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

1. Real Investments under Knightian UncertaintyJohan WaldenYale School of ManagementOctober 6, 2003

2. Agenda • 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

3. PRODUCTION EXAMPLE Classical expected utility theory breaks down under Knightian uncertainty Decision problem? Uncertain information “75% chance that A will win - quality is superior” Invest in A? Cash flow If the choice was the opposite: Would we really expect the firm to estimate B’s chance of success to 70%? Expert 1 No 0 Comple- mentary products, A and B A wins “80% chance that B will win - marketing is superior” -100+250= +150 Yes Expert 2 -100+0= -100 B wins Management chooses conservative estimate - Estimates probability for A to win to be 30% and does not invest

4. BROADBAND EXAMPLE 60 50 40 Price (EUR) 30 20 10 0 10 20 30 40 50 Household Penetration (%) Knightian uncertainty is important in many real life situations Content Access …But unclear who will capture value... Demand for service is high... DSL Movies Cable News Fiber Voice Wireless …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

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

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

7. 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 Decision makers (DMs): Investments: • Are “one-shot” (now or never) • Are irreversible • Have Knightian uncertainty • Are hedgeable • Are averse towards uncertainty • Are MEU optimizers

8. 2 PERIOD EXAMPLE Changed investment behavior is shown in a two period example (1/4) • 3 Projects with Payoffs • Logarithmic utility function • u(x)=log(x) • Multiple priors for horse lottery: • P(sH)=[0.95-19/20x ,0.95+x/20] • Probabilities for roulette lottery: • P(qH)=P(qL)=0.5 p0 p1 p2 (sH,qH) 1 1.3 0 1 0.9 0 (sH,qL) 1 0 0.2 (sL,qH) (sL,qL) 1 0 0.2 • Horse dimension • State space (sL,sH) • Roulette dimension • State space (qL,qH)

9. 2 PERIOD EXAMPLE 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)

10. 2 PERIOD EXAMPLE 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 ”

11. 2 PERIOD EXAMPLE 3. Uncertainty averse and risk averse decision makers choose different types of projects (4/4) • 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 “Let’s do it: It’s a no regret move” “Let’s skip it: Opportunities are limited anyway”

12. Implications of modified investment behavior • 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

13. BACK UP

14. 30 ? ? If you rank RL > BL and NRL > NBL, you are not a (subjective) expected utility maximizer 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 S = 90

15. BACK UP Spaces involved in in MEU setup

16. BACK UP “Kinked” demand curves arise

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

18. BACK UP 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”

19. VC EXAMPLE BACK UP High rates of return required for venture capital • Requirements on expected IRRs are high... • 50-70% For seed investments • 30-50% For third stage investments • … and realized IRRs seem to be too • 22.7% 1980-2000 according to Thomson Financial • >26% 1964-1987 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