estimation methods in portfolio selection and the effectiveness of short sales restrictions uk evidence forecasting the mean returns vector and the covariance matrix is a key feature in implementing portfolio theory the performance of the bayes stein method for forecasting these parameters for use in the markowitz model with and without short sales was compared with that of seven other estimation methods and three alternative portfolio selection techniques this paper represents the first large scale empirical investigation of the usefulness of the bayes stein approach using historical data this data was drawn from the london stock exchange in contrast to earlier studies the relative performance of bayes stein was mixed while it produced reasonable estimates of the mean returns vector there were superior methods e g overall mean for estimating the covariance matrix when short sales were permitted when short sales were prohibited actual portfolio performance was clearly improved although there was little to choose between the various estimation methods

are household portfolios efficient an analysis conditional on housing in this paper we argue that standard tests of portfolio efficiency are biased towards rejection because they neglect the existence of illiquid wealth in the case of household portfolios the most important illiquid asset is housing if housing stock adjustments are costly and therefore infrequent we show how the dynamic optimization problem produces optimal portfolios in periods of no adjustment that are affected by housing price risk through a hedge term when the housing stock is not adjusted we argue that tests for portfolio efficiency of financial asset must then be run conditionally upon housing wealth in our application we use italian household portfolio data from shiw 1998 and time series data on financial asset and housing stock returns to assess whether actual portfolios are efficient we first consider purely financial portfolios and portfolios that also treat the housing stock as another asset we then consider the consequences of treating the housing stock as given and test for efficiency in this framework our empirical results support the view that the presence of illiquid wealth can explain portfolio choice by home owners

downward sloping demand for environmental amenities and international compensation elephant conservation and strategic culling conventional wisdom holds that monetary compensation for positive transboundary externalities will promote conservation of resource amenities we demonstrate that in the case of elephant conservation international transfers may also result in strategic behavior by host countries with adverse implications for global welfare and in situ stocks

forward exchange bias hedging and the gains from international diversification of investment portfolios abstract the gains to the us investor from international diversification of investment portfolios are examined for portfolio strategies that hedge and strategies that do not hedge exchange rate risk via the interbank forward market using the sharpe performance index and stochastic dominance as performance measures almost all the unhedged strategies outperformed the hedged strategies for 1985 1988 the opposite held for 1981 1984 the results are explained by the biasedness of forward rates in predicting future spot rates jel f30

integrating replenishment decisions with advance demand information there is a growing consensus that a portfolio of customers with different demand lead times can lead to higher more regular revenues and better capacity utilization customers with positive demand lead times place orders in advance of their needs resulting inadvance demand information this gives rise to the problem of finding effective inventory control policies under advance demand information we show that state dependent s s and base stock policies are optimal for stochastic inventory systems with and without fixed costs the state of the system reflects our knowledge of advance demand information we also determine conditions under which advance demand information has no operational value a numerical study allows us to obtain additional insights and to evaluate strategies to induce advance demand information

delegated portfolio management and optimal allocation of portfolio managers in this article we investigate whether the application of the mean variance framework on portfolio manager allocation offers any out of sample benefits compared to a naive strategy of equal weighting based on an exclusive data set of high net worth hnw investors we utilize a wide variety of methodologies to estimate the input parameters including exponentially weighted moving average ewma generalized autoregressive conditional heteroscedasticity garch and bayes stein shrinkage estimation we apply nine different mean variance models but find that none of these present any consistent benefit over a naive strategy of equal weighting

improved estimates of higher order comoments and implications for portfolio selection in the presence of nonnormally distributed asset returns optimal portfolio selection techniques require estimates for variance covariance parameters along with estimates for higher order moments and comoments of the return distribution this is a formidable challenge that severely exacerbates the dimensionality problem already present with mean variance analysis this article extends the existing literature which has mostly focused on the covariance matrix by introducing improved estimators for the coskewness and cokurtosis parameters we find that the use of these enhanced estimates generates a significant improvement in investors welfare we also find that it is only when improved estimators are used that portfolio selection with higher order moments dominates mean variance analysis from an out of sample perspective the author 2009 published by oxford university press on behalf of the society for financial studies all rights reserved for permissions please email journals permissions oxfordjournals org oxford university press

measuring price risk in rating revenue coverage bs or no bs the black scholes bs option pricing model has been a cornerstone of modern financial theories since its introduction by black and scholes 1973 and its subsequent refinement by merton 1973 the model has realized widespread adoption for a number of purposes inherent in the model are a number of assumptions an important and potentially restrictive assumption is that the underlying asset price is log normally distributed among the many diverse uses of the bs model the model and underlying theory are used to derive measurements of the variance of expected harvest time prices for use in rating revenue coverage in the federal crop insurance program revenue coverage currently accounts for about 80 of the total liability insured in the program this liability frequently exceeds 100 billion and thus the accuracy of revenue premium rates is of vital importance the use of the bs model by the risk management agency rma of the usda has been the focus of recent criticisms of the program critics have argued in favor of retrospective measures of price variability that are based on historical price movements or have recommended other approaches to measuring price risk this article reports on a contracted review of revenue insurance rating methodology commissioned by rma we evaluate a number of alternative approaches to measuring expected price variability including several approaches recommended by critics of the federal program our results suggest that the bs model is preferred to recommended alternatives on the basis of numerous criteria

the behavior of flexible exchange rates evidence and implications for predicting currency price movements furthermore variations in nominal exchange rates are dominated by changes in real rates past rate changes will not be useful for predicting inflation or vice versa changes in money supplies real incomes interest rates and current or trade accounts appear not to be systematically related to changes in exchange rates in the absence of any systematic component that could be exploited for forecasting purposes what means are available for controlling exchange rate risk hedging can be used with some effect but the optimal hedging policy is still a matter of debate given the relatively low correlations between euromarket interest rates and returns on common stock indexes and relative changes in exchange rates diversification across international markets offers considerable potential for risk reduction

political risk and the benefits of international portfolio diversification this paper examines the benefits of portfolio investment in the stock markets of politically risky countries by evaluating the effects of political risk constraints on the performance of a portfolio of international stocks we use monthly data on political risk ratings and stock returns for a sample of thirty six countries from april 1982 to december 1991 ex post and ex ante portfolio selection strategies are developed to assess the gains from international diversification efficient sets are derived using a quadratic programming technique we use four ex ante portfolio strategies whose optimal portfolio weights are those of the equally weighted portfolio the minimum variance portfolio the certainty equivalence tangency portfolio and the bayes stein portfolio the empirical findings based on the performance tests of jobson and korkie 1981 suggest that diversification among politically risky countries improves the risk return characteristics of optimal portfolios however the most striking benefit of the inclusion of politically risk countries in an international portfolio is the reduction in overall portfolio risk

monetary conditions and international investing we examine the relationship between monetary conditions and global stock returns previous studies established that u s stock returns during expansive u s monetary periods are significantly higher than returns during restrictive periods we found that this pattern prevails in non u s markets furthermore the pattern exists relative to both local and u s monetary conditions by examining several investment strategies we show that investors could have improved portfolio performance in the period studied by using both u s and local monetary conditions to guide their portfolio allocations using monetary conditions to determine portfolio composition would have been consistently beneficial throughout the past 30 years

confidence based optimisation for the newsvendor problem under binomial poisson and exponential demand abstract we introduce a novel strategy to address the issue of demand estimation in single item single period stochastic inventory optimisation problems our strategy analytically combines confidence interval analysis and inventory optimisation we assume that the decision maker is given a set of past demand samples and we employ confidence interval analysis in order to identify a range of candidate order quantities that with prescribed confidence probability includes the real optimal order quantity for the underlying stochastic demand process with unknown stationary parameter s in addition for each candidate order quantity that is identified our approach produces an upper and a lower bound for the associated cost we apply this approach to three demand distributions in the exponential family binomial poisson and exponential for two of these distributions we also discuss the extension to the case of unobserved lost sales numerical examples are presented in which we show how our approach complements existing frequentist e g based on maximum likelihood estimators or bayesian strategies

adaptive ordering and pricing for perishable products we consider the combined problem of pricing and ordering for a perishable product with unknown demand distribution and censored demand observations resulting from lost sales faced by a monopolistic retailer we develop an adaptive pricing and ordering policy with the asymptotic property that the average realized profit per period converges with probability one to the optimal value under complete information on the distribution the pricing mechanism is modeled as a multiarmed bandit problem while the order quantity decision made after the price level is established is based on a stochastic approximation procedure with multiplicative updates

optimal portfolio of foreign currencies with borrowing and lending until the late sixties most american corporations held their liquid assets in the form of cash short term government notes and other highly liquid marketable securities since the early seventies more and more firms have begun to hold their current assets in foreign currencies beyond what would be required to conduct normal foreign operations in the last few years companies have accumulated and retained much more cash than they held in the past in order to understand the magnitude of this issue realize that at the end of 1977 cash and short term securities held by international business machines amounted to 5 4 billion by exxon 4 2 billion and ford and general motors held well above 3 billion obviously with this cash pile up most companies devote much attention to cash management even a slight improvement in the management of these assets means a substantial profit and firms have responded with highly trained staff in particular people familiar with the international money market and the investment opportunities available the change in attitude toward cash management may be summarized by the following quotation from a senior adviser to the j henry schroder bank and trust company companies are no longer looking at a bank balance they re looking at a

optimal policies and approximations for a serial multiechelon inventory system with time correlated demand since clark and scarf s pioneering work most advances in multiechelon inventory systems have been based on demand processes that are time independent this paper revisits the serial multiechelon inventory system of clark and scarf and develops three key results first we provide a simple lower bound approximation to the optimal echelon inventory levels and an upper bound to the total system cost for the basic model of clark and scarf second we show that the structure of the optimal stocking policy of clark and scarf holds under time correlated demand processes using a martingale model of forecast evolution third we extend the approximation to the time correlated demand process and study in particular for an autoregressive demand model the impact of lead times and autocorrelation on the performance of the serial inventory system

future capacity procurements under unknown demand and increasing costs in this paper we study a situation in which a broker must manage the procurement of a short life cycle product as the broker observes demand for the item she learns about the demand process however as is often the case in practice it becomes either more difficult or more expensive to procure the item as the selling season advances thus the broker must trade off higher procurement costs against the benefit of making ordering decisions with better information about demand problems of this type arise for example in the travel industry where a travel agent s cost of procuring airline and hotel reservations increases as the date of a vacation package approaches we develop a newsvendor like characterization of the optimal procurement policy in a numerical analysis we demonstrate how broker procurements tend to cluster just before price increases and how brokers can benefit from explicitly considering the effects of information about demand in their ordering policies

a time series framework for supply chain inventory management we consider a supply chain in which the underlying demand process can be described in a linear state space form inventory is managed at various points of the chain members based on local information that each member observes and continuously updates the key feature of our model is that it takes into account the ability of the members to observe subsets of the underlying state vector and adopt their forecasting and replenishment policies accordingly this enables us to model situations in which the members are privy to certain explanatory variables of the demand with the latter possibly evolving according to a vector autoregressive time series for each member we identify an associated demand evolution model for which we propose an adaptive inventory replenishment policy that utilizes the kalman filter technique we then provide a simple methodology for assessing the benefits of various types of information sharing agreements between members of the supply chain we also discuss inventory positioning and cost performance assessment in the supply chain our performance metrics and inventory target levels are usually presented in matrix forms allowing them to accommodate a relatively large spectrum of linear demand models and making them simple to implement several illustrations for possible applications of our models are provided

massaging mean variance inputs returns from alternative global investment strategies in the 1980s this paper explores the impact of adjustments to the inputs on total returns terminal wealth and portfolio turnover in an unconstrained monthly mean variance mv asset allocation over time it is well known that mv allocations are very sensitive to small forecast errors in the means and covariances this sensitivity is especially pronounced for errors in means one way to control this sensitivity to forecast errors is to use stein estimation we examined three naive applications of stein estimation for six individual country stock indexes five country bond indexes and five cash indexes this study has two major conclusions first any of the suggested adjustments to inputs dominate the results of an unadjusted input mv optimization adjusted input portfolios have higher mean return less variance and greater terminal wealth than unadjusted input portfolios second these improvements become even greater with transaction costs

international diversification of investment portfolios u s and japanese perspectives in this paper we analyze the gains from international diversification of investment portfolios from the japanese as well as the u s perspectives the major findings of this paper include first the potential gains from international as opposed to purely domestic diversification are much greater for u s investors than for japanese investors for u s investors the gains accrue not so much in terms of lower risk as in terms of higher return and the opposite holds for japanese investors second using various ex ante international investment strategies designed to control parameter uncertainty u s investors can realize substantial gains from international diversification in out of sample periods japanese investors however can gain relatively little third hedging exchange risk generally allows the u s but not japanese investors to benefit more from international diversification for u s investors the international bond diversification with exchange risk hedging offers a superior risk return trade off than the international stock diversification with or without hedging

money bonds and foreign exchange in the theory of finance capital markets provide securities which allow the ownership of productive assets to be allocated among investors according to their willingness to bear risk in exchange for return and independently of their tastes for the productive services provided by the assets this paper uses the theory of finance to study the role of money as a productive asset and the transformation of money into a portfolio asset true to its purpose the capital market provides securities nominal bonds that allow an allocation of the current services of the money supply according to its current productivity and without regard for its future purchasing power risk and an allocation of the future purchasing power risk of the money supply according to the willingness of investors to bear this risk in exchange for return and without regard for investor needs for the future transactions services of money in open

a dynamic globally diversified index neutral synthetic asset allocation strategy an investor with the ability to assess the prospective return and risk structure of the global capital markets can construct portfolios that over time will not only outperform actively or passively managed domestic asset portfolios but will also outperform passively managed global portfolios a bayesian approach to dynamic seemingly unrelated regression dsur is a robust and effective means to forecast the one step ahead conditional distribution of asset returns this approach recognizes the time varying nature of the global capital markets the predictive moments are used to derive a single factor return model once an index portfolio is specified the index portfolio represents an investor s underlying portfolio given the factor model that assesses the relative attractiveness and risk of the assets in relation to the index an index neutral portfolio is constructed as an overlay to enhance the returns of the index portfolio this portfolio is mean variance optimal is notional neutral i e the sum of the asset exposures is zero and has returns that are designed to be uncorrelated with the returns of the index portfolio the implementation of such an index neutral portfolio using derivative securities is simulated over the period january 1988 to december 1993

bayes stein estimation for portfolio analysis in portfolio analysis uncertainty about parameter values leads to suboptimal portfolio choices the resulting loss in the investor s utility is a function of the particular estimator chosen for expected returns so this is a problem of simultaneous estimation of normal means under a well specified loss function in this situation as stein has shown the clas sical sample mean is inadmissible this paper presents a simple empirical bayes estimator that should outperform the sample mean in the context of a portfolio simulation analysis shows that these bayes stein estimators provide significant gains in portfolio selection problems

disagreement portfolio optimization and excess volatility disagreement a key factor inducing trading has been receiving ever increasing attention in recent years most research has focused on disagreement about the expected returns several authors have shown that if the average belief coincides with the true expected return in the portfolio context prices are unaffected by disagreement in this paper we study the pricing effects of disagreement about return variances we show that i disagreement about variances has systematic and significant pricing effects more disagreement leads to higher prices and ii prices are very sensitive to the degree of disagreement even if the average belief about the variance is constant tiny fluctuations in the disagreement about the variance lead to substantial price fluctuations this second result may offer an explanation for the excess volatility puzzle when small changes in the degree of disagreement occur they induce relatively large price changes yet the changes in disagreement may be hard to directly detect empirically leading to apparent excess volatility

optimal minimum bids and inventory scrapping in sequential single unit vickrey auctions with demand learning abstract retailers often conduct sequential single unit auctions and need to decide the minimum bid in each auction to reduce inventory costs it may be optimal to scrap some of the inventory rather than holding it until it is auctioned off in some auctions the seller may be uncertain about the market response and hence may want to dynamically learn the demand by observing the number of posted bids we formulate a markov decision process mdp to study this dynamic auction design problem under the vickrey mechanism we first develop a clairvoyant model where the seller knows the demand distribution we prove that it is optimal to scrap all inventory above a certain threshold and then auction the remaining units we derive a first order necessary condition whereby the bidders virtual value at an optimal minimum bid equals the seller s marginal profit this is a generalization of riley and samuelson s result from the one single unit auction case when the virtual value is strictly increasing this necessary condition is also sufficient and leads to a structured value iteration algorithm we then assume that the number of bidders is poisson distributed but the seller does not know its mean the seller uses a mixture of gamma prior on this mean and updates this belief over several auctions this results in a high dimensional bayesian mdp whose exact solution is intractable we therefore propose and compare two approximation methods called certainty equivalent control cec and q function approximation numerical experiments suggest that q function approximation can attain higher revenues than cec

portfolio selection an alternative approach this paper provides a solution to the portfolio diversification problem based on finding optimal weights that will result in maximizing the risk adjusted return of the underlying portfolio subject to the budget constraint contrary to the standard approach that aims at finding the required weights based on minimizing the variance of the portfolio subject to the budget constraint a mathematical proof is given for the suggested solution an application is provided to the portfolio diversification opportunity between all the share market indexes of the two largest economies in the world the results show that the portfolio created by our suggested approach leads to almost one percent increase in the risk adjusted return compared to the portfolio created by the standard method

bayes solution to dynamic inventory models under unknown demand distribution this paper considers the periodic review inventory problem for which one or more parameters of the demand distribution are unknown with a known prior distribution chosen from the natural conjugate

performance of portfolios optimized with estimation error we explain the poor out of sample performance of mean variance optimized portfolios developing theoretical bias adjustments for estimation risk by asymptotically expanding future returns of portfolios formed with estimated weights we provide closed form non bayesian adjustments of classical estimates of portfolio mean and standard deviation the adjustments significantly reduce bias in international equity portfolios increase economic gains and are robust to sample size and to nonnormality dominant terms grow linearly with the number of assets and decline inversely with the number of past time periods under suitable conditions sharpe ratio maximizing tangency portfolios become more diversified using these approximation methods it may be possible to assess before investing the effect of statistical estimation error on portfolio performance

pre season stocking and pricing decisions for fashion retailers with multiple information updating abstract motivated by the industrial practice we investigate in this paper the pre season inventory and pricing decisions for fashion retailers before the selling season a retailer can place orders for a seasonal fashion product from her supplier at two distinct stages via two different delivery modes market information from the sales of a pre seasonal product is collected and used to update the demand forecast of the seasonal product at the succeeding stages by using bayesian approach we formulate a dynamic optimization problem and obtain the optimal stocking policy after the ordered seasonal product has arrived and just before the start of the selling season the retailer can determine the optimal selling price of the product with respect to the latest demand information and the amount of product on hand we study the pricing policy under different objectives sensitivity analysis is carried out and the features of the policies are revealed managerial insights are generated

cvar models with selective hedging for international asset allocation abstract we develop an integrated simulation and optimization framework for multicurrency asset allocation problems the simulation applies principal component analysis to generate scenarios depicting the discrete joint distributions of uncertain asset returns and exchange rates we then develop and implement models that optimize the conditional value at risk cvar metric the scenario based optimization models encompass alternative hedging strategies including selective hedging that incorporates currency hedging decisions within the portfolio selection problem thus the selective hedging model determines jointly the portfolio composition and the level of currency hedging for each market via forward exchanges we examine empirically the benefits of international diversification and the impact of hedging policies on risk return profiles of portfolios we assess the effectiveness of the scenario generation procedure and the stability of the model s results by means of out of sample simulations we also compare the performance of the cvar model against that of a model that employs the mean absolute deviation mad risk measure we investigate empirically the ex post performance of the models on international portfolios of stock and bond indices using historical market data selective hedging proves to be the superior hedging strategy that improves the risk return profile of portfolios regardless of the risk measurement metric although in static tests the mad and cvar models often select portfolios that trace practically indistinguishable ex ante risk return efficient frontiers in successive applications over several consecutive time periods the cvar model attains superior ex post results in terms of both higher returns and lower volatility

international effects of a compression of euro area yield curves abstract in this paper we use a bayesian global vector autoregressive model to analyze the macroeconomic effects of a flattening of euro area yield curves our findings indicate positive effects on real activity and prices both within the euro area as well as in neighboring economies spillovers transmit through an exchange rate channel and a broad financial channel we complement our analysis by conducting a portfolio optimization exercise our results show that multi step ahead forecasts conditional on the euro area yield curve shock improve sharpe ratios relative to other investment strategies

international portfolio diversification the basket peg regime abstract the paper compares and contrasts optimal investment strategies in two alternative monetary arrangements namely in the regime with freely floating bilateral exchange rates and the basket peg system it is shown that in the basket peg arrangement investors can form a domestic currency denominated risk free asset of the foreign risk free assets without entering into the forward currency markets furthermore investors have an incentive to hold fewer assets and the structure of capital flows tends to be more volatile but also more predictable in the basket peg system than in the regime with freely floating bilateral exchange rates

adapting the newsvendor model for infinite horizon inventory systems abstract we address inventory decisions in the context of the reorder point order quantity policy in infinite horizon stochastic lead time demand inventory systems in which the parameters may be non stationary we develop a heuristic policy based on the simple economic order quantity eoq model and the one period newsvendor model using illustrative numerical examples we demonstrate that our simple and easy to understand heuristic policy performs nearly as well as the optimal policy derived from complicated mathematical procedures our heuristic policy is simple easy to implement and flexible in that it can be easily adapted to situations when the parameters of the inventory system may change analytical modeling under non stationary parameters would be extremely complex and the derivation of closed form optimal policies is mathematically intractable in most cases in such cases practitioners will find our heuristic policy an attractive option

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

scarf s state reduction method flexibility and a dependent demand inventory model we consider a finite horizon inventory model with linear holding shortage and ordering costs the demand random variables are dependent and average demand is described by an exponential smoothing formula this model can be formulated as a two state variable inventory level weighted past demands dynamic program using a procedure first developed by scarf for a bayesian inventory model we are able to reformulate the model as a one state variable dynamic program resulting in a considerable computational saving over the two state variable formulation we also show that this dependent demand model orders less than or equal the amount ordered by a comparable independent demand model we establish this result under the assumption that demand represents failures that are repaired by the beginning of the next period

the benefits from international diversification for nordic investors abstract in this paper we investigate the magnitude of the benefits from international diversification from the nordic point of view special attention is paid to whether potentially increased co movement of stock markets together with more volatile nordic currencies have resulted in decreased benefits from international diversification towards the end of the 1980s moreover the paper presents evidence on the benefits from international diversification for a currency which has recently started its free float the finnish markka fim we find significant increases in stock market co movement both unhedged ex ante strategies as well as strategies hedged for exchange rate risk are investigated revealing substantial benefits from international diversification for the nordic countries however we obtain mixed results concerning the question of the optimality of hedging

were the returns from stocks and bonds of different countries really different in the 1980 s we analyzed the total equity returns of indexes from australia canada germany japan the uk and the us and total fixed income returns of indexes from all but australia excluded due to lack of data to see if the returns of stocks and bonds were statistically different across markets during the 1980s at the end of 1989 these countries represented over 87 of the market capitalization of the morgan stanley capital international msci world equity index and over 88 of the salomon brothers world bond index this study used monthly observations from january 1980 through december 1989 and examined returns based in local currency and hedged and unhedged us dollars we found that sample mean stock and bond returns during the 1980s were statistically indistinguishable across countries however because the sample variances were so large relative to the sample means it would have been difficult to detect differences in population means by any test we found evidence of variance heterogeneity which may be

exchange rate uncertainty forward contracts and international portfolio selection in this paper ex ante efficient portfolio selection strategies are developed to realize potential gains from international diversification under flexible exchange rates it is shown that exchange rate uncertainty is a largely nondiversiflable factor adversely affecting the performance of international portfolios therefore it is essential to effectively control exchange rate volatility for that purpose two methods of exchange risk reduction are simultaneously employed multicurrency diversification and hedging via forward exchange contracts the empirical findings show that international portfolio selection strategies designed to control both estimation and exchange risks almost consistently outperform the u s domestic portfolio in out of sample periods since grubel 11 applied modern portfolio theory mpt to international investment various authors such as levy and sarnat 17 solnik 20 and lessard 16 have examined the gains from international diversification of investment portfolios for the purpose of establishing the gains from international diversification these studies constructed international portfolios using historical risk and return data from a period of fixed or relatively stable exchange rates and showed that internationally diversified portfolios dominated purely domestic portfolios in terms of mean variance efficiency from the standpoint of today s investors however the previous studies fail to offer operational guidance for international diversification for two important reasons first it is now questionable whether the past findings are still relevant under the current flexible exchange rate regime second by being ex post in nature the past studies ignored the issue of estimation risk or parameter uncertainty and therefore may have overstated the realizable portion of the potential gains from international diversification fluctuating exchange rates are likely to mitigate the potential gains from international diversification by making investment in foreign securities more risky as will be shown later a fluctuating exchange rate contributes to the risk of foreign investment not only through its own variance but also through its positive covariances with the local stock market returns during our sample period of 1980 through 1985 for example exchange rate volatility is found to account for about fifty percent of the volatility of dollar returns from investment in the stock markets of such major countries as germany japan and the u k furthermore the exchange rate changes vis a vis the u s dollar are found to be

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

design for postponement a comprehensive characterization of its benefits under unknown demand distributions recent papers have developed analytical models to explain and quantify the benefits of delayed differentiation and quick response programs these models assume that while demands in each period are random they are independent across time and their distribution is perfectly known i e sales forecasts do not need to be updated as time progresses in this paper we characterize these benefits in more general settings where parameters of the demand distributions fail to be known with accuracy or where consecutive demands are correlated here it is necessary to revise estimates of the parameters of the demand distributions on the basis of observed demand data we analyze these systems in a bayesian framework assuming that our initial information about the parameters of the demand distributions is characterized via prior distributions we also characterize the structure of close to optimal ordering rules in these systems for a variety of types of order cost functions

optimal policy for a muti product multi period non stationary stochastic production and customization problem abstract this paper is concerned with a multi product multi period non stationary stochastic production and customization problem in which a firm wishes to satisfy multi period stochastic demands for m products the firm produces a generic product that can be customized into the m products the lead time to produce the generic product is one period the generic product can be customized into any of the m products immediately assume that the costs of production customization storage and shortage are linear also assume that the unsatisfied demands for the m products at the firm in each period are lost the objective of the firm is to find a production customization policy that minimizes the expected cost over a planning horizon we obtain the conditions that ensure that a myopic production customization policy is optimal

parameter based decision making under estimation risk an application to futures trading this study shows how the standard portfolio model of futures trading should be modified when there is less than perfect information about the relevant parameters estimation risk the standard and the optimal decision rules for futures trading in the presence of estimation risk are compared and discussed an operational model of futures trading for use under estimation risk is advanced in the presence of relevant prior and sample information the model can be used to optimally blend both types of information many of the contributions of economic theory to the study of financial markets involve the use of parameters that are assumed known or estimable by the economic agents examples include the risk premium coefficient 18 and the security market lines that underlie the capital asset pricing model the volatility measures required for option pricing and the minimum variance hedge ratio and expected basis used to construct portfolios of futures contracts and cash positions generally it is left to practitioners to provide estimates of these parameters which are then directly substituted for the actual parameter values of the theoretical model whenever textbooks demonstrate how these parameters can be estimated there is usually a cookbook formula provided that requires some relatively straightforward analysis of the relevant data e g marshall 1989 chapters 6 and 7 cox and rubinstein 1985 chapter 6 the problems with the procedure described above are twofold first the theory has been slow to acknowledge that the practical application of the model almost always involves parameter estimates generally the additional risk of not knowing the true parameters is completely neglected second practitioners or the market participants will often have some type of nonsample information such as insider information or subjective priors that seems relevant for decision making however this potentially important information is ignored altogether when only sample data are used to obtain the parameter estimates

a postponement model for demand management in this paper we analyze demand postponement as a strategy to handle potential demand surges under demand postponement a fraction of the demands from the regular period are postponed and satisfied during a postponement period this permits capacity to be procured to satisfy the postponed demands a reimbursement per unit is paid to customers whose demands are postponed the basic idea is that by preempting stockouts through demand postponement we can reduce overall stockout costs we formulate and solve a two stage capacity planning problem under demand postponement we propose a power range class of distributions to capture the nature of demand surges we establish the scalability and conjugate properties of the power range distributions under demand postponement which leads to a tractable analysis of the problem we analytically solve the problem of determining the optimal regular and postponement period capacities and the demand splitting rule to minimize the supplier s expected cost we show that a the value of postponement may be significant depending on cost and demand parameters b a postponement strategy may lead to reduced investment in initial capacity and c it may be optimal to do no demand postponement over a range of demands even after observing a higher demand signal we then relax several model assumptions and provide results for these extensions we conclude with managerial insights

daily exchange rate behaviour and hedging of currency risk textabstractwe construct models which enable a decision maker to analyze the implications of typical time series patterns of daily exchange rates for currency risk management our approach is bayesian where extensive use is made of markov chain monte carlo methods the effects of several model characteristics unit roots garch stochastic volatility heavy tailed disturbance densities are investigated in relation to the hedging strategies consequently we can make a distinction between statistical relevance of model specifications and the economic consequences from a risk management point of view we compute payoffs and utilities from several alternative hedge strategies the results indicate that modelling time varying features of exchange rate returns may lead to improved hedge behaviour within currency overlay management

confidence in the familiar an international perspective one striking feature of intemrnational portfolio investment is the extent to which equity portfolios are concentrated in the domestic equity market of the investor the home bias puzzle i examine the role of investors perception of foreign investment risk on their portfolio choices the expected retumrns and risk of foreign investment are specified through an asset pricing model with the home portfolio being the benchmark asset pastor s 2000 domestic capm the model serves as a reference point around which investors can center their prior beliefs i focus on investors prior beliefs that are consistent with the literature on confidence in the familiar foreign equities in terms of both expected returns and risk being viewed less favorably than domestic equities these prior beliefs are then combined with the data on g7 equities and the revised beliefs are used to obtain the global optimal asset allocation to hold predominantly domestic equities each g7 investor has to believe that the risk of foreign investment is several times higher than the actual risk the home bias is more of a puzzle for a u s investor during the 1970s specifying investors prior beliefs around the world capm does not help resolve the puzzle

bayesian and capm estimators of the means implications for portfolio selection abstract this paper compares active investment policies under three alternative models for estimating expected stock returns the historical sample mean a shrinkage or bayesian estimator and a capm based estimator the out of sample performance of actively managed u s industry portfolios is analyzed for these three estimators over the period 1931 to 1987 it is found that the classical method based on historical means and covariances leads to the worst forecasts and out of sample performance and is generally outperformed by shrinkage estimators an active portfolio with expected returns based on the capm produced the best results among all actively managed portfolios this strategy as we show closely matches a simple buy and hold the market rule

efficient portfolios when housing needs change over the life cycle abstract we address the issue of the efficiency of household portfolios in the presence of housing risk we treat housing stock as an asset and rents as a stochastic liability stream over the life cycle households can be short or long in their net housing position efficient financial portfolios are the sum of a standard markowitz portfolio and a housing risk hedge term that multiplies net housing wealth our empirical results show that net housing plays a key role in determining which household portfolios are inefficient the largest proportion of inefficient portfolios obtains among those with positive net housing who should invest more in stocks

loss averse newsvendor model with two ordering opportunities and market information updating abstract a fashion supply chain characterized by a long lead time and a short selling season is considered in this paper facing demand uncertainty the risk averse retailer has two opportunities to make order decisions before the demand is realized the risk aversion is modelled as a penalty to the decision maker the retailer if a target profit is not attained we derive the retailer s optimal ordering decisions and analyze the monotonicity behaviours of the critical market signal the optimal first stage order quantity and the optimal expected payoff with respect to the penalty coefficient we also examine the impact of demand forecast quality on the retailer s decisions and extend the study to the case where order cancellation is allowed

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

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

stopped myopic policies in some inventory models with generalized demand processes this paper considers single item inventory systems with immediate delivery and no economies of scale bounds are provided on the value loss relative to optimal cost for restricting attention to the class of inventory stocking policies that behave myopically up to a specified stopping time the stopping time may be random and may depend on demand histories as well as information exogenous to the firm the bounds are robust to the nature of the demand process faced after the stopping time so are applicable when the statistics of demand after the stopping time are unknown stopping times that are large with high probability imply that near term decisions are completely specified with high probability the general bounding results allow one to consider demand processes that may otherwise be analytically intractable it is shown that the class of demand models for which the assumption of additive i i d shocks is appropriate is the same class admitting effective myopic stocking policies the bounds also make rigorous the intuitive notion that myopic policies are least effective in systems with precipitous drops in demand coupled with an inability to recover cash invested in inventory the option of selling inventory at discount is a reality in many real systems and enhances the attractiveness of the myopic stocking policy in numerical examples the myopic policy is shown to be an effective competitor in a range of systems for which optimal policies are not known the results suggest that for systems with immediate delivery no economies of scale and no currently known optimal policy the myopic stocking rule is a reasonable default policy to adopt

a rational explanation for home country bias abstract while modern portfolio theory predicts that investors should diversify across international markets corporate equity is essentially held by domestic investors french and poterba 1991 french k poterba j 1991 investor diversification and international equity markets american economic review 81 222 226 suggest that in order for this bias to be justified investors must hold optimistic expectations about their domestic markets and pessimistic expectations about their foreign markets tesar and werner 1995 tesar l l werner i m 1995 home bias and high turnover journal of international money and finance 14 467 492 find existing explanations for the home equity bias unsatisfactory and conclude that the issue poses a challenge for portfolio theory we develop a model that incorporates both the foregone gains from diversification and the informational constraints of international investing and shows that home equity bias is consistent with rational mean variance portfolio choice specifically we prove that the nature of estimation risk in international markets can be responsible for this phenomenon we show that when the cross market variability in the estimation errors of international markets means far exceeds the cross market variability in the means themselves domestic dedication dominates international diversification an examination of 11 international markets returns over the last 25 years from the perspective of german japanese and us investors provides evidence consistent with this explanation

risk reduction by diversification in the nordic stock markets empirical examination of the ex post potential gains of risk reduction through international portfolio diversification started with grubel 1968 levy and sarnat 1970 solnik 1974 and lessard 1974 in their survey of international finance adler and dumas 1983 p 938 summed up the results the potential for international diversification to reduce risk seems unquestionable in the wake of increasing liberalization for international portfolio investment more recent contributions include jorion 1985 1989 grauer and hakansson 1987 and levy and lerman 1988 the results of the pioneers have been corroborated by contemporary research and according to jorion 1989 p 54 international diversification extolled by grubel as early as 1968 seems to have delivered on its promises despite the long tradition of studies in international portfolio diversification there has been no such work regarding the nordic markets this paper fills the gap through an analysis of potential gains from international diversification for different nordic investors danish finnish norwegian and swedish if they invest in all the nordic equity markets until the beginning of the 1980s nordic investors particularly in finland and sweden faced legal restrictions on investment abroad see nordiska radet 1987 adler and dumas 1983 have pointed out that such restrictions would lead to partially or fully segmented markets and hietala 1989 has shown the existence of premiums in the finnish stock market in our study we do not make any direct test of whether the nordic equity markets have been segmented or integrated but our results might provide some indirect evidence the nordic countries are generally viewed as fairly homogeneous from a social political and economic point of view while international diversifi

the empirical minimum variance hedge decision making under unknown true parameters estimation risk is discussed along with bayes and parameter certainty equivalent pce criteria bayes criterion incorporates estimation risk in a manner consistent with expected utility maximization the pce method which is the most commonly used is not consistent with expected utility maximization bayes criterion is employed to solve for the minimum variance hedge ratio empirical application of bayes minimum variance hedge ratio is addressed and illustrated simulations shoe that discrepancies between prior and sample parameters may lead to substantial differences between bayesian and pce minimum variance hedges

performance of currency portfolios chosen by a bayesian technique 1967 1985 abstract this paper is about normative currency portfolio rules it assumes logarithmic investors who maximize the expected utility from lognormal currency returns with and without short sales restrictions a number of implementable portfolio diversification policies are tried out on a large body of data covering nine major currencies and eighteen years of weekly observations in doing so we present ways of dealing with the estimation risk in an international context the necessary mean and covariance inputs are provided by a bayesian prior on the means and by sample means and covariance matrices which are estimated from weekly sample data while some policies do produce abnormal returns over and beyond proper reward for risk none does so in a statistically significant way this means that the evidence does not allow one to conclude that market participants are improperly diversified as a byproduct of this investigation techniques are found which would allow portfolio managers to earn a proper reward for risk by following a purely mechanical procedure such techniques may be valuable in a multi country world where the aggregate portfolio of currencies and securities is unknown and is not supposed to be efficient

selective hedging strategies for oil stockpiling abstract as a feasible option for improving the economics and operational efficiency of stockpiling by public agency this study suggests simple selective hedging strategies using forward contracts the main advantage of these selective hedging strategies over the previous ones is not to predict future spot prices but to utilize the sign and magnitude of basis easily available to the public using the weekly spot and forward prices of west texas intermediate for the period of october 1997 august 2002 this study adopts an ex ante out of sample analysis to examine selective hedging performances compared to no hedge and minimum variance routine hedging strategies to some extent selective hedging strategies dominate the traditional routine hedging strategy but do not improve upon the expected returns of no hedge case which is mainly due to the data characteristics of out of sample period used in this analysis

international portfolio diversification with estimation risk international portfolio diversification has long been advocated as a way of enhancing average returns while reducing portfolio risk for the investor who considers diversifying into foreign securities this proposition however relies on the assumption that the required inputs to the classical mean variance analysis are known with certainty typically expected returns variances and covariances are simply replaced by their ex post sample values and the optimal portfolio is derived without mentioning the uncertainty inherent in these parameter values but the rational investor should take this uncertainty into account when forming expectations and probably will consider estimators that are less subject to estimation error than the classical sample mean this paper investigates alternative estimators of expected returns and their implications for the alleged gains from diversification an important observation is the crucial influence that errors in estimating expected returns have on portfolio analysis a closer examiprevious studies of international portfolio diversification have relied on ex post meanvariance analysis without considering the problem of estimation risk typically past averages are substituted for expected returns and no allowance is made for the uncertainty inherent in these parameter values first i demonstrate the shortcomings of such an approach and second i investigate another method of estimating expected returns initially proposed by stein by shrinking the sample averages toward a common mean i find that the out of sample performance of the optimal portfolio is substantially increased one of the implications of this method is that the classical conclusions vastly overestimate the possible gains in average returns instead benefits from diversification are more likely to accrue from a reduction in risk this paper draws on part of my dissertation at the university of chicago i am grateful to arnold zellner michael mussa george constantinides and especially john bilson for useful discussions and comments numerous improvements were also suggested by the referee this research received the generous financial support of the college interuniversitaire d etudes doctorales dans les sciences du management

myopic solutions of markov decision processes and stochastic games sufficient conditions are presented for a markov decision process to have a myopic optimum and for a stochastic game to possess a myopic equilibrium point an optimum or an equilibrium point is said to be myopic if it can be deduced from an optimum or an equilibrium point of a static optimization problem or a static nash game the principal conditions are a each single period reward is the sum of terms due to the current state and action b each transition probability depends on the action taken but not on the state from which the transition occurs and c an appropriate static optimum or equilibrium point is ad infinitum repeatable these conditions are satisfied by several dynamic oligopoly models and numerous markov decision processes

gains from international diversification 1968 85 returns on portfolios of stocks and bonds this paper applies the multi period investment model to a universe of international securities on the basis of the simple probability assessment approach our principal findings are 1 the gains from including non u s asset categories in the universe were remarkably large in some cases statistically significant especially for the highly risk averse strategies 2 the gains from removing the no leverage constraint were more substantial than they were in the absence of non u s securities and 3 there is strong evidence of market segmentation in that the optimal levels of investment in u s securities were mostly zero in the presence of the non u s asset categories

a general equilibrium model of international portfolio choice we investigate in a two country general equilibrium model whether a bias in consumption towards domestic goods will necessarily lead to a preference for domestic securities we develop a model where investors are constrained to consume only from their domestic capital stock and where it is costly to transfer capital across countries in this model investors less risk averse than an investor with log utility bias their portfolios towards domestic assets investors more risk averse than log however prefer foreign assets thus this model suggests that it is unlikely that the portfolios observed empirically can be explained by the high proportion of domestic goods in total consumption we investigate in a two country general equilbrium model whether a bias in consumption toward domestic goods will necessarily lead to a preference for domestic assets in an investor s optimal portfolio we constrain investors to consume only from their domestic capital stock and introduce a proportional cost for transferring goods from one country this cost gives rise to endogenous deviations from the law of one price lop thus the home and foreign investors do not hold identical portfolios we show that an investor s optimal portfolio is biased towards domestic equity only if she is less risk averse than an investor with log utility investors with relative risk aversion greater than one exhibit a preference for the foreign asset this is because the exchange rate derived endogenously is negatively correlated with the return on the foreign asset and therefore the translated return on the foreign stock is less risky than that on the domestic stock thus the results of this model suggest that it is unlikely that the preference for domestic assets that is observed empirically can be explained by the high proportion of domestic goods in total consumption there exists a considerable body of literature documenting the gains from international diversification grubel 1968 was the first to propose that international diversification allows investors to attain lower return variances than those achievable by diversifying domestically this proposition relies on the correlation between stock indices across countries being significantly less

myopic policies for some inventory models with uncertain demand distributions the majority of papers on stochastic inventory theory make the assumption that the distribution of consumer demand in each time period is known with certainty while this assumption is unsupported in many applied contexts it is conventionally held that more realistic models are more difficult to solve and will not yield simple operational policies this paper shows that a simple inventory policy based upon a critical fractile can be optimal or near optimal in some inventory models with parameter adaptive demand processes in these some parameter of the demand distribution is not known with certainty and estimates of the parameter are updated in a statistical fashion as demand is observed through time examples include exponentially smoothed forecasts and bayesian updating of parameter estimates bounds on the value loss relative to optimal cost when using the critical fractile policy can be calculated directly from the problem data some numerical examples illustrate the technique

cluster analysis for portfolio optimization we consider the problem of the statistical uncertainty of the correlation matrix in the optimization of a financial portfolio by assuming idealized conditions of perfect forecast ability for the future return and volatility of stocks and short selling we show that the use of clustering algorithms can improve the reliability of the portfolio in terms of the ratio between predicted and realized risk bootstrap analysis indicates that this improvement is obtained in a wide range of the parameters n number of assets and t investment horizon the predicted and realized risk level and the relative portfolio composition of the selected portfolio for a given value of the portfolio return are also investigated for each considered filtering method we also show that several of the results obtained by assuming idealized conditions are still observed under the more realistic assumptions of no short selling and mean return and volatility forecasting based on historical data

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

multi level approaches to demand management in complex environments an analytical model abstract recent studies have shown that as demand becomes irregular and complex i e lumpy a possible approach for managing such uncertainty is to collect information directly from customers this implies that the sales units have to move closer to customers analyse their likely requirements and collect quantitative and structured data as well as qualitative and subjective insights however as integration with individual customers increases and data collection capabilities improve the organisational configuration of most companies becomes ever more complex and the aggregation of forecasts more difficult this paper discusses two approaches to managing demand uncertainty in complex environments in the first termed decentralised order overplanning sales units are responsible for forecasting the demand of each customer and defining requirements in the second termed centralised order overplanning forecasts provided by sales units are aggregated and further elaborated by manufacturing to define item requirements by means of an analytical model which describes the forecasting and planning process as a bayesian markovian process we show that the centralised method out performs the decentralised approach by virtue of the ability to exploit the additional information provided by commonalities between customers requests however this advantage has to be balanced against organisational costs since the centralised method splits responsibilities for forecasting and slack control between sales and manufacturing units major conflicts are likely to arise the focus and commitment on forecasting accuracy may be compromised and information may be lost when individual forecasts are sent to the manufacturing unit

adaptive inventory control for nonstationary demand and partial information this paper examines several different policies for an inventory control problem in which the demand process is nonstationary and partially observed the probability distribution for the demand in each period is determined by the state of a markov chain the core process however the state of this core process is not directly observed only the actual demand is observed by the decision maker given this demand process the inventory control problem is a composite state partially observed markov decision process pomdp which is an appropriate model for a number of dynamic demand problems in practice managers often use certainty equivalent control cec policies to solve such a problem however this paper presents results that demonstrate that there are other practical control policies that almost always provide much better solutions for this problem than the cec policies commonly used in practice the computational results also indicate how specific problem characteristics influence the performance of each of the alternative policies

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