Ch05-4e Essentials of Investment
Ch05Interest Rate Markets(期权,期货和其他衍生物-第五版)
Fundamentals of Futures and Options Markets, 4th edition © 2001 by John C. Hull
5.3
Zero Rates
A zero rate (or spot rate), for maturity T is the rate of interest earned on an investment that provides a payoff only at time T
Calculation of Forward Rates
Table 5.4, page 104
Zero Rate for Year (n ) 1 2 3 (% per annum) 10.0 10.5 10.8 11.0 11.4 Forward Rate (% per annum)
5.14
an n -year Investment for n th Year
可持续性资本理论
B OSTON U NIVERSITY Center for Energy and Environmental Studies Working Papers SeriesNumber 9501 September 1995 THE CAPITAL THEORY APPROACH TO SUSTAINABILITY:A CRITICAL APPRAISALbyDavid Stern675 Commonwealth Avenue, Boston MA 02215Tel: (617) 353-3083Fax: (617) 353-5986E-Mail: dstern@WWW: /sterncv.htmlThe Capital Theory Approach to Sustainability:A Critical AppraisalDavid I. SternBoston UniversityNovember 1995______________________________________________________________________________ Center for Energy and Environmental Studies, Boston University, 675 Commonwealth Avenue, Boston MA 02215, USA. Tel: (617) 353 3083 Fax: (617) 353 5986, E-Mail: dstern@The Capital Theory Approach to Sustainability:A Critical Appraisal______________________________________________________________________________ SummaryThis paper examines critically some recent developments in the sustainability debate. The large number of definitions of sustainability proposed in the 1980's have been refined into a smaller number of positions on the relevant questions in the 1990's. The most prominent of these are based on the idea of maintaining a capital stock. I call this the capital theory approach (CTA). Though these concepts are beginning to inform policies there are a number of difficulties in applying this approach in a theoretically valid manner and a number of critics of the use of the CTA as a guide to policy. First, I examine the internal difficulties with the CTA and continue to review criticisms from outside the neoclassical normative framework. The accounting approach obscures the underlying assumptions used and gives undue authoritativeness to the results. No account is taken of the uncertainty involved in sustainability analysis of any sort. In addition, by focusing on a representative consumer and using market (or contingent market) valuations of environmental resources, the approach (in common with most normative neoclassical economics) does not take into account distributional issues or accommodate alternative views on environmental values. Finally, I examine alternative approaches to sustainability analysis and policy making. These approaches accept the open-ended and multi-dimensional nature of sustainability and explicitly open up to political debate the questions that are at risk of being hidden inside the black-box of seemingly objective accounting.I.INTRODUCTIONThe Brundtland Report (WCED, 1987) proposed that sustainable development is "development that meets the needs of the present generation while letting future generations meet their own needs". Economists initially had some difficulty with this concept, some dismissing it1 and others proliferating a vast number of alternative definitions and policy prescriptions (see surveys by: Pezzey, 1989; Pearce et al., 1989; Rees, 1990; Lélé, 1991).In recent years, economists have made some progress in articulating their conception of sustainability. The large number of definitions of sustainability proposed in the 1980's have been refined into a smaller number of positions on the relevant questions in the 1990's. There is agreement that sustainability implies that certain indicators of welfare or development are non-declining over the very long term, that is development is sustained (Pezzey, 1989). Sustainable development is a process of change in an economy that does not violate such a sustainability criterion. Beyond this, the dominant views are based on the idea of maintaining a capital stock as a prerequisite for sustainable development. Within this school of thought there are opposing camps which disagree on the empirical question of the degree to which various capital stocks can be substituted for each other, though there has been little actual empirical research on this question.There is a consensus among a large number of economists that the CTA is a useful means of addressing sustainability issues.2 Capital theory concepts are beginning to inform policy, as in the case of the UN recommendations on environmental accounting and the US response to them (Beardsley, 1994; Carson et al., 1994; Steer and Lutz, 1993). There are, however, a growing number of critics who question whether this is a useful way to address sustainability (eg. Norgaard, 1991; Amir, 1992; Common and Perrings, 1992; Karshenas, 1994; Pezzey, 1994; Common and Norton, 1994; Faucheux et al., 1994; Common, 1995). The literature on sustainable development and sustainability is vast and continually expanding. There are also a large number ofsurveys of that literature (eg. Tisdell, 1988; Pearce et al., 1989; Rees, 1990; Simonis, 1990; Lélé, 1991; Costanza and Daly, 1992; Pezzey, 1992; Toman et al., 1994). I do not intend to survey this literature.The aim of this paper is to present a critique of the capital theory approach to sustainability (CTA henceforth) as a basis for policy. This critique both outlines the difficulties in using and applying the CTA from a viewpoint internal to neoclassical economics and problems with this approach from a viewpoint external to neoclassical economics. I also suggest some alternative approaches to sustainability relevant analysis and policy. The neoclasscial sustainability literature generally ignores the international dimensions of the sustainability problem. I also ignore this dimension in this paper.The paper is structured as follows. In the second section, I discuss the background to the emergence of the capital theory approach, while the third section briefly outlines the basic features of the approach. The fourth section examines the limitations of the CTA from within the viewpoint of neoclassical economics and the debate between proponents of "weak sustainability" and "strong sustainability". The following sections examine the drawbacks of this paradigm from a viewpoint external to neoclassical economics and discuss alternative methods of analysis and decision-making for sustainability. The concluding section summarizes the principal points.SHIFTING DEBATE: EMERGENCE OF THE CAPITAL THEORY II. THEAPPROACHMuch of the literature on sustainable development published in the 1980's was vague (see Lélé, 1991; Rees, 1990; Simonis, 1990). There was a general lack of precision and agreement in defining sustainability, and outlining appropriate sustainability policies. This confusion stemmed in part from an imprecise demarcation between ends and means. By "ends" I mean the definition ofsustainability ie. what is to be sustained, while "means" are the methods to achieve sustainability or necessary and/or sufficient conditions that must be met in order to do the same. As the goal of policy must be a subjective choice, considerable debate surrounded and continues to surround the definition of sustainability (eg. Tisdell, 1988). As there is considerable scientific uncertainty regarding sustainability possibilities, considerable debate continues to surround policies to achieve any given goal.Sharachchandra Lélé (1991) stated that "sustainable development is in real danger of becoming a cliché like appropriate technology - a fashionable phrase that everyone pays homage to but nobody cares to define" (607). Lélé pointed out that different authors and speakers meant very different things by sustainability, and that even UNEP's and WCED's definitions of sustainable development were vague, and confused ends with means. Neither provided any scientific examination of whether their proposed policies would lead to increased sustainability. "Where the sustainable development movement has faltered is in its inability to develop a set of concepts, criteria and policies that are coherent or consistent - both externally (with physical and social reality) and internally (with each other)." (613). Judith Rees (1990) expressed extreme skepticism concerning both sustainable development and its proponents. “It is easy to see why the notion of sustainable development has become so popular ... No longer does environmental protection mean sacrifice and confrontation with dominant materialist values” (435). She also argued that sustainable development was just so much political rhetoric. A UNEP report stated: "The ratio of words to action is weighted too heavily towards the former" (quoted in Simonis, 1990, 35). In the early days of the sustainability debate, vagueness about the meaning of sustainability was advantageous in attracting the largest constituency possible, but in the longer run, greater clarity is essential for sustaining concern.In the 1990's many people have put forward much more precisely articulated definitions of sustainable development, conditions and policies required to achieve sustainability, and criteria toassess whether development is sustainable. This has coincided with a shift from a largely politically-driven dialogue to a more theory-driven dialogue. With this has come a clearer understanding of what kinds of policies would be required to move towards alternative sustainability goals, and what the limits of our knowledge are. There is a stronger awareness of the distinction between ends and means. Most, but not all (eg. Amir, 1992), analysts agree that sustainable development is a meaningful concept but that the claims of the Brundtland Report (WCED, 1987) that growth just had to change direction were far too simplistic.There is a general consensus, especially among economists, on the principal definition of sustainable development used by David Pearce et al. (1989, 1991): Non-declining average human welfare over time (Mäler, 1991; Pezzey, 1992; Toman et al., 1994).3 This definition of sustainability implies a departure from the strict principle of maximizing net present value in traditional cost benefit analysis (Pezzey, 1989), but otherwise it does not imply a large departure from conventional economics. John Pezzey (1989, 1994) suggests a rule of maximizing net present value subject to the sustainability constraint of non-declining mean welfare. It encompasses many but not all definitions of sustainability. For example, it excludes a definition of sustainability based on maintaining a set of ecosystem functions, which seems to be implied by the Holling-sustainability criterion (Common and Perrings, 1992; Holling, 1973, 1986) or on maintaining given stocks of natural assets irrespective of any contribution to human welfare. A sustainable ecosystem might not be an undesirable goal but it could be too strict a criterion for the goal of maintaining human welfare (Karshenas, 1994) and could in some circumstances lead to declining human welfare. Not all ecosystem functions and certainly not all natural assets may be necessary for human welfare. Some aspects of the natural world such as smallpox bacteria may be absolutely detrimental to people. In the context of the primary Pearce et al. definition, the Holling-sustainability criterion is a means not an end.The advantage of formalizing the concept of sustainability is that this renders it amenable to analysis by economic theory (eg. Barbier and Markandya, 1991; Victor, 1991; Common and Perrings, 1992; Pezzey, 1989, 1994; Asheim, 1994) and to quantitative investigations (eg. Repetto et al., 1989; Pearce and Atkinson, 1993; Proops and Atkinson, 1993; Stern, 1995). Given the above formal definition of sustainability, many economists have examined what the necessary or sufficient conditions for the achievement of sustainability might be. Out of this activity has come the CTA described in the next section. The great attractiveness of this new approach is that it suggests relatively simple rules to ensure sustainability and relatively simple indicators of sustainability. This situation has seemingly cleared away the vagueness that previously attended discussions of sustainability and prompted relatively fast action by governments and international organizations to embrace specific goals and programs aimed at achieving this notion of the necessary conditions for sustainability.III. THE ESSENCE OF THE CAPITAL THEORY APPROACHThe origins of the CTA are in the literature on economic growth and exhaustible resources that flourished in the 1970s, exemplified by the special issue of the Review of Economic Studies published in 1974 (Heal, 1974). Robert Solow (1986) built on this earlier literature and the work of John Hartwick (1977, 1978a, 1978b) to formalize the constant capital rule. In these early models there was a single non-renewable resource and a stock of manufactured capital goods. A production function produced a single output, which could be used for either consumption or investment using the two inputs. The elasticity of substitution between the two inputs was one which implied that natural resources were essential but that the average product of resources could rise without bound given sufficient manufactured capital.The models relate to the notion of sustainability as non-declining welfare through the assumption that welfare is a monotonically increasing function of consumption (eg. Mäler, 1991). The path ofconsumption over time (and therefore of the capital stock) in these model economies depends on the intertemporal optimization rule. Under the Rawlsian maxi-min condition consumption must be constant. No net saving is permissible as this is regarded as an unjust burden on the present generation. Under the Ramsey utilitarian approach with zero discounting consumption can increase without bound (Solow, 1974). Here the present generation may be forced to accept a subsistence standard of living if this can benefit the future generations however richer they might be. Paths that maximize net present value with positive discount rates typically peak and then decline so that they are not sustainable (Pezzey, 1994). Pezzey (1989) suggested a hybrid version which maximizes net present value subject to an intertemporal constraint that utility be non-declining. In this case utility will first increase until it reaches a maximum sustainable level. This has attracted consensus as the general optimizing criterion for sustainable development. Geir Asheim (1991) derives this condition more formally.Under the assumption that the elasticity of substitution is one, non-declining consumption depends on the maintenance of the aggregate capital stock ie. conventional capital plus natural resources, used to produce consumption (and investment) goods (Solow, 1986). Aggregate capital, W t,and the change in aggregate capital are defined by:W t=p Kt K t + p Rt S t (1)∆W t=p Kt∆K t + p Rt R t (2)where S is the stock of non-renewable resources and R the use per period. K is the manufactured capital stock and the p i are the relevant prices. In the absence of depreciation of manufactured capital, maintenance of the capital stock implies investment of the rents from the depletion of the natural resource in manufactured capital - the Hartwick rule (Hartwick 1977, 1978a, 1978b). Income is defined using the Hicksian notion (Hicks, 1946) that income is the maximum consumption in a period consistent with the maintenance of wealth. Sustainable income is,therefore, the maximum consumption in a period consistent with the maintenance of aggregate capital intact (Weitzman, 1976; Mäler, 1991) and for a flow of income to be sustainable, the stock of capital needs to be constant or increasing over time (Solow, 1986).The initial work can be extended in various ways. The definition of capital that satisfies these conditions can be extended to include a number of categories of "capital": natural, manufactured, human, and institutional.4 Natural capital is a term used by many authors (it seems Smith (1977) was the first) for the aggregate of natural resource stocks that produce inputs of services or commodities for the economy. Some of the components of natural capital may be renewable resources. Manufactured capital refers to the standard neoclassical definition of "a factor of production produced by the economic system" (Pearce, 1992). Human capital also follows the standard definition. Institutional capital includes the institutions and knowledge necessary for the organization and reproduction of the economic system. It includes the ethical or moral capital referred to by Fred Hirsch (1976) and the cultural capital referred to by Fikret Berkes and Carl Folke (1992). For convenience I give the name 'artificial capital' to the latter three categories jointly. None of these concepts is unproblematic and natural capital is perhaps the most problematic. Technical change and population growth can also be accommodated (see Solow, 1986).Empirical implementation of the CTA tends to focus on measurement of sustainable income (eg. El Serafy, 1989; Repetto, 1989) or net capital accumulation (eg. Pearce and Atkinson, 1993; Proops and Atkinson, 1993) rather than on direct estimation of the capital stock.5 The theoretical models that underpin the CTA typically assume a Cobb-Douglas production function with constant returns to scale, no population growth, and no technological change. Any indices of net capital accumulation which attempt to make even a first approximation to reality must take these variables into account. None of the recent empirical studies does so. For example, David Pearce and Giles Atkinson (1993) present data from eighteen countries on savings and depreciation of natural andmanufactured capital as a proportion of GNP. They demonstrate that only eight countries had non-declining stocks of total capital, measured at market prices, and thus passed a weak sustainability criterion of a constant aggregate capital stock, but their methodology ignores population growth, returns to scale or technological change.IV.INTERNAL APPRAISAL OF THE CAPITAL THEORY APPROACHIn this section, I take as given the basic assumptions and rationale of neoclassical economics and highlight some of the technical problems that are encountered in using the CTA as an operational guide to policy. From a neoclassical standpoint these might be seen as difficulties in the positive theory that may lead to difficulties in the normative theory of sustainability policy. In the following section, I take as given solutions to these technical difficulties and examine some of the problems inherent in the normative neoclassical approach to sustainability.a.Limits to Substitution in Production and "Strong Sustainability"Capital theorists are divided among proponents of weak sustainability and strong sustainability. This terminology is confusing as it suggests that the various writers have differing ideas of what sustainability is.6 In fact they agree on that issue, but differ on what is the minimum set of necessary conditions for achieving sustainability. The criterion that distinguishes the categories is the degree of substitutability believed to be possible between natural and artificial capital.7The weak sustainability viewpoint follows from the early literature and holds that the relevant capital stock is an aggregate stock of artificial and natural capital. Weak sustainability assumes that the elasticity of substitution between natural capital and artificial capital is one and therefore that there are no natural resources that contribute to human welfare that cannot be asymptotically replaced by other forms of capital. Reductions in natural capital may be offset by increases inartificial capital. It is sometimes implied that this might be not only a necessary condition but also a sufficient condition for achieving sustainability (eg. Solow, 1986, 1993).Proponents of the strong sustainability viewpoint such as Robert Costanza and Herman Daly (1992) argue that though this is a necessary condition for sustainability it cannot possibly be a sufficient condition. Instead, a minimum necessary condition is that separate stocks of aggregate natural capital and aggregate artificial capital must be maintained. Costanza and Daly (1992) state: "It is important for operational purposes to define sustainable development in terms of constant or nondeclining total natural capital, rather than in terms of nondeclining utility" (39).8 Other analysts such as members of the "London School" hold views between these two extremes (see Victor, 1991). They argue that though it is possible to substitute between natural and artificial capital there are certain stocks of "critical natural capital" for which no substitutes exist. A necessary condition for sustainability is that these individual stocks must be maintained in addition to the general aggregate capital stock.The weak sustainability condition violates the Second Law of Thermodynamics, as a minimum quantity of energy is required to transform matter into economically useful products (Hall et al., 1986) and energy cannot be produced inside the economic system.9 It also violates the First Law on the grounds of mass balance (Pezzey, 1994). Also ecological principles concerning the importance of diversity in system resilience (Common and Perrings, 1992) imply that minimum quantities of a large number of different capital stocks (eg. species) are required to maintain life support services. The London School view and strong sustainability accommodate these facts by assuming that there are lower bounds on the stocks of natural capital required to support the economy, in terms of the supply of materials and energy, and in terms of the assimilative capacity of the environment, and that certain categories of critical natural capital cannot be replaced by other forms of capital.Beyond this recognition it is an empirical question as to how far artificial capital can substitute for natural capital. There has been little work on this at scales relevant to sustainability. However, the econometric evidence from studies of manufacturing industry suggest on the whole that energy and capital are complements (Berndt and Wood, 1979).In some ways the concept of maintaining a constant stock of aggregate natural capital is even more bizarre than maintaining a non-declining stock of total capital. It seems more reasonable to suggest that artificial capital might replace some of the functions of natural capital than to suggest that in general various natural resources may be substitutes for each other. How can oil reserves substitute for clean air, or iron deposits for topsoil? Recognizing this, some of the strong sustainability proponents have dropped the idea of maintaining an aggregate natural capital stock as proposed by Costanza and Daly (1992) and instead argue that minimum stocks of all natural resources should be maintained (Faucheux and O'Connor, 1995). However, this can no longer really be considered an example of the CTA. Instead it is an approach that depends on the concept of safe minimum standards or the precautionary principle. The essence of the CTA is that some aggregation of resources using monetary valuations is proposed as an indicator for sustainability.The types of models which admit an index of aggregate capital, whether aggregate natural capital or aggregate total capital, is very limited. Construction of aggregate indices or subindices of inputs depend on the production function being weakly separable in those subgroups (Berndt and Christensen, 1973). For example it is only possible to construct an index of aggregate natural capital if the marginal rate of substitution between two forms of natural capital is independent of the quantities of labor or capital employed. This seems an unlikely proposition as the exploitation of many natural resources is impractical without large capital stocks. For example, in the production of caught fish, the marginal rate of substitution, and under perfect competition the price ratio, between stocks of fresh water fish and marine fish should be independent of the number of fishingboats available. This is clearly not the case. People are not likely to put a high value on the stock of deep sea fish when they do not have boats to catch them with.If substitution is limited, technological progress might reduce the quantity of natural resource inputs required per unit of output. However, there are arguments that indicate that technical progress itself is bounded (see Pezzey, 1994; Stern, 1994). One of these (Pezzey, 1994) is that, just as in the case of substitution, ultimately the laws of thermodynamics limit the minimization of resource inputs per unit output. Stern (1994) argues that unknown useful knowledge is itself a nonrenewable resource. Technological progress is the extraction of this knowledge from the environment and the investment of resources in this activity will eventually be subject to diminishing returns.Limits to substitution in production might be thought of in a much broader way to include nonlinearities and threshold effects. This view is sometimes described as the "ecological" viewpoint on sustainability (Common and Perrings, 1992; Common, 1995) or as the importance of maintaining the "resilience" of ecological systems rather than any specific stocks or species. This approach derives largely from the work of Holling (1973, 1986). In this view ecosystems are locally stable in the presence of small shocks or perturbations but may be irreversibly altered by large shocks. Structural changes in ecosystems such as those that come about through human interference and particularly simplification, may make these systems more susceptible to losing resilience and being permanently degraded. There is clearly some substitutability between species or inorganic elements in the role of maintaining ecosystem productivity, however, beyond a certain point this substitutability may suddenly fail to hold true. This approach also asks us to look at development paths as much less linear and predictable than is implied in the CTA literature.All things considered, what emerges is a quite different approach to sustainability policy. It is probable that substitution between natural and artificial capital is limited, as is ultimately technicalchange. Additionally the joint economy-ecosystem system may be subject to nonlinear dynamics. This implies that eventually the economy must approach a steady state where the volume of physical economic activity is dependent on the maximum economic and sustainable yield of renewable resources or face decline ie. profit (or utility) maximizing use of renewable resources subject to the sustainability constraint. As in Herman Daly's vision (Daly, 1977) qualitative change in the nature of economic output is still possible. Sustainability policy would require not just maintaining some stocks of renewable resources but also working to reduce "threats to sustainability" (Common, 1995) that might cause the system to pass over a threshold and reduce long-run productivity.The notion of Hicksian income originally applied to an individual price-taking firm (Faucheux and O'Connor, 1995). However, even here it is not apparent that the myopic policy of maintaining capital intact from year to year is the best or only way to ensure the sustainability of profits into the future. If a competing firm makes an innovation that renders the firm's capital stock obsolete, the latter's income may drop to zero. This is despite it previously following a policy of maintaining its capital intact. The firm's income measured up to this point is clearly seen to be unsustainable. In fact its policy has been shown to be irrelevant to long-run sustainability. In the real world firms will carry out activities that may not contribute to the year to year maintenance of capital and will reduce short-run profits such as research and development and attempts to gain market share.10 These activities make the firm more resilient against future shocks and hence enhance sustainability.b.Prices for AggregationSupposing that the necessary separability conditions are met so that aggregation of a capital stock is possible, analysts still have to obtain an appropriate set of prices so that the value of the capital stock is a sustainability relevant value. The CTA is more or less tautological if we use the "right" prices. However, these correct "sustainability prices" are unknown and unknowable. A number of。
Coordination of Supply Chains with risk-averse agents
Coordination of Supply Chainswith Risk-Averse AgentsXianghua Gan,Suresh P.Sethi,and Houmin YanAbstract The extant supply chain management literature has not addressed the issue of coordination in supply chains involving risk-averse agents.We take up this issue and begin with defining a coordinating contract as one that results in a Pareto-optimal solution acceptable to each agent.Our definition generalizes the standard one in the risk-neutral case.We then develop coordinating contracts in three specific cases(1)the supplier is risk neutral and the retailer maximizes his expected profit subject to a downside risk constraint,(2)the supplier and the retailer each maximizes his own mean-variance trade-off,and(3)the supplier and the retailer each maximizes his own expected utility.Moreover,in case(3)we show that our contract yields the Nash Bargaining solution.In each case,we show how we can find the set of Pareto-optimal solutions,and then design a contract to achieve the solutions.We also exhibit a case in which we obtain Pareto-optimal sharing rules explicitly,and outline a procedure to obtain Pareto-optimal solutions. Keywords Capacity•Coordination•Nash bargaining•Pareto-optimality•Risk averse•Supply chain managementX.Gan(*)Department of Logistics and Maritime Studies,The Hong Kong Polytechnic University,Hung Hom,Kowloon,Hong Konge-mail:lgtxgan@.hkS.P.SethiSchool of Management,SM30,The University of Texas at Dallas,800W.Campbell Road, Richardson,TX75080-3021,USAe-mail:sethi@H.YanDepartment of Systems Engineering and Engineering Management,The Chinese University of Hong Kong,Shatin,NT,Hong Konge-mail:yan@.hkT.-M.Choi and T.C.Edwin Cheng(eds.),Supply Chain Coordination under Uncertainty,3 International Handbooks on Information Systems,DOI10.1007/978-3-642-19257-9_1,#Springer-Verlag Berlin Heidelberg20114X.Gan et al. 1IntroductionMuch of the research on decision making in a supply chain has assumed that the agents in the supply chain are risk neutral,i.e.,they maximize their respective expected profits.An important focus of this research has been the design of supply contracts that coordinate the supply chain.When each of the agents maximizes his expected profit,the objective of the supply chain considered as a single entity is unambiguously to maximize its total expected profit.This fact alone makes it natural to define a supply chain to be coordinated if the chain’s expected profit is maximized and each agent’s reservation profit is met.A similar argument holds if each agent’s objective is to minimize his expected cost.In this paper we consider supply chains with risk-averse agents.Simply put,an agent is risk averse if the agent prefers a certain profit p to a risky profit,whose expected value equals p.In the literature,there are many measures of risk aversion; see Szeg€o(2004)for examples.Regardless of the measure used,when one or more agents in the supply chain are risk averse,it is no longer obvious as to what the objective function of the supply chain entity should be.Not surprisingly,the issue of coordination of supply chain consisting of risk-averse agents has not been studied in the supply chain management literature.That is not to say that the literature does not realize the importance of the risk-averse criteria.Indeed,there are a number of papers devoted to the study of inventory decisions of a single risk-averse agent.These include Lau(1980),Bouakiz and Sobel(1992),Eeckhoudt et al. (1995),Chen and Federgruen(2000),Agrawal and Seshadri(2000a),Buzacott et al. (2002),Chen et al.(2007),and Gaur and Seshadri(2005).There also have been a few studies of supply chains consisting of one or more risk-averse u and Lau(1999)and Tsay(2002)consider decision making by a risk-averse supplier and a risk-averse retailer constituting a supply chain.Agrawal and Seshadri(2000b) introduce a risk-neutral intermediary to make ordering decisions for risk-averse retailers,whose respective profits are side payments from the intermediary.Van Mieghem(2003)has reviewed the literature that incorporates risk aversion in capacity investment decisions.While these papers consider risk-averse decision makers by themselves or as agents in a supply chain,they do not deal with the issue of the supply chain coordination involving risk-averse agents.It is this issue of coordination of supply chains consisting of one or more risk-averse agents that is the focus of this paper.That many decision makers are risk-averse has been amply documented in thefinance and economics literature;see, for example,Van Neumann and Morgenstern(1944),Markowitz(1959),Jorion (2006),and Szeg€o(2004).We shall therefore develop the concept of what we mean by coordination of a supply chain,and then design explicit contracts that achieve the defined coordination.For this purpose we use the Pareto-optimality criterion,used widely in the group decision theory,to evaluate a supply chain’s performance.We define each agent’s payoff to be a real-valued function of a random variable representing his profit,and propose that a supply chain can be treated as coordinated if no agent’s payoff can beCoordination of Supply Chains with Risk-Averse Agents5 improved without impairing someone else’s payoff and each agent receives at least his reservation payoff.We consider three specific cases of a supply chain(1)the supplier is risk neutral and the retailer maximizes his expected profit subject to a downside risk constraint,(2)the supplier and the retailer each maximizes his own mean-variance trade-off,and(3)the supplier and the retailer each maximizes his own expected utility.We show how we can coordinate the supply chain in each case according to our definition.In each case we do this byfinding the set of Pareto-optimal solutions acceptable to each agent,and then constructing aflexible contract that can attain any of these solutions.Moreover,the concept we develop and the contracts we obtain generalize the same known for supply chains involving risk-neutral agents.The remainder of the paper is organized as the follows.In Sect.2we review the related literature in supply chain management and group decision theory.In Sect.3 we introduce a definition of coordination of a supply chain consisting of risk-averse agents.In Sect.4we characterize the Pareto-optimal solutions andfind coordinating contracts for the supply chains listed as thefirst two cases.In Sect.5wefirst take up the third case using exponential utility functions for the agents,and design coordinating contracts as well as obtain the Nash Bargaining solution.Then we examine a case in which the supplier has an exponential utility followed by a linear utility.Section6provides a discussion of our results.The paper concludes in Sect.7 with suggestions for future research.2Literature ReviewThere is a considerable literature devoted to contracts that coordinate a supply chain involving risk-neutral agents.This literature has been surveyed by Cachon(2003). In addition,the book by Tayur et al.(1999)contains a number of chapters addressing supply contracts.In light of these,we limit ourselves to reviewing papers studying inventory and supply chain decisions by risk-averse agents.First we review papers dealing with a single risk-averse agent’s optimal inventory decision.Then we review articles dealing with decision making by risk-averse agents in a supply chain.Chen and Federgruen(2000)re-visit a number of basic inventory models using a mean-variance approach.They exhibit how a systematic mean-variance trade-off analysis can be carried out efficiently,and how the resulting strategies differ from those obtained in the standard analyses.Agrawal and Seshadri(2000a)consider how a risk-averse retailer,whose utility function is increasing and concave in wealth,chooses the order quantity and the selling price in a single-period inventory model.They consider two different ways in which the price affects the distribution of demand.In thefirst model,they assume that a change in the price affects the scale of the distribution.In the second model, a change in the price only affects the location of the distribution.They show that in comparison to a risk-neutral retailer,a risk-averse retailer will charge a higher price6X.Gan et al. and order less in thefirst model,whereas he will charge a lower price in the second model.Buzacott et al.(2002)model a commitment and option contract for a risk-averse newsvendor with a mean-variance objective.The contract,also known as a take-or-pay contract,belongs to a class of volumeflexible contracts,where the newsvendor reserves a capacity with initial information and adjusts the purchase at a later stage when some new information becomes available.They compare the performance of strategies developed for risk-averse and risk-neutral objectives. They conclude that the risk-averse objective can be an effective approach when the quality of information revision is not high.Their study indicates that it is possible to reduce the risk(measured by the variance of the profit)by six-to eightfold,while the loss in the expected profit is almost invisible.On the other hand,the strategy developed for the expected profit objective can only be consid-ered when the quality of information revision is high.They show furthermore that thesefindings continue to hold in the expected utility framework.The paper points out a need for modeling approaches that deal with downside risk considerations.Lau and Lau(1999)study a supply chain consisting of a monopolistic supplier and a retailer.The supplier and the retailer employ a return policy,and each of them has a mean-variance objective u and Lau obtain the optimal wholesale price and return credit for the supplier to maximize his utility.However,they do not consider the issue of improving the supply chain’s performance,i.e.,improving both players’utilities.Agrawal and Seshadri(2000b)consider a single-period model in which multiple risk-averse retailers purchase a single product from a common supplier.They introduce a risk neutral intermediary into the channel,who purchases goods from the vendor and sells them to the retailers.They demonstrate that the intermediary, referred to as the distributor,orders the optimal newsvendor quantity from the supplier and offers a menu of mutually beneficial contracts to the retailers.In every contract in the menu,the retailer receives afixed side payment,while the distributor is responsible for the ordering decisions of the retailers and receives all their revenues.The menu of contracts simultaneously(1)induces every risk-averse agent to select a unique contract from it;(2)maximizes the distributor’s profit; and(3)raises the order quantities of the retailers to the expected value maximizing (newsvendor)quantities.Tsay(2002)studies how risk aversion affects both sides of the supplier–retailer relationship under various scenario of relative strategic power,and how these dynamics are altered by the introduction of a return policy.The sequence of play is as follows:first the supplier announces a return policy,and then the retailer chooses order quantity without knowing the demand.After observing the demand, the retailer chooses the price and executes on any relevant terms of the distribution policy as appropriate(e.g.,returning any overstock as allowed).Tsay shows that the behavior under risk aversion is qualitatively different from that under risk neutrality.He also show that the penalty for errors in estimating a channel partner’s risk aversion can be substantial.Coordination of Supply Chains with Risk-Averse Agents7 In a companion paper(Gan et al.2005),we examine coordinating contracts for a supply chain consisting of one risk-neutral supplier and one risk-averse retailer. There we design an easy-to-implement risk-sharing contract that accomplishes the coordination as defined in this paper.Among these supply chain papers,Lau and Lau(1999)and Tsay(2002)consider the situation in which both the retailer and the supplier in the channel are risk averse.However,neither considers the issue of the Pareto-optimality of the actions of the agents.The aim of Agrawal and Seshadri(2000b)is to design a contract that increases the channel’s order quantity to the optimal level in the risk-neutral case by having the risk-neutral agent assume all the risk.Once again,they do not mention the Pareto-optimality aspect of the decision they obtain.Finally since our definition of coordination is based on the concepts used in the group decision theory,we briefly review this stream of literature.From the early fifties to the early eighties,a number of papers and books appeared that deal with situations in which a group faces intertwined external and internal problems.The external problem involves the choice of an action to be taken by the group,and the internal problem involves the distribution of the group payoff among the members. Arrow(1951)conducted one of the earliest studies on the group decision theory, and showed that given an ordering of consequences by a number of individuals,no group ordering of these consequences exists that satisfies a set of seemingly reasonable behavioral assumptions.Harsanyi(1955)presented conditions under which the total group utility can be expressed as a linear combination of individuals’cardinal utilities.Wilson(1968)used Pareto-optimality as the decision criterion and constructed a group utility function tofind Pareto-optimal solutions. Raiffa(1970)illustrates the criterion of Pareto-optimality quite lucidly,and discusses how to choose a Pareto-optimal solution in bargaining and arbitration Valle(1978)uses an allocation function to define Pareto-optimality. Eliashberg and Winkler(1981)investigate properties of sharing rules and the group utility functions in additive and multilinear cases.3Definition of Coordination of a Supply Chainwith Risk-Neutral or Risk-Averse AgentsIn this section we define coordination of a supply chain consisting of agents that are risk neutral or risk averse.We use concepts developed in group decision theory that deals with situations in which a group faces intertwined external and internal problems.The external problem involves the choice of an action to be taken by the group,and the internal problem involves the distribution of the group payoff among the members.In group decision problems,a joint action of the group members is said to be Pareto-optimal if there does not exist an alternative action that is at least as acceptable to all and definitely preferred by some.In other words,a joint action is Pareto-optimal if it is not possible to make one agent better off without makinganother one worse off.We call the collection of all Pareto-optimal actions as the Pareto-optimal set .It would not be reasonable for the group of agents to choose a joint action that is not Pareto-optimal.Raiffa (1970)and LaValle (1978)illustrate this idea quite lucidly with a series of examples.A supply chain problem is obviously a group decision problem.The channel faces an external problem and an internal problem.External problems include decisions regarding order/production quantities,item prices,etc.The internal problem is to allocate profit by setting the wholesale price,deciding the amount of a side payment if any,refund on the returned units,etc.Naturally,we can adopt the Pareto-optimality criterion of the group decision theory for making decisions in a supply chain.Indeed,in the risk-neutral case,the optimal action under a coordinating contract is clearly Pareto-optimal.In general,since the agents in the channel would not choose an action that is not in the Pareto-optimal set,the first step to coordinate a channel is to characterize the set.Following the ideas of Raiffa (1970)and LaValle (1978),we formalize below the definition of Pareto-optimality.Let (O ;F ;P )denote the probability space and N denote the number of agents in the supply chain,N r 2.Let S i be the external action space of agent i ;i ¼1;...;N ,and S ¼S 1ÂÁÁÁÂS N .For any given external joint action s ¼s 1;...;s N ðÞ2S ,the channel’s total profit is a random variable P s ;o ðÞ;o 2O .Let E and V denote the expectation and variance defined on (O ;F ;P ),respectively.Now we define a sharing rule that governs the splitting of the channel profit among the agents.Let Y be the set of all functions from S ÂO to R N .Definition 1.A function u ðs ;v Þ2Q is called a sharing rule if P i u i ðs ;v Þ¼1almost surely.Under the sharing rule u ðs ;o Þ,agent i’s profit is represented byP i ðs ;v ;u ðs ;v ÞÞ¼u i ðs ;v ÞP ðs ;v Þ;i ¼1;...;N :Often,when there is no confusion,we write P ðs ;v Þsimply as P ðs Þ,u ðs ;v Þas u ðs Þ,and P i ðs ;v ;u ðs ;v ÞÞas P i ðs ;u ðs ÞÞ.A supply chain’s external problem is to choose an s 2S and its internal problem is to choose a function u ðs Þ2Y .Thus the channel’s total problem is to choose a pair ðs ;u ðs ÞÞ2S ÂY .Now we define the preferences of the agents over their random profits.Let G denote the space of all random variables defined on O ;F ;P ðÞ.For X ;X 02G ,the agent i ’s preference will be denoted by a real-valued payoff function u i ðÁÞdefined on G .The relation u i ðX Þ>u i ðX 0Þ,u i ðX Þ<u i ðX 0Þand u i ðX Þ¼u i ðX 0Þindicate X is preferred to ,less preferred to ,and equivalent to X 0,respectively.It should be noted that this definition of payoff function allows for ordinal as well as cardinal utility functions.We provide following examples of payoff functions.Example 1.If agent i wants to maximize his mean-variance trade-off,then his payoff function is u i ðX Þ¼E ðX ÞÀl V ðX Þ;X 2G ,for some l >0.Example 2.Assume that agent i maximizes his expected profit under the constraint that the probability of his profit being less than his target profit level a does not exceed a given level b ;0<b b 1.Then his payoff u i can be represented as8X.Gan et al.u iðXÞ¼EðXÞ;if P X b aðÞb b;À1;if P X b aðÞ>b:&Example3.Suppose agent i has a concave increasing utility function g i:R1!R1 of wealth and wants to maximize his expected utility.Then the agent’s payoff function is u iðXÞ¼E g iðXÞ½ ;X2G.Remark1.In Raiffa(1970)and LaValle(1978),each agent is assumed to have a cardinal utility function of profit,and his objective is to maximize his expected utility.However,some preferences,such as the one in Example2,cannot be represented by a cardinal utility function.A point a2R N is said to be Pareto-inferior to or Pareto-dominated by another point b2R N,if each component of a is no greater than the corresponding compo-nent of b and at least one component of a is less than the corresponding component of b.In other words,we say b is Pareto-superior to a or b Pareto-dominates a.A point is said to be a Pareto-optimal point of a subset of R N,if it is not Pareto-inferior to any other point in the subset.With these concepts,we can now define Pareto-optimality of a sharing rule uðsÞand an action pairðs;uðsÞÞ.Definition2.Given an external action s of the supply chain,uÃðsÞis a Pareto-optimal sharing rule,ifðu1ðP1ðs;uÃðsÞÞÞ;ÁÁÁ;u NðP Nðs;uÃðsÞÞÞÞis a Pareto-optimal point of the setfðu1ðP1ðs;uðsÞÞÞ;ÁÁÁ;u NðP Nðs;uðsÞÞÞÞ;u2Y g;where u iðP iðs;uðsÞÞÞis the payoff of the i th agent.Definition3.ðsÃ;uÃðsÃÞÞis a Pareto-optimal action pair if the agents’payoffsðu1ðP1ðsÃ;uÃðsÃÞÞÞ;ÁÁÁ;u NðP NðsÃ;uÃðsÃÞÞÞÞis a Pareto-optimal point of the setfðu1ðP1ðs;uðsÞÞÞ;ÁÁÁ;u NðP Nðs;uðsÞÞÞÞ;ðs;uðsÞÞ2SÂY g:Clearly ifðsÃ;uÃðsÃÞÞis a Pareto-optimal action pair,then uÃðsÃÞis a Pareto-optimal sharing rule given sÃ.We begin now with an examination of the Pareto-optimal set in a supply chain consisting of risk-neutral agents.If an external action maximizes the supply chain’s expected profit,then it is not possible to make one agent get more expected profit without making another agent get less.More specifically,we have the following proposition.Coordination of Supply Chains with Risk-Averse Agents9Proposition1.If the agents in a supply chain are all risk neutral,then an action pairðs;uðsÞÞis Pareto-optimal if and only if the channel’s external action s maximizes the channel’s expected profit.Proof.The proof follows from the fact that in the risk-neutral case,for each s,Xu iðP iðs;uðsÞÞÞ¼XE P iðs;uðsÞÞ¼EXP iðs;uðsÞÞ¼E PðsÞ:Thus,everyðsÃ;uðsÃÞÞ2SÂY is Pareto-optimal provided sÃmaximizes E PðsÃÞ.□Since agents in a supply chain maximize their respective objectives,the agents’payoffs might not be Pareto-optimal if their objectives are not aligned properly.In this case,it is possible to improve the chain’s performance,i.e.,achieve Pareto-superior payoffs.The agents can enter into an appropriately designed contract, under which their respective optimizing actions leads to a Pareto-superior payoff.In the supply chain management literature,a contract is defined to coordinate a supply chain consisting of risk-neutral agents if their respective optimizing external actions under the contract maximize the chain’s expected profit.Then,according to Propo-sition1,a coordinating contract is equivalent to a Pareto-optimal action in the risk-neutral case.It is therefore reasonable to use the notion of Pareto-optimality to define supply chain coordination in the general case.Definition4.Supply Chain Coordination.A contract agreed upon by the agents of a supply chain is said to coordinate the supply chain if the optimizing actions of the agents under the contract1.Satisfy each agent’s reservation payoff constraint.2.Lead to an action pairðsÃ;uÃðsÃÞÞthat is Pareto-optimal.Besides Pareto-optimality of a contract,we have introduced the individual-rationality or the participation constraints as part of the definition of coordination. The constraints ensure that each agent is willing to participate in the contract by requiring that each gets at least his reservation payoff.It is clear that each agent’s reservation payoff will not be less than his status-quo payoff,which is defined to be his best payoff in the absence of the contract.Thus,we need consider only the subset of Pareto-optimal actions that satisfy these participating constraints.The reservation payoff of an agent plays an important role in bargaining,as we shall see in the next section.Now we illustrate the introduced concept of coordination by an example. Example4.Consider a supply chain consisting of one supplier and one retailer who faces a newsvendor problem.Before the demand realizes,the supplier decides on his capacityfirst,and the retailer then prices the product and chooses an order quantity.The supplier and the retailer may enter into a contract that specifies the retailer’s committed order quantity and the supplier’s refund policy for returned items.In this channel,the external actions are the supplier’s capacity selection and the retailer’s pricing and ordering decisions.These are denoted as s.The internal 10X.Gan et al.Coordination of Supply Chains with Risk-Averse Agents11 actions include decision on the quantity of commitment,the refundable quantity, and the refund credit per item.These internal actions together lead to a sharing rule denoted by uðsÞ.Once the contract parameters are determined,the agents in the supply chain choose their respective external actions that maximize their respective payoffs.Ifðs;uðsÞÞsatisfies the agents’reservation payoffs and is Pareto-optimal, then the channel is coordinated by the contract.The definition of coordination proposed here allows agents to have any kind of preference that can be represented by a payoff function satisfying the complete and transitive axioms specified earlier.For example,all of the seven kinds of preferences listed in Schweitzer and Cachon(2000),including risk-seeking preferences,are allowed.Since often in practice,an agent is either risk neutral or risk averse,we restrict our attention to only these two types.Remark2.Our definition applies also to a T-period case.For this,we define the payoff function of player i asu iðP1iðsÃ;uÃðsÃÞÞ;P2iðsÃ;uÃðsÃÞÞ;ÁÁÁ;P T iðsÃ;uÃðsÃÞÞÞ:G T!R1;where P t iðsÃ;uÃðsÃÞÞis agent i’s profit in period t.4Coordinating Supply ChainsEach Pareto-optimal action pairðs;uðsÞÞresults in a vector of payoffsðu1ðP1ðs;uðsÞÞÞ;ÁÁÁ;u NðP Nðs;uðsÞÞÞÞ;where u iðP iðs;uðsÞÞÞis the payoff of the i th agent.LetC¼fðu1ðP1ðs;uðsÞÞÞ;ÁÁÁ;u NðP Nðs;uðsÞÞÞÞjðs;uðsÞÞis Pareto-optimal;ðs;uðsÞÞ2SÂY g;denote the set of all Pareto-optimal payoffs,and let F&C be the subset of Pareto-optimal payoffs that satisfy all of the participation constraints.We shall refer to F as Pareto-optimal frontier.We will assume that F is not empty.To coordinate a supply chain,thefirst step is to obtain the Pareto-optimal frontier F.If F is not a singleton,then agents bargain to arrive at an element in F to which they agree.A coordinating contract is one with a specific set of parameters that achieves the selected solution.A contract is appealing if it has sufficientflexibility.In Cachon(2003),a coordinating contract is said to beflexible if the contract,by adjustment of some parameters,allows for any division of the supply chain’s expected profit among the risk-neutral agents.This concept can be extended to the general case as follows.12X.Gan et al. Definition 5.A coordinating contract isflexible if,by adjustment of some parameters,the contract can lead to any point in F:We shall now develop coordinating contracts in supply chains consisting of two agents:a supplier and a retailer.We shall consider three different cases.In each of these cases,we assume that agents have complete information.In Case1,the supplier is risk neutral and the retailer has a payoff function in Example2,i.e.,the retailer maximizes his expected profit subject to a downside constraint.In Case2, the supplier and the retailer are both risk averse and each maximizes his own mean-variance trade-off.In Case3,the supplier and the retailer are both risk averse and each maximizes his own expected concave utility.We consider thefirst two cases in this section and the third case in Sect.5.In each case,let us denote the retailer’s and the supplier’s reservation payoffs as p r r0and p s r0,respectively.Wefirst obtain F and then design aflexible contract that can lead to any point in F by adjusting the parameters of the contract.4.1Case1:Risk Neutral Supplier and Retailer Averseto Downside RiskWe consider the supplier to be risk neutral and the retailer to maximize his expected profit subject to a downside risk constraint.This downside risk constraint requires that the probability of the retailer’s profit to be higher than a specified level is not too small.The risk neutrality assumption on the part of the supplier is reasonable when he is able to diversify his risk by serving a number of independent retailers,which is quite often the case in practice.When the retailers are independent,the supply chain can be divided into a number of sub-chains,each consisting of one supplier and one retailer.This situation,therefore,could be studied as a supply chain consisting of one risk-neutral supplier and one risk-averse retailer.We say that an action pairðs;uðsÞÞis feasible if the pair satisfies the retailer’s downside risk constraint.We do not need to consider a pairðs;uðsÞÞthat is not feasible since under the pair the retailer’s payoff isÀ1and he would not enter the contract.We denote PðsÞ,P rðs;uðsÞÞ,and P sðs;uðsÞÞas the profits of the supply chain,the retailer,and the supplier,respectively.Other quantities of interest will be subscripted in the same way throughout the chapter,i.e.,subscript r will denote the retailer and subscript s will denote the supplier.Then we have the following result.Theorem1.If the supplier is risk neutral and the retailer maximizes his expected profit subject to a downside risk constraint,then a feasible action pairðs;uðsÞÞis Pareto-optimal if and only if the supply chain’s expected profit is maximized over the feasible set.Proof.ONLY IF:It is sufficient to show that if E PðsÞis not maximal over the feasible set,thenðs;uðsÞÞis not Pareto-optimal.。
CH05 相关模型(三)
rt
N (d )
2
–ቤተ መጻሕፍቲ ባይዱ
d
1
ln V / X
r y / 2 t
2
t
d d
2 1
t
三、說明
– V：未開發資源的當前市場價值，根據開發 獲得現金收益的滯後期折現 – X：資源開發成本的現值 – r：對應於相應期權壽命週期的無風險利率 – y：每年自資源開發中，所獲得的淨現金流 量，根據市場價值的百分比表示 – ：標的資源市場價值的方差 – t：保有資源開發權得時間，或者預期資源 將被消耗殆盡的時間
二、模型
–穩定增長階段公司 –高增長階段公司
P
0
BV
0
P BV ROE
支付比率
1 g (1 g) 1 1 r
n n
r g
支付比率 (1 g) 1 g ( r g )( 1 r )
n n n n n
三、說明
– g ：前n年的異常增長率 – gn：n年後的永續增長率
四、適用性
–製造業有存量資產 –不當評估價值
五、注意事項
第三節 價格/銷售收入比率 （基礎財務變量模型）
一、意義
–價格/銷售收入比率，即P/S，可以用股息 折現模型中所決定價值的相同基礎財務 指標顯現。
二、模型
–穩定增長階段公司
2
四、適用性
–起步公司 –產品價值大
五、侷限性
–考慮技術變化 –基本分析
一、意義
–價格/收益比率，即市盈率，可以用股息 折現模型中所決定價值的相同基礎財務 指標顯現。
二、模型
ch5 Fixed income securities课后习题答案
ANSWERS TO QUESTIONS: 1. a b. c. d. e. Indenture - the contract between the issuing firm and the lenders in a debt obligation, specifying the nature of the debt issue, the manner in which the principal must be paid, and the restrictions (covenants) placed on the firm by the lenders. Covenants – the indenture lists any restrictions placed on the firm by the lenders. These restrictions are called covenants, and the firm must satisfy them to keep from defaulting on its obligations. Trustee - the bondholders representative in a public debt offering. The trustee is responsible for monitoring the borrower's compliance with the terms of the indenture. Call feature - a provision that permits the bond issuer to retire the obligation prior to its maturity. Sinking fund - a method of providing for the gradual retirement of a bond issue. The sinking fund requirement can be met by depositing a certain amount of money annually in a sinking fund account. Alternatively, the firm can either purchase a portion of the debt each year in the open market or, if the debt is callable, use a lottery technique to determine which actual bonds will be called and retired each year. Conversion feature - a provision that allows the holder to exchange the bond for shares of the company's common stock at the option of the holder. Coupon rate - the annual rate of interest paid to bondholders. It is expressed as a percentage of par value. Yield to maturity - a bond is the discount rate that equates the present value of all expected interest payments and the repayment of principal from a bond with the present bond price. Yield to call – for bonds with a call feature, the expected yield to call can also be computed. This is done by replacing the maturity value by the call price and the number of years until maturity by the number of years until the company can call the bond.
Ch05HullFundamentals9thEd
Investment assets are assets held by many traders purely for investment purposes (Examples: gold, silver) Consumption assets are assets held primarily for consumption (Examples: copper, oil)
Fundamentals of Futures and Options Markets, 9th Ed, Ch 5, Copyright © John C. Hull 2016
13
Valuing a Forward Contract
A forward contract is worth zero (except for bidoffer spread effects) when it is first negotiated Later it may have a positive or negative value Suppose that K is the delivery price and F0 is the forward price for a contract that would be negotiated today
Fundamentals of Futures and Options Markets, 9th Ed, Ch 5, Copyright © John C. Hull 2016
9
When Interest Rates are Measured with Continuous Compounding
Fundamentals of Futures and Options Markets, 9th Ed, Ch 5, Copyright © John C. Hull 2016
CH5 国际商法-ray·august奥古斯特
Regional Investment Policies
Nations in a particular region may agree to general standards for investment in their region. One such region is the Association of Southeast Asian Nations (ASEAN). This region is a leading recipient of foreign direct investment (FDI). ASEAN countries act individually and collectively to attract investment. Exhibit 5-3 shows a sample of the investment incentives implemented by ASEAN countries
5-10
© 2009 Pearson Education, Inc publishing as Prentice Hall
Screening Investment Proposals
There are many varied criteria by which countries screen proposals. Some examples of proposals that will be screened include:
5-11
© 2009 Pearson Education, Inc publishing as Prentice Hall
Tiered Screening and Special Screening of Proposals
公司理财精要版原书第12版中文Ch05估值导言Calculator课件
• 你想开始为你女儿的大学教育存钱，你估计她 在17年后需要15万美元。如果你自信你可以每 年赚8%，你现在需要投资多少？
▪ N = 17; I/Y = 8; FV = 150,000
▪ CPT PV = -40,540.34
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution with
现值
• 我今天需要投资多少才能在未来得到一 些钱？
▪ FV = PV(1 + r)t ▪ 重新整理得 PV = FV / (1 + r)t
• 当我们讨论折现时，我们指的是找出未 来金额的现值
• 当我们谈论某物的“价值”时，我们谈论
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution with
现值 – 重要关系一
• 对于给定的利率，时间越长，现值越低
▪ 5年后500美元的现值是多少？十年？折现率 是10%
▪ 5年: N = 5; I/Y = 10; FV = 500 CPT PV = -310.46
▪ 10年: N = 10; I/Y = 10; FV = 500 CPT PV = -192.77
快速测验 – 第二部分
• 现值和终值之间的关系是什么？ • 假设3年后你需要15000美元。如果你每年能赚
6%，你现在需要投资多少？
• 如果你能以8%的利率投资，你会投资更多还是 更少？多少钱？
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• Non-Life Companies
– Invest premiums not paid back to policyholders for loss – Hedge against potential claims
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Bodie • Kane • Marcus
Essentials of Investments
Fourth Edition
Investment Policy: Active or Passive
Active Trying to secure better than average performance Must balance returns and costs Passive Trying to get average returns rather than do better than the market Mix of Passive and Active
2
Bodie • Kane • Marcus
Essentials of Investments
Fourth Edition
Overview of the Investment Process
• • • • • Specify objectives Identify constraints Formulate an investment policy Monitor performance Reevaluate and modify portfolio as determined from monitoring
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© 2001 The McGraw-Hill Companies, Inc. All rights reserved.
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Bodie • Kane • Marcus
Essentials of Investments
Fourth Edition
Specifying Objectives: Personal Trusts and Mutual Funds
7
Bodie • Kane • Marcus
Essentials of Investments
Fourth Edition
Specify Objectives: Banks
• Sources of funds: deposits and borrowed funds • Investment of funds: predominately in loans and fixed income securities • Active in the securitized loan and asset markets • Not active in equity except in the Trust Function
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Irwin / McGraw-Hill
© 2001 The McGraw-Hill Companies, Inc. All rights reserved.
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Bodie • Kane • Marcus
Essentials of Investments
Fourth Edition
Specifying Objectives: Pension Funds and Endowments
Irwin / McGraw-Hill
© 2001 The McGraw-Hill Companies, Inc. All rights reserved.
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Bodie • Kane • Marcus
Essentials of Investments
Fourth Edition
Investment Policy: Asset Allocation Decision
• Personal Trusts
– Determined by the individual for whom the funds are being managed
• Mutual Funds
– Varies with type of fund – Detailed in the prospectus
1
Bodie • Kane • Marcus
Essentials of Investments
Fቤተ መጻሕፍቲ ባይዱurth Edition
Chapter 5
Investors and the Investment Process
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© 2001 The McGraw-Hill Companies, Inc. All rights reserved.
Example - an all stock mutual fund would want nearly 100% in stock Sector or Region allocations
Irwin / McGraw-Hill
© 2001 The McGraw-Hill Companies, Inc. All rights reserved.
Tax Considerations - special considerations related to tax position of the investor Unique Needs- special considerations related to the underlying investors Diversification requirements related to employment
Individual - depends on life cycle
Younger Older Higher equity 75% Lower safe assets 25% Lower equity 40% Higher safe assets 60%
Institutional - depends on objectives
Irwin / McGraw-Hill
© 2001 The McGraw-Hill Companies, Inc. All rights reserved.
8
Bodie • Kane • Marcus
Essentials of Investments
Fourth Edition
Investor Constraints
6
Bodie • Kane • Marcus
Essentials of Investments
Fourth Edition
Specifying Objectives: Insurance Companies
• Life Companies
– Investments are hedged against potential claims of policy holders
Liquidity - speed and ease with which as asset can be converted into cash Investment Horizon - the planned liquidation date Regulations - specific regulations that may apply to the investor Prudent Man Rule Mutual Fund Diversification Charitable contribution limits
Irwin / McGraw-Hill
© 2001 The McGraw-Hill Companies, Inc. All rights reserved.
3
Bodie • Kane • Marcus
Essentials of Investments
Fourth Edition
Specifying Objectives: Individual Investors
Shelter Options • Deferral of taxes on capital gains • Tax Deferred Retirement Plan
– IRA – 401(k) – Taxes are paid on the income from retirement and not on returns from investment
Irwin / McGraw-Hill
© 2001 The McGraw-Hill Companies, Inc. All rights reserved.
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Bodie • Kane • Marcus
Essentials of Investments
Fourth Edition
Investor Constraints
Irwin / McGraw-Hill
© 2001 The McGraw-Hill Companies, Inc. All rights reserved.