Real investments under knightian uncertainty johan walden yale school of management october 6 2003
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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

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Real investments under knightian uncertainty johan walden yale school of management october 6 2003
Real Investments under Knightian UncertaintyJohan WaldenYale School of ManagementOctober 6, 2003


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

    • What are the implications of the changed behavior?

  • Discussion


Classical expected utility theory breaks down under knightian uncertainty

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


Knightian uncertainty is important in many real life situations

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


Classical theory can be modified to take knightian uncertainty into account meu setup 1 2

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


Classical theory can be modified to take knightian uncertainty into account meu results 2 2

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


Meu theory changes decision makers investment behavior

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


Real investments under knightian uncertainty johan walden yale school of management october 6 2003

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)


Real investments under knightian uncertainty johan walden yale school of management october 6 2003

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)


2 when uncertainty increases fewer npv positive projects will be wanted by decision maker 3 4

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 ”


Real investments under knightian uncertainty johan walden yale school of management october 6 2003

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”


Real investments under knightian uncertainty johan walden yale school of management october 6 2003

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



Ellsberg example

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


Real investments under knightian uncertainty johan walden yale school of management october 6 2003

BACK UP

Spaces involved in in MEU setup


Real investments under knightian uncertainty johan walden yale school of management october 6 2003

BACK UP

“Kinked” demand curves arise


Real investments under knightian uncertainty johan walden yale school of management october 6 2003

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”


Real investments under knightian uncertainty johan walden yale school of management october 6 2003

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”


Real investments under knightian uncertainty johan walden yale school of management october 6 2003

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