fin5b - Portfolio Tools 1 Econ 333 Spring 08 1 Portfolio...

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Econ 333 Spring 08 1 Portfolio Tools 1
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Econ 333 Spring 08 2 Portfolio Tools 1 Before one turns to modeling asset pricing it is essential to understand the determinants of the demand for securities of various risk classes (Individuals demand securities (in exchange of current purchasing power) in their attempt to redistribute income across time and states of nature). When talking of the “risk” of an investment, people generally have in mind uncertainty in the future cash-flow stream: much lower payments may be received in some states than in others. Thus cash flow in any future period is a random variable. Consider the following investments: (Table 1) 1,600 1,050 -1000 Investment 3 1,600 500 -1000 Investment 2 1,200 1,050 -1000 Investment 1 Asset 2 Asset 1 State probab. π 1 = 2 = 1/2 Value at t =1 Cost at t=0
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Econ 333 Spring 08 3 Portfolio Tools 1: Concept of Dominance Investment 3 dominates investments 1 and 2 in the sense that it pays as much in all states of nature and strictly more in at least one state. This refers to the state-by-state dominance , the strongest form of dominance. Without any qualification, a rational individual should prefer investment 3 to the two others i.e. the typical individual desires more rather than less of the consumption goods these payoffs allow to buy. When using dominance, the choice problem is obvious and in some sense the issue of risk is irrelevant. But this concept is incomplete: Comparing investment 2 and 3, neither dominates the other. The concept of risk enters necessarily. Investment 2 and 3 are comparatively riskier than investment 1: 3 dominates 1 BUT preference for smooth consumption implies that the large variation associated with 3 is undesirable in itself. These comparisons can alternatively, and often more conveniently, be represented if investments are described in terms of their performance on a per dollar basis: Usefulness of state contingent rates of return (ROR).
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Econ 333 Spring 08 4 Portfolio Tools 1: Concept of Dominance Table 2: State contingent RORs Once again, all rational individuals should prefer investment 3 to 1 and 2. But the fact that 2 is riskier than 1 doesn’t
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This note was uploaded on 04/01/2008 for the course ECON 3330 taught by Professor Mbiekop during the Spring '08 term at Cornell University (Engineering School).

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fin5b - Portfolio Tools 1 Econ 333 Spring 08 1 Portfolio...

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