Consider the Following Problem with Four States of Nature,three Decision

question 27

Essay

Consider the following problem with four states of nature,three decision alternatives,and the following payoff table (in $'s): $$\begin{array} { l | c c c c } & s _ { 1 } & s _ { 2 } & s _ { 3 } & s _ { 4 } \\\hline d _ { 1 } & 200 & 2600 & - 1400 & 200 \\d _ { 2 } & 0 & 200 & - 200 & 200 \\d _ { 3 } & - 200 & 400 & 0 & 200\end{array}$$ The indifference probabilities for three individuals are: $$\begin{array} { r c c c } \text { Payoff } & \text { Person 1 } & \text { Person 2 } & \text { Person 3 } \\\hline\$ 2600 & 1.00 & 1.00 & 1.00 \\\$ 400 & .40 & .45 & .55 \\\$ 200 & .35 & .40 & .50 \\\$ 0 & .30 & .35 & .45 \\- \$ 200 & .25 & .30 & .40 \\- \$ 1400 & 0 & 0 & 0\end{array}$$
a. Classify each person as a risk avoider, risk taker, or risk neutral.
b. For the payoff of $400, what is the premium the risk avoider will pay to avoid risk? What is the premium the risk taker will pay to have the opportunity of the high payoff?
c. Suppose each state is equally likely. What are the optimal decisions for each of these three people?

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Definitions:

Market Price

Market price refers to the present cost at which a service or asset is available for purchase or sale in a market.

Face Value

The nominal or original value printed on a financial instrument like a bond, distinct from its market value.

Market Yield

The annual income return on an investment, expressed as a percentage of the market price, reflecting the current consensus on the investment's future performance.

Coupon Bond

A bond that pays the holder a fixed interest payment (coupon) periodically until the maturity date, when the principal amount is reimbursed.