limit cycles in intertemporal adjustment models theory and applications this paper starts from well behaved i e concave one state variable optimal control models the crucial feature is that indigenous growth is present the replacement of the control by an adjustment process and presumably penalizing these adjustments may convert stable and only stable fixed point equilibria into limit cycles indeed given positive growth and proper externalities such that discounting exceeds growth one can generate stable limit cycles with ease e g for a separable framework examples from such diverse fields as renewable resources optimal saving and public choice highlight the economic applicability

capital flow controls international asset pricing and investors welfare a multi country framework this paper investigates the impact of capital flow restrictions on the pricing of securities on the optimal portfolio composition for investors of different nationalities and on their welfare under capital flow controls the equilibrium price of a security is determined jointly by its international and national risk premiums and investors acquire nationality specific portfolios along with a market wide proxy for the world market portfolio removal of investment barriers generally leads to an increase in the aggregate market value of the affected securities and all investors favor a move toward market integration introduction of different types of index funds in the world market generally increases world market integration and investor welfare in recent years the international capital markets have undergone numerous important changes that have increased the international linkage of national markets these changes include the creation of national index funds e g mexico korea taiwan india france and scandinavia and selective liberalization e g brazil india korea sweden and japan despite their potential impact on the national economies and global finance it is not clear what consequences these integrating changes entail for example is welfare increased by allowing cross border investment that is restricted to purchasing the entire national portfolio of which the national index fund is a class unfortunately with the exception of subrahmanyam 1975a who studies the pricing and welfare effects of fully integrating heretofore completely segmented markets other international asset pricing models that incorporate capital flow restrictions for instance black 1974 stulz 1981b lessard et al 1983 errunza and losq 1985 cooper and kaplanis 1986 and eun and janakiramanan 1986 analyze the pricing but not the welfare effects of investment barriers to analyze systematically the welfare implications of various structural changes in the current market environment this paper follows the lead of subrahmanyam and recasts the analysis in two important respects

on universal currency hedges this paper identifies five universal currency hedge ratio uhr definitions these are hedge positions in foreign bonds stated as a fraction of national or global equity portfolios that are the same for all investors regardless of nationality the first three involve the total demand for foreign bonds and depend on equities not being held for hedging purposes the last two are associated with variance minimizing regression hedges these hold in general but are designed exclusively for hedging other traded asset positions jensen s inequality makes the choice of measurement currency irrelevant and makes the hrs universal without affecting their values

real and monetary cycles in models of keynes wicksell type abstract we formulate a descriptive dynamic macroeconomic model of the keynes wicksell type which incorporates goods labour and financial markets the model has well specified budget constraints with respect to the economic agents households firms and government within it we introduce some standard nonlinearities into the goods and labour markets the dynamics of the general model consist of five differential equations we analyse two and three dimensional subcases to show the existence of real and monetary cycles whose interaction will determine the full dynamics we use numerical simulation to study the dynamics of the full model and the impact of various government fiscal and monetary policies

sharing the emission reduction burden in an uneven world in the climate agreement reached in paris on the 12th of december 2015 the participating countries agreed to provide information about their intended nationally determined contribution and also to assess its fairness and ambition this study contributes a transparent empirical econometric tool for such an assessment it shows that using a formal decomposition framework that uniquely disentangles the macroeconomic and other influences on emissions effort sharing in global greenhouse gas reductions can be achieved in a way that promotes innovation and environmental efficiency to reduce emissions without interfering with the right of poor countries to catch up economically based on gdp projections by the imf and the oecd in a sample of about 185 countries it presents country level co2 emission targets applicable as benchmarks to assess the adequacy and fairness of national contributions

heterogeneous beliefs and adaptive behaviour in a continuous time asset price model abstract this paper extends the analysis of the seminal work of brock and hommes 1997 brock and hommes 1998 on heterogeneous beliefs and rational routes to randomness in discrete time models to a continuous time model of asset pricing the resulting model characterised mathematically by a system of stochastic delay differential equations provides a unified approach to deal with adaptive behaviour of heterogeneous agents and market stability impact of lagged price used by chartists to form their expectations for the underlying deterministic model we show not only that the result of brock and hommes on rational routes to market instability in discrete time holds in continuous time but also a double edged effect of an increase in lagged price used by the chartists on market stability for the stochastic model we demonstrate that the interaction and boundedly rational behaviour of heterogeneous agents can generate various market phenomena such as bubbles and crashes and replicate stylised facts including volatility clustering and long range dependence in volatility

the structure of residential energy demand in greece abstract this paper attempts to shed light on the determinants of residential energy demand in greece and to compare it with some other oecd countries from the estimates of the short run and long run elasticities of energy demand for the period 1965 1999 we find that residential energy demand appears to be price inelastic also we do not find evidence of a structural change probably because of the low efficiency of the energy sector we find however that the magnitude of the income elasticity varies substantially between greece and other oecd countries

carbon dioxide emissions allocation a review carbon dioxide co2 emissions allocation plays a fundamental role in determining reduction responsibility at economy level or emission permits at firm level past decades have seen the development and applications of various methods for co2 emissions allocation this paper provides a literature review of co2 emissions allocation with emphasis on the evolution of allocation methods used it begins with a summary of the most popular allocation principles and criteria that lay a foundation for the development of allocation methods we then classify the existing allocation methods into four groups namely indicator optimization game theoretic and hybrid approaches the main features and findings of past studies are identified and summarized while the fairness principle prevails in earlier studies the efficiency principle has been found to receive increasing attention recently we also present a comparison of the empirical results based on ten popular indicator methods to show how indicator choice affects the allocation results issues related to selecting appropriate methods in co2 emissions allocation are finally discussed further research may be carried out to strike a balance between fairness and efficiency so that the allocation results become more widely acceptable and economically feasible

a keynes goodwin model of the business cycle abstract the paper puts forward a dynamic is lm model in four state variables representing real balances inflation income distribution and a so called state of confidence local in stability is characterized by high low interest elasticities of money demand also a hopf bifurcation can be shown to exist freezing inflation and distribution makes a mathematical analysis of the main stability mechanisms in the outer regions possible the global dynamics of the full system is studied by means of numerical simulations it gives rise to unique and stable limit cycles lastly a sensitivity analysis inquires into the impact of parameter changes on the main cycle features

unemployment income distribution and debt financed investment in a growth cycle model abstract as recent experience suggests the most significant economic fluctuations are those that combine real and financial factors this paper works out a simple model that couples a version of goodwin s 1967 growth cycle model of real fluctuations with insights drawn from a model of financial fluctuations based on minsky s financial instability hypothesis vercelli 2000 sordi and vercelli 2006 sordi and vercelli 2012 the model suggested substantially modifies that of keen 1995 who combined insights from goodwin and minsky within a model of fluctuating growth in the real part of the model we introduce the possibility of disequilibrium in the goods market and formalize a mechanism of output adjustment based on the conventional dynamic multiplier the model so obtained may exhibit persistent dynamics and provide insights to enable better understanding of the nature of real world fluctuations

on the effects of barriers to international investment a simple model is presented in which it is costly for domestic investors to hold foreign assets the implications of the model for the composition of optimal portfolios at home and abroad are derived it is shown that all foreign assets with a beta larger than some beta plot on either one of two security market lines some foreign assets with a beta smaller than are not held by domestic investors even if their expected return is increased slightly while it is obviously not true that asset markets are completely segmented between countries there is evidence of barriers to international investment although reality seems to lie in that grey area between complete segmentation and no segmentation at all most international asset pricing models are concerned with the extreme case of no barriers to international investment no effort seems to have been made to study the effect on portfolio choice of such barriers which make it costly to hold foreign securities as opposed to domestic securities but which do not in general render international diversification so onerous that investors avoid foreign securities completely casual empiricism suggests that models without barriers to international investment should be suspect those models cannot explain why it appears that in every country investors on average hold more domestic securities than would be required if they held the world market portfolio 2 this paper constructs a model of international asset pricing in which there is a cost associated with holding either long or short risky foreign securities for the sake of simplicity in most of the paper we assume that while domestic investors face barriers to international investment foreign investors face no such barriers it turns out that nothing significant is lost with such an assumption the main conclusions of this paper for the case in which foreign investors face no barriers to international investment are 1 in the presence of barriers to international investment some risky foreign

the time variation of risk and return in the foreign exchange and stock markets this paper attempts to determine whether the fluctuations of conditional first and second moments which are observed for many assets are consistent with the sharpelintner mossin capital asset pricing model we test the mean variance model under several different assumptions about the time variation of conditional second moments of returns using weekly data from july 1974 to december 1986 that include returns on a portfolio composed of dollar deutsche mark sterling and swiss franc assets together with the u s stock market the results indicate that estimated conditional variances cannot explain the observed time variation of risk premia rates of return on international financial assets are characterized by statistical properties that are quite common to all financial markets they are highly volatile and largely unpredictable these properties make it very difficult to extract statistically reliable estimates of systematic exchange rate and assetprice movements and are at the root of the generally poor empirical performance of international asset pricing models nevertheless two important results have been uncovered by empirical researchers and can be considered a fair characterization of the data a expected returns on foreign assets vary over time cumby and obstfeld 1981 and the numerous articles that followed recently surveyed by frankel and meese 1987 b the volatility of returns of foreign assets also changes over time cumby and obstfeld 1984 hodrick and srivastava 1984 and hsieh 1988 among others as giovannini and jorion 1987 suggest the

an electricity generation planning model incorporating demand response abstract energy policies that aim to reduce carbon emissions and change the mix of electricity generation sources such as carbon cap and trade systems and renewable electricity standards can affect not only the source of electricity generation but also the price of electricity and consequently demand we develop an optimization model to determine the lowest cost investment and operation plan for the generating capacity of an electric power system the model incorporates demand response to price change in a case study for a u s state we show the price demand and generation mix implications of a renewable electricity standard and of a carbon cap and trade policy with and without initial free allocation of carbon allowances this study shows that both the demand moderating effects and the generation mix changing effects of the policies can be the sources of carbon emissions reductions and also shows that the share of the sources could differ with different policy designs the case study provides different results when demand elasticity is excluded underscoring the importance of incorporating demand response in the evaluation of electricity generation policies

debt cycles instability and fiscal rules a godley minsky synthesis wynne godley and hyman minsky were two macroeconomists who saw the crisis coming this paper develops a simple macrodynamic model that synthesises some key perspectives of their analytical frameworks the model incorporates godley s financial balances approach and postulates that private sector s propensity to spend is driven by a stock flow norm the target net private debt to income ratio that changes endogenously via a minsky mechanism it also includes two fiscal rules a maastricht type fiscal rule according to which the fiscal authorities adjust the government expenditures based on a target net government debt ratio and a godley minsky fiscal rule which links government expenditures with private indebtedness following a counter cyclical logic the analysis shows that i the interaction between the propensity to spend and net private indebtedness can generate cycles and instability ii instability is more likely when the propensity to spend responds strongly to deviations from the stock flow norm and when the expectations that determine the stock flow norm are highly sensitive to the economic cycle iii the maastricht type fiscal rule is destabilising while the godley minsky fiscal rule is stabilising iv the paradox of debt can apply both to the private sector and the government sector

effort sharing in ambitious global climate change mitigation scenarios abstract the post 2012 climate policy framework needs a global commitment to deep greenhouse gas emission cuts this paper analyzes reaching ambitious emission targets up to 2050 either 10 or 50 from 1990 levels and how the economic burden from mitigation efforts could be equitably shared between countries the scenarios indicate a large low cost mitigation potential in electricity and industry while reaching low emission levels in international transportation and agricultural emissions might prove difficult the two effort sharing approaches triptych and multistage were compared in terms of equitability and coherence both approaches produced an equitable cost distribution between countries with least developed countries having negative or low costs and more developed countries having higher costs there is however no definitive solution on how the costs should be balanced equitably between countries triptych seems to be yet more coherent than other approaches as it can better accommodate national circumstances last challenges and possible hindrances to effective mitigation and equitable effort sharing are presented the findings underline the significance of assumptions behind effort sharing on mitigation potentials and current emissions the challenge of sharing the effort with uncertain future allowance prices and how inefficient markets might undermine the efficiency of a cap and trade system

futures markets and commodity options hedging and optimality in incomplete markets abstract this paper examines the allocational roles of futures markets and commodity options in multi good and multi period economies in a continuous time model with time additive utilities and homogeneous beliefs trading in unconditional futures contracts the market portfolio and a riskless asset gives any pareto optimal allocation individuals optimal holdings of futures contracts in the continuous time model are related to their consumption bundles and to their risk tolerances it is shown that both hedging and reverse hedging behavior are possible in the general model with discrete trading options on portfolios of commodity options are shown to permit any unconstrained pareto optimal allocation

dynamic analysis of policy lag in a keynes goodwin model stability instability cycles and chaos abstract in this paper we investigate the impact of government s stabilization policy on the dynamic behavior of the economic system in an analytical framework of a keynes goodwin model of the growth cycle in particular we study the effects of the policy lag on macroeconomic stability analytically and numerically it is shown that the increase of the policy lag contributes to destabilize the system and cyclical behavior and chaotic motion emerge in some ranges of the parameter values

international equity and differentiation in global warming policy ne of the major obstacles to reaching a comprehensive agreement on global warming is the setting of greenhouse gas emission reduction targets for individual countries long standing tensions between industrialized and developing countries have raised the issue of equity in burden sharing moreover individual industrialized nations have pleaded special circumstances and have sought differentiation in their obligations this paper analyzes alternative rules for distributing tradable carbon dioxide emissions permits a non linear programming model which distinguishes between allocation based and outcome based rules is used to analyze the relative welfare outcomes the model is applied to the world body of nations and yields several important policy implications

abatement costs of post kyoto climate regimes abstract this article analyses the abatement costs of three post kyoto regimes for differentiating commitments compatible with stabilising atmospheric greenhouse gases concentrations at 550 ppmv co 2 equivalent in 2100 the three regimes explored are 1 the multi stage approach assumes a gradual increase in the number of parties involved who are adopting either emission intensity or reductions targets 2 the brazilian proposal approach i e the allocation or reductions based on countries contribution to temperature increase 3 contraction convergence with full participation in convergence of per capita emission allowances in 2050 the global costs increase up to about 1 of the world gdp ranging from 0 5 to 1 5 depending on baseline scenario and marginal abatement costs four groups of regions can be identified on the basis of similar costs expressed as the percentage of gdp these are 1 oecd regions with average costs 2 fsu the middle east and latin america with high costs 3 south east asia and east asia incl china with low costs and 4 south asia incl india and africa with net gains from emissions trading for most regimes the brazilian proposal approach gives the highest costs for groups 1 and 2 the distribution of costs for the contraction convergence approach highly depends on the convergence year the multi stage approach and contraction convergence convergence year 2050 seem to result in relatively the most even distribution of costs amongst all parties

reviving kalecki s business cycle model in a growth context abstract in 1935 kalecki formulated the first fully specified model of a macroeconomic dynamics in which he studied an endogenous and most elementary business cycle mechanism to revive his insights the present paper adapts his stationary economy to a growth context introducing a reasonable nonlinearity into the investment function it then takes care that the model exhibits persistent cyclical behaviour that is characterized by a unique globally attracting limit cycle this feature is a robust property a calibration of the numerical parameters achieves desired values for the cycle period as well as the amplitudes of the output capital ratio and the capital growth rate it is moreover demonstrated that a one time shock to the dynamics can easily have long lasting effects on the amplitudes despite common misgivings about delay differential equations which here result from kalecki s implementation lag the analysis can be conducted with a limited mathematical effort

emission allowances and mitigation costs of china and india resulting from different effort sharing approaches to meet ambitious global climate targets mitigation effort in china and india is necessary this paper presents an analysis of the scientific literature on how effort sharing approaches affect emission allowances and abatement costs of china and india we find that reductions for both china and india differ greatly in time across and within approaches and between concentration stabilisation targets for china allocated emission allowances in 2020 are substantially below baseline projections moreover they may be below 2005 emission levels particularly for low concentration targets below 490 ppm co2 eq effort sharing approaches based on allocating reduction targets lead to relatively lower reductions for china than approaches that are based on allocating emission allowances for 2050 emission allowances for china are 50 80 below 2005 levels for low concentration targets with minor differences between approaches still mitigation costs of china including emissions trading remain mostly below global average according to literature chinese emission allowances peak before 2025 2030 for low concentration targets india s emission allowances show high increases compared to 2005 levels if emission trading is allowed financial revenues from selling credits might compensate mitigation costs in most approaches even for low concentration targets india s emission allowances peak around 2030 2040 for all concentration targets c 2012 elsevier ltd all rights reserved

effective demand class struggle and cyclical growth the paper presents an analytical model of endogenous cyclical growth in a pure capitalist economy the model integrates keynesian ideas on effective demand with a marxian emphasis on class struggle and the reserve army of labor for reasonable parameter values the model has a unique nontrivial balanced growth equilibrium the equilibrium is unstable and using the poincare bendixson theorem it is shown that the economy will exhibit perpetual fluctuations around the balanced growth path copyright 1989 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

pathways to a low carbon economy for the uk with the macro econometric e3mg model this paper examines different carbon pathways for achieving deep co2 reduction targets for the uk using a macro econometric hybrid model e3mg which stands for energy economy environment model at the global level the e3mg with the uk as one of its regions combines a top down approach for modeling the global economy and for estimating the aggregate and disaggregate energy demand and a bottom up approach energy technology submodel etm for simulating the power sector which then provides feedback to the energy demand equations and the whole economy the etm submodel uses a probabilistic approach and historical data for estimating the penetration levels of the different technologies considering their economic technical and environmental characteristics three pathway scenarios cfh clc and cam simulate the co2 reduction by 40 60 and 80 by 2050 compared to 1990 levels respectively and are compared with a reference scenario ref with no reduction target the targets are modeled as the uk contribution to an international mitigation effort such as achieving the g8 reduction targets which is a more realistic political framework for the uk to move towards deep reductions rather than moving alone this paper aims to provide modeling evidence that deep reduction targets can be met through different carbon pathways while also assessing the macroeconomic effects of the pathways on gdp and investment

currency hedging for international portfolios this paper examines the benefits from currency hedging both for speculative and risk minimization motives in international bond and equity portfolios the riskreturn performances of globally diversified portfolios are compared with and without forward contracts over the period 1974 to 1990 inclusion of forward contracts results in statistically significant improvements in the performance of unconditional portfolios containing bonds conditional strategies are also implemented both in sample and out of sample and are shown to both significantly improve the risk return tradeoff of global portfolios and to outperform unconditional hedging strategies whether international portfolios should be hedged against currency risks is the subject of an active debate the theoretical side of the debate has been closely associated with two strands in the academic literature international asset pricing and optimal hedging in the futures markets in the international asset pricing model iapm of solnik 1974 optimal portfolios contain positions in forward contracts or equivalently foreign currency denominated bills these positions which can differ from the positions in foreign stocks have since been termed hedges black 1990 shows that under additional assumptions the hedge ratios should be identical for all investors regardless of their nationality universality and that investors should never fully hedge their foreign currency exposures similarly theoretical models from the futures literature produce demands for hedging instruments that contain both speculative and hedging components the empirical issue unanswered so far is whether adding forward contracts to international portfolios significantly improves the risk return profile of global investments empirical research has barely begun to respond to the challenges of theoretical models there exists little empirical evidence on either the relevance of black s universal hedge ratios or the optimality of hedge ratios less than one instead researchers have concentrated on the benefits of fully hedging exchange risk for example eun and resnick 1988 indicate that stock portfolios perform better when fully hedged but offer no statistical tests

an analysis of the greek energy system in view of the kyoto commitments the current state of the greek energy system is analysed together with alternative energy policies a by sector analysis provides an overview of the inputs that have been used for this investigation a combination of a demand forecast performed together with an analysis based on the r markal and wasp iv models give an evaluation of the alternative policies to be applied and a determination of additional measures required in order to achieve the kyoto targets three scenarios are developed depicting the evolution of the greek energy system under alternative policies taking into consideration medium and high oil prices incremental investments and differential costs are then calculated between kyoto and non kyoto scenarios and they are compared to emission permits costs

a post kyoto analysis of the greek electric sector abstract the obligations resulting from the kyoto protocol kp are implemented by many participants e g greece by a combination of two methods a application of regional measures which restrict co2 emissions and b procurement of green certificates e g in a climate exchange market cex therefore the cost for compliance with the kp depends on the extent each method is used and also on the traded values in the cex the energy policy and planning to be considered are long term items and now extension of the kp to a post kp is discussed which reaches year 2020 in greece the electricity sector is with a weighted co2 contribution of 73 the dominantly emission sector the paper analyzes the cost and other merits of different scenarios for the expansion of electrical power system in greece for different scenarios the total cost of the electrical power system expansion is calculated as a function of the price of emission certificates it has been shown that there is a price of 27 5 tco2 above which specific mitigation measures may lead to cost optimum solutions a sensitivity analysis is also presented concerning the variation of key parameters like the participation in the system expansion of new supercritical coal units the price evolution of natural gas the res usage rate and the discount rates of the expansion investments results may be of interest for a decision on the cost optimum electrical power system expansion

the effects of income distribution and fiscal policy on aggregate demand investment and the budget balance the case of europe this paper develops a multi country post kaleckian model that incorporates the role of the government one key novelty of the model is that it integrates cross country effects of both changes in income distribution and fiscal policy the model is used to estimate econometrically the effects of income distribution and fiscal policy on the components of aggregate demand and the budget balance in eu15 countries the results show that a simultaneous increase in the wage share in all eu15 countries would increase demand and the primary budget balance in all countries a simultaneous increase in government spending turns out to boost economic activity in all the eu15 countries indicating the positive economic effects of expansionary fiscal policy moreover a progressive tax policy that would be implemented simultaneously at the eu level would lead to an increase in output in all countries

taxation income redistribution and debt dynamics in a seven equation model of the business cycle abstract in this paper we investigate the economic dynamics of a seven equation model of the business cycle the main distinctive features of the model are related to a the role played by the public sector in redeploying income between workers and capitalists since it is assumed that the bargaining power of the two classes affects tax rates and transfers levied upon them b the influence that past events have on the agents current behavior with particular regard to consumption patterns c the specification of firms investment function which incorporate keynesian and harrodian elements by assuming that investments are a function of both the difference between interest and profit rate and the discrepancy between actual and desired capital to output ratio since all these assumptions imply possible balance sheets disequilibrium particular regard is dedicated to the analysis of macroagents debt dynamics special emphasis is placed on the analysis of the destabilization of equilibria via hopf bifurcations which leads to the emergence of an interesting and rich cyclical dynamics

dynamics of moving average rules in a continuous time financial market model within a continuous time framework this paper proposes a stochastic heterogeneous agent model ham of flnancial markets with time delays to unify various moving average rules used in discrete time hams the time delay represents a memory length of a moving average rule in discrete time hams intuitive conditions for the stability of the fundamental price of the deterministic model in terms of agents behavior parameters and memory length are obtained it is found that an increase in memory length not only can destabilize the market price resulting in oscillatory market price characterized by a hopf bifurcation but also can stabilize an otherwise unstable market price leading to stability switching as the memory length increases numerical simulations show that the stochastic model is able to characterize long deviations of the market price from its fundamental price and excess volatility and generate most of the stylized facts observed in flnancial markets

allocation of co2 emission permits economic incentives for emission reductions in developing countries the economic impacts on developing regions following a global cap and trade system for carbon dioxide are assessed through the use of an energy economy systems model both an equal per capita allocation and a contraction and convergence allocation with convergence of the per capita emissions by 2050 are shown to offer economic incentive for africa india and probably also latin america to accept binding emissions commitments under a 450 ppm carbon dioxide stabilization scenario the gain for latin america is mainly a result of increased export revenues from sales of bio fuels as a result of the climate policy it is on the other hand unlikely that these allocation approaches would offer an economic incentive for china to join the regime because of its high economic growth present higher per capita emissions than india and africa and more costly mitigation options than latin america a more stringent allocation for developing countries such as contraction with convergence of the per capita emissions by the end of this century is estimated to generate reduced net gains or increased net losses for the developing regions though africa is still expected to gain

equilibrium exchange rate hedging we assume a world like the one that gives the capital asset pricing model but with many goods and many countries we assume that investors in a given country have homothetic utility functions with the same weights and a currency that has a sure endof period value using a price index with those weights siegel s paradox derived from jensen s inequality makes investors want a positive amount of exchange risk when average risk tolerance is the same across countries every investor will hold the same mix of market risk through the world market portfolio of all assets and exchange risk in a diversified basket of foreign currencies in fact the ratio of exchange risk to market risk is equal to the average investor s risk tolerance we can write the ratio of exchange risk to market risk and the fraction of the market s exchange risk that investors hedge as depending on an average of world market risk premia an average of world market volatilities and an average of exchange rate volatilities the weights in these averages are the same as the weights of the different countries in the currency basket given these averages the ratio and the fraction hedged will not depend directly on exchange rate means or covariances in equilibrium we can use the ratio of exchange risk to market risk to measure average risk tolerance in this model risk tolerance is observable

universal hedging optimizing currency risk and reward in international equity portfolios investors can increase their returns by holding foreign stocks in addition to domestic ones they can also gain by taking the appropriate amount of exchange risk but what amount is appropriate assume that investors see the world in light of their own consumption goods and count both risk and expected return when figuring their optimum hedges assume that they share common views on stocks and currencies and that markets are liquid and there are no barriers to international investing in this perfect world it is possible to derive a formula for the optimal hedge ratio this formula requires three basic inputs the average across countries of the expected returns on the world market portfolio the average across countries of the volatility of the world market portfolio and the average across all pairs of countries of exchange rate volatility these values can be estimated from historical data the formula in turn gives the circumstances for three rules 1 hedge foreign equity 2 hedge less than 100