Topic 7 PDF

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topic 7, Michael McCloskey. everything on powerpoint slides ...

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Loss Matrix  Indicates $ amounts (costs) associated with each combo of: 1. Risk Management Alternatives 2. Future states of the world Example 1: assume first 2 future states of the world  Loss (total loss, no partial loss) o Loss= fire  no loss o no Loss= no fire  building replacement cost is $424,000  possible risk management options o retention o retention plus safety measures  loss prevention that reduces frequency but not security  costs $12,000 o full insurance  face amount (amount insurance will pay) of $424,000  premium of $20,000 o assume tax rate of 20%  Taxes? What are tax deductibles? o $424,000 loss o $20,000 insurance premium o safety program o cost of uninsured loss  probabilities o without safety  fire- 3%  no fire- 97% o with safety  fire- 1%  no fire- 99% possible losses- future states of the world Possible decision Fire No Fire P* (Expected Value) Retention $424,000 ($ out) $0 ($ out) (254,400x.03) + (0x.97) = $424,000(.6) = $254,400 $0 (After tax cost) $7632 (After tax cost) Retention+ $424,000+$12,000= $0+$12,000 = $12,000 (261,000x.01) + ($7200x.99) = Safety $436,000 ($ out) $12,000(.6) = $$7,200 $9744 $436,000(.6) =$261,000 Full Insurance $20,000 $20,000 $12,000 (with a probability of $20,000(.6)= $12,000 $20,000(.6) = $12,000 1 or 100% bc theyre the same)

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What decision would you pick? IF the decision rule is to choose the alternative that minimizes expected loss- pick the cheapest option o Pick retention o Retention < retention + safety < full insurance Each decision (alternatives) has 2 types of “costs” o Monetary costs= expected cost o Nonmonetary costs= cost of uncertainty (worry value)  Worry value is the cost associated with decision making  Cost of anxiety concerning a decision  Unique to the decision maker Estimation of the worry value for retention  loss of $254,400  probability of .03 or 3%  loss of $0  probability or .97 or 97%  P* = $7632  Ask the key decision maker if they would choose retention or full insurance with an “actuarially fair premium”  Actuarially fair premium  P*= $7632  If price of insurance was $7632 (P*) would you pick insurance or retention?  Insurance  If price of insurance was $7632 (P*) + 1 or $7633would you pick insurance or retention?  Insurance  As soon as you say no, you’ve hit the MAX  Pmax = most individuals will pay for insurance for a particular risk  Pmax – P*= worry value  Worry value is the max above and beyond P* that a person is willing to pay to reduce uncertainty Ranking of worry value  WV1= worry value for retention  WV2= worry value for retention plus safety  WV3= worry value for full insurance  WV1 > WV2 > WV3 McCluskey’s Worry Value  WV1= $5,000  WV2= $3000  WV3= $0  Total Cost  Retention= $7632 + $5000= $12,632  Retention + safety= $$9744 + $3000= $12,744  Full insurance= $12000 + 0= $12,000 

IF the decision rule is to choose the alternative that minimizes total costs

 Pick insurance Side Example #1 (Taxes)  For a firm: revenue- expenses= taxable income o Revenue of $2000 with no expenses o Taxable income of $2,000  $2000 x .4 = $800 of tax obligation  Revenue of $2000 with $400 of insurance premium expenses  Taxable income of $1600  $1600 x .4 = $640 of tax obligation  After tax savings cost  400(800-640) = $240  After tax savings cost of a tax-deductible expenditure of $X  ($X)(1-tax rate)  FOR THE EXAMPLE ABOVE  (400)(1-.4)= $240 Example 2: you are the owner of a real estate development company you you’re worried about losses during the year  the tax rate is 30%  ($X)(1- tax rate)= ($X)(1-.3)= ($X)(.7)  Probability distribution – future states of the world Outcomes Probabilities $0 loss 80% $20,000 loss 10% $25,000 loss 9% $65,000 loss 1% Risk Management Alternatives 1. Retention 2. Buy insurance policy a. Face amount of $25,000 (limit of coverage) b. Premium of $4,000 3. Buy insurance policy a. Face amount of $75,000 (limit of coverage) b. Premium of $7,000 c. Deductible of $5,000 4. Buy insurance policy a. Face amount of $75,000 (limit of coverage) b. Premium of $12,000 5. Implement loss prevention program and purchase insurance a. Face amount of $25,000 (limit of coverage) b. Premium of $3,000 c. Program cost of $500 d. Probability changes i. $0 loss, 85% ii. $20,000 loss, 5% What decision would you pick?

IF the decision rule is to pick the alternative that minimizes expected loss (pick cheapest option or whichever has the lowest P*) Choose option 5- implementation of loss prevention program and insurance IF the decision rule is to pick the alternative that minimizes total cost – you must factor in worry value WV1= $6000 WV2= $5000 WV3= $1000 WV4= $0 WV5= $5500 TC= $9430 TC2= $8080 TC3= $6600 TC4= $8400 TC5= $8230 WV= WORRY VALUE TC= TOTAL COST Choose option 3- buy insurance policy #3 Example 3  probability distribution – future states of the world $0 – no loss 90% $1000 – partial loss 7% $10,000 – partial loss 2.9% $100,000 – full loss .1% Risk Management Alternative 1. Retention 2. Partial Insurance a. Face amount of $10,000 (limit of coverage) b. Premium of $550 3. Buy full insurance a. Face amount of $100,000 (limit of coverage) b. Premium of $700 4. Buy deductible insurance policy a. Face amount of $100,000 (limit of coverage) b. Premium of $550 c. Deductible of $1,000 Total Cost for Each Option – P* + Worry Value 1. Retention= $460 + WV1 2. Partial Insurance = $640 + WV2 3. full insurance = $700 + WV3 a. WV3= 0 because there is no uncertainty because of full insurance 4. deductible insurance policy = $650 + WV4 Compare Worry Value (P* + WV)  Retention (1) VS. Full Insurance (3) o A person would prefer full insurance over retention when: o TC of full insurance < TC of retention o 700 + WV3 < 460 + WV1 o 700-460 < WV1 – WV3 o 240 < WV1 If WV1> 240 pick full insurance If WV1 < 240 pick retention

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If WV1= 240 we are indifferent Retention (1) VS. Deductible Insurance (4) o A person would prefer deductible insurance over retention when: o TC of deductible insurance < TC of retention o 650 + WV4 < 460 + WV1 o 650- 460 < WV1 – WV4 o 190 < WV1 – WV4  If 190 < WV1 – WV4 pick deductible insurance  If 190 > WV1 – WV4  If 190 = WV1 – WV4 we are indifferent

A person or firms worry value (WV) will increase when:  The variability of losses increases  The level of confidence in the estimate of P* decreases  The size of the maximum possible loss increases  The probability of the maximum possible loss increases  The financial strength of the firm/individual decreases  The level of insurance coverage decreases (assuming all other things are equal)...