Risk analysis using maximin criterion, minimax regret criterion, expected value criterion and decision trees
Conceptual foundations of decision and risk analysis.
The method of analysis depends on whether a risk involves certainty or uncertainty.
Decision analysis criteria depend on uncertainty and probabilities of outcomes.
States of nature refer to the possible outcomes in a decision situation over which the decision maker has no control.
Payoff is the outcome (positive or negative) for any combination of alternative and state of nature. The payoffs associated with all possible combinations of alternatives and states of nature constitute a payoff table
Payoff is the outcome (positive or negative) for any combination of alternative and state of nature. The payoffs associated with all possible combinations of alternatives and states of nature constitute a payoff table
A small electronics company is investigating an investment in a surface-mount machine, but they were uncertain about the extent of the investment needed. Initial research led them to identify three potential courses of action (alternatives):
The company also identified three potential directions that they believed the market demand for surface-mounted components could take (states of nature).
- [A1] A large investment, which would involve purchasing a full-scale surface-mount system, including robotics, thus allowing them to bid on the majority of present manufacturing contracts. This equipment would give them greater capability.
- [A2] A medium investment, which would give them the same general capability as alternative A, but the equipment would operate at a much lower speed. This would prevent them from bidding on large contracts.
- [A3] A small investment, which would limit them to bidding on less than half of the potential contracts.
The company also identified three potential directions that they believed the market demand for surface-mounted components could take (states of nature).
- [S1] Rapidly increasing demand due to the capability of the surface-mount equipment
- [S2] Moderately increasing demand
- [S3] Slight increase in demand as more businesses added their own surface-mount capability
How and who determines the payoff and cash flow values?
The maximax criterion is an optimistic decision criterion. For each alternative, the decision maker finds the maximum possible payoff and then selects the alternative with the greatest maximum payoff.
A small electronics company is investigating an investment in a surface-mount machine, but they were uncertain about the extent of the investment needed. Initial research led them to identify 3 potential courses of action (alternatives). They also identified 3 potential directions that they believed the market demand for surface-mounted components could take (states of nature).
The maximin criterion is a pessimistic decision criterion. For each alternative, the decision maker finds the minimum possible payoff and then selects the alternative with the greatest minimum payoff.
A small electronics company is investigating an investment in a surface-mount machine, but they were uncertain about the extent of the investment needed. Initial research led them to identify 3 potential courses of action (alternatives). They also identified 3 potential directions that they believed the market demand for surface-mounted components could take (states of nature).
The minimax regret criterion considers the results of selecting the wrong alternative. For each state of nature, the decision maker finds the difference between the best payoff and each other alternative and uses these values to construct an regret (opportunity loss) table. Next, the decision maker identifies the maximum regret value for each alternative and selects the alternative with the lowest maximum regret value.
An inventor is considering production of a novelty item for golfers that will be sold through pro shops. The inventor has decided on a selling price of £3.50 for the item. The cost of production is £2.00 per unit, with an initial setup cost of £3,750. Based on feedback from local sporting goods retailers, the inventor believes the demand for the item will be either 2,000 units, 3,000 units, 4,000 units, or 5,000 units. Determine the number of units that the inventor should produce for sale.
When the probabilities of each outcome are available, the expected value criterion is used to select the alternative that will produce the greatest average payoff or minimum average loss.
A real estate investor is considering 3 investment alternatives. Returns from each investment depend on future population growth. The investor has developed 3 growth scenarios (states of nature). Which investment alternative should the investor select?
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Decision trees are diagrams that illustrate the chronological ordering of actions and events in a decision analysis problem. Each action node represents a choice of alternatives and each event node represents a set of possible outcomes (states of nature).
All outcomes for an event must be exclusive. If one outcome occurs, then it should not be possible for any of the other outcomes from the same event to occur.
Use the time information and a discount rate to calculate present values of all future values in a decision tree.
Below is an example of converting a discount rate of 8.4% per annum to a discount rate per 6-months.
The variable W is the discount rate per 6-months and the 2 exponent represents the fact that there are 2 six-months investment periods per year.
The variable W is the discount rate per 6-months and the 2 exponent represents the fact that there are 2 six-months investment periods per year.
(1 + W)^2 = (1 + 0.084)^1
W = SQRT(1 + 0.084) � 1 = 0.041 = 4.1%
W = SQRT(1 + 0.084) � 1 = 0.041 = 4.1%
Aquatech currently holds the lease to a site with good potential for geothermal development to generate electricity. Aquatech is now looking at 3 alternatives for the site.
If the company extends the lease in order to sell the property later without drilling, the sale price will be determined by the demand for electricity. Market research indicates 3 levels of demand (states of nature) and their projected sale prices.
If the company decides to extend the lease in order to drill, future revenue from the site would be determined by the pressure and temperature of the water. Preliminary analysis was conducted of 3 possible temperature ranges (states of nature) to estimate the projected drill revenues.
Use a decision tree and the expected value criterion to determine the best alternative for Aquatech. Use a discount rate of 8% to calculate present values.
If the company extends the lease in order to sell the property later without drilling, the sale price will be determined by the demand for electricity. Market research indicates 3 levels of demand (states of nature) and their projected sale prices.
If the company decides to extend the lease in order to drill, future revenue from the site would be determined by the pressure and temperature of the water. Preliminary analysis was conducted of 3 possible temperature ranges (states of nature) to estimate the projected drill revenues.
Use a decision tree and the expected value criterion to determine the best alternative for Aquatech. Use a discount rate of 8% to calculate present values.
Common decision scenarios involving risk analysis:
- use vs. build
- buy vs. build
- buy vs. lease
- insurance premium vs. cost of actual problem
- invest now vs. savings later
- invest now vs. income later
- spend on testing vs. spend on quality
Use the results of your financial and risk analysis in your writing. But, do not repeat the step by step description of the calculations.
The expected value criterion does not take into account the attitude to risk of the decision maker.
E(x) = (0.2 x -10) + (0.8 x 15) = 10
E(z) = (0.6 x -50) + (0.4 x 120) = 18
E(x) = (0.2 x -10) + (0.8 x 15) = 10
E(z) = (0.6 x -50) + (0.4 x 120) = 18
The expected value criterion assumes a linear value function for money. This assumption may be false for some decisions.
An increase from zero to £1 million may be regarded by the decision maker as much more preferable than an increase from £9 million to £10 million.
Consider, if you are unemployed, a job with a £20,000 annual salary is very attractive.
By comparison, if you currently have a job with a £200,000 annual salary, then it is less attractive to work on the weekends in order to earn £20,000 of additional income.
By comparison, if you currently have a job with a £200,000 annual salary, then it is less attractive to work on the weekends in order to earn £20,000 of additional income.
Consider both quantitative and qualitative factors when evaluating a decision.