RISK MANAGEMENT

INTRODUCTION TO RISK MANAGEMENT

HOMEWORK ASSIGNMENT 3 (30 POINTS)

SPRING 2017

Due on Friday February 24th, 2017 AT THE BEGINNING OF CLASS

Be careful to follow the Guidelines for Homework Document located on Blackboard. Follow those directions

exactly!!!

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 that United Delivery Service (UDP), a mail service company, has distribution centers all along

the East coast. UDP uses a fleet of 900 delivery trucks in its operations dispersed among the various

distribution centers. From past information the Chief Risk Officer for UDP has constructed the following

probability distribution for the number of losses per truck per month.

# of losses per truck per month Probability

0 0.30

1 0.25

2 0.20

3 0.16

4 0.09

a. Calculate expected value of frequency per truck per month. (2 points)

b. Calculated the variance. (2 points)

2. Now assume that when truck losses do occur, they are non-random and always equal to $800.

a. Calculate the expected loss per truck per month? (2 points)

b. Calculate the expected loss for ALL trucks per month. (2 points)

c. Calculate the expected loss for ALL trucks for the year. (1 point)

3. UDP has one major competitor on the East Coast, Speedy Delivery (SD). SD has similar operations and

services as does UDP. However SD has a smaller fleet of trucks, with 500 trucks dispersed throughout

the region. From past information SD has collected the following data for the number of losses per truck

per month.

# of losses per truck per month # of trucks having these losses

0 200

1 150

2 100

3 ???

4 10

2

a. As a new hire in SD’s risk management department, you are asked to derive the probability

distribution for frequency based on the information provided above. (2 points)

b. Now you are an insurance underwriter, looking at submissions from both UDP and SD. You

would like to know which company faces the most risk? Show/Explain how you came to this

answer (3 points)

4. From past information, SD has constructed the following distribution related to dollar amount of losses

when accidents do occur.

$ amount of losses Probability of dollar loss

100 0.60

600 0.30

1200 0.07

2000 0.03

a. Calculate the expected value of severity for SD. (3 points)

b. Calculate the expected loss per truck per month. (3 points)

5. Miranda’s Muffins sells muffins in Philadelphia. They have been baking and selling muffins in the city

for 5 years. While they generally produce just enough to sell for the week, there are occasions when they

bake more than they can sell, sometimes way more than they can sell, which forces them to throw the

product out. Here is the data that Miranda’s Muffins has collected over the last 5 years in weeks:

Muffins Wasted Number of Weeks

0 140

25 60

50 40

100 15

200 5

a. What is the probability of each loss (Create a probability distribution)? (2 points)

b. Calculate the variance of the muffin loss. (1 point)

c. Calculate the coefficient of variance for the muffin loss. (1 point)

6. Amazon has three packages (Package A, Package B, and Package C) that is to be shipped to Bill’s

address. Package A is worth $50, Package B is worth $150, and Package C is worth $250. All three

packages have a 80% chance of arriving and a 20% chance of being lost in transit. Set up a probability

distribution with the appropriate probabilities for each possible outcome. (3 points) What is the expected

loss (P*)? (2 points) How much risk does Amazon face in this delivery purchase. (i.e. –what is the

coefficient of variation)? (1 point)

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