INTRODUCTION TO RISK MANAGEMENT:
Hint: Read the questions carefully and be sure that what you write answers the questions. Many times students give correct information in an answer but that information is not the answer to the question.
Be careful as your writing skills, proper grammar, punctuation, capitalization etc. constitute part of the homework grade.
1. Assume a firm owns a small warehouse worth $300,000.
Assume that the warehouse is subject to the risk of a fire. They believe that the probability of loss is 3%. Also assume that when a loss occurs, it will be a total loss. Assume this firm’s marginal tax rate is 20%.
The firm has four current risk management options to use to manage this risk.
[1] The firm can purchase full insurance for the risk of physical damage/destruction to the warehouse for a premium of $7,500.
[2] The firm is also considering retention as an alternative to full insurance.
[3] The firm is considering a loss control measure (LC) to use in conjunction with both retention and full insurance (so options 3 and 4 are essentially options 1 and 2 but with loss control added).
The cost of loss control is $1200
The impact of loss control is to reduce the probability of loss from 3% to 1.5%.
The insurer agrees to reduce the insurance premium from $7,500 to $6,000 if/when the loss control measure is introduced.
a. Construct an after tax loss matrix. Assume that the firm’s marginal tax rate is 20%.
b. Suppose the risk manager wants to minimize expected loss as her decision rule. What risk management alternative does she choose? Show all expected loss calculations and work and explain why the risk manager chooses the option.
c. Assume that the risk manager has a worry value (WV) equal to $5,000 for retention. Assume also that the WV for retention falls to $3,500 when the probability of the loss falls due to the loss control measure, (i.e., the WV for retention with loss control is now equal to $3,500.)
If the risk manager decides to minimize TOTAL COST, what risk management alternative does she choose? Show all total cost calculations and work and explain why the risk manager selects the option.
2. Assume that a department store has the following probability distribution related to property losses for its physical plant. The physical plant is worth $2,000,000.
Loss is dollars ($) Probability of the loss
0 0.78
10,000 0.10
100,000 0.07
250,000 0.04
2,000,000 0.01
The firm is considering retention and three different insurance options or as risk management alternatives.
Partial insurance:
• Face amount of the policy = $100,000
• Premium = $10,000.
Deductible insurance:
• Face amount of the policy = $250,000
• Deductible = $5,000
• Premium = $20,000
Full insurance:
• Face amount of the policy = $2,000,000
• Premium = $55,000.
a. Construct the the loss matrix
b. If the risk manager makes decisions by minimizing TOTAL COST, show what conditions on the WVs would make:
Full insurance preferred to Deductible Insurance? Show all work and explain the numerical answer.
Partial insurance preferred to Retention? Show all work and explain the numerical answer.
For ease of exposition call the WVs:
WVR (retention) WVP (partial insurance)
WVD (deductible insurance) WVF (full insurance)
3. Refer to class notes and the article This is What a Health Insurance Death Spiral Looks Like, and answer the following questions:
a. What is the name of the concept covered in Topic 9 that would lead to the “death spiral” discussed in the article?
b. Why does removing the “individual mandate” lead to this death spiral? (Hint: use P*, Pi, Pmax, and participants in the risk pool to describe the pattern)
4. Refer to class notes and the article Social Security Jitters? Better Prepare Now, and answer the following questions:
a. In what year was the Social Security system established in the US?
b. Name one potential strategy discussed in the article that could be used to address the financial stability of Social Security above, and describe how/why it could have the desired effect of stabilizing the financials.