Decision Making under Risk: Criteria of EMV & EOL

-

Decision Making under Risk: Criteria of EMV & EOL

Decision-making under risk involves choosing between alternatives when the probabilities of various outcomes are known. Two key criteria used in this context are Expected Monetary Value (EMV) and Expected Opportunity Loss (EOL). Both criteria help decision-makers evaluate and compare the potential outcomes of different choices, enabling them to select the most rational option under uncertainty.

Expected Monetary Value (EMV)

EMV is a decision rule used to calculate the average outcome when the future includes scenarios that may or may not happen. The EMV criterion helps in making decisions that are statistically expected to yield the best monetary return over time.

Calculation of EMV: EMV=∑(Pi×Vi)

Where:

  • Pi​ = Probability of outcome i
  • Vi​ = Monetary value of outcome i

Steps to Calculate EMV:

  • List Possible Outcomes: Identify all potential outcomes for each decision alternative.
  • Assign Probabilities: Determine the probability associated with each outcome.
  • Determine Values: Estimate the monetary value (gain or loss) for each outcome.
  • Calculate EMV: Multiply the monetary value of each outcome by its probability and sum these products for each decision alternative.

Example: Suppose a company is considering launching a new product. There are two possible market responses:

  • High demand (probability = 0.7, profit = $100,000)
  • Low demand (probability = 0.3, loss = $50,000)

The EMV for launching the product would be: EMV = (0.7×100,000)+(0.3×−50,000)=70,000−15,000=55,000

Thus, the EMV of launching the product is $55,000, indicating that, on average, the decision would result in a profit of $55,000.

Expected Opportunity Loss (EOL)

EOL is another decision-making criterion that focuses on minimizing the potential regret or loss from not choosing the best alternative. It is also known as the Expected Regret.

Calculation of EOL:

  • Determine the Opportunity Loss Matrix: For each possible state of nature, calculate the difference between the payoff of the best decision and the payoff of each alternative decision.
  • Calculate the Expected Opportunity Loss: Multiply the opportunity loss for each outcome by its probability and sum these products for each decision alternative.

Steps to Calculate EOL:

  • List Possible Outcomes and Probabilities: Similar to EMV, identify all possible outcomes and their probabilities.
  • Create Payoff Matrix: Develop a matrix of payoffs for each decision alternative.
  • Calculate Opportunity Loss: For each outcome, subtract the payoff of each decision from the highest payoff in that outcome.
  • Compute EOL: Multiply each opportunity loss by its probability and sum these products for each decision alternative.

Example: Using the previous example:

  • High demand (probability = 0.7, best payoff = $100,000)
  • Low demand (probability = 0.3, best payoff = -$50,000)

Suppose the company considers not launching the product (payoff = $0 for both outcomes). The opportunity loss matrix would be:

  • High demand: 100,000−0 = 100,000
  • Low demand: 0−(−50,000) = 50,0000

The EOL for launching the product would be: EOL=(0.7×0)+(0.3×50,000) =0+15,000=15,000

The EOL for not launching the product would be: EOL=(0.7×100,000)+(0.3×0)=70,000+0=70,000

Thus, the EOL of launching the product is $15,000, and the EOL of not launching is $70,000. The lower EOL for launching indicates it is the better choice to minimize potential regret.

Comparison of EMV and EOL

  • Focus: EMV focuses on maximizing expected returns, while EOL focuses on minimizing potential regret or loss.
  • Application: EMV is generally preferred when probabilities and monetary values of outcomes are well-defined and the decision-maker is risk-neutral. EOL is useful when decision-makers are concerned with the regret of not choosing the best option.
  • Decision Rule: Choose the alternative with the highest EMV or the lowest EOL.

Both EMV and EOL provide valuable insights and frameworks for making informed decisions under risk, each with its perspective on handling uncertainty and evaluating potential outcomes.