mixed integer programming approaches for index tracking and enhanced indexation we consider the problem of reproducing the performance of a stock market index but without purchasing all of the stocks that make up the index index tracking we also consider the problem of out performing the index enhanced indexation we present mixed integer linear programming formulations of these problems our formulations include transaction costs a constraint limiting the number of stocks that can be purchased and a limit on the total transaction cost that can be incurred as our formulations of these problems are mixed integer linear programs we can use a standard solver cplex numeric results are presented for eight data sets drawn from major markets the largest of these data sets involves over 2000 stocks

debt leases taxes and the endogeneity of corporate tax status we provide evidence that corporate tax status is endogenous to financing decisions which induces a spurious relation between measures of financial policy and many commonly used tax proxies using a forward looking estimate of before financing corporate marginal tax rates we document a negative relation between operating leases and tax rates and a positive relation between debt levels and tax rates this is the first unambiguous evidence supporting the hypothesis that low tax rate firms lease more and have lower debt levels than high tax rate firms many theories of capital structure imply that all else equal the incentive to use debt financing increases with a firm s marginal tax rate due to the tax deductibility of interest expense e g modigliani and miller 1963 deangelo and masulis 1980 conversely leasing models generally predict that firms with low marginal tax rates employ relatively more leases than do firms with high marginal tax rates the logic behind the leasinlg prediction is that leases allow for the transfer of tax shields from firms that cannot fully utilize the associated tax deduction lessees to firms that can lessors e g myers dill and bautista 1976 smith and wakeman 1985 ross westerfield and jaffe 1996 despite these straightforward predictions empirically testing for tax effects is difficult because a spurious relation exists between the financing decision and many commonly used tax proxies specifically both interest expense and lease payments are tax deductible thus a firm that finances its operations with debt or leases reduces its taxable income potentially lowering its expected marginal tax rate if not properly addressed this endogeneity of the tax rate can bias an experiment in favor of finding a negative

do banks provide financial slack we study the decision to choose bank debt rather than public securities in a firm s marginal financing choice using a sample of 500 firms over the 1980 to 1993 time period we find that firms are relatively more likely to choose bank loans when variables that measure asymmetric information problems are elevated the sensitivity of the likelihood of choosing bank debt to information problems is greater for firms with no public debt outstanding these results are consistent with the hypothesis that banks help alleviate asymmetric information problems and that firms weigh these information benefits against a wide range of contracting costs when choosing bank financing why do some firms borrow from public sources while others rely exclusively on private lenders the answer to this question is not well understood existing theories suggest that a firm must consider the tradeoff between the benefits and costs of bank debt financing relative to other potential financing choices the potential benefits of bank financing include low moral hazard and adverse selection costs and ease of renegotiation in financial distress 1 the potential costs of bank financing include monitoring costs suboptimal liquidation outcomes and distortions induced by information monopolies 2 the goal of this paper is to identify whether adverse selection problems influence a firm s choice between new bank debt public debt or common stock in particular we are interested in assessing the empirical validity of the hypothesis that banks have the ability to accurately price a firm s claims thus inducing a preference for firms that are undervalued by the market to

pricing risk adjusted deposit insurance an option based model this paper presents a methodology for arriving at empirical estimates of deposit insurance premiums from market data by using isomorphic relationships betweeen equity and a call option and insurance and a put option the data utilizes the market value of equity to solve for the asset value and its volatility market perceptions of fdic bailout policies are explicitly modeled so as to eliminate the bias in inverted values of assets and their volatility sensitivity analyses are performed to show that rank orderings based on premiums are robust to changes in specification thus facilitating allocation of aggregate premium across banks while economists have long argued in favor of risk adjusted deposit insurance as both more equitable and more efficient than the current system of flatrate premiums various recent developments have further contributed to an increasing dissatisfaction with the current system first both the banking industry and the government seem to be tending to the view that deregulation of the banking industry would be necessary in order to meet more sophisticated future demands on the industry as well as desirable as a policy means of stimulating greater competition among banks moreover a sudden rise in the incidence of bank failures 1 and the vulnerability of the u s banks to the socalled international debt crisis have served to bring to the fore concern about the health of the banking industry in the absence of deposit insurance riskier banks will be able to attract deposits only at higher rates and these higher costs of funding serve as built in market regulated incentives to limit excessive risk taking by banks as introduction of deposit insurance makes deposits equally risk free across banks these incentives disappear and regulation and close supervision of the banking industry must necessarily replace them as deterrents to excessive risk taking thus when insurance is offered at a flat premium regulation is designed to ensure that the risk posed to the insurer both asset and financial risk is appropriately uniform

mean var portfolio optimization a nonparametric approach portfolio optimization involves the optimal assignment of limited capital to different available financial assets to achieve a reasonable trade off between profit and risk we consider an alternative markowitz s mean variance model in which the variance is replaced with an industry standard risk measure value at risk var in order to better assess market risk exposure associated with financial and commodity asset price fluctuations realistic portfolio optimization in the mean var framework is a challenging problem since optimizing var leads to a non convex np hard problem which is computationally intractable in this work an efficient learning guided hybrid multi objective evolutionary algorithm mode gl is proposed to solve mean var portfolio optimization problems with real world constraints such as cardinality quantity pre assignment round lot and class constraints a learning guided solution generation strategy is incorporated into the multi objective optimization process to promote efficient convergence by guiding the evolutionary search towards promising regions of the search space the proposed algorithm is compared against the non dominated sorting genetic algorithm nsga ii and the strength pareto evolutionary algorithm spea2 experimental results using historical daily financial market data from s p 100 and s p 500 indices are presented experimental results shows that mode gl outperforms two existing techniques for this important class of portfolio investment problems in terms of solution quality and computational time the results highlight that the proposed algorithm is able to solve the complex portfolio optimization without simplifications while obtaining good solutions in reasonable time and has significant potential for use in practice

the debt equity choice when firms adjust their capital structures they tend to move toward a target debt ratio that is consistent with theories based on tradeoffs between the costs and benefits of debt in contrast to previous empirical work out tests explicitly account for the fact that firms may face impediments to movements toward their target ratio and that the target ratio may change over time as the firm s profitability and stock price change a separate analysis of the size of the issue and repurchase transactions suggests that the deviation between the actual and the target ratios plays a more important role in the repurchase decision than in the issuance decision

financial intermediation delegated monitoring and long term relationships abstract this paper considers the consequences of enduring relationships for bank structure and policy in an information based banking model adding a richer time dimension allows repeated lending between the intermediary and borrower this contract lets a bank produce information and enforce compliance more easily than direct monitoring of the borrower s organization this implies an asymmetric banking structure banks enter long term relationships with borrowers but not with depositors next it shows how enduring relationships solve problems with loan participations and security underwriting by commercial banks

political promotion ceo incentives and the relationship between pay and performance both theory and empirical evidence suggest that managers career concerns can serve as an important source of implicit economic incentives we examine how incentives for political promotion are related to compensation policy and firm performance in chinese state owned enterprises we find that the likelihood that the ceo receives a political promotion is positively related to firm performance we also find that ceos with a higher likelihood of political promotion have lower pay levels and lower pay performance sensitivity overall the evidence suggests that competition in the political job market helps mitigate weak monetary incentives for ceos in china data are available at https doi org 10 1287 mnsc 2017 2966 this paper was accepted by lauren cohen finance

bank information monopolies and the mix of private and public debt claims this article examines the determinants of the mix of private and public debt using detailed information on the debt structure of 250 publicly traded corporations from 1980 through 1990 we find that the relationship between bank borrowing and the importance of growth opportunities depends on the number of banks the firm uses and whether the firm has public debt outstanding for firms with a single bank relationship the reliance on bank debt is negatively related to the importance of growth opportunities in contrast among firms borrowing from multiple banks the relationship is positive

on the effectiveness of scenario generation techniques in single period portfolio optimization in single period portfolio selection problems the expected value of both the risk measure and the portfolio return have to be estimated historical data realizations used as equally probable scenarios are frequently used to this aim several other parametric and non parametric methods can be applied when dealing with scenario generation techniques practitioners are mainly concerned on how reliable and effective such methods are when embedded into portfolio selection models in this paper we survey different techniques to generate scenarios for the rates of return we also compare the techniques by providing in sample and out of sample analysis of the portfolios obtained by using these techniques to generate the rates of return evidence on the computational burden required by the different techniques is also provided as reference model we use the worst conditional expectation model with transaction costs extensive computational results based on different historical data sets from london stock exchange market ftse are presented and some interesting financial conclusions are drawn

disproportional control rights and the governance role of debt we examine the governance role of debt in the context of u s based dual class ownership structures we hypothesize that the use of debt alleviates the conflict between shareholder classes by balancing the power of controlling insiders we document that dual class firms have higher leverage and a greater propensity to issue private debt they also more frequently use cash sweeps and performance based covenants dual class firms with greater agency conflicts and a greater need to access the capital market appear to rely more extensively on debt these findings are consistent with controlling insiders bonding against the agency costs associated with dual class ownership the governance role of debt is further corroborated by the valuation effect of debt for dual class companies private debt issuances trigger greater positive market reactions to the inferior dual class stock in relation to both the superior dual class stock and a matched sample of single class firms further leverage attenuates the previou

optimal capital structure a multi period programming model for use in financial planning abstract this paper describes a multi period chance constrained mathematical programming model to compute for each period the firm s optimal debt to equity ratio and the optimal maturity distribution of its debt the model assumes that the firm s objective is to maximize total value of the firm and that the firm operates in a world of uncertainty with corporate income taxes and bankruptcy costs finally the actual coupon rate paid by the firm which is commensurate to the risk of default is endogenously determined by the model

optimal portfolio selection and dynamic benchmark tracking abstract this paper analyzes different approaches to portfolio selection when the requirement to portfolio performance is formulated relative to a given benchmark for example it may be desirable to track a market index as closely as possible we develop several portfolio selection algorithms based on different perceptions of risk and different risk target measures ranging from the traditional variance to the more modern value at risk in a dynamic setting we address the issue of optimal portfolio rebalancing we develop an algorithm for determining whether or not to rebalance a given portfolio based on transaction costs and new information about market conditions our approaches are tested on a set of stock data from the oslo stock exchange

what s different about banks abstract negotiable certificates of deposit cd s trade in the capital market in competition with other securities like commercial paper and bankers acceptances if cd s must pay lenders competitive monetary interest the reserve tax on cd s is borne by bank borrowers viability of the tax means there must be something special about bank loans that makes some borrowers willing to pay higher interest rates than those on other securities of equivalent risk moreover there must be something special about banks that prevents other intermediaries from competing to assure that it never pays to finance loans with cd s

an evolutionary heuristic for the index tracking problem abstract index tracking is a popular form of passive fund management the index tracking problem is the problem of reproducing the performance of a stock market index but without purchasing all of the stocks that make up the index our formulation of the problem explicitly includes transaction costs associated with buying or selling stocks and a limit on the total transaction cost that can be incurred our formulation also includes a constraint limiting the number of stocks that can be purchased an evolutionary heuristic population heuristic is presented for the solution of the index tracking problem reduction tests are also presented computational results are presented for five data sets drawn from major world markets these data sets are made publicly available for use by other workers

information reliability and a theory of financial intermediation this paper is an analysis of when it will be beneficial for agents engaged in the production of information to form coalitions the model is cast in a financial market framework thus leading to an identification of conditions sufficient for the existence of financial intermediaries intermediation is shown to improve welfare if informational asymmetries are present and the information generated to rectify these asymmetries is potentially unreliable the usual appeal to transactions costs to explain intermediation is not needed

the real consequences of market segmentation we study the real effects of market segmentation due to credit ratings using a matched sample of firms just above and just below the investment grade cutoff these firms have similar observables including average investment rates however flows into high yield mutual funds have an economically significant effect on the issuance and investment of the speculative grade firms relative to their matches especially for firms likely to be financially constrained the effect is associated with the discrete change

debt and the marginal tax rate abstract do taxes affect corporate debt policy this paper tests whether the incremental use of debt is positively related to simulated firm specific marginal tax rates that account for net operating losses investment tax credits and the alternative minimum tax the simulated marginal tax rates exhibit substantial variation due to the dynamics of the tax code tax regime shifts business cycle effects and the progressive nature of the statutory tax schedule using annual data from more than 10 000 firms for the years 1980 1992 i provide evidence which indicates that high tax rate firms issue more debt than their low tax rate counterparts

does corporate lending by banks and finance companies differ evidence on specialization in private debt contracting this paper establishes empirically the existence of specialization in private market corporate lending adding a new dimension to the public versus private debt distinctions now common in the literature comparing corporate loans made by banks and by finance companies we find that the two types of intermediaries are equally likely to finance information problematic firms however finance companies tend to serve observably riskier borrowers particularly more leveraged borrowers evidence supports both regulatory and reputation based explanations for this specialization in passing we shed light on various theories of debt contracting and intermediation and present facts about finance companies

an empirical analysis of the determinants of corporate debt ownership structure i examine the relation between corporate debt ownership structure and several firm characteristics suggested by recent theory the results demonstrate the importance of monitoring and information costs the likelihood and costs of inefficient liquidation and borrowers incentives in affecting firms debt source preferences several theoretical predictions receive support while others do not the results also suggest important differences between bank and private non bank debt which contrasts with most theoretical models additionally i find evidence of systematic use of bank debt by firms with access to public debt suggesting the benefits attributed to bank debt in theoretical models remain important after firms gain access to public debt markets although different lenders appear to have different maturity preferences the results also suggest debt maturity and debt ownership decisions may be separable

optimal construction and rebalancing of index tracking portfolios abstract index funds aim to track the performance of a financial index such as e g the standard poor s 500 index index funds have become popular because they offer attractive risk return profiles at low costs the index tracking problem considered in this paper consists of rebalancing the composition of the index fund s tracking portfolio in response to new market information and cash deposits and withdrawals from investors such that the index fund s tracking accuracy is maximized in a frictionless market maximum tracking accuracy is achieved by investing the index fund s entire capital in a tracking portfolio that has the same normalized value development as the index in the presence of transaction costs which reduce the fund s capital one has to manage the trade off between transaction costs and similarity in terms of normalized value developments existing mathematical programing formulations for the index tracking problem do not optimize this trade off explicitly which may result in substantial transaction costs or tracking portfolios that differ considerably from the index in terms of normalized value development in this paper we present a mixed integer linear programing formulation with a novel optimization criterion that directly considers the trade off between transaction costs and similarity in terms of normalized value development in an experiment based on a set of real world problem instances the proposed formulation achieves a considerably higher tracking accuracy than state of the art formulations

financial intermediation and delegated monitoring this paper develops a theory of financial intermediation based on minimizing the cost of monitoring information which is useful for resolving incentive problems between borrowers and lenders it presents a characterization of the costs of providing incentives for delegated monitoring by a financial intermediary diversification within an intermediary serves to reduce these costs even in a risk neutral economy the paper presents some more general analysis of the effect of diversification on resolving incentive problems in the environment assumed in the model debt contracts with costly bankruptcy are shown to be optimal the analysis has implications for the portfolio structure and capital structure of intermediaries

the determinants of the maturity of corporate debt issues we document the determinants of the term to maturity of 7 369 bonds and notes issued between 1982 and 1993 our main finding is that large firms with investment grade credit ratings typically borrow at the short end and at the long end and of the maturity spectrum while firms with speculative grade credit ratings typically borrow in the middle of the maturity spectrum this pattern is consistent with the theory that risky firms do not issue short term debt in order to avoid inefficient liquidation but are screened out of the long term debt market because of the prospect of risky asset substitution traditionally capital structure research has focused on how much of a firm s future cash flows should be paid out to debtholders instead of equityholders an equally important issue is when future cash flows should be paid out to debtholders a firm that finances its projects with short term debt risks serious financial difficulty if the debt cannot be extended similarly a firm that finances its activities with long term debt can sacrifice profits by needlessly risking mismanagement of resources after cash flows are returned from investments but before they are due to debtholders this study investigates the factors that firms consider when choosing the maturity of their liabilities we document the determinants of the maturity of 7 368 public debt issues made by u s corporations between 1982 and 1993 our empirical tests are based on existing theoretical models that relate the maturity of a firm s borrowings to the riskiness of its cash flows the time until investments pay off the quality of information held by outsiders the expected

performance replication of the spot energy index with optimal equity portfolio selection evidence from the uk us and brazilian markets abstract this paper reproduces the performance of a geometric average spot energy index by investing only in a subset of stocks from the dow jones composite average the ftse 100 and bovespa composite indexes and in two pools that include only energy sector stocks from the us and the uk respectively daily data are used and the index tracking problem for passive investment is addressed with two evolutionary algorithms the differential evolution algorithm and the genetic algorithm the performance of the suggested investment strategy is tested under three different scenarios buy and hold quarterly and monthly rebalancing accounting for transaction costs where necessary

real and nominal determinants of real exchange rates in latin america short run dynamics and long run equilibrium this article analyses the factors that determine the long run real exchange rate in argentina colombia and mexico distinguishing between real and nominal determinants cointegration analysis is utilised to establish that the real exchange rate has an equilibrium relationship with real variables the terms of trade capital flows productivity and government share of gdp which excludes nominal variables nominal exchange rate money and central bank intervention variance decompositions reveal that among the real variables that determine the real exchange rate the terms of trade and productivity explain much of the variation in the real exchange rates when nominal variables are included in the model the nominal exchange rate accounts for most of the variation in the real exchange rates of all three countries the impulse response functions are broadly consistent with theoretical predictions and shocks to the nominal variables have only transitory effects on the real exchange rate

optimal debt structure and the number of creditors within an optimal contracting framework we analyze the optimal number of creditors a company borrows from we also analyze the optimal allocation of security interests among creditors and intercreditor voting rules that govern renegotiation of debt contracts the key to our analysis is the idea that these aspects of the debt structure affect the outcome of debt renegotiation following a default debt structures that lead to inefficient renegotiation are beneficial in that they deter default but they are also costly if default is beyond a manager s control the optimal debt structure balances these effects we characterize how the optimal debt structure depends on firm characteristics such as its technology its credit rating and the market for its assets

the variety of maturities offered by firms and institutional investment in corporate bonds we study how a firm s decision to offer bonds of various maturities affects the portfolio allocations of institutional investors we argue that because of lower information collection costs institutional investors tilt their portfolios towards firms that offer bonds of various maturities we show that this translates into lower bond yields both in the primary and in the secondary bond markets

tax planning regulatory capital planning and financial reporting strategy for commercial banks we test whether banks investment and financing policies can be explained by tax status we document changes in bank holdings of municipal bonds in response to changes in tax rules relating to deductibility of interest expense we also document an association between banks marginal tax rates and their investment and financing decisions which is consistent with the existence of tax clienteles however banks do not sort themselves perfectly into investment and financing clienteles because of adjustment costs we posit specific types of transaction cost impediments to tax planning and document that banks apparently trade off these costs against tax planning benefits article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

horses and rabbits trade off theory and optimal capital structure this paper examines optimal capital structure choice using a dynamic capital structure model that is calibrated to reflect actual firm characteristics the model uses contingent claim methods to value interest tax shields allows for reorganization in bankruptcy and maintains a long run target debt to total capital ratio by refinancing maturing debt using this model we calculate optimal capital structures in a realistic representation of the tra ditional trade off model in contrast to previous research the calculated optimal capital structures do not imply that firms tend to use too little leverage in practice we also esti mate the costs borne by a firm whose capital structure deviates from its optimal target debt to total capital ratio the costs of moderate deviations are relatively small suggesting that a policy of adjusting leverage infrequently is likely to be reasonable for many firms

the capital structure puzzle revisited corporate finance researchers have long been puzzled by low corporate debt ratios given debt s corporate tax advantage this article recognizes that firm value typically reflects a growing stream of earnings while current debt reflects a nongrowing stream of interest payments debt to value is therefore a distorted measure of corporate tax shielding even with very small debt related costs this may explain the observed magnitude and cross sectional variation of debt ratios since this variation may be independent of tax shielding debt ratios provide an inappropriate framework for empirically examining the trade off theory of capital structure article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

evidence on the role of cash flow for investment abstract recent work in macroeconomics argues that imperfections in capital markets may lead to business cycle fluctuations by propagating relatively modest shocks evidence for such a mechanism also known as the financial accelerator consists largely of firm level studies showing that cash flow is an important predictor of investment but this evidence is often viewed with skepticism because cash flow is also a good indicator of investment opportunities in this paper we develop a framework for estimating the extent to which the predictive power of cash flow can be attributed to its role as a fundamental versus its role in alleviating credit frictions for firms with access to commercial paper and bond markets we find that the perfect capital markets model of investment can fully account for the role of cash flow for firms with only limited access to capital markets as indicated by lack of participation in public debt markets however investment appears to be excessively sensitive to fluctuations in cash flow these results thus clarify the role of cash flow in investment equations and provide support for the existence of a financial accelerator

the determinants of contract terms in bank revolving credit agreements the paper examines the determinants of contract terms on bank revolving credit agree ments revolvers of medium large publicly traded companies we model the duration maturity secured status and pricing decisions within a simultaneous decision frame work thereby overcoming the biased and inconsistent estimates in prior single equation studies of debt contract terms we find strong interrelationships between contract terms with significant bi directional relationships between duration and secured status and be tween the all in spread and commitment fees and a unidirectional relationship from both duration and secured status to all in spread we also illustrate how several single equa tion studies of contract terms draw incorrect conclusions because of their inappropriate assumption that other contract terms and leverage were exogenous finally our results sup port the hypothesis that the setting of contract terms plays an important role in alleviating contracting problems

equity bonds and bank debt capital structure and financial market equilibrium under asymmetric information this paper proposes a model of financial markets and corporate finance with asymmetric information and no taxes where equity issues bank debt and bond financing coexist in equilibrium the relationship banking aspect of financial intermediation is emphasized firms turn to banks as a source of investment mainly because banks are good at helping them through times of financial distress this financial flexibility is costly since banks face costs of capital themselves which they attempt to minimize through securitization to avoid this intermediation cost firms may turn to bond or equity financing but bonds imply an inefficient liquidation cost and equity an informational dilution cost we show that in equilib rium the riskier firms prefer bank loans the safer ones tap the bond markets and the ones in between prefer to issue both equity and bonds this segmentation is broadly consistent with stylized facts

does the source of capital affect capital structure prior work on leverage implicitly assumes capital availability depends solely on firm characteristics however market frictions that make capital structure relevant may also be associated with a firm s source of capital examining this intuition we find firms that have access to the public bond markets as measured by having a debt rating have significantly more leverage although firms with a rating are fundamentally different these differences do not explain our findings even after controlling for firm characteristics that determine observed capital structure and instrumenting for the possible endogeneity of having a rating firms with access have 35 more debt copyright 2006 oxford university press

the maturity structure of corporate debt we provide an empirical examination of the determinants of corporate debt maturity our evidence offers strong support for the contracting cost hypothesis firms that have few growth options are large or are regulated have more long term debt in their capital structure we find little evidence that firms use the maturity structure of their debt to signal information to the market the evidence is consistent however with the hypothesis that firms with larger information asymmetries issue more short term debt we find no evidence that taxes affect debt maturity

deep time series forecasting for enhanced index tracking we consider the problem of enhanced index tracking whose objective is to construct a portfolio that maximizes the excess return and minimizes the tracking error between the returns of the tracking

how do firms choose their lenders an empirical investigation this article investigates which companies finance themselves through intermediaries and which borrow directly from arm s length investors our empirical results show that large companies with abundant cash and collateral tap credit markets directly these markets cater to safe and profitable industries and are most active when riskless rates or intermediary earnings are low we show that determinants of lender selection sharpen during investment downturns and that there are substantial asymmetries in the way firms enter and exit capital markets these results support a theoretical framework where intermediaries have better reorganizational skills but a higher opportunity cost of capital than bondholders

the priority structure of corporate liabilities most discussions of corporate capital structure effectively assume that all debt is the same yet debt differs by maturity covenant restrictions conversion rights call provisions and priority here we examine priority structure across a sample of 4995 compustat industrial firms from 1981 to 1991 we analyze the variation in the use of capital leases secured debt ordinary debt subordinated debt and preferred stock both as a fraction of the firm s market value and as a fraction of total fixed claims our evidence provides consistent support for contracting cost hypotheses mixed support for tax hypotheses and little support for the signaling hypothesis

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