risk management hw

RMI 2101

Fall 2016

Homework Assignment 7

28 Points

Due on Wednesday, November 2, 2016 AT THE BEGINNING OF CLASS

1. Manaca Company owns a small office building worth $100,000. Art Vandelay is the risk

manager. Manaca faces the risk of fire which would completely destroy their building.

The probability of a fire is known to be 5%.

Manaca is considering the following risk management options to address the risk of fire

to their building:

[1] Retention

[2] Full Insurance for a premium of $4,000

[3] Safety Program + Retention

[4] Safety Program + Full Insurance [premium falls to $3,000]

The cost of the Safety Program is $600. It has the impact of lowering the probability of a

fire from 5% to 3%. However, if a fire does occur it is still a total loss.

a. Construct a loss matrix. [4 point]

b. What is the actuarially fair premium [AFP] in this case? [1 point]

c. What is the AFP when safety is introduced? [2 points]

Assume Art’s worry value for retention (WVR) is $2,000 and for retention and safety

(WVRS) is $1,200.

d. If Art decides to minimize TOTAL COST, what risk management option does he

choose? Make sure that you show all calculations and clearly define TOTAL

COST in each case. [4 points]

e. What is Art’s PMAX for full insurance? [1 point]

f. During a meeting, the Chief Risk Officer (CRO) told Art that the most he would

pay for full insurance is $7,500. What is the CRO’s WVR? [1 point]

g. Who is more risk averse, the CRO or Art? Explain. [2 points]

2. Kramerica Company has a small plant worth $60,000. The plant is subject to physical

damages and total destruction as a result of fire.

From over 10,000 industry observations, the firm has derived the following probability

distribution of fire losses for its physical plant.

Loss Amount ($) Probability of Loss

0 0.4

20,000 0.3

40,000 0.2

60,000 ?

Kramerica is considering the following risk management options:

[1] Retention

[2] Partial insurance - Face Amount = $50,000; Premium = $1,200

[3] Deductible insurance - Face Amount = $60,000; Deductible per occurrence =

$800; Premium = $1,500

[4] Full insurance - Face Amount = $60,000; Premium = $7,000

a. Construct the loss matrix. [4 points]

b. Assume that the firm decides to choose a risk management alternative without

including valuation for subjective risk. What risk management option is chosen?

Show all work and calculations. [4 points]

c. What worry value(s) would make full insurance preferred to partial insurance?

Show all work and calculations and explain your numerical answer. [2 points]

d. What worry value(s) would make deductible insurance preferred to partial

insurance? Show all work and calculations and explain your numerical answer.

[3 points]