investment decision under uncertainty: choice theoretic approaches

1. investment decision under uncertainty: choice theoretic approaches Andy Wibisono (37407048) Marcell Wu (37407061) Thresia Hilda (37408023) Felix Thio (37408035) Nikken Nuartiana (37408037) Amanda Fabiola (37408044)

2. Irving Fisher • Theory of investment decision

3. Interpretation and Reformulation The time preference function for the j-th individual may be denoted: present consumption future consumption

4. It is useful to distinguish three different categories within the opportunity set: • endowment, is the individual’s initial position. • financial opportunities, and • productive opportunities

6. investment • a rate of exchange between units of present consumption (present dollars) and of future consumption (future dollars) can be expressed as

7. In figure 1 the financial opportunities facing the investor are shown by the "market line" MM’ through Y. • along this market line wealth equals a constant, so that the market line is a budget or wealth constraint.

8. the time preference optimum for the individual under pure exchange (financial opportunities only) is M* • at the interest rate r he seeks to invest (lend) the amount

9. under pure exchange the social totals of present and of the future consumption and are conserved, while the social total of investment is zero (for each borrower there is a lender).

10. The basic equations under pure exchange: time-preference function wealth constraint, or financial opportunities

11. Time-preference optimum Conservation equations The social total of investment is zero, as required for pure exchange.

12. Figure II

13. In figure II, the individual investor attains his utility optimum at X* . • The productive investment is and he borrows to replenish current consumption.

14. The elements (Po,Pi) of the “productive solution” P* appear as variables : Time-preference function wealth constraint, or financial opportunities. Time-preference optimum Productive opportunity set Productive optimum

15. Then, it represent attainment of maximum wealth or “present value” Conservation equations The social total of current investment :

16. in figure II, the individual investor attains his utility optimum at X* by a two step procedure. • first, he moves from his endowment Y along his productive opportunity locus PP to his productive optimum P*. • The productive investment is and he borrows to replenish current consumption.

17. Figure II

18. The elements (Po,Pi) of the “productive solution” P* appear as variables : Time-preference function wealth constraint, or financial opportunities. Time-preference optimum Productive opportunity set Productive optimum

19. Then, it represent attainment of maximum wealth or “present value” Conservation equations The social total of current investment : • We specify : • Firms do not consume • Firms have null endowments • All productive opportunity appertain to firms

20. Figure III

21. With the introduction of firms, the equation system may be represent : Time-preference fuction Wealth constraint With no “equity” funds, the effect of profitable investment is an increment ef to the equity in time “1” Time-preference optimum Productive opportunity set Productive optimum

22. The productive decisions are all made by the firms : Firm’s Financial Distributions Since the firm does not consume, it must distribute its productive gross earnings, q1. this amount is divided between repayment of debt and equity income to owners. Conservation equations

23. An alternative form of the wealth of financial constraints is also useful. Po = price of c0 P1 = price of c1 And if Co is taken as numeraire, we got : Po = 1 and P1 = 1/(1+r). Then : And after dividing through by (1+r), equation (6”) becomes : Wealth of the firm, is the sum of the values of the debt and equity.

24. II. CHOICE-THEORETIC APPROACHES TO INVESTMENT DECISION UNDER UNCERTAINTY A model containing the following features : a. Objects of choice (commodities), and decision-making units (economic agent) b. A preference function ordering such objects, for each economic agent c. An opportunity set, for its agent, which is equivalent to specifying the constraints upon the agent’s range of choice. d. Balancing or conservation equations, which specify the social interactions among the individual decisions. The most direct theoretical formulation of this decision is the Asset-preference approach. This postulates that asset themmselves are the desired objects of choice.

25. Disadvantages : • That assets are clearly not the elemental desired objects. • Will reappear below in connection with each of the various types of assets cannot be assumed fixed, even under pure exchange. The approach currently most popular in the ananlysis of investment decision under uncertainty postulates that the fundamental objects of choice, standing behind the particularities of individual asset, are the mean and the variability of future return – where variability refers to probabilistic rather than chronological fluctuation.

26. III. THE MEAN, VARIABILITY APPROACH The mean, variability approach to investment decision under uncertainty selects as the objects of choice expected returns and variability of returns from investment.

27. Variability approach have concentrated upon the problem of portfolios, i.e., holdings of financial assets (securities)

28. A specification of a concave-downward utility-of-income v(X) function shown in Figure VI

29. VI. THE STATE-PREFERENCE APPROACH

31. All investors adapt their subjective marginal rates of time preference to the market rate of interest is the following: marginal rate of time and state preference to the market discount rate. • Optimum requires adjusting the marginal personal rate of time preference to the objective market rate.

32. The Final elements in the choice system are the conservation. These take on almost trivially simple form; in each separate time-state, the total social endowment must be conserved (under pure exchange)

33. Time and state Preference Function Wealth Constraint

34. THIS FORMULATION EMPHASIZES THAT UTILITY DEPENDS UPON THE SUBJECTIVE PROBABILITY ESTIMATES: Conservation equation Optimum Condition

35. Example: each individual has an endowment distributed as fellow: 100 busherls of present corn (Y0) and contingent claims to the future corp Y1a= 150 and y1b= 50. Thus, the individual is entitled to 150 bushels if state-a obtains, but only 50 bushels if state b obtains- only these two states, regarded as equally probable, being consided possible for the future corp. In a pure-exchange situation, it is impossible to change these endowments by planting seed, carry-over of corp, or ‘consumption of capital”.

36. Relation defining the riskless discount rate in terms of more basic time and risk exchange: This following immidiately from P1 = P1a + P1b. That is, the price of a riskless holding is simply the sum of the prices of a corresponding holding for each possible contingency.

37. The Generatization to T times and S states, it is possible in a few sentences to sum up the main nature of the result yielded by the time-and state preference approach. The discount rates are determined by the interaction of individual of individual attempts move to preferred time and state consumption combination by productive and financial transformation. • The equilibrium depend upon composition of endowments among individuals, states, and times

38. V. RISK AVERSION AND THE UNIQUENESS ASSUMPTION Ordinary definition of Risk Aversion: “Given an initial combination along the certainty line, a fair gamble would not be accepted.” Consideration to be examined further in this section: whether some types of behaviour that seem to violate risk aversion can be rationalized in terms of state-preference approach

39. A Family man vs. A Bachelor Behaviour explanation : Their consumption opportunity contingent upon their death do not have the same appeal. • The more general consideration : We have to distinguish between true gambles and natural hazards. • A particular individual might weight his present choices in such a way as to have more income in depression than in prosperity.

41. We would observe risk-taking at fair odds in the sense that the preferred state distributions would not be along the certainty line. • That is, we would have differing conditional utility-of-income functions v1a(c1a) and v1b(c1b). • We can find the utility of any prospect (c1a, c1b; πa, πb) via the expected-utility theorem: U (c1a, c1b; πa, πb) = πa v1a(c1a) + πb v1b(c1b)

42. The marginal utilities of income in state a are unaffected by the level of consumption available for state b, and vice versa. • The equilibrium condition: • In the hazard situations people will be inclined to take risks. The “risk” is undertaken because quantitative equality of incomes in the two states does not properly balance the marginal utility.

43. The state-preference approach leads to a generalized concept which might be called “conservative behaviour” – of which ordinary risk aversion in the sense of minimizing variability of outcome is only a special case.

44. VI. CONCLUDING REMARK One surprising aspect of the time-and-state preference model is that it leads to a theory of decision under uncertainty while entirely excluding the “vagueness” we usually associate with uncertainty.

45. The Expected Utility Theorem • The Equivalence of Nulls  Since we cannot do worse than zero in either state, a title or claim to zero in a particular state is worthless. Thus :

47. The expected-utility theorem can then be used with the scales to calculate the over-all preference ordering of any income distribution over these states.

48. T H A N K Y O U . . . .