Econ 4010 Lecture 7

Econ 4010 Lecture 7 - 5. Uncertainty Expected...

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<Lecture 7> 5. Uncertainty We have so far assumed that prices, incomes, and other variables are known with certainty. However, many of the choices that people make involve considerable uncertainty. Sometimes we must choose how much risk to bear. To solve this problem, we must examine the ways that people can compare and choose among risky alternatives. In order to compare the riskness of alternative choices, we need to quantify risk. To describe risk quantitatively, we begin by listing all the possible outcomes of a particular action or event, as well as the likelihood that each outcome will occur: Probability. Probability is used in calculating two measures that help us describe and compare risky choices. Expected Value Probability-weighted average of the payoffs associated with all possible outcomes Suppose that you are considering investing in a company that explores for offshore oil. If the exploration effort is successful, the company's stock will increase form $30 to $40 per share; if not, the price will fall to $20 per share. Possible Outcomes: 1. Success and $40 per share price 2. Failure and $20 per share price Probability: 1. 1/4 2. 3/4 E.V. = Pr[Success]*Payoff[Success] + Pr[Failure]*Payoff[Failure] = (1/4)($40) + (3/4)($20) = $25 E(X) = P(X 1 )X 1 + P(X 2 )X 2 + … + P(X n )X n Variability Extent to which possible outcomes of an uncertain event differ Measures of variability: Standard deviation and Variance (the square of the standard deviation) Standard Deviation: Square root of the average of the squares of the deviations of the payoffs associated with each outcome from their expected values Suppose you are choosing between two sales jobs. The first is based entirely on commission. There are two equally likely payoffs for this job: $2000 (successful sales) and $1000 (less successful). Outcome Pr. Payoff ($) E(X) Deviation D. Squared Weighted Average D. S. Standard Deviation 1st .5 2,000 1,500 + 500 250,000 250,000 500 2nd .5 1,000 - 500 250,000 The second is salaried. $1510 (99%) and $510 (1%, the company will go out of business) Outcome Pr. Payoff ($) E(X) Deviation D. Squared Weighted Average D. S. Standard Deviation 1st .99 1,510 1,500 + 10 100 9,900 99.4987 2nd .01 510 - 990 980,100 1
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In this case, the second job is much less risky than the first, because the standard deviation of the incomes is much lower. Q1. Why is the variance a better measure of variability than the range?
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This note was uploaded on 03/31/2009 for the course ECON 4010 taught by Professor Cheng during the Spring '09 term at USC.

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Econ 4010 Lecture 7 - 5. Uncertainty Expected...

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