B.  Risk Analysis

1.  Concepts

a.  Certainty - only one possible outcome, known precisely

b.  Risk - more than one possible outcome, probability of outcome known

c.  Uncertainty - more than one possible outcome, probabilities unknown

d.  Strategy - alternative courses of action that can be undertaken

e.  States of nature - conditions in future that have an effect on the outcome of a strategy

f.  Payoff matrix - shows possible outcomes of each strategy for different states of nature

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2.  Measuring risk

• Probability - the chance or odds that an event will occur

• Probability distribution - list of all possible outcomes and the probability they occur

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a.  Expected value

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b.  Standard deviation

• Use as the measure of risk

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c.  Coefficient of variation

• Allows different situations to be compared

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3.  Utility and risk preference

• Need to look at utility associated with monetary outcomes

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• Risk averter - choose less risky project if expected values are the same

• Risk seeker - choose more risky project

• Risk neutral - indifferent

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4.  Adjusting the valuation model for risk

• Value of firm:

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a.  Risk-adjusted discount rate

• Use trade off between risk and return

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b.  Certainty-equivalent approach

• Certainty-equivalent - the certain sum that yields the same utility as the risky sum

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• Adjust valuation model accordingly

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5.  Decision trees

• Shows sequence of possible decisions and expected outcomes under different states of nature

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6.  Decision making under uncertainty

a.  Maximin criterion

• Determine worst possible outcome of each strategy

• Choose strategy the gives the best of the worst possible outcomes

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b.  Minimax regret criterion

• Choose strategy that minimizes the maximum opportunity cost (regret) of the wrong decision

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7.  Information and risk

a.  Asymmetric information

• One party to a transaction has more information than another

Ex. - Used cars

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• Adverse selection - lower quality drives out higher quality

Ex. - Insurance

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• Can be dealt with by providing more information or guarantees

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b.  Moral hazard

• More risky behavior undertaken when there is insurance

• Insurance reduces the loss from risky behavior

Ex. - Auto insurance, life insurance

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• Insurance companies may require certain precautions be taken

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c.  Principal-agent problem

• Principals - owners of a company

• Agents - managers of the company

• Separation between ownership and management in a corporation

• Interests of the two may differ

Ex. - Takeover bids

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• Golden parachutes - financial payments to executives if they are forced out as a result of a takeover

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d.  Auctions

(1)  English auction

• Sold to highest bidder

• Sequential, ascending bid auction

• May not get maximum bid (reservation price)

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(2)  First-price sealed bid auction

• Bids made secretly, highest bidder wins

• More likely to get maximum bid

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(3) Second-price sealed bid (Vickrey) auction

• Bids made secretly, highest bidder wins but pays amount of second highest bid

• Has same effect as English auction

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(4) Dutch auction

• Starts at a high price, price lowered until someone accepts

• Descending bid auction

• Has same effect as first-price sealed bid auction

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• Winners Curse - overpaying for an item by placing the winning bid

- More likely in first-price sealed bid and Dutch auctions - less information than in English auction