mimicking portfolios and exact arbitrage pricing we characterize the sets of mimicking positions with returns that can serve in place of factors in an exact k factor arbitrage pricing relation for a set of n assets all of the sets are k dimensional nonsingular linear transformations of each other we interpret three examples of such transformations and discuss empirical considerations we provide conditions under which the mimicking positions can be expressed as portfolios and we characterize the relation between mimicking portfolios and the minimumvariance frontier

index changes and losses to index fund investors because of arbitrage around the time of index changes investors in funds linked to the s p 500 index and the russell 2000 index lose between 1 0 billion and 2 1 billion a year for the two indices combined the losses can be higher if benchmarked assets are considered the pre reconstitution period is lengthened or involuntary deletions are taken into account the losses are an unexpected consequence of the evaluation of index fund managers on the basis of tracking error minimization of tracking error coupled with the predictability and or pre announcement of index changes creates the opportunity for a wealth transfer from index fund investors to arbitrageurs

the effects of regulatory policies on the cost of debt for electric utilities an empirical investigation this article develops a model of debt cost determination for regulated electric utilities based on an application of finance theory estimation of the model allows the hypothesis that regulatory policy directly influences the cost of debt to be tested and also enables the specific effects attributable to individual regulatory policy variables to be examined regulatory decisions are found to have statistically and economically significant effects on the cost of debt for electric utilities and the most important effects are associated with the treatment of construction work in progress for ratemaking purposes the extent of regulatory delay and whether or not interim rate relief is provided copyright 1989 by the university of chicago

on the frequency of large stock returns putting booms and busts into perspective textabstractnumerous articles have investigated the distribution of share prices and find that the returns are fat tailed nevertheless there is still controversy about the amount of probability mass in the tails and hence about the most appropriate distribution to use in modeling returns this controversy has proven hard to resolve as the alternatives are non nested we employ extreme value theory focusing exclusively on the larger observations in order to assess the tail shape within a unified framework we find that at least the first two moments exist this enables one to generate robust probabilities on large returns which put the recent stock market swings into historical perspective

optimal currency composition for china s foreign reserves a copula approach this paper investigates the optimal currency composition for a country s foreign reserves in the context of china we examine the asymmetric fat tail and complex dependence structure in distributions of currency returns a skewed fat tailed and pair copula construction is then built to capture features of higher moments in a d vine copula approach we show that under the disappointment aversion effect the central bank in our model can achieve sizeable gains in expected economic value from switching from the mean variance to copula modelling we find that this approach will lead to an optimal currency composition that allows china to have more space for international currency diversification while maintaining the leading position of the us dollar in the currency shares of china s reserves

another look at portfolio optimization under tracking error constraints research has shown that adding constraints to total portfolio volatility can substantially improve the performance of managed portfolios although other work has considered constant tracking error volatility frontiers in this study tracking error was allowed to vary but the risk aversion was fixed the resulting optimal portfolios have several desirable properties

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

ipssis an integrated multicriteria decision support system for equity portfolio construction and selection abstract a fundamental principle of modern portfolio theory is that comparisons between portfolios are generally made using two criteria corresponding to the first two moments of return distributions namely the expected return and portfolio variance according to this model and according to most of the portfolio models derived from the stochastic dominance approach the group of portfolios open to comparisons is divided into two parts on the one hand there are the efficient portfolios those that are not dominated by any other portfolio in the group and on the other those that are dominated in other words these models do not solve for one optimal portfolio but rather solve for an efficient set of portfolios among which the investor must choose given his preference system one criticism over these models which has often been addressed both by practitioners and academics is that they fail to embody the objectives of the decision maker dm through the various stages of the decision process our purpose in this article is to present an integrated and innovative methodological approach for the construction and selection of equity portfolios which will take into account the inherent multidimensional nature of the problem while allowing the dm to incorporate his preferences in the decision process the proposed approach which grounds its basis on the field of multiple criteria decision making mcdm and more specifically on multiobjective mathematical programming mmp is implemented in the ipssis integrated portfolio synthesis and selection information system decision support system dss the validity of the proposed approach is tested through an illustrative application in the athens stock exchange ase

portfolio selection with mental accounts and delegation das et al 2010 develop an elegant framework where an investor selects portfolios within mental accounts but ends up holding an aggregate portfolio on the mean variance frontier this investor directly allocates the wealth in each account among available assets in practice however investors often delegate the task of allocating wealth among assets to portfolio managers who seek to beat certain benchmarks accordingly we extend their framework to the case where the investor allocates the wealth in each account among portfolio managers our contribution is threefold first we provide an analytical characterization of the existence and composition of the optimal portfolios within accounts and the aggregate portfolio second we present conditions under which such portfolios are not on the mean variance frontier and conditions under which they are third we show that the aforementioned analytical characterization is also applicable within the framework of das et al and thus improves upon their numerical approach

export diversification through resource based industrialization the case of natural gas for small resource rich developing economies specialization in raw exports is usually considered to be detrimental to growth and resource based industrialization rbi is often advocated to promote export diversification this paper develops a new methodology to assess the performance of these rbi policies we first formulate an adapted mean variance portfolio model that explicitly takes into consideration i a technology based representation of the set of feasible export combinations and ii the cost structure of the resource processing industries second we provide a computationally tractable reformulation of the resulting mixed integer nonlinear optimization problem finally we present an application to the case of natural gas comparing current and efficient export oriented industrialization strategies of nine gas rich developing countries

the rationale of the mean standard deviation analysis skewness preference and the demand for money publisher summary this chapter discusses the rationale of the mean standard deviation analysis skewness preference and the demand for money in january 1969 issue of the review of economic studies karl borch and martin feldstein separately criticized the widely used mean variance analysis of portfolio selection borch contended that any system of upward sloping mean standard deviation e s indifference curves can be shown to be inconsistent with the basic axiom of choice under uncertainty he pointed out that one can always pick any two points on an upward sloping indifference curve to represent two bernoulli distributions with probability 1 p of gaining the same amount x in both the cases and probability p of gaining y1 in the case of one distribution and y2 in the case of the second distribution with y2 y1 if the second distribution represents the point to the northeast of the other point then by the dominance axiom the second distribution must be preferred to the first which contradicts the basic meaning of indifference curves feldstein by using a log utility function and a lognormal distribution for investment outcome showed that e s indifference curves for a risk averter need not be convex downwards though upward sloping they would change from convex to concave once the standard deviation of the outcome exceeds the mean multiplied by on the face of it this seems to suggest that risk aversion might decrease as risk is increased beyond a certain extent

too risky to hold the effect of downside risk accumulated equity wealth and firm performance on ceo equity reduction although the alignment effect of equity ownership is often studied with emphasis on changes in firm strategy the exposure of ceos firm specific wealth to firm risk is more easily controlled by changing their level of equity holdings than by changing firm strategic risk we rely on prospect theory and the behavioral theory of the firm to examine the antecedents of ceo equity reduction and investigate whether it serves to decouple ceo wealth from firm risk given its central role in loss avoidance we underline the effect of the firm s downside risk and distinguish the total loss potential on equity holdings from the loss potential due to firm specific factors allowing for own performance referents we also consider firm performance and the value of a ceo s equity holdings in the analysis based on a sample of 208 u s ceos for the years 1997 1999 we find empirical support for the role of downside risk and firm performance in ceo equity reductions implications on incentive alignment through equity ownership are presented

on the impossibility of informationally efficient markets comment in a recent paper in this review sanford grossman and joseph stiglitz challenge the efficient markets notion that in an asset market at any time prices fully reflect all available information p 404 the purpose of this comment is to argue that certain theorems and comments of grossman and stiglitz do not necessarily follow when an error in the specification of the informed trader s demand function for the risky asset is corrected in theorem 5 b p 401 grossman and stiglitz show that when informed traders have perfect information concerning a risky asset s yield no overall equilibrium will exist that is there will be no equilibrium value for the proportion of informed traders x inspection of equations 8 8 and 9 p 396 helps to give intuitive reasons why this is so if no individual purchases an observation of the information point 0 that is if x 0 then for a sufficiently small value of c the cost of obtaining an observation of the information point 0 an individual could increase his expected utility by purchasing the information if some fraction of traders purchase the information point 0 that is if x 0 from equation 8 it is seen that as 0 2 0 as informed traders obtain better information small movements in 0 have a nearly infinite effect upon the informed trader s demand for the risky asset and hence upon the asset s price thus according to grossman and stiglitz for a fixed x 0 as q2 0 the price system becomes perfectly informative as to the informed trader s observation of 0 thus for x 0 and a 2 0 no individual will wish to purchase 0 at cost c but for xa c2 0 and small c it pays an individual to purchase 0 clearly then for q 2 0 no equilibrium exists equation 8 plays a crucial role in theorem 5 b however equation 8 ignores the fact that x1i the ith informed trader s demand for the risky asset is constrained by his wealth woi in fact if the informed trader has perfect information so that 0 is the return on the risky asset then the informed trader simply invests in the asset with the higher yield thus for ue2 0 equation 8 ought to read

revisiting the home bias puzzle downside equity risk deviations from normality in financial return series have led to the development of alternative portfolio selection models one such model is the downside risk model whereby the investor maximizes his return given a downside risk constraint in this paper we empirically observe the international equity allocation for the downside risk investor using nine international markets returns over the last 34 years the results hold for both daily and monthly data and also from an international perspective due to greater downside risk investors may think globally but instead act locally the model s results therefore provide an alternative view of the home bias puzzle

portfolio selection based on return risk and relative performance markowitz introduced the concept of portfolio selection based on return and variance recognition that many investors evaluate performance relative to a benchmark led to the idea of portfolio selection based on return and relative risk for many investors both approaches fail to yield satisfactory results although they acknowledge the importance of benchmarks in the decision process they are not indifferent to the variance of absolute returns in this situation a utility function that measures return variance and tracking error is more appropriate analysis of this utility function shows that its set of efficient portfolios includes the mean variance efficient set the mean tracking error efficient set and all convex combinations of these two sets optimization with this utility function may find solutions that investors will actually use

the optimal value at risk hedging strategy under bivariate regime switching arch framework unlike the majority of other hedging literatures in which variance is taken as the risk indicator this article uses the value at risk var as the risk management tool of the hedged portfolio this article adopts a bivariate markov regime switching autoregressive conditional heteroscedastic swarch model to formulate the optimal var hedging strategy and then compares it with the other dynamic futures hedging strategies mentioned in the literature in hedging performance using taiwan stock exchange capitalization weighted stock index taiex futures data the in sample and out of sample results shows that when var is used as the criterion to measure the futures hedging effectiveness the performance of the dynamic hedging strategy is superior to that of the static hedging strategy and the performance of the optimal var hedging strategy is better than that of the minimum variance and mean variance hedging strategies besides from the standpoint that the volatility of hedge ratio and hedged portfolio var

basel s value at risk capital requirement regulation an efficiency analysis abstract we analyze the optimal portfolio policies of expected utility maximizing agents under var capital requirement var cr regulation in comparison to the optimal policy under exogenously imposed var limit var l and limited expected loss lel regulations with var cr regulation the agent strategy consists of simultaneous decisions on both the portfolio var and on the implied amount of required eligible capital as a result the performance of var cr regulation depends on its design the parameter n and the agent preferences we show that an optimal var cr regulation allows the regulator on the one hand to completely eliminate the exposure to the largest losses which may jeopardize the existence of the institution and on the other hand to restrain the portfolio exposure to all other losses these results rationalize the current basel regulations however the analysis shows also that there is an optimal level of required eligible capital from the regulator standpoint counter intuitively any requirement above this optimal level is inefficient as it leads to a smaller amount of actually maintained eligible capital and thereby to a larger exposure to the most adverse states of the world unfortunately the current basel s range of required levels n 3 4 is within this inefficient range moreover with an inefficient regulation the agent might employ an inefficient reporting and disclosure procedure

optimal algorithms and lower partial moment ex post results portofolio management in the finance literature has typically used optimization algorithms to determine security allocations within a portfolio in order to obtain the best trade off between risk and return these algorithms despite some improvements are restrictive in terms of an investor s risk aversion utility function since individual investors have different levels of risk aversion this paper proposes two portfolio optimization algorithms that can be tailored to the specific level of risk aversion of the individual investor and performs ex postevaluation tests of the algorithm performance

the statistical distribution of exchange rates empirical evidence and economic implications the abundant evidence that changes in exchange rates have distributions with fatter tails than the normal distribution has led researchers to consider non normal distributions including the student the stable paretian and mixtures of distributions this paper compares the empirical fits of three non normal candidates and the normal distribution for daily changes in the logarithms of exchange rates using maximum likelihood estimation of the parameters and chi square goodness of fit tests the student and mixture of two normals provide the best fits but there is evidence that the distribution parameters may vary over time

the relation between mean variance efficiency and arbitrage pricing the mean standard deviation diagram has proven to be a valuable tool for understanding equilibrium asset pricing theory first introduced by markowitz 1952 1959 and tobin 1958 the diagram helps students and researchers alike to develop intuition about the capital asset pricing model capm its properties are useful for analyzing the conditions under which the market portfolio is mean variance efficient and for linking the location of the market portfolio in the diagram with the validity of the capm in addition its simple geometry seems to be the critical inspiration for roll s 1977 argument that the capm cannot feasibly be tested because the market portfolio is unobservable and because of a mathematical equivalence between the individual return beta linearity relation and the market portfolio s mean variance efficiency p 129 recent research on equilibrium asset pricing both theoretical and empirical has tended to focus on multibeta pricing models especially the arbitrage pricing theory apt this paper will show that the simple intuition derived from the

bank regulation and international financial stability a case against the 2006 basel framework for controlling tail risk in trading books abstract in attempting to promote international financial stability the basel committee on banking supervision 2006 provided a framework that sought to control the amount of tail risk that large banks around the world would take in their trading books relative to their corresponding minimum capital requirements however many of these banks suffered significant trading losses during the recent financial crisis our paper examines whether the basel framework allowed banks to take substantive tail risk in their trading books without a capital requirement penalty we find that it allowed banks to do so and that its minimum capital requirements can be notably procyclical hence focusing on the way the basel framework sought to control the amount of tail risk in trading books relative to their corresponding minimum capital requirements our paper supports the view that it was not properly designed to promote financial stability we also discuss alternative regulatory frameworks that would potentially be more effective than the basel framework in preventing banks from taking substantive tail risk in their trading books without a capital requirement penalty

optimal portfolio selection in a value at risk framework abstract in this paper we develop a portfolio selection model which allocates financial assets by maximising expected return subject to the constraint that the expected maximum loss should meet the value at risk limits set by the risk manager similar to the mean variance approach a performance index like the sharpe index is constructed furthermore when expected returns are assumed to be normally distributed we show that the model provides almost identical results to the mean variance approach we provide an empirical analysis using two risky assets us stocks and bonds the results highlight the influence of both non normal characteristics of the expected return distribution and the length of investment time horizon on the optimal portfolio selection

regulation and preemptive technology adoption two rival firms must decide if and when to adopt a new technology knowing how adoption costs decline over time and how profit flows vary with adoption patterns in many cases price and entry regulations beneficially slow technology adoption by making preemption strategies less attractive in some cases these regulations can so discourage a firm from preemption as to change the order in which firms adopt new technologies speeding one firm s adoption date and slowing the other s in the context of a particular scenario for cable and telephone companies adoption of new fiber optic technologies the case for lifting the cross ownership ban depends on the extent to which telephone companies are able to implement a superior technology reregulation of cable companies strengthens this case

shortfall as a risk measure properties optimization and applications motivated from second order stochastic dominance we introduce a risk measure that we call shortfall we examine shortfall s properties and discuss its relation to such commonly used risk measures as standard deviation var lower partial moments and coherent risk measures we show that the mean shortfall optimization problem unlike mean var can be solved e7ciently as a convex optimization problem while the sample mean shortfall portfolio optimization problem can be solved very e7ciently as a linear optimization problem we provide empirical evidence a in asset allocation and b in a problem of tracking an index using only a limited number of assets that the mean shortfall approach might have advantages over mean variance 2003 elsevier b v all rights reserved

regulatory delay and the timing of product innovation abstract this paper examines how regulatory delay affects innovation by a regulated firm when product introduction costs fall over time an extra day of regulatory delay increases time to introduction by more than a day when the uncertainty of regulatory delay increases a risk neutral firm responds by moving up the product introduction the model places testable restrictions on the empirical relationship between introduction delay and regulatory delay and is consistent with data gathered from a large u s telecommunications provider

speculation optimism and differential information speculative trading has for quite some time been an important question for at least two reasons firstly as a positive question of whether speculative behavior basically is caused by differences in information or by differences in aversion to risk secondly the question is related to the informational efficiency of decentralized market systems if access to information not currently available to the market makes possible a speculative profit the incentive to acquire information may be too excessive from a social point of view the aim of this paper is to clarify the relationship between information and speculation in his seminal article on information acquisition in decentralized market economies hirshleifer 12 showed that the private value of acquiring information depends critically on the speculative profits to be made from this information hirshleifer 12 distinguished between information foreknowledge which affects productive decisions and information which only has implications for exchange similarly fama and laffer 5 distinguish between operational information which improves a firms operating decisions and trading information which only affects trading decisions it is argued due to the speculative profits to be made from having access to information not available to the market that there are excessive private incentives to acquire information without any relevance for productive decisions

incentive fees who wins who loses 1987 incentive fees who wins who loses financial analysts journal vol 43 no 1 pp 27 38

capital structure with countervailing incentives the regulatedjirm s choice of capital structure is affected by countervailing incentives the jirm wishes to signal high value to capital markets to boost its market value while also signalling high cost to regulators to induce rate increases when the jim s investment is large countervailing incentives lead both high and low cost jims to choose the same capital structure in equilibrium thus decoupling capital structure from private information when investment is small or medium sized the model may admit separating equilibria in which high cost jirrns issue greater equity and low cost jims rely more on debt jinancing

conditional risk and return in asian emerging markets evidence from the banking sector previous studies reach no consensus on the relationship between risk and return using data from one market this study argues that the market factor should be noticed in assessing the risk return relationship in a partially integrated emerging market the analysis aims to provide new insight into the nature of the risk return relationship by a conditional factor garch m framework that controls for time series effects to investigate the banking sector in five asian emerging markets of china hong kong indonesia malaysia and taiwan during the period 1995 to 2004 finally the study provides evidence on these relations before and after the asian financial crisis of 1997 the results are generally consistent across the markets and with expectations and have implications for empirical assessments of the risk return relationship and diversification

a simple approximation for semivariance abstract semivariance can differentiate among skewed return distributions but variance is unable to do so thus semivariance has been used as a risk surrogate in portfolio analysis and capital budgeting problems unfortunately semivariance analysis is relatively unknown and poses difficult analytic and computational problems in this paper an expression is derived which very closely approximates semivariance this expression is simple in form and uses only familiar statistics namely mean variance critical value and cumulative probability below the critical value

asset pricing in a generalized mean lower partial moment framework theory and evidence a new asset pricing model that generalizes earlier results in the downside risk literature is developed and empirically tested using a multivariate approach by specifying risk as deviations below any arbitrary target rate of return the generalized mean lower partial moment mlpm model overcomes the limited appeal of earlier formulations and moreover a large class of extant pricing models using alternative risk measures variance semivariance semideviation probability of loss etc becomes special cases of the new framework empirical tests indicate that the new model cannot be rejected against an unspecified alternative for a large set of target rates of return the traditional capm on the other hand is rejected as a well specified alternative the mlpm target rates inferred from market data appear to be related to equity market mean returns rather than to the riskfree rate the target rate that is implicit in the capm and explicit in earlier downside risk formulations the attractiveness of downside risk measures for decision making purposes has been noted in the financial economic literature for over a quarter of a century 1 risk from this perspective is measured in terms of deviations below some exogenously prespecified target rate of return and a formal analysis of these risk measures for various utility functions has been presented by bawa 1975 in terms of the lower partial moment lpm of the asset distributions the appeal of these risk measures has been based in part on their consistency with the way individuals actually perceive risk notwithstanding its intuitive appeal this area of research has been virtually neglected in recent years we believe that this disaffection with downside risk models tends from two sources first earlier models of this genre exogenously specify the target rate to equal the risk free interest rate in the absence of a satisfactory theory for explaining how investors establish their target rates this assumption as argued herein has been motivated more by technical reasons than economic considerations second empirical tests

portfolio selection with a drawdown constraint abstract when identifying optimal portfolios practitioners often impose a drawdown constraint this constraint is even explicit in some money management contracts such as the one recently involving merrill lynch management of unilever s pension fund in this setting we provide a characterization of optimal portfolios using mean variance analysis in the absence of a benchmark we find that while the constraint typically decreases the optimal portfolio s standard deviation the constrained optimal portfolio can be notably mean variance inefficient in the presence of a benchmark such as in the merrill lynch unilever contract we find that the constraint increases the optimal portfolio s standard deviation and tracking error volatility thus the constraint negatively affects a portfolio manager s ability to track a benchmark

two moment decision models and expected utility maximization two moment decision models are consistent with expected utility maximization only if the choice set or the agent s preferences are restricted this paper identifies a restriction which is sufficient to ensure this consistency and confirms that it holds in many economic models the implications for economic analysis are then derived two different approaches to representing an agent s preferences over strategies yielding random payoffs are in wide use under the mean standard deviation ms approach the agent is assumed to rank the alternatives according to the value of some function defined over the first two moments of the random payoff while the expected utility eu criterion assumes that the expected value of some utility function defined over payoffs is used instead the fact that there are these two competing approaches has generated a considerable literature some authors are concerned with the advantages and disadvantages of each while others deal with conditions under which the potentially different approaches would yield the same results or at least approximately so space does not

fuzzy multi period portfolio selection with different investment horizons abstract this paper considers a fuzzy multi period portfolio selection problem with v shaped transaction cost compared with the traditional studies assuming that assets have the same investment horizon we handle the practical but complicated situation in which assets have different investment horizons within the framework of credibility theory a mean variance model is formulated with the objective of maximizing the terminal return under the total risk constraint over the whole investment alternatively a variation is given by minimizing the total risk under the terminal return constraint a fuzzy simulation based genetic algorithm fsga is designed and three numerical examples are given to illustrate the effectiveness of the proposed approach

regulation innovation and the introduction of new telecommunications services i examine the effects of fcc regulation on the innovation and introduction of advanced telecommunications services in the united states an interim of lighter regulation provides an experiment to test the regulatory regime s impact the econometric model comprises an arrival process for service innovation followed by a duration process for regulatory delay the number of services the firms created during the interim is 60 99 higher than the model predicts they would have created if the stricter regulation had still been in place overall firms would have introduced 62 more services to consumers during the study period if the regulation had not been in place

comparative statics under uncertainty the case of mean variance preferences we analyze the comparative statics of optimal decisions under uncertainty when preferences are represented by twomoment mean variance utility functions we relate our findings to concepts for risk attitudes that are familiar from the expected utility approach in the two parameter approach a number of plausible comparative static effects already emerges under the assumption of decreasing absolute risk aversion to determine comparative static effects of changes in background risks stronger concepts are needed risk vulnerability temperance and standardness imply appropriately transferred to the mean variance framework the plausible effect that risk taking will be reduced if background risks increase 2002 elsevier b v all rights reserved

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

a dynamic autoregressive expectile for time invariant portfolio protection strategies constant proportion portfolio insurance cppi is nowadays one of the most popular techniques for portfolio insurance strategies it simply consists of reallocating the risky part of a portfolio with respect to market conditions via a leverage parameter called the multiple guaranteeing a predetermined floor we propose to introduce a conditional time varying multiple as an alternative to the standard unconditional cppi method directly linked to actual risk management problematics this ex ante approach for the conditional multiple aims to diversify the risk model associated for example with the expected shortfall es or extreme risk measure estimations first we recall the portfolio insurance principles and main properties of the cppi strategy including the time invariant portfolio protection tipp strategy as introduced by estep and kritzman 1988 we emphasize the existence of an upper bound on the multiple for example to hedge against sudden drops in the market then we provide the main properties of the conditional multiples for well known financial models including the discrete time portfolio rebalancing case and levy processes to describe the risky asset dynamics for this purpose we precisely define and evaluate different gap risks in both conditional and unconditional frameworks as a by product the introduction of discrete or random time portfolio rebalancing allows us to determine and or estimate the density of durations between rebalancements finally from a more practical and statistical point of view due to trading restrictions we present the class of dynamic autoregressive expectile dare models for estimating the conditional multiple this latter approach provides useful complementary information about the risk and performance associated with probabilistic approaches to the conditional multiple

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

exchange rate regimes and the price of exchange rate risk abstract we investigate the price of exchange rate risk in the us stock market across exchange rate regimes we find that exchange rate risk is a priced factor and that the sign of the price of risk is affected by the exchange rate regime the results have important implications for risk management policies

a variance equality test of the icapm on philippine stocks post asian financial crisis period the study examines whether fama s discrete version of merton s intertemporal capm icapm can explain the negative market risk premium and the cross sectional variability of philippine stock returns after the onset of the asian financial crisis in july 1997 the change in foreign exchange rate in addition to the change in market risk premium is used as a state variable of hedging concern to investors the relationship of fama s multifactor minimum variance mmv portfolio to the markowitz minimum variance mv portfolio is characterized in terms of the equality of the return variances for the same expected return a test due to basak et al 2002 is then used to verify the equality of the return variance of a derived tangency portfolio along the mmv frontier to an mv portfolio with the same sample mean return the results do not reject the icapm during the period covered by the study thus the model provides a plausible explanation both for the cross sectional variability of stock returns and the nega

the evolution of markets under entry and standards regulation the case of global mobile telecommunications abstract we analyze the effects of government policies on the evolution of an industry the global mobile telecommunications market i we find a relatively slow diffusion convergence between countries this follows partly from regulatory delay in issuing first licenses yet persisting initial cross country differences also contribute to a lack of convergence ii introducing competition has a strong immediate impact on diffusion but a weak impact afterwards sequential entry is preceded by pre emptive behavior by incumbents this is consistent with the presence of consumer switching costs iii setting a single technological standard accelerates the diffusion of analogue technologies considerably for digital technologies it is too early to draw reliable conclusions yet the available evidence suggests that setting single standards has similar beneficial effects

beyond portfolio theory the next frontier logically investment theory s next frontier is to put into practice the rich set of tools that academia has bestowed on the investment community starting with harry markowitz s seminal article on portfolio selection in 1952 or is it in fact the next frontier lies beyond simply engineering the implementation of new investment decision tools the time has come to integrate the powerful insights offered by information theory and principal agent theory into a holistic comprehensive theory of investing only such an expanded theory offers any material hope of improving the economic prospects of the millions of clients beneficiaries of today s mutual funds pension funds endowments and foundations

management compensation and market timing under portfolio constraints abstract this paper shows that portfolio constraints have important implications for management compensation and performance evaluation in particular in the presence of portfolio constraints allowing for benchmarking can be beneficial benchmark design arises as an alternative effort inducement mechanism vis a vis relaxing portfolio constraints numerically we solve jointly for the manager s linear incentive fee and the optimal benchmark the size of the incentive fee and the risk adjustment in the benchmark composition are increasing in the investor s risk tolerance and the manager s ability to acquire and process private information

downside risk and portfolio diversification in the euro zone equity markets with special consideration of the crisis period abstract this study examines the value at risk for ten euro zone equity markets individually and also divided into two groups piigs portugal italy ireland greece and spain and the core austria finland france germany and the netherlands employing four var estimation and evaluation methods considered over the full period and the pre and post global crisis subperiods 1 and 2 the backtesting results are also evaluated according to the basel capital requirements the results demonstrate that the cevt methods meet all the statistical criteria the best for most individual equity indices over the full period but these results over the two subperiods for those two methods are mixed compared to those the dpot methods moreover the two optimal group portfolios of the piigs and the core as well as the grand portfolio that combines the ten indices do not show much diversification benefits the piigs portfolio selects spain s ibex only while that of the core opts for austria s atx only in the full period and subperiod 1 however germany s dax overwhelmingly dominates both the core and the grand portfolios in subperiod 2

downside loss aversion and portfolio management downside loss averse preferences have seen a resurgence in the portfolio management literature this is due to the increasing use of derivatives in managing equity portfolios and the increased use of quantitative techniques for bond portfolio management we employ the lower partial moment as a risk measure for downside loss aversion and compare mean variance m v and mean lower partial moment m lpm optimal portfolios under nonnormal asset return distributions when asset returns are nearly normally distributed there is little difference between the optimal m v and m lpm portfolios when asset returns are nonnormal with large left tails we document significant differences in m v and m lpm optimal portfolios this observation is consistent with industry usage of m v theory for equity portfolios but not for fixed income portfolios

mean variance analysis of a single supplier and retailer supply chain under a returns policy abstract in the literature most of the supply chain coordinating policies target at improving the supply chain s efficiency in terms of expected cost reduction or expected profit improvement however optimizing the expected performance alone cannot guarantee that the realized performance measure will fall within a small neighborhood of its expected value when the corresponding variance is high moreover it ignores the risk aversion of supply chain members which may affect the achievability of channel coordination as a result we carry out in this paper a mean variance mv analysis of supply chains under a returns policy we first propose an mv formulation for a single supplier single retailer supply chain with a newsvendor type of product the objective of each supply chain decision maker is to maximize the expected profit such that the standard deviation of profit is under the decision maker s control we study both the cases with centralized and decentralized supply chains we illustrate how a returns policy can be applied for managing the supply chains to address the issues such as channel coordination and risk control extensive numerical studies are conducted and managerial findings are proposed

options and structured products in behavioral portfolios abstract options and structured products have no roles in mean variance portfolios but they have roles in behavioral portfolios behavioral portfolios are composed of mental account sub portfolios each associated with a goal such as retirement income or bequest investors optimize each mental account by finding the assets and asset allocation that maximizes the expected return of each mental account sub portfolio subject to the condition that the probability of failing to reach a preset threshold aspiration level not exceed a preset probability put options are useful in downside protection mental accounts whose goal is avoiding poverty whereas call options are useful in upside potential mental accounts whose goal is a shot at riches we also explore the roles in behavioral portfolios of option collars capital guaranteed notes and barrier range notes

multivariate dependence and portfolio optimization algorithms under illiquid market scenarios we propose a model for optimizing structured portfolios with liquidity adjusted value at risk lvar constraints whereby linear correlations between assets are replaced by the multivariate nonlinear dependence structure based on dynamic conditional correlation t copula modeling our portfolio optimization algorithm minimizes the lvar function under adverse market circumstances and multiple operational and financial constraints when we consider a diversified portfolio of international stock and commodity market indices under multiple realistic portfolio optimization scenarios the obtained results consistently show the superiority of our approach relative to other competing portfolio strategies including the minimum variance risk parity and equally weighted portfolio allocations

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

markowitz revisited social portfolio engineering abstract in recent years socially responsible investing has become a popular subject with both private and institutional investors at the same time a number of scientific papers have been published on socially responsible investments sris covering a broad range of topics from what actually defines sris to the financial performance of sri funds in contrast to non sri funds in this paper we revisit markowitz portfolio selection theory and propose a modification allowing to incorporate not only asset specific return and risk but also a social responsibility measure into the investment decision making process applied in an a posteriori fashion the model results in a three dimensional capital allocation plane illustrating the complete set of feasible optimal portfolios it enables investors to custom tailor their asset allocations and incorporate all personal preferences regarding return risk and social responsibility in an empirical analysis with a data set of over 6000 international companies including the complete universe of social responsibility rated stocks we find that investors opting to maximize the social impact of their investments do indeed face a statistically significant decrease in expected returns however the social responsibility risk optimal portfolio yields a statistically significant higher social responsibility rating than the return risk optimal portfolio

analysis of the conditional stock return distribution under incomplete specification abstract the analysis of the distribution of the stock returns plays an important role in financial theory since a distributional assumption is required for mean variance portfolio theory theoretical models of capital asset prices determining the price of derivative products efficient estimation by maximum likelihood procedure and establishing forecasting confidence intervals up to now most of the studies analyze the unconditional distribution of the stock returns using the likelihood ratio test the schwarz information criterion or by graphical analysis however the analysis of the conditional distribution is very important since most of the empirical financial studies use high frequency data and these data present dynamic structure in this paper we focus on the conditional distribution we design different bootstrap mechanisms for comparing the goodness of fit of several functional forms postulated under the null hypothesis for individual spanish stocks and for the general index of the madrid stock market we use the cramer von mises test statistic based on the standardized residuals and assuming that the null distribution can depend on some unknown parameters

the pricing of interest rate risk evidence from the stock market this paper addresses the issue of whether firms are required to pay an ex ante premium to investors for bearing the risk of interest rate changes a two factor apt model with the market and changes in the yield on long term government bonds as factors is employed the paper shows that empirically most of the interest sensitive stocks are in the utility industries and that there is reasonable evidence that the interest factor is priced in the sense of the apt several sources for the interest sensitivity are considered and regulatory lags are focused on as a likely candidate some firms exhibit ex post sensitivity in their stock returns to unanticipated changes in interest rates are these firms required to pay investors ex ante for bearing this risk of interest rate changes the framework for examining pricing of unanticipated interest rate changes is a two factor apt model with the market and changes in the yield on long term government bonds as factors the issue is whether the interest rate change premium is significant to study this the paper uses full information maximum likelihood fiml estimation on groups of twenty five individual firms with both cross equation constraints and withinequation nonlinear constraints on the parameters as mandated by the apt model whether the risk of unanticipated changes in interest rates is priced in the market is of particular interest with regard to regulated firms regulated firms especially electric utilities turn out to comprise the big majority of firms that are sensitive to unanticipated interest rate changes after some preliminary investigation the analysis focuses on electric utilities much empirical work on the apt relies on factor analysis e g roll and ross 30 bower bower and logue 5 use factor analysis in comparing the apt and the capm to explain utilities returns the present paper however uses observable variables at the macro level chan chen and hsieh cch 7 and chen roll and ross crr 8 also examine apt models with specific macroeconomic factors cch and crr use a traditional fama macbeth type of cross sectional estimation approach in the premia calculations rather than a fiml approach gibbons and stambaugh have applied fiml techniques to models using only the market as an explanatory variable gibbons 20 used a noniterative algorithm on portfolios of firms equivalent to a two step cross sectional approach stam

portfolio frontiers with restrictions to tracking error volatility and value at risk abstract asset managers are often given the task of restricting their activity by keeping both the value at risk var and the tracking error volatility tev under control however these constraints may be impossible to satisfy simultaneously because var is independent of the benchmark portfolio the management of these restrictions is likely to affect portfolio performance and produces a wide variety of scenarios in the risk return space the aim of this paper is to analyse various interactions between portfolio frontiers when risk managers impose joint restrictions upon tev and var specifically we provide analytical solutions for all the intersections and we propose simple numerical methods when such solutions are not available finally we introduce a new portfolio frontier

on the unimodality of the price setting newsvendor problem with additive demand under risk considerations abstract we present a mean variance analysis of the single product single period price setting newsvendor problem with additive price dependent demand the main goal of this paper is to use a mean variance framework to solve any risk sensitive instance and find conditions under which the unimodality of the problem is guaranteed we introduce such conditions via the lost sales rate elasticity the elasticity of the optimal price and the elasticity of the expected safety stock surplus to provide managerial insight in terms of the newsvendor s level of service we also simplify the optimization problem in case that those conditions do not hold the main contribution of this paper is that by evaluating the unimodality of the problem for any possible risk attitude it extends previously published results found for the concavity of the solution in risk neutral and moderately risk sensitive cases

forecasting the volatility of crude oil futures using intraday data abstract we use the information in intraday data to forecast the volatility of crude oil at a horizon of 1 66 days using a variety of models relying on the decomposition of realized variance in its positive or negative semivariances part and its continuous or discontinuous part jumps we show the importance of these decompositions in predictive in sample regressions using a number of specifications nevertheless an important empirical finding comes from an out of sample analysis which unambiguously shows the limited interest of considering these components overall our results indicates that a simple autoregressive specification mimicking long memory and using past realized variances as predictors does not perform significantly worse than more sophisticated models which include the various components of realized variance

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

non separation in the mean lower partial moment portfolio optimization problem abstract with a number of advantages lower partial moments lpm serve as alternatives to variance as measures of portfolio risk for two specific targets a separation property holds in the context of mean lpm portfolio optimization that allows investors to separate the decision about investment proportions among risky assets from the decision about how much to invest in risky versus risk free assets for other targets however separation is not guaranteed and this case has not received much attention in the literature we show in the case of non separation that investment curves are not common to all optimizing investors but that they are convex in mean lpm space and their lower envelope is the efficient frontier we consider the interesting behavior of investment curves and optimal risky portfolios we also show empirically that an investor who mistakenly assumes separation holds will not experience significant excess portfolio risk in all practical cases

portfolio optimization under loss aversion abstract we present an integrated methodological approach for selecting portfolios the proposed methodology is focused on incorporation of investor s preferences in the mean risk framework we propose a risk measure calculated with the downside part of the portfolio return distribution which we argue captures better the practical behavior of the loss averse investor we establish its properties study the link with stochastic dominance criteria point out the relations with conditional value at risk and lower partial moment of first order and give the explicit formula for the case of scenario based portfolio optimization the proposed methodology involves two stages firstly the investment opportunity set efficient frontier is determined and secondly one single preferred efficient portfolio is selected namely the one having the highest expected utility value three classes of utility functions with loss aversion corresponding to three types of investors are considered the empirical study is targeted on assessing the differences between the efficient frontier of the proposed model and the classical mean variance mean cvar and mean lpm1 frontiers we firstly analyze the loss of welfare incurred by using another model instead of the proposed one and measure the corresponding gain loss of utility secondly we assess how much the portfolios really differ in terms of their compositions using a dissimilarity index based on the 1 norm we describe and interpret the optimal solutions obtained and emphasize the role and influence of loss aversion parameters values and of constraints three types of constraints are studied no short selling allowed a certain degree of diversification imposed and short selling allowed

an mcdm approach to portfolio optimization abstract we propose a model for portfolio optimization extending the markowitz mean variance model based on cooperation with standard and poor s we use five specific objectives related to risk and return and allow consideration of individual preferences through the construction of decision maker specific utility functions and an additive global utility function numerical results using customized local search simulated annealing tabu search and genetic algorithm heuristics show that problems of practically relevant size can be solved quickly

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

portfolio optimization under lower partial moments in emerging electricity markets evidence from turkey abstract optimization of the electricity markets under modern portfolio theory has a crucial role for financial decision makers power suppliers in deregulated electricity markets need to optimize their generation capacities and bidding strategies so as to effectively participate in bilateral contract and spot markets market players have to deal with continuously changing electricity prices in competitive electricity market environment during their daily routine system operations electricity not like the others is a unique product service and cannot be stored economically however it should be generated and consumed simultaneously in addition to all power suppliers face with fuel price water regime delivery and network risks in view of the scene described above prudent decision making methodologies are of critical importance to maximize profit while minimizing managing risks this paper presents a comprehensive comparison of mean variance down side and semi variance methods for optimization in electricity markets and the corresponding methodologies to maximize the return while minimizing risk real turkish day ahead market data set between december 2009 and december 2012 is used in numerical calculations generation cost data of hydraulic plants lignite coal fired thermal power plants and natural gas combined cycle power plants are taken into consideration in the course of optimization evaluations in the present of real data these methods can also be applied to renewable energy generation types these three methods were able to be applied to all case scenarios effectively and produced efficient frontiers optimal minimal portfolios and utility functions successfully the results have revealed that the methods significantly provide decisions for power suppliers with different risk aversion levels and for various instruments to maximize the profit while minimizing the associated market risks and to meet generation obligations consequently financial optimization under lower partial moments constraints would give notable results in analyzing the efficient frontiers for electricity markets in turkey

does it all add up benchmarks and the compensation of active portfolio managers in this article the authors examine theoretically the use of benchmark portfolios in the compensation of privately informed portfolio managers they find that the use of a benchmark and particularly the types of benchmarks often observed in practice cannot be easily rationalized specifically commonly used benchmark adjusted compensation schemes are generally inconsistent with optimal risk sharing and do not lead to the choice of an optimal portfolio for the investor moreover benchmarks do not help in solving potential contracting problems such as inducing the manager to expend effort or trying to screen out uninformed managers copyright 1997 by university of chicago press

mean lower partial moment valuation and lognormally distributed returns in this paper we develop a capital asset pricing model in a mean lower partial moment framework specifically we show that when partial moments are computed about the expected risky portfolio return optimal portfolio choice in a mean lower partial framework permits a two fund portfolio separation between a riskless asset and a market portfolio of risky assets in this new framework risk is measured as semideviation for second degree stochastic dominance and semivariance for third degree stochastic dominance further when security returns are lognormally distributed and small risk this new mean lower partial moment valuation specializes to the mean logarithmic variance capital asset pricing model

a risk return model with risk and return measured as deviations from a target return two attribute risk and return models are very popular in the economics and finance literature for analyzing decisions under uncertainty their popularity stems primarily from the intuitive appeal of the dichotomy into risk and return and from the ease with which the concepts can be diagrammed in two dimensions the most commonly used risk return model is the mean variance model in which risk is measured as the variance and return by the mean of the probability distribution over outcomes the mean variance model has a number of shortcomings which are widely known but of particular concern here are the facts that 1 mean variance dominance is neither necessary nor sufficient for second degree stochastic dominance 2 unless the form of the probability distribution is restricted mean variance is consistent with von neumann morgenstern utility theory only if the utility function is quadratic and 3 as peter fishburn has noted

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

optimizing tracking error constrained portfolios active portfolios subject to tracking error te constraints are the typical setup for active managers tasked with outperforming a benchmark the risk and return relationship of such constrained po

incentive fees some problems and some solutions 1987 incentive fees some problems and some solutions financial analysts journal vol 43 no 1 pp 21 26

selecting a portfolio with skewness recent evidence from us european and latin american equity markets abstract polynomial goal programming in which investor preferences for skewness can be incorporated is utilized to determine the optimal portfolio from latin american us and european capital markets the empirical findings suggest that the incorporation of skewness into an investor s portfolio decision causes a major change in the resultant optimal portfolio the empirical evidence indicates that investors do trade expected return of the portfolio for skewness

the impact of financial leverage on risk of equity measured by loss oriented risk measures an option pricing approach abstract we investigate how financial leverage influences the risk of equity in companies with limited liability in our study the risk is measured by loss oriented risk measures var downside deviation etc also the dependence of the risk premium on risk is under consideration var based and downside risk measures are considered in similar frameworks and risk premium is introduced which is symmetrical to these risk measures the value of equity is modeled by the price of a call option in most cases there is a positive relationship between the level of leverage measured by the debt ratio and the risk measured by the loss oriented risk measures however there exist exceptions the risk premium is not a linear function of the risk still for a reasonable range of leverage the dependence of the risk premium on risk is approximately linear in most cases

adoption of cost saving innovations by a regulated firm regulatory lag is generally credited with providing monetary incentives for the adoption of cost saving technological changes by regulated firms because regulators can not instantaneously adjust price ceilings in response to cost changes these incentives are inherent to the process of price regulation in a dynamic world a firm which decreases production costs through technological innovation will enjoy excess profits until the regulators lower price to a level consistent with the new conditions the longer the delay before regulatory response to a decrease in cost the greater are the profits which can be derived from a cost reduction and therefore the greater is the incentive for adoption of technological change 2 the passive nature of this incentive mechanism is an important characteristic although regulatory agencies typically have authority to force price decreases upon firms which do not take advantage of potential cost savings this power is limited by the difficulty of proving that a firm is laggard rather than the victim of unfortunate circumstances thus the regulated firm which foregoes potential profit from adopting a costsaving innovation today may generally reap that profit at some convenient time tomorrow indeed it is the main contention of this paper that in many circumstances a regulated monopolist can maximize the present value of profits only by delaying adoption of an innovation that is rather than completely adopting a cost saving innovation when it becomes available a profit maximizing regulated firm will choose to adopt the innovation only gradually through time the profitability of such delaying procedure may be illustrated by a simple example consider a situation in which the price of a firm s product is fixed by a regulatory authority but periodically adjusted according to the following cost plus markup scheme at each review price for the following period is set equal to average cost of the previous period plus an allowed markup that is price in period i 1 is set equal to m times average cost in period i m 1 this situation is illustrated in figure 1 a firm is initially producing output qo at cost co qo with price set by the regulators at mco qo qo suppose a cost saving innovation is discovered which if employed would decrease average production cost to c1 q q if the firm were to adopt this innovation immediately it would earn a profit equal to the area of the rectangle abcd in figure ia at the next regulatory review price would be lowered to the level m times the new average cost i e to p1 and profit would fall to that amount represented by the area aefg this amount of profit would be earned each period thereafter however suppose that the firm were to adopt this innovation in two steps rather than completely adopting the innovation when it first becomes available this option is sketched in figure lb in the initial period the firm adopts the innovation throughout approximately half its operations thereby lowering average cost only to oh in the next period the firm completes the adoption process lowering average cost to the final level oa although this procedure would yield profit equal only to hicd in the initial period it would result in a price in the next period equal to p1 i e equal to m times oh since average cost in that period would fall to oa profit would equal ajkl in the next period price would be at the new equilibrium level og and profit would equal aefg this amount of profit would be earned each period thereafter given the demand and cost functions illustrated in figure 1 the second alternative assistant professor of economics vanderbilt university see william baumol and alfred kahn ch 2 2see elizabeth bailey

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