Real Investments under Knightian Uncertainty Johan Walden Yale School of Management October 6, 2003

Presentation Why is Knightian uncertainty important for real investments? How does it modify decision makers’ behavior? Expected utility theory Investment decisions What are the implications of the changed behavior? Discussion Agenda

Classical expected utility theory breaks down under Knightian uncertainty Expert 1 Expert 2 Decision problem?Uncertain information “75% chance that A will win - quality is superior” “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 If the choice was the opposite: Would we really expect the firm to estimate B’s chance of success to 70%? PRODUCTION EXAMPLE Cash flow = = -100 Invest in A? No Yes 0 A wins B wins Comple- mentary products, A and B

ContentAccess DSL Cable Fiber Wireless Voice News Movies Demand for service is high... …But unclear who will capture value... …And regulations prohibit hedging Restrictions on horizontal integration Restrictions on vertical integration Even though the business case is solid, uncertainty make investors reluctant Consequently, roll-out has been slow in many European and Asian markets BROADBAND EXAMPLE Knightian uncertainty is important in many real life situations

MEU MODEL * Multiple priors Expected Utility In classical setup: “I give you probabilities, you choose lottery” In MEU setup: “I give you information, you choose probabilities and lottery” Structure of decision maker’s choice Classical theory can be modified to take Knightian uncertainty into account - MEU* setup (1/2)

MEU MODEL Decision theoretic axioms: Weak order Continuity Monotonicity Nondegeneracy C-Independence Uncertainty aversion Decision maker is rational with respect to axioms “I prefer situations with known probabilities” C MEU Theorem: Classical theory can be modified to take Knightian uncertainty into account - MEU results (2/2)

Are averse towards uncertainty Are MEU optimizers Are “one-shot” (now or never) Are irreversible Have Knightian uncertainty Are hedgeable When uncertainty increases, decision maker: 1. Acts as if cost of capital has increased 2. Supplements NPV rule with other value measures 3. Invests differently than under increased risk aversion MEU theory changes decision makers’ investment behavior Investments:Decision makers (DMs):

3 Projects with Payoffs Logarithmic utility function u(x)=log(x) Multiple priors for horse lottery: P(s H )=[ /20 ,0.95+  /20] Probabilities for roulette lottery: P(q H )=P(q L )=0.5 Horse dimension State space (s L,s H ) Roulette dimension State space (q L,q H ) 2 PERIOD EXAMPLE (s H,q H ) (s H,q L ) (s L,q H ) (s L,q L ) p0p0 p1p1 p2p Changed investment behavior is shown in a two period example (1/4)

2 PERIOD EXAMPLE 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: “Nondegeneracy”

2. When uncertainty increases, fewer NPV positive projects will be “wanted” by decision maker (3/4) Results hold for multi-period investments with general utility functions under additional assumptions on projects: “Strong moment conditions ” 2 PERIOD EXAMPLE

For hedgeable investments, a low risk aversion will explain behavior For small investments, a high risk aversion is needed to explain behavior Results hold in multiperiod framework 2 PERIOD EXAMPLE 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”

Value of being able to hedge increases drastically Barriers to hedging become very costly Challenging to develop incentive schemes for uncertainty averse managers Uncertainty could be incorporated into firms’ investment analyses Implications of modified investment behavior

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Ellsberg example Information: Urn contains 90 balls Each ball is either red, blue or yellow There are 30 red balls 4 Games: Pick ball from urn RL: $10 if red BL: $10 if blue NRL: $10 if not red NBL: $10 if not blue If you rank RL > BL and NRL > NBL, you are not a (subjective) expected utility maximizer 30 ? ?  = 90

BACK UP Spaces involved in in MEU setup

BACK UP “Kinked” demand curves arise

Results hold for multi-period investments with general utility functions under additional assumptions on ordering of outcomes: “Normality” Demand for risky projects decrease BACK UP

Results hold for multi-period investments with general utility functions under additional assumptions on ordering of outcomes: “Weak moment conditions” BACK UP Fewer projects are preferred to riskfree project

Requirements on expected IRRs are high % For seed investments 30-50% For third stage investments … and realized IRRs seem to be too 22.7% according to Thomson Financial >26% according to Venture Economics. However, recent studies suggest that they could be lower... As (high) risks are largely idiosyncratic, this seems to be in violation of standard NPV rule VC EXAMPLE BACK UP High rates of return required for venture capital