a behavioral framework for time diversification the box of factors that we call risk is both too large and too small the box is large enough to include many sometimes conflicting measures of risk variance and semivariance probabilities of losses and their amounts but the box is too small to include factors that affect choices but fall outside the boundaries of risk frames and cognitive errors self control and regret we explore the role of these factors in time diversification the belief that time diversification reduces risk underlies the current drive to invest social security funds in stocks but is such investment prudent we discuss the role of advisors in providing prudent advice changes in the standards of prudence over time the use of time diversification in guiding investors to prudent portfolios and its use in the current debate on social security

a note on environmental risk and the rate of discount abstract this paper examines the use of risk adjusted discount rates to evaluate future environmental risks it is determined that the risk adjusted discount rate should be lower not higher than the risk free rate if evaluation of future environmental risks is to point toward optimality

a note on environmental risk and the rate of discount comment abstract the sign of the adjustment to the riskless discount rate for environmental risk depends on whether the price of avoiding the consequences of the externality is seen as reducing expected net benefits or increasing expected costs the conclusion is that the risk adjustment is positive when the externality is defined as reducing expected net benefits

risk rationality and time diversification the validity of the concept of time diversification is the subject of long running debate supporters of the concept argue that risk decreases as investment horizon increases detractors suggest that the concept is false on the face of it we argue that time diversification is consistent both theoretically and empirically with current conceptions of risk and rationality and we also note the implications of changes in investment horizon for stock market behavior

on the risk of stocks in the long run a note in a recent article in this journal zvi bodie used a simplified black scholes model to prove that the cost of insuring a long term stock portfolio against earning less than the risk free rate increases over time bodie believes that this means the risk of investing in common stocks increases over time and that the conventional wisdom of the investment community concerning time diversification is a fallacy bodie s proof relies on a constant standard deviation for common stock over all holding periods this assumption however may not be appropriate for long term stock portfolios this article is not available online

factor and spread analysis of the convertible securities market factor decomposition demonstrates that during certain time periods the convertible market has offered excess returns over a well allocated bond equity portfolio moreover because the magnitude of these returns spans a wide range of values investors can use this valuation framework as a tool for estimating the relative attractiveness of convertibles compared with their underlying equity and fixed income components analysis of yield spreads demonstrates the changing nature of valuation levels embedded in convertible securities a factor analysis of a market weighted equity index underlying convertibles shows that their equity component is well diversified across two major dimensions value versus growth and large cap versus small cap

general equilibrium with endogenously incomplete financial markets abstract the present paper studies a class of general equilibrium economies with imperfectly competitive financial intermediaries and price taking consumers intermediaries optimally choose the securities they issue and the bid ask spread they charge financial intermediation is costly and hence markets are endogenously incomplete an appropriate equilibrium concept is developed and existence is proved competitive equilibria for this class of economies display full indexation of securities payoffs and monetary neutrality even if intermediaries are restricted to issue nominal securities and financial markets turn out to be incomplete this is in sharp contrast with the indeterminacy and non neutrality results established in the literature for incomplete markets economies with exogenously given nominal securities journal of economic literaturclassification numbers d52 g20

does sunspot monetary policy matter abstract in this note we examine the effectiveness of pure random monetary policies i e changes in the money supply with no direct redistributive effects conditioned only on some extrinsic source of uncertainty in the framework of a general infinite horizon economy with uncertainty we show that these policies affect the agents insurance opportunities and hence have in general real effects when markets are incomplete and some nominal assets are traded the result is shown to extend though in a slightly weaker form to the case in which monetary policy is conditioned only on the intrinsic uncertainty in the economy

quasi option value some misconceptions dispelled abstract we discuss a couple of important issues in the recent literature on quasi option value we show that the assertion that quasi option value can be negative in a model with independent learning is based on confusion between quasi option value which is always positive and the net benefit of preservation of a natural environment subject to development which is not we also explore the significance of different assumptions about the nature of learning and show that the result that quasi option value is positive is surprisingly robust

behavioral finance and its implications for stock price volatility an increasing number of academic and professional articles are being published about research on and potential applications of behavioral finance this article offers a more complete picture of the origin content and rationale behind this emerging area of study than previously presented in the process the traditional dominance in finance of the economic concepts of subjective expected utility and rationality are discussed in addition the article argues that the newer theories of chaos and adaptive decision making which have a place in behavioral finance can help explain the puzzle of stock price volatility

the economics of the greenhouse effect the recognition that economic activity is contributing to climatic change with attendant costs that may be of large magnitudes has set in motion a substantial research effort this paper seeks to review the contribution of economics to analysis of the greenhouse effect and to the policies and instruments suggested as means of mitigating its damage a brief overview of the causes and consequences of global warming is given and a number of energy economy forecasting models are examined as the costs of global warming depend upon the extent to which preventative and adaptive measures are undertaken the techniques available to evaluate these costs are surveyed we examine extant targets for greenhouse gas emissions reduction and explore the frameworks within which optimal policy targets can be designed the paper also considers the narrower question of minimized abatement costs and surveys the types of models used to estimate them the merits of alternative policy instruments are examined paying particular attention to the role that risk and uncertainty and the costs of monitoring and implementation of policy under conditions of imperfect information may play in the choice of instruments problems of international co operation in the development of abatement policy are examined and we consider the compensations across both nations and generations that are likely to be necessary conditions for effective action

the problem of global environmental protection what distinguishes global common property problems and global unidirectional externalities from the ones that arise under a single jurisdiction is that there is no global authority empowered to intervene and regulate use of global environmental resources cooperation is needed the paper discusses when cooperation is most needed and how it might be obtained cooperation might emerge from a noncooperative setting if supergames are played if the actions of any one country are explicitly contingent on the actions undertaken by other countries or if moral concerns lead countries to consider the consequences of their actions for others cooperation emerges in an explicit though limited form when countries commit to regulate themselves in signing international agreements in these cases the signatories cooperate but the agreements are self enforcing an attempt is made to relate these theoretical concepts to the practice of global environmental protection copyright 1990 by oxford university press

ecological economics and scientific controversies lessons from some recent policy making in the eec abstract contrasting the very limited scientific evidence on the forest dieback issue with the sudden adoption of policies on air pollution decided in the frg 1983 1984 and extended to the european community 1985 we propose an interpretative framework for the real internalization process at work in what was tantamount to a social crisis for public opinion the media and political actors we conclude that open scientific controversies on some environmental issues effects causes solutions pave the way for some actors to use the issue for their own techno industrial strategies quite alien to ecological constraints in cases of very high uncertainties on impacts it becomes impossible to apply conventional social cost benefit analysis scba as an optimizing tool we propose to develop economic analysis as a negotiation language and to give pride of place to the value of learning time and to the crucial role of technological pluralism as a condition for flexibility in the future

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

an experiment on risk taking and evaluation periods does the period over which individuals evaluate outcomes influence their investment in risky assets results from this study show that the more frequently returns are evaluated the more risk averse investors will be the results are in line with the behavioral hypothesis of myopic loss aversion which assumes that people are myopic in evaluating outcomes over time and are more sensitive to losses than to gains the results have relevance for the equity premium puzzle and also for the marketing strategies of fund managers

on the risk of stocks in the long run a resolution to the debate in response to the ongoing debate in this journal about whether the risk of investments in the stock market is increased or decreased by lengthening the investment period we show that bodie s attempt to identify market risk with the price of put options leads to a circular argument within the workings of arbitrage free option pricing models thus bodie failed to rebut the conventional view that longer investment horizons may be thought of as less risky bodie s put option prices are relevant however to determining market prices of stock investment insurance

misconceptions about optimal equity allocation and investment horizon our analysis and results offer some resolution to a debate that has continued for 30 years we demonstrate that in contrast to prior claims no conflict exists between the implications of economic models of choice under uncertainty and a rational investor preference for larger equity allocations at longer investment horizons using examples of expected utility of wealth and mean variance utility we show that the effect of a longer horizon on risky asset allocation is consistent with increasing or decreasing optimal equity allocations even under the assumption of constant relative risk aversion

the time diversification controversy some financial theorists reject the widely held practitioner belief in time diversification the theorists argue that given serially uncorrelated returns holding a risky asset over longer periods of time will not reduce its inherent riskiness the argument is supported by references to economic models of risk aversion such as mean variance optimization and expected utility theory mean variance optimizers however are not indifferent to investment horizon and investment horizon indifference is only a special case within expected utility theory furthermore to the extent that models reject the notion of time diversification they are inadequate because they are inconsistent with common sense measures of risk at very long horizons

the nature of market growth risk and return in the model of asset appreciation advanced here the market economy and the market of asset claims on the economy are modeled as organic or exponential growth processes similar to those commonly seen in nature and the biological sciences in dempsey s organic growth model of appreciation dogma investors have a log wealth utility function within the framework the market risk premium is derived as the premium that balances supply and demand among risky and risk free assets the model indicates that the premium is less than is indicated by ex post returns observed on u s stock markets the model is consistent however with empirical observations that idiosyncratic risk and small company size are rewarded by the markets in terms of the model investors choose to allocate their portfolios long in both the risky market and the risk free asset furthermore their portfolios are independent of the investment time horizon

the greenhouse effect and intergenerational transfer abstract the scientific basis for understanding the economic issues involved in the greenhouse effect is outlined four important aspects of the problem are identified and discussed irreversibility international and institutional constraints uncertainty and intergenerational equity attention is focused upon the intertemporal choice problem a model describing the potential for intergenerational transfers under the uncertainty of climatic change due to fossil fuel combustion is presented we conclude intergenerational compensation can be achieved by investment in capital or technology or by bequest and is ethically required regardless of any other action

the relevance of financial policy when the asset market is incomplete equilibrium allocations are not invariant to changes in the financial policies of firms in the presence of secondary assets such as options whose payoffs depend nonlinearly on the price of equity the range of attainable reallocations of revenue varies as a firm alters its position in the asset market corporate financial policy is thus relevant when assets are nominal monetary policy implemented through open market operations is also effective

a theory of anticipated utility abstract a new theory of cardinal utility with an associated set of axioms is presented it is a generalization of the von neumann morgenstern expected utility theory which permits the analysis of phenomena associated with the distortion of subjective probability

investments with downside insurance and the issue of time diversification of two insurance policies that guarantee the same minimum rate of return on a portfolio and differ only in their time horizons which is riskier this study shows that if the minimum rate is lower than the risk free rate and if the risk is measured by the cost of insurance then the degree of risk is not a monotonic function of the policy s time horizon for every positive level of concession rate defined as the risk free rate minus the insured rate the cost of such insurance peaks at a finite time horizon this peak cost horizon is typically between 5 and 15 years the higher the concession rate or the lower the volatility of the insured portfolio the shorter this peak cost time horizon is thus although a 5 year insurance policy can be much riskier than a 1 year policy it can also be riskier than a 30 year policy

on the non neutrality of money with incomplete markets abstract in this paper we show that if markets are incomplete and there are nominal assets whose payoff is denominated in money monetary policy will be in general non neutral the mechanism through which monetary policy operates is a change in the structure of the rates of return by changing the level of money prices monetary policy affects the payoffs of nominal assets this differs from previous arguments for non neutrality we also show that a consideration of this effect of monetary policy may allow us to claim the superiority from a welfare point of view of a random money growth rate over a deterministic one journal of economic literature classification numbers d52 e50 g10

time diversification definitions and some closed form solutions abstract we establish general conditions under which younger investors should invest a larger proportion of their wealth in risky assets than older ones in the finite horizon dynamic setting we show that such phenomenon known as time diversification can occur in the presence of human wealth guaranteed consumption or mean reverting stock returns we formalize two alternative notions of time diversification commonly confounded in the literature analytic solutions are provided for both time series and cross sectional forms of time diversification to our best knowledge this paper is the first to solve in closed form the hedging demand for a cara investor with inter temporal consumption and a finite horizon facing mean reverting expected returns our results indicate that horizon can have a significant effect on the portfolio demand of a cara investor due to inter temporal hedging

on the risk of stocks in the long run a familiar proposition is that investing in common stocks is less risky the longer an investor plans to hold them if this proposition were true then the cost of insuring against earning less than the risk free rate of interest should decline as the investment horizon lengthens this paper shows that the opposite is true even if stock returns are mean reverting in the long run the case for young people investing more heavily than older people in stocks cannot therefore rest solely on the long run properties of stock returns for guarantors of money fixed annuities the proposition that stocks in their portfolios are a better hedge the longer the maturity of their obligations is unambiguously wrong

option value an exposition and extension this article examines the role of the discount rate in making decisions that will have significant implications for the environment the authors begin by providing a rationale for discounting in general and by describing the main factors that determine

time diversification perspectives from option pricing theory despite repeated theoretical arguments to the contrary many investment professionals subscribe to the principle of time diversification this principle states that equity investments become less risky if held for longer periods of time we apply option pricing theory to the question of how the investment horizon affects equity risk financially engineered securities that guarantee a minimum return allow for greater equity market participation if the investor commits to a longer time horizon in other words the fair cost of insuring a minimum return in terms of foregone market participation is lower for longer horizons the lower cost of risk reduction suggests that risk itself is lower consistent with the pervasive practitioner belief in time diversification

thinking economically about climate change abstract uncertainty over both the regional impacts and timing of climatic changes the way they tend to magnify the likelihood of so called natural disasters and their irreversibility require careful analysis of policy options from an economic standpoint the best approach is to apply cost benefit thinking the essential trade off is between doing nothing now and investing in either important preventive or adaptive measures the choices involve analysis of incurring costs now against the benefits of reducing vulnerability and future damage costs for any given level of warming the aim is to minimize the sum of policy costs and costs of adaptation by individuals any resulting policy decision will have to address issues of international cooperation and compensation these considerations may in turn influence the resulting policy choices between carbon taxes marketable permits and regulatory restrictions

the contribution of efficient energy pricing to reducing carbon dioxide emissions abstract carbon dioxide co2 emissions from energy utilization are a major factor contributing to the greenhouse effect removing existing price distortions and imposing privately efficient energy pricing makes a substantial impact on energy demand the estimated reduction in co2 emissions in the usa china and india by adopting privately efficient electricity pricing is just less than the uk s total annual emissions of co2 from fossil fuel combustion however privately efficient pricing does not ensure the optimal social level of energy production that is necessary for averting the greenhouse effect further policy instruments and considerations need to be adhered to in order to attain this optimum level globally