This preview shows page 1. Sign up to view the full content.
Unformatted text preview: Risk Management Decisions Risk Management Decisions Including risk management costs in the total cost of risk means that we have defined a situation of risk as one that results in only costs (no benefits) to the individual or firm This means that we should make risk management decisions to minimize the cost of risk TCOR TCOR Total cost of risk includes: E(direct loss) E(indirect loss) Costs of risk management Costs associated with uncertainty Cost of Uncertainty? Cost of Uncertainty? Discomfort or worry at being in a situation of uncertainty (riskaverse individuals) Real (opportunity) costs of being in a situation of uncertainty (even if not riskaverse) May need to hold more cash reserves Contractual terms are worsened May miss opportunities for increased earnings Increased uncertainty affects contractual terms with managers, workers, suppliers, customers, creditors Divert attention to managing risks Fail to gain outside resources needed Relate to our Usual Objectives Relate to our Usual Objectives Risk management decisions should be made using the same objectives as in other decisions: Maximize the utility of an individual Maximize the value of a firm Maximize the welfare of society Individual Utility = (Hypothetical) Bliss Point – TCOR Firm Value = (Hypothetical) Maximum Value – TCOR Social Welfare = (Hypothetical) Max Welfare – TCOR Normative Models of Decision-making Normative Firms: Maximize Expected Value Maximize ΣtE(Revenuet-Costt) Maximize (1 + r)t (1 Individuals: Maximize Expected Utility Maximize ΣtE(U(Wealtht)) Maximize (1 + r)t (1 Value of a Firm Value of a Firm Managers should make risk management decisions to maximize the value of the firm Value of the firm = the discounted stream of expected “net cash flows” or “profits” (revenues minus costs) This is the expected value of the firm to its shareholders (the owners of the firm) Implications for Corporate Risk Implications for Corporate Risk Management Managers should make risk management Managers decisions to maximize the expected discounted value of net cash flows discounted Risk Aversion and Corporations Risk Aversion and Corporations We should not expect (large) corporations to behave in a risk averse manner, even if the individual owners of the corporation are risk averse Firms should not try to reduce uncertainty for its own sake Shareholder diversification reduces risk Shareholder diversification potentially substitutes for risk management to reduce the cost of uncertainty to shareholders Example: Diversification Example: Diversification
$1000 investment: 50% chance of $2000 (100% gain) 50% chance of $500 (50% loss) Consider 10 (independent) $100 investments with same payoff structures: 50% chance of $200 50% chance of $50 What is E(payoff) and Variance(payoff) to the investor in each situation? Math: Var(aX) = a2Var(X) Var(X/10) = Var(X)/100 10Var(X/10) = Var(X)/10 Uncertainty can be Costly Uncertainty can be Costly
V = Σ E[Revenue – Cost ] t t t t (1 + r) Uncertainty can reduce firm value: Lost investment opportunities Lost productivity Increased bankruptcy probability Affects contractual terms with Managers Workers Suppliers Customers Creditors These will reduce E(Revenue) or increase E(Cost) Uncertainty Costs for a Firm Uncertainty Costs for a Firm The cost of uncertainty will vary with: The amount of uncertainty faced The characteristics and situation of the firm Uncertainty costs are associated with the possibility of losses that are large relative to a firm’s ability to bear losses Risk Aversion Risk Aversion
A risk averse person prefers a known amount of wealth to a risky situation with the same expected value of wealth
A risk averse person would not accept a “fairodds” gamble: 50% chance of winning $100 50% chance of losing $100 Expected Utility Theory Expected Utility Theory Individuals maximize utility Utility depends on wealth (money) For risk averse individuals utility is increasing in wealth, but increases by less than one unit with a one unit increase in wealth If wealth is uncertain (e.g. individuals face a possible loss) individuals maximize the expected value of utility Diminishing marginal utility of wealth Risk Aversion and Utility Risk Aversion and Utility
Utility U(Wealth) Wealth Expected Utility: Example Expected Utility: Example
U(Wealth) = (Wealth)1/2 Risky situation: Initial wealth: $500 Face potential loss of $400 Probability of loss = 0.2
Expected Loss: .2($400) = $80 Expected Wealth: .8($500) + .2($100) = $420 Example, cont. Example, cont.
U(Wealth) = (Wealth)1/2 U(Initial wealth) = U($500) = U(Wealth if loss) = U($100) = Expected Utility: .8($500)1/2 + .2($100)1/2 = Utility Expected Utility Expected Utility
W0 = 500 L = 400 pL = .2 100 500 Wealth Expected Utility Expected Utility
Utility U(420) EU EU = .8U(500) + .2U(100) < U(420) 100 420 500 Wealth The cost of uncertainty will vary with: Uncertainty Costs for an Uncertainty Costs for an Individual The amount of uncertainty faced The characteristics and situation The degree of risk aversion Uncertainty can have real costs for an individual just as it can for a firm E.g., reduced ability to plan, higher borrowing costs A risk averse person may care about even small amounts of uncertainty ...
View Full Document
This note was uploaded on 05/07/2009 for the course PAM 4230 taught by Professor Tennyson during the Spring '07 term at Cornell University (Engineering School).
- Spring '07