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Real Investments under Knightian Uncertainty Johan Walden Yale School of Management October 6, 2003. Agenda. Presentation Why is Knightian uncertainty important for real investments? How does it modify decision makers’ behavior? Expected utility theory Investment decisions
“75% chance that A will win - quality is superior”
Invest in A?
If the choice was the opposite: Would we really expect the firm to estimate B’s
chance of success to 70%?
A and B
“80% chance that B will win - marketing is superior”
Management chooses conservative estimate - Estimates probability for A to win to be 30% and does not invest
Household Penetration (%)Knightian uncertainty is important in many real life situations
…But unclear who will capture value...
Demand for service is high...
…And regulations prohibit hedging
Structure of decision maker’s choice
* Multiple priors Expected Utility
“I prefer situations with known probabilities”Classical theory can be modified to take Knightian uncertainty into account - MEU results (2/2)
Decision theoretic axioms:
Decision maker is rational with respect to axioms
1. Acts as if cost of capital has increased
2. Supplements NPV rule with other value measures
3. Invests differently than under increased risk aversionMEU theory changes decision makers’ investment behavior
Decision makers (DMs):
Changed investment behavior is shown in a two period example (1/4)
Results hold for multi-period investments with general utility functions under additional assumptions on projects: “Nondegeneracy”
1. When uncertainty increases, required minimum IRR to invest in a project increases (2/4)
Results hold for multi-period investments with general utility functions under additional assumptions on projects: “Strong moment conditions ”
3. Uncertainty averse and risk averse decision makers choose different types of projects (4/4)
“Let’s do it: It’s a no regret move”
“Let’s skip it: Opportunities are limited anyway”
If you rank RL > BL and NRL > NBL, you are not a (subjective) expected utility maximizerEllsberg example
S = 90
Spaces involved in in MEU setup
“Kinked” demand curves arise
Demand for risky projects decrease
Results hold for multi-period investments with general utility functions under additional assumptions on ordering of outcomes: “Normality”
Fewer projects are preferred to riskfree project
Results hold for multi-period investments with general utility functions under additional assumptions on ordering of outcomes:
“Weak moment conditions”
High rates of return required for venture capital
As (high) risks are largely idiosyncratic, this seems to be in violation of standard NPV rule