Question

Assume that a risk manager would like to purchase property insurance on a building. She is analyzing two insurance coverage bids. The bids are from comparable insurance companies, and the coverage amounts are the same. The premiums and deductibles, however, differ. Insurer A’s coverage requires an annual premium of $70,000 with a $3000 per-claim deductible.
Insurer B’s coverage requires an annual premium of $25,000 with a $9,000 per-claim deductible. The risk manager wonders whether the additional $55,000 in premiums is warranted to obtain the lower deductible. Using some of the loss forecasting methods just described, the risk manager predicts the following losses will occur:

Expected Number of Losses Expected Size of Losses
9 $35000
5 $7,000
3 over $9,000

Answer 1

Answer :

1)

Expected number of losses = 9 and Expected size of losses $35,000

Therefore total loss = 9*35000 = $315000

Insurer A

Deductible = Number of losses * Deduction per claim = 9*3000 = $27000

Hence benefit received = Total losses - Total deductible = $315000 - $27000 = $288000

Risk reward ratio = Benefit received / Annual premium = $288000/70000 = 4.11

Insurer B

Deductible = 9*9000 = $81000

Benefit received = $315000-$81000 = $234000

Risk reward ratio = $234000/25000 = 9.36

The risk reward ratio of Insurer B is higher than Insurer A which means policy B gives higher return in comparison to A.Hence policy B is recommended.

2)

Expected number of losses = 5 and Expected size of losses $7000

Therefore total loss = 5*7000 = $35000

Insurer A

Deductible = Number of losses * Deduction per claim = 5*3000 = $15000

Hence benefit received = Total losses - Total deductible = $35000 - $15000 = $20000

Risk reward ratio = Benefit received / Annual premium = $20000/70000 = 0.29

Insurer B

Deductible = 5*9000 = $45000 i.e upto $35000

Since the deduction is $45000 nothing will be received as claim from policy B insurer.Hence policy A is better than B.

3)

Expected number of losses = 3 and Expected size of losses $10000 (Assumed over $9000)

Therefore total loss = 3*10000 = $30000

Insurer A

Deductible = Number of losses * Deduction per claim = 3*3000 = $9000

Hence benefit received = Total losses - Total deductible = $30000 - $9000 = $21000

Risk reward ratio = Benefit received / Annual premium = $21000/70000 = 0.30

Insurer B

Deductible = 3*9000 = $27000

Benefit received = $30000-$27000 = $3000

Risk reward ratio = $3000/25000 = 0.12

The risk reward ratio of Insurer A is higher than Insurer B which means policy A gives higher return in comparison to B.Hence policy A is recommended.