of sample performance of an optimal portfolio constructed on the basis of time varying return and volatility forecasts from this specification approach our overall results show that using this technique it is possible to reduce risk and out perform the naive rule which is usually employed in this type of investment these findings are relevant not only for academics but also for practitioners especially for professional managers of sri portfolios

asset prices with locally constrained entropy recursive multiple priors utility control problems with recursive multiple priors utility rmpu are highly non linear so that rmpu asset prices have been studied in very simple exchange economies only we identify a continuous time exchange equilibrium with locally constrained entropy rmpu lce rmpu that is tractable even in the presence of a stochastic opportunity set and incomplete markets we find that time variation in the lce based ambiguity set is able to capture important features of consumption and asset markets data

learning by doing and the value of optimal experimentation abstract recent research on learning by doing has provided the limit properties of beliefs and actions for a class of learning problems in which experimentation is an important aspect of optimal decision making however under these conditions the optimal policy cannot be derived analytically because bayesian learning about unknown parameters introduces a nonlinearity in the dynamic optimization problem this paper utilizes numerical methods to characterize the optimal policy function for a learning by doing problem that is general enough for practical economic applications the optimal policy is found to incorporate a substantial degree of experimentation under a wide range of initial beliefs about the unknown parameters dynamic simulations indicate that optimal experimentation dramatically improves the speed of learning and the stream of future payoffs furthermore these simulations reveal that a policy which separates control and estimation and does not incorporate experimentation frequently induces a long lasting bias in the control and target variables while these sequences tend to converge steadily under the optimal policy they frequently exhibit non stationary behavior when estimation and control are treated separately

value of information in portfolio selection with a taiwan stock market application illustration abstract despite many proposed alternatives the predominant model in portfolio selection is still mean variance however the main weakness of the mean variance model is in the specification of the expected returns of the individual securities involved if this process is not accurate the allocations of capital to the different securities will in almost all certainty be incorrect if however this process can be made accurate then correct allocations can be made and the additional expected return following from this is the value of information this paper thus proposes a methodology to calculate the value of information a related idea of a level of disappointment is also shown how value of information calculations can be important in helping a mutual fund settle on how much to set aside for research is discussed in reference to a taiwan stock exchange illustrative application in which the value of information appears to be substantial heavy use is made of parametric quadratic programming to keep computation times down for the methodology

inventories and sticky prices more on the microfoundations of macroeconomics the role of inventories in making prices sticky is studied by analyzing a dynamic linear quadratic model of a monopoly firm facing stochastic demand but able to store its finished goods in inventory it is shown that in contrast to the usual presumption firms that exhibit the smallest output responses to demand fluctuations may also exhibit the smallest price fluctuations specifically firms which have very flexible inventory storage facilities or are subjected to very transitory demand shocks will rely on inventories as buffers and will change neither production nor price very much on the other hand firms which have very inflexible storage facilities or whose demand shocks are quite permanent will display large swings in both price and output the standard assumption about inventory carrying costs that has been used in the literature that they are linear is shown to imply that production is impervious to fluctuations in demand it is also established that prices may respond more strongly to positive demand shocks than to negative ones if it is impossible to hold negative inventories i e to have unfilled orders the model offers an explanation for stickiness in relative prices however under certain circumstances it may help explain the persistence of inflation this abstract was borrowed from another version of this item

the dynamic black litterman approach to asset allocation abstract we generalize the black litterman bl portfolio management framework to incorporate time variation in the conditional distribution of returns in the asset allocation process we evaluate the performance of the dynamic bl model using both standard performance ratios as well as other measures that are designed to capture tail risk in the presence of non normally distributed asset returns we find that the dynamic bl model outperforms a range of different benchmarks moreover we show that the choice of volatility model has a considerable impact on the performance of the dynamic bl model

can the production smoothing model of inventory behavior be saved the production smoothing model of inventory behavior has a long and venerable history and theoretical foundations that seem very strong yet certain overwhelming facts seem not only to defy explanation within the production smoothing framework but actually to argue that the basic idea of production smoothing is all wrong most prominent among these is the fact that the variance of detrended production exceeds the variance of detrended sales this paper first documents the stylized facts then it derives the production smoothing model rigorously and explains how the model can be amended to make it consistent with the facts finally it reviews the theoretical and empirical evidence and tries to draw some tentative conclusions

more possessions more worry abstract a common wisdom asserts that the wider the universe of assets to choose from the greater the investor s welfare we show that this is not the case in practice where parameters have to be estimated even when the estimates are unbiased surprisingly risk aversion plays a crucial role corresponding to the desirability of asset expansion by dividing investors in three groups investors with very low risk tolerance and investors with very high risk tolerance are better off with asset expansion and investors with moderate risk tolerance are worse off despite the option to refrain from investing in the additional asset

why empirical international portfolio models fail evidence that model misspecification creates home asset bias abstract international portfolio models consistently predict that investors should put much more of their wealth into foreign assets than they actually do a result known as home asset bias we use actual international portfolio data to show how model misspecification contributes to this bias we find that three widely used simplifying assumptions produce optimal portfolio weights that are significantly different from the weights produced by an unsimplified model in particular imposing the invalid assumption that ppp holds exaggerates the degree of home asset bias these findings suggest that researchers should pay greater attention to empirical model specification in the future