Suggested Solutions Assignment 06
Risk Financing
RSK4803
Department of Finance, Risk Management and
Banking
RSK4803: ASSIGNMENT 06 2021
CONTENTS
Page
1
INTRODUCTION ..........................................................................................................3
2
SUGGESTED SOLUTIONS .........................................................................................3
3
IN CLOSING ................................................................................................................9
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RSK4803: ASSIGNMENT 06 2021
Dear Student
1 INTRODUCTION
Assignment 06 was the final written assignment as part of the assessment plan of the module.
It is important that students at a postgraduate level are able to critically read, analyse and to
address complex problems by drawing systematically on the body of knowledge and
appropriate methods in the field of study. The presentation of the work should also be at a
postgraduate level, and it seems that many students need to improve their academic writing
skills.
Please take note of the general comments below and ensure that you do not, where
applicable, repeat the same mistakes when attempting the examination.
2
SUGGESTED SOLUTIONS
Presentation
Part of the learning outcomes of this module and as regulated by the National Qualification
Framework is that students must communicate and present their findings at a postgraduate
level. Good academic writing skills are therefore essential, and it is recommended that you
invest some time into improving your academic writing skills. Many videos are available on
YouTube to assist where necessary. It is also important to use the correct number formats
and conventions, and you lost one (4%) or two marks (8%) where the incorrect convention.
Although there was a significant improvement, a minority of students did not follow a structured
approach to do and present their calculations and answers. It is strongly recommended that
you do the calculations in tables. When answering essay type questions, use
headings/subheadings, bullets and paragraphs to improve the readability of your answers.
References
Students who did not reference lost where possible two marks (8%). Many students who
referred to incorrect references which do not cover the topic were penalised with one mark
(4%).
There were examples where students copied components of the assignment from other
students, internet sources and the learning material. Where it was identified, no marks were
allocated for the question. You may be awarded a zero mark in the examination.
General comments
You will earn more marks to approach the calculation in logical steps. However, keep in mind
that you must approach the question from the perspective of the Chief Risk Officer (CRO) and
not the insurer.
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RSK4803: ASSIGNMENT 06 2021
Question 1
Calculate the optimum deductible according to the total expected cost (TEC) rule Show all calculations.
Year
No. of vehicles
1
2
3
4
5
20
20
25
30
50
145
29
Total
Average
Quote number
Average loss per event
Quoted annual
premium
1
2
3
4
5
R15,000,000.00
R10,000,000.00
R8,500,000.00
R6,000,000.00
R5,000,000.00
No of accidents
R1,500,000
R2,200,000
R1,750,000
R2,000,000
R3,500,000
Annual limit for
damage to motor fleet
R60,000,000
R30,000,000
R25,000,000
R20,000,000
R10,000,000
(8 marks)
Total cost for the year
10
12
15
20
25
82
16.4
R15,000,000
R26,400,000
R26,250,000
R40,000,000
R87,500,000

Deductible
R0
R25,000
R50,000
R70,000
R100,000
Calculate the optimum deductible according to the total expected cost (TEC) rule and decide according to the TEC which quote is the most
appropriate.
q = 0.565517241 or 0.57 
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RSK4803: ASSIGNMENT 06 2021
Quote number
Premium quoted (R)
1
2
3
4
5
q
Deductible (R)
R15,000,000.00
R10,000,000.00
R8,500,000.00
R6,000,000.00
R5,000,000.00
0.566
0.566
0.566
0.566
0.566
TEC
R0
R25,000
R50,000
R70,000
R100,000
R15,000,000.00
R10,014,137.93
R8,528,275.86
R6,039,586.21
R5,056,551.72
Some students calculated the premium per vehicle, calculated the dectible and multiplied the answer to determine the amount for the total portfolio
which was also acceptable.
Annual premium
No of accidents Deductible
R15,000,000.00
R10,000,000.00
R8,500,000.00
R6,000,000.00
R5,000,000.00
25
25
25
25
25
Potential max deductibles to be paid Total cost
R0
R25,000
R50,000
R70,000
R100,000
Maximum of 8 marks allocated.
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R0
R625,000
R1,250,000
R1,750,000
R2,500,000
R15,000,000.00
R10,625,000.00
R9,750,000.00
R7,750,000.00
R7,500,000.00
RSK4803: ASSIGNMENT 06 2021
Question 2
Considering the loss history of the company and your answer above, argue which quote is the most appropriate for the company.
Annual
premium
No of
accide
nts
R15,000,000.00
R10,000,000.00
R8,500,000.00
R6,000,000.00
R5,000,000.00
25
25
25
25
25
Deductible
R0
R25,000
R50,000
R70,000
R100,000
Potential max
deductibles to be
paid
Total cost
R0
R625,000
R1,250,000
R1,750,000
R2,500,000
R15,000,000.00
R10,625,000.00
R9,750,000.00
R7,750,000.00
R7,500,000.00
Expected
economic loss
R87,500,000
R87,500,000
R87,500,000
R87,500,000
R87,500,000
Limit
R60,000,000
R30,000,000
R25,000,000
R20,000,000
R10,000,000
(5 marks)
Unreimbursed
losses
R27,500,000
R57,500,000
R62,500,000
R67,500,000
R77,500,000
Based on the TEC rule, option 5 appears to be the best solution. The TEC rule, however, does not consider the total cost.  When the total
cost, i.e. deductibles for the expected number of accidents and cover limit, are considered, option 1 appears to be the best solution. 
There is an upward trend in the number of accidents and the number of vehicles. Using the information from the last year will thus be more
appropriate. Many students referred to implementing action to improve drivers' skills and road conditions; however, it will be more prudent to
consider past experience before incorporating the potential improvement measures to reduce losses.
General comments
Many students use the average loss history to calculate the potential unreimbursed losses. The potential problem with this approach is that there
is an upward trend in the number of vehicles and the number of accidents. It would therefore be more prudent to use the information of the last
year to consider other factors such as policy limits. Students received a mark for indicating that Option 1 is the preferred alternative.
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RSK4803: ASSIGNMENT 06 2021
Question 3
The management of Healthy Fish Ltd plans to purchase a logistics company. As a result, the due diligence team obtained the following loss data
from the records of the target company.
Expected number of accidents
Expected total claims cost per event
25
35
20
15
12
10
Expected probability of losses
R 100 900
R 130 203
R 150 304
R 170 212
R 180 386
R 200 560
0.15
0.25
0.2
0.15
0.1
0.15
a. Calculate the maximum probable yearly loss (MPY) according to the Chebyshev method by using the following formula:
𝑀𝑃𝑌𝐶 = 𝐸(𝑋) + 𝑘𝜎(𝑋). The k value obtained from a consultant was 1.17.
Expected
number of
accidents
25
35
20
15
12
10
Expected
total
claims
cost per
event
R100,900.00
R130,203.00
R150,304.00
R170,212.00
R180,386.00
R200,560.00
Expected
total claims
(X-µ)
Expected
probability of
losses
0.15
0.25
0.2
0.15
0.1
0.15
R2,522,500.00
R4,557,105.00
R3,006,080.00
R2,553,180.00
R2,164,632.00
R2,005,600.00
E(X) =
R378,375.00
R1,139,276.25
R601,216.00
R382,977.00
R216,463.20
R300,840.00
R3,019,147.45
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-R496,647.45
R1,537,957.55
-R13,067.45
-R465,967.45
-R854,515.45
-R1,013,547.45
(X-µ)2
246658689591.50
2365313425602.00
170758249.50
217125664459.50
730196654288.70
1027278433401.50
Var (σ2) =
σ=
(7 marks)
(X-µ)2P(X)
36,998,803,439
591,328,356,401
34,151,650
32,568,849,669
73,019,665,429
154,091,765,010
888,041,591,597
R942,359.59
RSK4803: ASSIGNMENT 06 2021
𝑀𝑃𝑌𝐶 = 𝐸(𝑋) + 𝑘𝜎(𝑋)
R3,019,147.45 + (1.17 x R942,359.59) =
𝑀𝑃𝑌𝐶 =
R4,121,708.45
R4,121,708.17
b. Argue how you will use the MPY to negotiate insurance cover.






(5 marks)
Describe/define the term.
Explain that the purpose of quantifying the probable loss is to have insight into the loss history and trends, which will enable the enterprise to
determine its exposure to make informed decisions on risk retention strategies.
The amount of risk retention will be guided by the financial ability of the enterprise and the risk appetite.
Different types of decutibles are available which can be considered to structure the policy.
The cover limit for the insurance policy can also be negotiated as the enterprise will have a reasonable estimate of the potential losses.
The enterprise can also opt for coinsurance to optimise the insurance cover.
General discussion
Most students defined/described the term before discussing how the calculated amount would be used to commence the insurance
cover with the broker/insurer. Many students also included discussions on how the insurer uses the MPY/MPL to price insurance
premiums.
Please keep in mind that you are regarded as the chief risk officer (CRO) in this module, and your approach should be from the
perspective of the proposed insured.
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RSK4803: ASSIGNMENT 06 2021
References
University 0f South Africa. 2020. Topic 3: Risk Financing Concepts. Pretoria: University of
South Africa. Available from: https://mymodules.unisa.ac.za/portal/site/RSK4803-21Y1/tool/cac44e50-205a-4a3d-86ea-99f9b631c83d (Accessed 20 October 2021)
University 0f South Africa. 2020. Topic 4: Risk Financing- Risk Retention. Pretoria: University
of South Africa. Available from: https://mymodules.unisa.ac.za/portal/site/RSK4803-21Y1/tool/5f15224b-b382-415e-8bcf-74544113c50f (Accessed 20 October 2021)
3 IN CLOSING
Compare your answers with the suggested solutions and reflect on your approach to the case
study and assignment.
Although the examination will include theoretical questions, the examination will include
questions based on a case study, and it is important that you are able to analyse case studies
and apply the body of knowledge to solve risk financing problems. You need to know the work
to solve practical problems – do not fall into the trap to think that open book assessments are
necessarily easier than, for example, a traditional venue based examination.
Refer to the Housekeeping Section for the process that must be followed if you want to query
your assignment mark.
Dr J van Huyssteen
LECTURER: RSK4803
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