Real Investments under Knightian Real Investments under Knightian UncertaintyUncertainty

Johan WaldenJohan WaldenYale School of ManagementYale School of Management

October 6, 2003October 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

AgendaAgenda

Classical expected utility theory breaks Classical expected utility theory breaks down down under Knightian uncertainty 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’schance of success to

70%?

PRODUCTION EXAMPLE

Cash flow

-100+250=+150

-100+0= -100

Invest in A?

No

Yes

0

A wins

B wins

Comple-mentary products, A and B

Content Access

DSL

Cable

Fiber

WirelessVoice

News

Movies

0

10

20

30

40

50

60

Pri

ce (

EU

R)

10 20 30 40 50Household Penetration (%)

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 Knightian uncertainty is important in many real life situationsreal 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 Classical theory can be modified to take Knightian uncertainty into account - MEU* Knightian uncertainty into account - MEU* setup (1/2)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 Classical theory can be modified to take Knightian uncertainty into account - MEU Knightian uncertainty into account - MEU results (2/2)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 increased2. Supplements NPV rule with other value measures3. Invests differently than under increased risk aversion

MEU theory changes decision makers’ MEU theory changes decision makers’ investment behaviorinvestment behavior

Investments:Decision makers (DMs):

•3 Projects with Payoffs

•Logarithmic utility function•u(x)=log(x)

•Multiple priors for horse lottery:•P(sH)=[0.95-19/20,0.95+/20]

•Probabilities for roulette lottery:•P(qH)=P(qL)=0.5

•Horse dimension •State space (sL,sH)

•Roulette dimension•State space (qL,qH)

2 PERIOD EXAMPLE

(sH,qH)

(sH,qL)(sL,qH)(sL,qL)

p0 p1 p2

1

1

1

1

1.3

0.9

0

0

0

0

0.2

0.2

Changed investment behavior is shown in a Changed investment behavior is shown in a two period example (1/4)two period example (1/4)

2 PERIOD EXAMPLE

1. When uncertainty increases, required 1. When uncertainty increases, required minimum minimum IRR to invest in a project increases (2/4)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 2. When uncertainty increases, fewer NPV positive positive projects will be “wanted” by decision projects will be “wanted” by decision maker (3/4)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 3. Uncertainty averse and risk averse decision decision makers choose different types of projects makers choose different types of projects (4/4)(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 Implications of modified investment behaviorbehavior

BACK UP

Ellsberg example 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 UPSpaces involved in in MEU setupSpaces involved in in MEU setup

BACK UP ““Kinked” demand curves ariseKinked” 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 decreaseDemand 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 Fewer projects are preferred to riskfree projectproject

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

VC EXAMPLE

BACK UP

High rates of return required for venture High rates of return required for venture capitalcapital