1. Choice under uncertainty Assistant professor Bojan Georgievski PhD 1

2. 2 1.Describing Risk Probability Expected value Variability Decision Making

3. 2.Preferences towards risk Different preferences toward risk 3

4. 3.Reducing Risk Diversification Insurance Additional information 4

5. 4.The demand of risky assets Assets Asset returns The trade –off between Risk and Return The investor Choice Problem 5

6. Risk is the potential that a chosen action or activity (including the choice of inaction) will lead to a loss (an undesirable outcome ) Economic risks can be manifested in lower incomes or higher expenditures than expected 6

7. In business we are forced to make decisions involving risk— that is, where the consequences of any action we take is uncertain due to unforeseeable events. 7

8. Analyzing the Problem—Preliminary Steps Listing the available alternatives, not only for direct action but also for gathering information on which to base later action; Listing the outcomes that can possibly occur (these depend on chance events as well as on the decision maker’s own actions); Evaluating the chances that any uncertain outcome will occur; and Deciding how well the decision maker likes each outcome. 8

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10. Probability is a numerical measure of the likelihood of an event occurring 10

11. Objective versus Subjective Probabilities Repeatable experiments (tossing a die, flipping a coin) generate objective probabilities. Non-repeatable experiments necessarily involve assigning hypothetical or subjective probabilities to particular outcomes. 11

12. According to the subjective view, the probability of an outcome represents the decision maker’s degree of belief that the outcome will occur. 12

13. The following gives the subjective view of a manager concerning the probability distribution for the first year’s outcome of a new product launch. 13

14. Expected value In probability theory, the expected value (or expectation, mathematical expectation, EV, mean, or the first moment) of a random variable is the weighted average of all possible values that this random variable can take on 14

15. Computing Expected Value or E(v) Suppose the decision maker faces a risky prospect than has n possible monetary outcomes, v1, v2,..., vn, predicted to occur with probabilities p1, p2,..., pn. Then the (monetary) expected value is found by: E(v) for the new product launch is given by 15

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17. 17 Expected value of the drilling option

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19. Our next decision tree will take into account three (3) risks affecting the profits derived from drilling: The cost of drilling—which depends on the depth at which oil is found (or not found); The amount of oil discovered; and The price of oil. 19

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21. Expected Profit Drilling at 3,000 Feet At node D (drilling at 3,000 feet, 5,000 barrels discovered), expected profit is equal to: (0.2)(700) + (0.5)(0.3)(150)=$360 thousand But we might have discovered 8,000 barrels or 16,000 barrels by drilling at 3,000 feet. Thus at node E expected profit is equal to $636 thousand and at node F $1,372 thousand. Thus the expected profit of drilling at 3,000 feet is calculated by: (0.15)(360) + (0.55)(636) + (0.3)(1,372) = $815.4 thousand 21

22. Now we just multiply the expected value of each outcome (find oil at 3,000 feet, find oil at 5,000 feet, and not find oil) by its probability and sum together. Thus we have: (0.13)(815.4) + (0.21)(353.8) + (0.66)(-400) = -$83.7 thousand 22

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24. R & D Decision 24

25. Let G denote the biogenetic approach and C is the biochemical approach. The expected profit (π) of the 2 approaches is calculated as follows: 25

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28. Risk Aversion 28

29. A person who prefers a certain income to a risky job with the same income is described as being risk averse A person who is risk neutral is indifferent between a certain income and an uncertain income with the same expected value Risk premium is the amount of money that risk averse person would pay to avoid risk 29

30. Reducing risk Diversification Insurance The value of information 30

31. Thank You For Your Time and Consideration!