On the Roots of Risk Management

1
On the Roots of Risk Management

• By
• Richard MacMinn

2
Objectives

• Risk
• Choice
• Expected Utility
• Risk Aversion
• The risk premium
• Comments on risk aversion
• Insurance
• Demand
• Moral hazard
• Adverse selection

3
Risk

• Historical roots
• Problem of points
• Expected value
• Saint Petersburg Paradox
• Expected utility

4
Rational Behaviour
Expected utility theory is an attempt to explain
how rational individuals behave in the face of
risk.

• Let X, Y, and Z denote risks
• Axioms
• Transitivity. If X is preferred to Y and Y is
  preferred to Z then X is preferred to Z.
• Continuity. If X is preferred to Y and Y is
  preferred to Z then there is some lottery with X
  and Z as prizes with probability of winning X
  equal to ?, i.e., l X (1 - l) Z, such that the
  individual is indifferent between that lottery
  and Y
• Independence. If X is preferred to Y is preferred
  to Z then, if we make a lottery where the
  probability of winning X is ?, the lottery with X
  and Y as prizes is preferred to one with X and Z.

5
Expected Utility

• If the axioms hold, then it can be shown
  selecting the preferred risk is equivalent to the
  choice that maximizes expected utility, i.e., X
  preferred to Y if an only if Eu(X) gt Eu(Y)
• This is known as the expected utility theorem
  the theorem forms the basis for the current
  paradigm.
• There are other non-expected utility paradigms
  that make similar predictions about risk
  management

6
Risk again

• The Rothschild-Stiglitz Theorem
• Let X and Y denote two non-negative risks. Then
  the following are equivalent statements
• Y is riskier than X if all risk averse
  individuals prefer X to Y.
• Y has more weight in the tails of its
  distribution
• Y equals X plus noise

What does this theorem imply about capital market
values?
7
Risk Aversion

• The Arrow-Pratt risk premium
• Comments on risk bearing

8
Insurance

• Demand
• Agency Problems
• Moral hazard
• Adverse selection
• Rothschild-Stiglitz model

9
Concluding Remarks

• What is a risk?
• Where are we in the theory of risk management?
  For individuals? For corporations?
• What are the determinant of insurance demand?
• What is missing in the analysis?