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Equilibrium Risk Premia for Risk SeekersPowerPoint Presentation

Equilibrium Risk Premia for Risk Seekers

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Motivation and Background Risk Premium Puzzle

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

- Mehra and Prescott (1985)

Research Question

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

Results

- 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.

Results

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

Our Economy Individuals choose between the X-good today and the Y-good tomorrow. There is a fixed quantity of X and Y. Perfect Competition – Aumann (1964)

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

Homogenous Agents

- 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.

Social Indifference Curve

Two Agent Case

Y

Ymax

Agent 1

Agent 1 holds all X

Agent 2 holds all Y

Agent 2

Xmax

X

Perfect Competition

- 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.

Heterogeneous Agents

- 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.

Efficient Allocation

- 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.

Risk Averse Economy

- 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.

Conclusions and Implications

- 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.

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