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Equilibrium Risk Premia for Risk SeekersPowerPoint Presentation

Equilibrium Risk Premia for Risk Seekers

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Equilibrium Risk Premia for Risk Seekers

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Equilibrium Risk Premia for Risk Seekers

Douglas W. Blackburn

Andrey D. Ukhov

Indiana University

- Risk Seeking Behavior
- Friedman and Savage (1948)
- Kahneman and Tversky (1979)
- Green and Rydqvist (1997,1999)
- Jackwerth (2000)

- Mehra and Prescott (1985)

- Can individuals exhibit risk seeking behavior while at the same time exist in an economy that demands a risk premium?

- Yes!
- An economy of homogeneous risk seekers, under perfect competition, will exhibit risk neutral behavior.
- If agents’ wealth is distributed over an interval, then the economy’s indifference curve is strictly convex and differentiable.

- For every risk averse economy there exists a supporting economy comprised entirely of risk seekers that replicates this economy.

- Utility functions are convex and time separable.
- Individuals are risk seekers.
- Concave indifference curves.

- N agents have same convex utility function and same initial endowment.
- Economy efficiently allocates Ymax of Y and no X to all investors.
- Strategy – Trade the X good for the maximum amount of Y possible while maintaining each individual’s current utility.

y

ymax

For each agent i=1 to N

x A

x B

x

xmax

N-1 agents hold all X or all Y.

One agent holds both X and Y.

Two Agent Case

Y

Ymax

Agent 1

Agent 1 holds all X

Agent 2 holds all Y

Agent 2

Xmax

X

Five Agent Case

Y

Ymax

Xmax

X

- Allowing N ∞ while holding Ymax and Xmax constant:
- Each agent’s initial endowment of Y becomes smaller.
- The “humps” of each agent’s indifference curve become arbitrarily small.
- The social indifference curve converges to a straight line – risk neutrality.

- All agents have the same utility function
- Agents are divided into two wealth classes – the rich and the poor.
- The rich are initially endowed with a larger quantity of the Y-good than the poor.

- Two Cases:
- Indifference Curves Have Same Curvature.
- Then rates of substitution are the same across both wealth classes.

- Indifference Curves Curve At Different Rates.
- Rates of substitution are not the same.
- Allocate the X good to the wealth class with the greatest rate of substitution.

- Indifference Curves Have Same Curvature.

y

Rich

Poor

x

Y

Poor: NP=2

Rich: NR=2

X

Y

Poor: NP ∞

Rich: NR ∞

X

Y

Ymax

Xmax

X

- Suppose the economy is risk averse.
- Social indifference curve is convex and differentiable.

- By following our line of reasoning backwards, we can build an economy of risk seekers, with a particular wealth distribution, that replicates the risk averse economy.

- An economy of risk seekers can, in the aggregate, demand a risk premium.
- The distribution of wealth and the budget constraint may be of same importance as the individual’s utility function.
- Caution must be taken when making implications about individuals using aggregate data.