iii[ 
• ~ 
Strathmore 
UNIVERSITY 
Motor Private Vehicle Rating Model 
Pokar Heta Vinod, 084720 
Submitted in partial fulfillment of the requirements for the Degree of 
BBS Actuarial Science at Strathmore University 
Strathmore Institute of Mathematical Science 
Strathmore University 
Nairobi, Kenya 
November, 2017 
This Research Project is available for Library use on the understanding that it is 
copyright material and that no quotation from the Research Project may be 
published without proper acknowledgement. 
DECLARATION 
I declare that this work has not been previously submitted and approved for the 
award of a degree by this or any other University. To the best of my knowledge and 
belief, the Research Proposal contains no material previously published or written by 
another person except where due reference is made in the Research Proposal itself. 
© No pmt of this Research Proposal may be reproduced without the permission of 
the author and Strathmore University 
.~ ~0 .~ .. .. ~.~.T~ ... . .'!.J.t:':I..Q?.: ........... ... ... [Name of Candidate] 
.... . f.!:#:c(t. ~?P..t!. .......... ... ....... .... ................. . [Signature] 
... .. ?1:-.T.f.~!J#P.!. f.: ...... ... .... ...................... [Date] 
This Research Proposal has been submitted for examination with my approval as the 
Supervisor. 
..... 0fu.f..~f... ...... Q:P.<§ .:f.: .~ . ." ... .. ..... [Name of Supervisor] 
.............. ..... . ~. .... ... .... [Signature] 
"27/ \ 1 (;;zo(7_ 
.. . . . .... . . ... .......... .. ... ...... .......... ....... ..... ... .. . [Date] 
Strathmore Institute ofMathematical Sciences 
Strathmore University 
ACKNOWLEDGEMENTS 
I would like to appreciate my immediate supervisor Mr. George Odera for his guidance, 
insights and encouragements where necessary. Without his support, it was impossible to 
accomplish the research. His contributions and immediate feedback to this research has 
made it a success. I am forever grateful. 
I would like to pay special thankJulness, warmth and appreciation to my parents, 
lecturers, friends and classmates who contributed in assessing my research topic. Their 
moral support and company has made the research very successful. 
My sincere gratitude goes to Strathmore University for considering me to pursue this 
course and undertake this project. Their mentorship and basic support have made the 
entire journey of my undergraduate degree fruitful. 
Above all, I would like to thank God for his blessings on me. 
II 
Tab le of Contents 
INTRODUCTION ..... .. ...... .. .. ...... .. .... .. ... ... .... ........... .. .... .. .... ..... ........... .... ... ...... ..... .. .. 1 
1.0 Background Information ....... .. ... .. .......... ... ... ... ........ ......... ....... .. .... ........ ... ... ........ 1 
1.0.1 Definitions ..... .. ........ ...... .. ...... .... .... ..... .... ... ..... ...... .... ... ..... ...... ...... ... .... ......... I 
1.0.2 Insurance .... ...... .... ... ....... ... ........... ............... ...... ... .... .... .... .. .. ... ...... ... .. .. .. .... .. 1 
1.0.3 General Insurance .. ..... ........ .... ... ...... ... ....... ......... .. ...... ... ..... .... .. ..... ............ ... 2 
1.0.4 Motor Insurance Covers ...... ......... .... .. .. ........ ..... ..... ... .... .... .... ..... ... .... ... .... .... 3 
1.0.5 Risk Classification .... ...... ..... .... .... ....... ... ................ .............. .............. ..... ..... 3 
1.0.6 Trends in Motor Insurance ........ ... ....... ....... ... .. .. ...... ...... .. .. .. ........ ...... ... ... ..... 5 
1.1 Problen1 Statement .. ... .... .... .... .. .. ...... .. ...... .... ......... ... .... .. .... ........ ..... ...... ........ .. .... 6 
1.2 Research objectives ........ ...... .. ...... ......... ... .... ... .... .... .. .... ......... ... ...... .. ....... .... ... ... . 7 
1.3 Research questions ..... ... .. ..... ... ..... ..... ... .... ... .... ...... .. ..... .... ..... .. ... ... ................. ..... 7 
1.4 Significance of the study ..... ... ... ...... .. .. .. .... ...... ...... ..... .... ... .... ..... ... ... ...... ... ........ .. 8 
2 LITERATURE REVIEW ..... .... .. ........ ..... .... ....... .............. .. ....... ...... ...... ........ ... .... .. .... 9 
2.0 Introduction ...... ..... ..... .. ..... ....... ... ... .... ..... ..... .. ... .. .. .... .. ........ .... ... ... ..... .... ... ..... ... .. 9 
2.1 Theoretical Studies ... ............. ... ... .... ........ ... ................. ...................... ...... ... .. .. ... .. 9 
2.1.1 Additive and Multiplicative Models ....... ......... .. ... ..... .... ... ..... .... ........ ... ... .... 9 
2.1.2 Simple Pure Premium Model .......... .. .. ...... .......................... .. .. .. .......... .... .. .. . 9 
2.2 En1pirical studies .. ....... .. ............ .... ....... .. ........ .... ............ .... .......... .. ...... ...... .. ... .. 1 0 
2.2.1 Considerations when selecting rating factors .... .. .. .. .. .. ........ .. .. ...... .. .... ...... . 10 
2.2.2 Rating factors .. ..... ... ..... ... .... .... .. ... ........ ...... ... ... ... ........ .. ... ... .... .... ... ............ 12 
2.2.3 Pure premium models .............. ........ .... .......... .. .... ...... .. .. ........ ............ .... .... 16 
2.3 Conceptual framework .. .. .. .. .. ...... .. ....... ............ .. .. .... ........ ...... .. .... .. .. .......... ...... . 19 
2.4 Research gaps .... .. .. ...... ...... .. .... ...... ................ .. .. .... ..... .... ...... .. .... .. .. .... .. .. ... .. ...... 19 
3 RESEARCH METHODOLOGY .......... .. ... ..... ...... ...... ........ ...... .. .......... .. .... ............. 20 
3.0 Introduction .. ....... ........ ....... .. ... .. ........ ... ...... .. ..... .... .. .... ....... ... ... ..... ..... .. ... .......... 20 
3.1 Research Design ........................ .. ........ ...... ....... .. ..... .. .... ... .... .. ...... .. .. ............ ..... 20 
3.2 Target population and Sample Technique ................ ............. .. .. ........................ 20 
3.3 Data collection .. ........................................................................ .. ....................... 20 
3.4 Data Analysis .. .. ......... ... .. .. .......................... ............... .. .............. .. .. ...... .. ..... ...... 21 
3.4.1 Frequency of clain1s .... ..... .. .. ................. .. ................. ... ........................ .. ..... 21 
Ill 
3.4.2 Severity of claim amounts ... ... ... ...... ....... .... .... .... ........ ....... ....... ....... ...... ..... 22 
3.4.3 Pure Premitnn .... .... .... ......... .... ............. .......... ... .... ... ........ ....... ............ .... .... 22 
3.4.4 Total Premium Main Cover .. .. .................. ............ ... .................. ... .... .... ..... 23 
3.4.5 Total Premium Payable ... .. .. .... ...... ... ......................... ..... .... ...... .. .... .... ... ..... 23 
4 RESULTS AND ANALYSIS ... ..... .... ...... ... ..... ................ .... ..... .. .............. ..... ....... .... 24 
4.0 Introduction ........ ........ .. .. .......... ... ... ..... .. ... ......... ......... .. ............ .......... ......... .... .. 24 
4.1 Preliminary Analysis ............. ..... .. ... ...... .. ........ .. .... ......... ......... ................... ...... . 24 
4.2 Model Rating factors .............. .... ......... .......... .... ... ... .. ......... .... ................. ...... .... 26 
4.3 Assu1nptions ..... .... ..... ... .......... ..... ..... ............... ... ..... ...... ......................... .. .. .. ..... 26 
4.4 Model Description .. .... ....... ....... ...... ..... .... .... .... .. ... ......... ...... ............ ..... .. ........ ... 27 
4.5 Analysis of the findings ... .... ..... .. ............. ... ...... ..... ..... ... .... ... ....... .... ....... .. ... ...... 29 
4.5.1 Year ofmanufachire ...... ... ... ............ ....... ...... ......... ..... ... .... ..... ..... ..... ... ....... 29 
4.5.2 Engine Rating (CC) ..... ......................................... .. .. ........... ......... ..... ...... ... 29 
4.5.3 Color ....................................... ...... ...... ...... ......... ... .... ........ ..... .... ... .. ......... ... 30 
4.5 .4 Bodyofthecar .................... .. ............................. .... ......... ... ..... ....... ............ 31 
4.5 .5 Carry capacity ......... ...... ......... ... ..... ...... .... .. ... ... ..... .... ............. ................ ... . 31 
4.5.6 Make and model .......... ... .......... .................... ......... ............ ....... ..... ..... .. ...... 31 
4.6 Scenario Analysis ........... .. .. ........ .. ... .. .. ..... ............ ........................ .... ..... .... ........ 31 
4.7 Sensitivity of analysis ................................ ...... .... .. ..... .. .. .. ........... .. .. ....... .... .. ..... 32 
5 DISCUSSIONS ........... ......... ........ ..... ..... ..... ........ ............. .... .......... .... ..... .... ............. . 34 
5.0 Introduction ....... ........ ........ .......... ................ ........ ...... ... .. .. .... .... ....... .. ........ ... ... .. 34 
5.1 Conclusions .. .. ... ......... ... ... .............. .......... ... ... ................... .......... ...................... 34 
5.2 Limitations ... ..... .. .. ... .. .... ...... ..... .. .. ........... ........ ........ ............. ..... ......... ...... ... .... .. 34 
5.3 Recommendations .... ... ...... .. .. ...... .... ...... .......... .. .. .. .... .... .... ...... ... ... ...... .. .. ..... ..... 35 
6 REFERENCES ...... .. .. .... ........ .... .......... ... .... ...... ... .. ... .......... .... .... ..... ........... .... ...... .... 36 
IV 
LIST OF FIGURES 
Figure 1 Pure Loss Ratio ...................... .. ............................... ............. ...... .. ...... ..... ........... .. 6 
Figure 2 Concept11al framework ......... .. ... .. ...... .... .. .......... ..................................... .... ...... . 19 
Figure 3 Geometric Pure Premium ............... ..... .. ....... .. ... ...... ........ .... .. ...... .... ... ...... ......... 28 
Figure 4 Model Output. ..... .... ..... ...... ..... ....... ... .... ..... ..... ..... .. ... ......... .. ..................... .... ... .. 29 
Figure 5 Spread of Premium ........... .. ..... ........ .......... ......... ................................. ......... ..... 33 
LIST OF TABLES 
Table 1 Vehicle Year of manufacture and accident rate ... ...... ..... .. ........ ...... ...... .......... .... 15 
Table 2 Description of Inputs ...... .. ..... .... .. ........ ....... ... ..... .... ...... ........ ............ ... ..... ..... ... .. . 21 
Table 3 Overall Statistics from 2005-2016 .... .... ....... ............... ............ .. ..... .... ... ... .. ......... 24 
Table 4 Data Percentage Captured ........ .. ......... ..... ..................... ...................................... 25 
Table 5 Overview Statistics from 2009-2015 ... ...... ......... .. .. ...... .. ....... ... ........... .... ........ .. 26 
Table 6 Number of policies per type of cover. .... .... ........... .... ........... .............. .. .... ..... .. ... . 26 
Table 7 Exposure of Engine Rating ............................................... .... ............... ..... .... .... .. 30 
Table 8 Scenario Analysis .. ... ... ... ... ....................... ......... .. .. .. ....... ........ .............. .. ........ ..... 32 
ABBREVIATIONS 
1. IRA: Insurance Regulatory Authority 
2. AKI: Association of Kenya Insurers 
3. KNBS: Kenya National Bureau of Statistics 
v 
ABSTRACT 
Most motor insurance companies in Kenya collect about 5-l 0 rating factors in their 
proposal fonns . Despite having these data, these companies have in the past used the 
minimum rates prescribed by the Insurance Regulatory Authority (IRA). This implies 
that they are less likely to be aware of rating factors and their importance in pricing. This 
may justify one of the major reasons as to why motor insurance companies have been 
loss making. Although the minimum rates were specified, there was no regulation that 
compelled insurance companies not to price using rating factors . Thus although they 
collected data on the rating factors, they used the minimum rates possibly due to 
competitive pressure and market practice. However, IRA has recently issued a circular1 
to insurance companies that abolishes the use of minimum rates from 2018 thus 
insurance companies will be required to price based on their own experience. Rating 
factors fom1 the basis for pricing. Therefore, the overall objective of this study is to 
assess the use of rating factors to price motor premiums in light of the new IRA 
regulations. The past experience and data will be used to evaluate the use of relevant 
rating factors to price motor insurance policies and develop a simplified pricing model to 
compute premiums. A motor rating factor model is a simplified model that enables you 
to calculate the premium to be charged on a particular motor depending on the various 
rating factor such as type of cover, year of manufacture, engine rating, body type, make, 
color, carrying capacity, value of the car, age and profession of policyholder. Each of 
these factors contribute to the pure risk premium. The total premium payable is the 
combination of pure risk premium, expense premium, commission premium, profit 
loadings premiums and any other optional benefits. The findings of this model show that 
the premium rate varies significantly from the cuiTent model that assumes a fixed 
minimum rate on the value of the car. 
1 IRA Circular No IC & RE 12/2016 CONFIIRA/00/001/03A 
VI 
1 INTRODUCTION 
1.0 Background Information 
1.0.1 Definitions 
A policyholder is a person who purchases an insurance cover. An insurer is an individual 
or organization that provides insurance covers. The policyholder may be faced with an 
event leading to a loss and the insurer provides compensation against the loss in retum 
of regular payments paid by the policyholder. 
An insurance policy is therefore a promise by the insurer to the policyholder to pay for 
future claims in retum for specified payments paid upfront by the policyholder. The 
upfront payments are known as premiums. The total premiums contributed to the insurer 
has to be sufficient to meet all expected cost of losses incun·ed within the duration of 
cover as well as other operational costs. 
1.0.2 Insurance 
Insurance is a way of cushioning against risks. Risk exists when people are exposed to 
the likelihood of a future loss, which is uncertain. In most instances people are risk 
averse, i.e. instead of being exposed to a risk, they would prefer bearing a certain loss, 
even if its amount exceeds their expected loss under the risk. One of the most important 
feature of the insurance mechanism is the reduction of risk by pooling, (Skogh, 1991 ). 
Smith (1994) emphasized on operation of the law of large numbers, which states that 
uncertainty decreases when many similar but independent risks are brought together. 
However, it is highly uncertain for instance, whether one particular driver will be 
involved in a car accident in future and how serious the damage will be. The insurer will 
only take up the individual risks against a premium which will cater for the expected 
loss administering costs and profit loadings, only if the individual risks can be 
minimized by pooling, (Wils, 1994). 
Shavell ( 1979) noted that one of the major setback with insurance is moral hazard, which 
is the possible negative effect of insurance on loss prevention effects . In the absence of 
insurance, those individuals highly engaged in risky activities are incentivized to prevent 
losses by either reducing their activity level or by taking precautions when conducting the 
activity, (Shavell S. , 1987). Insurance sabotages the loss prevention incentives only if the 
premiums are not related to the risky activity or event. Therefore, differentiated premiums 
may be more valid as a means of improving the loss prevention incentives. 
Akerlof (1970), poses a very complex drawback in insurance markets because the 
individuals willing to buy insurance usually !mow more about their risk characteristics 
than it is possible for an insurer. The asymmetric infonnation leads to adverse selection 
within the insurance pool as most of the high-risk individuals realize that insurance is a 
good deal for them. This leads to a point where the insurance pool is highly constih1ted 
with high-risk individuals which means high payouts by the insurance company. The cost 
of providing insurance to the insurer increases due to adverse selection as most low-risk 
individuals tend to opt out, (Dionne G. R., 2014). 
1.0.3 General Insurance 
General insurance is non-life insurance which includes different classes such as Aviation, 
Engineering, Fire Domestic, Fire Industrial, Liability, Marine, Motor Private, Motor 
Commercials, Personal Accident, Theft, Workman's Compensation, Medical and 
Miscellaneous. These classifications are as per the Insurance Act (CAP 487). 
Motor insurance covers a policyholder against loss or damage to his/her own vehicle due 
to accidents, fire and theft. It also covers against third- party bodily injury or death and 
third-party property loss or damage. Motor insurance is usually offered on a short tem1, 
usually 1 year in duration. The first party in motor insurance contracts is the policyholder 
and the second party is the insurer. The third party is a person who suffers property damage 
or loss or death or bodily injury as a result of an accident involving the motor vehicle of 
the policyholder. A third party may be any person including a property owner, a 
pedestrian, a driver or passengers in another vehicle. There are various classes of motor 
insurance under Kenyan Laws; Public Service Vehicles (P .S.V), Commercial, Private and 
Motor cycles. 
2 
P.S .V are classified as class A and it includes all passenger service vehicles that are fare 
paying, e.g. buses, matatus, taxis, tuk-tuks (3-wheel cabin motor cycles). Commercial 
vehicles are classified as class B and includes vehicles used for commercial purposes e.g. 
lorries, trailers, pick-ups and any institutional vehicles that transport or carry goods. 
Private vehicles are classified as class C and includes vehicles that are used for social and 
domestic purposes. Motor cycle are classified as class D. 
1.0.4 Motor Insurance Covers 
The major types of Motor Insurance Covers include; Third-party cover, Third-party fire 
and theft and the Comprehensive cover. 
Third party cover is the bare legal requirement made compulsory by the Govenunent of 
Kenya. It covers third party bodily injury/death and property damage tlu·ough accidents 
which are caused by the Motor vehicle. 
The Third-party Fire and Theft policy covers the third party bodily injury/death, 
property damage caused by the vehicle and in addition any loss or damages to the motor 
vehicle due to theft and fire. 
The Comprehensive policy covers any third-party liability or property damage or 
damages that arise from fires or theft are covered. In addition, any damages to the 
vehicle due to accidents are also covered. 
1.0.5 Risk Classification 
Risk classification is a key component of insurance pricing. Di01me G. R. (20 14 ), defines 
risk classification as the use of observable characteristics by insurers to group individuals 
with similar risks for the purpose of computing approp1iate premiums. Risk classification 
is therefore grouping of different risks according to their estimated cost or likely impact 
or likelihood of occurrence. 
Motor rating factors are factors or variables which are measurable and have a correlation 
with the likely claims experience. Some of them include age, gender, value, make, body, 
year of manufactme, color, carry capacity and engine rating. A risk class or risk 
3 
characteristic represents the various subsections in the rating factors that have different 
risk exposures. 
J ee (1989), states that the purpose of risk classification system is to group homogeneous 
risks and charge each rating factor a premium corresponding with the average expected 
loss of its risk characteristic. This means that individuals with similar risk characteristics 
are treated in a consistent manner. Furthem1ore, it enables insurers to charge 
differentiated premiums corresponding to an insured's expected loss . This way, cross 
subsidies associated with an average pricing model would be avoided i.e. low risk 
individuals will pay a premium below the overall average and high-risk individuals will 
pay a premium above the overall average. 
Risk classification therefore groups individuals with similar risk characteristics based on 
a rating factor and subsequently charging an appropriate premium. This approach of rating 
is known as experience rating. 
Risk classification systems have been used as an initial step to deal with the practical 
problem of how to determine the expected costs of coverage based on the available 
infonnation. Each outcome reflects the frequency and the severity. For instance, if a class 
includes a number of risks, its probabilities can be estimated by observing outcomes over 
time. These estimates can be used in tum to estimate the estimated coverage costs for the 
risks in the risk class. Thus, an effective risk classification system facilitates the estimates 
of expected costs. A risk classification system can promote internal consistency of the 
estimates, decrease the likelihood of adverse selection2 and aid the tracking of data, 
(Dickie, 2011). 
However, a major drawback in risk classification is that it assumes that each individual in 
the risk class behaves in a similar way. Although, this may not be the case as every 
individual is unique. This would therefore, no longer be fair to some individuals . 
2 Adverse selection refers to a situation whereby the policyholder (or the insurer) takes an action that is to 
his financial advantage based on the information that he has but the other party (insurer) does not have. 
4 
\ 
I 
! 
\ 1.0.6 Trends in Motor Insurance 
Motor insurance is compulsory in Kenya under the Insurance Act CAP 405 of motor 
vehicle third party risks. This Act requires that all drivers in the country, to insure their 
vehicles against any third-party injuries or damages to property. Therefore, it is illegal 
for any person to drive a motor vehicle in Kenya without, at a minimum, third-party 
msurance cover 
According to KNBS 3, the number of new registration of road motor vehicles per year 
has increased from 205,841 in 2009 to 218,057 in 2014. Car Registrations4 in Kenya 
averaged 14,385 from 2006 until2016. This exhibits that the market for motor insurance 
is highly attractive and large. 
According to IRA Annual Reports, Motor Private Insurance has been one of the most loss-
making class of business under General Insurance. It shows that in 2009, the total Gross 
Loss recorded amounted to Kshs 1.278 billion, which has increased to Kshs 1.923 billion 
in the year 2015 . Furthem1ore, IRA through AKI, introduced minimum rates for motor 
insurance. These rates were based on average industry experience and were not based on 
any rating factors. Most insurers, to remain competitive, use this minimum rate (as a 
percentage of the estimated value of motor vehicle), as a price ceiling rather than a price 
floor. 
Therefore, some drivers are paying higher premiums while others are paying a lower 
premium than they should. This, therefore shows a need to change the premium pricing 
approach used for motor insurance in order to ensure that the correct premium is charged 
and the current losses curtailed. IRA has recently issued a circular5 to insurance 
companies that abolishes the use of minimum rates from 2018 thus insurance companies 
will be required to price their own experience. Rating factors form the basis for pricing. 
3 Kenya National Bureau of Statistics 2015 
4 Kenya New Vehicle Registration 
5 IRA Circular No IC & RE 12/2016 CONF/1 RA/00/00 l/03A 
5 
When pricing, two major aspects are supposed to be considered. First the relative premium 
levels need to be detennined, for instance, it is important to charge correct premium for 
inexperienced drivers' relative to experienced drivers, new cars relative to old cars. The 
second aspect is that the overall level of premiums must be adequate to meet the particular 
profit objectives, (Brockman & Wright, 1992). 
Differentiated pricing using rating factors can be used to compute premiums that best 
reflect the risk profile of a particular applicant. The motor rating factors that can be used 
in the pricing basis either relate to the policyholder or the vehicle or the type of cover 
purchased. This implies that for the same individual, the premiums charged could vary if 
different cars are insured. Having considered the above, an analysis is perf01med to 
compare the performance of a counh·y (South Africa) that use rating factors as a pricing 
basis for motor insurance to that of Kenya which has not been using these factors. 
The analysis demonstrated a more stable pure loss ratios for a country that applies rating 
factors as compared to Kenya. This could be illustrated as shown in figure 1. 
0.8000 
0 0.7000 
·.;::; 
0 .6000 ro a:: 
"' 0.5000 
"' 0 
--' 0.4000 
"0 
QJ 
c 0.3000 
:.c 
E 0.2000 
0 
u 0.1000 
- Kenya 
-- SA 
Figure I Pure Loss Ratio 
.... 
2011 
0.5746 
0.66 
Pure Loss Ratio 
-
2012 
0.6502 
0.66 
-
2013 
0.6847 
0.67 
- = =-
2014 
0.7273 
0.65 
2015 
0.7511 
0.64 
Source: IRA Reports, AnJJital reviews, hllp:llwww.saia.co.zal info-cenledsaia-documenlslpublicalioJISiannual-reviewsl 
1.1 Problem Statement 
Most motor insurance companies 111 Kenya collect about 5-l 0 rating factors in their 
proposal fom1s. Despite having these data, these companies have in the past used the 
6 
minimum rates prescribed by the IRA. This implies that they are less likely to be aware of 
rating factors and their importance in pricing. This may justify one of the major reasons 
as to why motor insurance companies have been loss making. Although the minimum 
rates were specified, there was no regulation that compelled insurance companies not to 
price using rating factors thus although they collected data on the rating factors, they used 
the minimum rates possibly due to competitive pressure and market practice. 
Looking into the comparison done between South Africa and Kenya, it is clear that in 
South Africa where motor insurance companies use rating factors as pricing basis, tends 
to make high profits compared to countries that do not incorporate rating factors. 
Having considered the above, the insurers are expected to change their premium pricing 
approach. Given the new regulation by IRA, the change in premium pricing should 
incorporate the use of rating factors. Therefore, to fill in this gap, the study intends to 
suggest a simplified motor rating factor model that uses rating factors and is simple for 
the insurers to understand. 
1.2 Research objectives 
The overall objective of this study is to assess the use of rating factors to price motor 
premiums in light of the new IRA regulations. The past experience and data will be used 
to: 
a) Evaluate the use of rating factors and the relevant rating factors for the pricing of 
motor insurance policies. 
b) Develop a simplified pricing model to compute premiums using the rating factors. 
1.3 Research questions 
a) What rating factors are relevant for the pricing of motor insurance policies 
b) How can a simplified model be used to compute premiums using these rating 
factors? 
7 
1.4 Significance of the study 
The study will be beneficial to insurers in dete1mining the premiums for the different risk 
profiles. The findings could also be used for research by doing further analysis on the 
more risky profiles. 
The study will be beneficial to the potential policyholders who will be keen to !mow the 
different premiums that could be charged by various insurance companies based on a 
specific car. 
The st11dy will also be helpful to potential students interested in motor insurance related 
subjects. 
8 
2 LITERATURE REVIEW 
2.0 Introduction 
This section contains empirical and theoretical studies on the use of rating factors as a 
basis for premium pricing and the various statistical models done to estimate pure 
premiums. 
2.1 Theoretical Studies 
2.1.1 Additive and Multiplicative Models 
Most pricing models have a combination of multiplicative and additive models. A 
multiplicative model implies the multiplication of two or more variables while an 
additive model involves the summation of two or more variables. 
There tends to be a con-elation between different rating factors within a model and thus a 
diversification benefit needs to be allowed for. 
This can be done via the use of correlation matrix or a simplified approach such as the 
square root of sum of squares. 
2.1.2 Simple Pure Premium Model 
Pure risk premiums are based on frequency and severity of claim amounts. Frequency 
represents the incidence rate of claims occuring in a given year. The severity of a claim 
represents the average claim cost associated with each claim. In most studies carried out, 
severity and frequency are treated independently, (Weisberg, 1982). The expected value 
of the observed pure premium for a rating factor is then computed as; 
(1) 
Where i!.i represents the incidence rate related to the risk class i under the rating factor; 
~i corresponds to the average claim cost attached to the corresponding risk class. For 
instance, in a motor insurance company, risk class could be Toyota or Jaguar or many 
others, i!.i could represent the proportion of the number of Toyota cars which were 
9 
claimed in a particular duration and the total number policies ofToyotas for a particular 
type of motor cover. 
For various rating factors the overall1isk premium is the square root of sum of squares 
of all the rating factors 
(2) 
2.2 Empirical studies 
2.2.1 Considerations when selecting rating factors 
Dickie (20 11 ), stated that when coming up with a risk classification system, an insurer 
has to consider the selection of 1isk classes under each rating factors is large enough to 
measure costs with accuracy. Having fewer risk classes means each risk class will have a 
greater volume of historical data on which to base estimates of its risk probabilities. This 
is important because a small group may not necessmily reflect the expected loss 
accurately as there is a greater probability that the group may be biased and have a 
volatile expe1ience due to insufficient volume. 
Abraham (1985), points out that homogeneity needs to be considered when selecting the 
rating vmiables. Homogeneity indicates that since all individuals belonging to a 
particular risk class pay same premiums, their risk of loss should be very similar. He 
further adds on that the rating variable should be highly stable and reliable. Reliability 
measures how much simple and evident differences are utilized to classify the insured in 
an accurate way. 
In addition to the above considerations made by Abraham (1985), PoiTini (20 15), points 
out that separation, causality and incentive worth should be considered when selecting 
rating variables. The separation measures all risk classes ' mean expected losses which 
ought to be sufficiently different in terms of loss expectation to wanant their 
identification as a separate class. Causality measures whether category distinctions are 
supported by characte1istics associated with loss. Incentive worth means that a good 
10 
category ought to classify the characteristics inside the insured ' s control so as to produce 
the inducement to adopt low-risk characteristics. 
Insurers sell insurance covers at prices that are sufficient to cover the anticipated cost of 
claims, expenses and usually a profit loading, (an expected profit to compensate for the 
cost of capital necessary to support the sale of cover). The insurers aim to classify risks 
they underw1ite in order to charge premiums commensurate to risks undertaken. 
Anderson (2005), explains that the amount of loss to the insurer depends on two major 
variables. The first one is the frequency of losses which is the number of losses that will 
occur in a specified period. The other major variable is the severity of losses which is the 
average cost of claims. These two variables affect pure premium. Therefore, when 
selecting rating variables, the insurer should ensure that 1isk classes under each rating 
factor reflects the different premium values. 
A key consideration when selecting a rating factor is legislation in that particular 
jurisdiction. The rating factor should not be restricted under the laws. If it is restricted, 
then insurers are not pem1itted to apply these rating factors to premium pricing. 
For maintaining a viable insurance system, the risk classification should be fair, should 
reflect expected cost differences, should distinguish among risks on the basis of relevant 
cost-related factors and should be practical and cost-effective. In addition to these, the 
risk classification system should be accepted by the public. 
Rating factors could fall under tlu-ee major categories; factors associated with the 
policyholder the vehicle and the coverage. Some of the factors related to the 
policyholder include age, profession, gender and marital status. Factors related to the 
vehicle include year of manufacture, make, body, vehicle, can-y capacity, engine 
capacity and color. Factors related to the coverage may include type of cover purchased 
by the policyholder. 
It is worth noting that motor rating in countries like UK uses up-to 20 rating factors , 
many of which are gathered when a policy is taken out. In Kenya, insurance companies 
collect between 5-10 rating factors . As earlier stated, these factors have not been used in 
the actual pricing process . 
1 1 
Dahlby (1983), found evidence that low-risk individuals (safer drivers) tend to leave the 
market when risk classification in automobile is excluded. 
Dionne G. G. ( 1998), studied motor insurance markets and concluded that risk 
classification removes residual adverse selection. The same authors in the later years, 
(Dionne G. G. , 2001), showed that adverse selection in motor insurance market could be 
controlled by using an appropriate risk classification system. 
However Schwarzwe (2005), showed that risk classification was inefficient in the 
German automobile insurance market during the 1990s. In addition, risk classification is 
viewed as an effort in avoiding risk. Such a competition based on use of rating factors 
has a limited value in producing a public good. 
2.2.2 Rating factors 
2.2.2.1 Age 
McKnight & McKnight (2003), noted that young individuals are risk takers. This means 
that they are more likely to take higher 1isks compared to the rest of the population. This 
can be explained by lack of diiving experience. 
Kelly & Nielson (2006), can·ied out a study which examined the use of age in the 
delivery of personal insurance to Canadians. The use of age as a rating factor had been 
justified on the basis of its existing strong intuitive causal relationship. In addition, they 
reviewed the relationship between age and driving ability in relation to young d1ivers 
and old drivers. Also, they considered the various 1isk-taking behaviors of the young 
individuals, the time duration for an individual to d1ive proficiently and the effects of 
these on the level of accidents caused by young drivers. They examined between ageing, 
sensory and the cognitive skills required for an individual to drive. This study 
demonstrated functional limitations and the environmental factors that are highly 
coiTelated with age and that make both young and elderly drivers high risk drivers. This 
study reflected that young drivers are more likely to be involved in road accidents that 
tend to have a significant impact. 
12 
In UK, Groupe Consultatif Actuariel Europeen (20 11 ), assessed the use of age as a 
rating factor and found that males aged 17 are over are 8 times more expensive than 
males aged 65 in regard to claims experience over the insured individuals. 
Braver & Trempel (2004) and Teff (2008) exhibited higher accident tendencies for 
young and elderly drivers. Their analysis resulted to aU shape curve for loss against . 
age. Such results were applied in this study for Kenyan insurance company reflecting 
higher rate coefficients upon young and elder drivers. 
A study by Bennet, eta! (2008) in UK examined the implications of removing age as a 
rating factor. It concluded that the cost of motor insurance of young individuals, (under 
25 years), would drop by approximately 17%. This would imply that motor insurance 
will become more affordable for these individuals. Therefore, encouranging most young 
individuals to buy higher powered motor cars. This would increase the number of motor 
vehicles being bought by these individuals which will reflect an increase in the expected 
claim costs as more inexperienced drivers on the road results to more accidents of 
significant impacts. 
Groupe Consultatif Actuariel Europeen (20 11 ), illustrated that age is an essential risk 
factor in managing adverse selection to an acceptable level for particular types of 
insurance. Adverse selection could cause a market to be unsustainable. On the other 
hand, if age were not used in pricing, insurance covers would become unfair for low-risk 
individuals and high-risk individuals would tend to drive recklessly as the premium rates 
are to their advantage. 
In addition to this, it is believed that young drivers tend to use cell phones while driving 
and thereby resulting to an increase in the number of accidents. 
2.2.2.2 Gender 
Gender is one of the most basic rating factors which the insurance industry uses to 
classify individuals. Storie (1977) carried out a study that presented the differences in 
driving characteristics between male and female based on speed, skill and attitude. The 
major findings for this study reflected that females are more likely to drive at lower 
13 
speeds and overtake more carefully while males are more likely to drive in a 1isky 
manner. 
Butler, Butler, & Williams (1988) analyzed motor accidents records for both male and 
female drivers using US actual data. Based on the claim losses and the premiums 
collected, the study reflected that females were overcharged for their vehicle. 
Using data from three personal vehicle insurance policies in Georgia, USA, Puelz & 
Kemmsies (I993) examined how gender and other demographic variables impacted on 
premium pticing. This study demonstrated that gender significantly affects premium 
rates although its level of impact is relatively less than rating factors such as driving 
record, location, vehicle type and age. 
Waylen and McKe1ma (2002) noted that the pattern of road accident differs by gender. 
Men are more likely than women to be involved in crashes that occur on bends, in the 
dark or those that involve overtaking. Women, on the other hand, have a greater 
frequency of crashes occurring at junctions than men. This supports the suggestion by 
Storie (1977), that men are more at risk from accidents involving high speed while 
women are at more likely to be involved in accidents resulting from perceptual 
judgement eiTors. 
In addition, there is a high probability of men driving at night or midnight are under the 
influence of drugs or alcohol. Noting the eye vision is impaired at night, there are high 
chances of accidents with higher severity of loss. On this basis, men tend to drive in a 
risky manner and causing more accidents compared to women. 
As at December 20 I1, across Europe, gender had been used as a rating factor by insurers 
in many insurance markets. However, from December 2012, insurers in Europe had been 
restricted to treat men and women differently in computing premiums and benefits for 
any new insurance contracts. This was as result of a landmark ruling on 1 March 20II 
by the European Court of Justice, (Groupe Consultatif Actuariel Europeen, 20 II). 
2.2.2.3 Color 
Newstead & D'Elia (2007) analyzed the relationship between the color of the vehicle 
and the accident risk using data from two Australian states and found a clear statistically 
14 
significant relationship between the two. The study showed that vehicles with lower 
visibility colors tend to have a higher accident risk as compared to those with higher 
visibility colors. White vehicles were proved to be the safest in terms of accident risk. In 
addition, the study also mentioned that environmental factors could modify the 
relationship between the vehicle color and accident risk. 
2.2.2.4 Year of manufacture 
National Highway Traffic Safety Administration (2013) examined how a vehicle's age 
would relate to the driver's injury severity in fatal crash. The study demonstrated that the 
percentage killed is lowest among newer cars and highest for old vehicles. 
National Highway Traffic Safety Administration (20 13), analyzed how age of vehicle at 
time of crash and the vehicle's model year are correlated with the accident rate. The 
results of this study can be summarized below: 
Vehicle Age (years) by Vehicle MY MY 2008-2012 MY 2003-2007 MY 1998-2002 MY 1993-1997 
Age G-3 0.29 0.33 0.35 0.37 
Age 4-7 0.31 0.35 0.38 0.40 
Age 8-11 0.33 0.37 0.39 0.42 
Age 12-14 0.35 0.40 0.42 0.45 
Age 15-17 0.38 0.43 0.45 0.48 
Age 18+ 0.42 0.46 0.48 0.50 
Table I Vehicle Year of manufacture and accident rate 
Source: https:/lwww.google.com/webhp?sourceid=chrome-instant&ion =I &espv= 2 &ie= UTF-
8#q=discount+FACTOR+FORMULA 
MY 1985-1992 
0.42 
0.45 
0.47 
0.49 
0.52 
0.56 
The above results could be attributed to increased safety record of newer car models 
compared to older car models. 
2.2.2.5 Type of cover 
Claims from comprehensive motor insurance covers are higher than third party covers 
since additional payments are made to cover the cost of material damage to the vehicle. 
Under both types of cover, third party claims are payable owing to damage to property or 
injury to persons inside and outside the car. 
2.2.2.6 Make and models 
Claims analysis from a local underwriter in the Kenyan market indicates that the claims 
experience differed significantly between different car makes and models. Toyota forms 
15 
the largest proportion of cars in the Kenyan market, followed by Nissan. Due to law of 
large numbers, the claims experience associated with a car brand that has significant 
volumes like Toyota is expected to be more stable and less volatile compared to a brand 
that has fewer cars. 
The repair costs associated with a car brand that has few volumes is also higher than a car 
brand that has larger volumes due to lack of readily available spare parts. 
2.2.2. 7 Engine rating 
The engine rating of a car is directly proportional to the speed and power output. Cars 
with very high engine ratings are likely to be expensive, have extra safety features and 
are likely to be purchased by owners who either have a driver or are experienced in 
driving, having owned another car. 
Cars with a low engine rating are likely to be cheaper, have basic features and are 
popular with individuals as an entry level car 
2.2.3 Pure premium models 
A number of studies have been conducted on the use of models to compute pure risk 
premiums based on multiple rating factors . Researchers have suggested various 
statistical procedures for risk classification. A functional form for a statistical model is 
required to estimate pure premiums using regression methods. 
Ahner ( 1957), conducted a study on modelling of pure premiums within the risk 
classification system. He emphasized on a multiplicative model for use with rating 
factors with the general form: 
(3) 
Where Pij represents the claim proportion for class ij; P0 represents the overall mean; 
ai bj represent the effect of the levels i and j for rating factors a and b respectively; eij 
represents the error tem1. He used weighted least squares approach as an estimation 
method and found a fine goodness of fit of residuals being generated by equalization and 
not by random choice of factors. 
16 
Bailey & Simon (1960) examined loss ratios for additive model and multiplicative 
model. The additive model could be expressed as follows; (Bailey & Simon, Two 
studies in Automobiloe Insurance Ratemeking 
(4) 
Bailey & Simon (1960) analyzed Canadian automobile insurance data and showed that 
the multiplicative models produced systematic overestimates for the highest risk driver 
classes. He used minimum chi squares as an estimation method . 
Bailey R. (1963) examined the multiplicative model using the minimum bias method. 
His study provided evidence that a multiplicative form is preferable if all factors are 
percents and additive approach is preffered if all rating factors are cents. 
Jung (1968) tested the multiplicative model using the Heuristic method, (Modified chi-
square minimum) and found out that multiplicative model will result to biasness. 
Chang (1979) used a loglinear form of function to derive the parameters for the 
multiplicative model. He demonstrated that loglinear models tend to overestimate high 
risks by double counting classification factors. The estimation method used was 
weighted least squares. The study showed that predictive accuracy of the additive model 
was better. Furthem1ore the study suggested separate estimation for claim frequency and 
severity. 
Ajne (1980) analyzed multiplicative model using method of moments, (modified chi-
square minimum). Based on the analysis, the study demonstrated that the estimator may 
have a positive finite sample bias . 
Sant (1980) realized the need to apply statistical modelling and parameter estimation. He 
suggested a multiplicative model and applied the principle of least squares to get the 
relativities. One of the major findings was bias for high risks and low. 
Fairley, Tomberlin, & Weisberg (1981) analyzed New Jersy data by applying additive 
log-linear models using weighted least squares. This study noted the tendency of log-
linear models to overestimate high risks. 
17 
DuMouchel (1983) introduced a hybrid functional fom1 expressed as; 
(5) 
For which Ti represents the additional parameter for the multiplicative factor for class-ij. 
He estimated pure premiums using iterative wieghted least squares and demonstrated 
that pure premiums are determined by a Bayesian credibility scheme. 
Harrington ( 1986) used auto insurance claims data from the state of Massachusetts and 
from United Kingdom to estimate pure premiums using maximum likelihood estimation. 
In addition the study tested for functional fonn using the power transfom1ation 
suggested by Box and Cox. The study concluded that estimation and testing of 
functional form using Box and Cox procedure may provide more accurate predictions 
than simply assuming either a linear or log-linear model. In overall the sh1dy findings 
reflected that flexible functional fom1s produce better goodness fit and more accurate 
estimates. 
J ee ( 1989), carried out a comparative analysis of altemative pure premium models in the 
automobile risk classification system. The altemative pure premium models were 
compared in terms of their predictive accuracy and adequacy of underlying distributional 
assumptions. These models include Box and Cox heteroskedastic model and the Bayes 
estimation models . 
Furthennore, Noriszura & Abdul (2005), demonstrated the Generalized Poisson 
Regression models as an altemative to risk classifcation. It showed that Generalized 
Poisson distribution is superior to Poisson distribution. Thus contributing to a more 
accurate claim frequency rates. 
18 
2.3 Conceptual framework 
The conceptual framework for this study could be illustrated as shown below; 
Figure 2 Conceptua/ji-amework 
2.4 Research gaps 
Insurers in Kenya have the necessary rating factor data required to estimate pure 
premiums. Despite having this data, they are unable to incorporate it on the pure 
premium pricing mainly because they lack knowledge on the use of rating factors as 
they have never been applying minimum rates. 
The study emphasizes on the use of the simple approach to estimate the pure premiums 
charged to a policyholder incorporating the vatious rating factors. This is because most 
insurers in Kenya have less lmowledge on the use of rating factors and therefore 
applying a complicated model to estimate pure premiums may not be understood by the 
salesforce and clients. The use of a simple approach can be easily communicated and 
understood by the insurers. 
In addition, most of the pure premium models are time consuming and expensive to 
monitor. 
19 
3 RESEARCH METHODOLOGY 
3.0 Introduction 
This chapter provides an outline of the data and methodology used in the study. It 
explains the research design, target population, sample design and sampling technique, 
data collection and data analysis. 
3.1 Research Design 
The study is descriptive and quantitave in nature as it tends to assess the various rating 
factors to be used in premium pricing as well as computing a simplified model for 
premium pricing which uses numeric claims data. 
3.2 Target population and Sample Technique 
The target population for this study are the existing insurers in Kenya. There are about 
37 general insurance companies out of which 35 companies underw1ite motor private 
insurance. Sample selection is based on non-probabilistic sampling method because 
strongly established company is required to be selected as a good representative of a 
motor p1ivate insurance provider in the industry. 
3.3 Data collection 
The data collection will be cross-sectional in nature. This is because the study involves 
claims data collection over a period of time i.e. from 2009 to 2015. Past claims data will 
be collected from a local Kenyan insurance company. About 65, 003 policies have been 
obtained from the company as sample data corresponding to the indushy The total sum 
assured and the total premium collected from this data are KES 32,489,574,214 and 
KES I ,435,208,226. 
For each policy, the following information will be required; 
Inputs Description of the inputs 
Motor Vehicle Registration Number 
Policy Number Claim Verification purposes 
Age Policyholder related Rating factors 
20 
Inputs Description of the inputs 
Profession Policyholder related Rating factor 
Value of the vehicle 
Make of the vehicle 
Type of body 
Engine Rating Vehicle related Rating factors 
Color 
Year of manufacture 
Seating capacity 
Type of cover 
Other benefits paid out such as Policy related Rating factors 
windscreen 
Claims paid out, (Yes/No) 
Claim Number Claims Data 
Claim Amounts paid 
Premiums charged 
Sum assured Collected for analysis purposes 
Table 2 Description of Inputs 
3.4 Data Analysis 
A motor rating factor model is a simplified model that enables a company to calculate 
the premium to be charged on a particular vehicle depending on the various motor rating 
factors. Each of these rating factors contribute to the pure risk premium charged to the 
policyholders. 
Each rating factors could be split into the type of motor covers. For example, a rating 
factor such as make of vehicle will have the available makes for each type of motor 
cover. This would make it easier when performing analysis. Analysis on each rating 
factor could be divided into two; Frequency of claims and severity of claim amounts. 
3.4.1 Frequency of claims 
For analyzing the claims frequency, we need to have the total number of policies, the 
total number of policies claimed and total premium paid out. 
21 
The frequency or incidence of claims can be computed using the formula below; 
Frequency or Incidence (6) 
Number of policies claimed in a risk class 
Total number of policies exposed per risk class 
For instance, assuming a pmiicular company provided motor cover to 1000 Toyotas, out 
of which only 100 Toyota policies had been claimed during some time interval. The 
frequency of Toyota claims could be represented as; 
100 
Frequency or Incidence = -- = 10% 
1000 
3.4.2 Severity of claim amounts 
Severity represents the average claim amount paid out. 
Severity 
Total claim amount for a risk class 
Total number of claims per risk class 
(7) 
For instance, assuming a pariicular insurance company received 10,000 Toyota claims 
within some time interval for which the total claim amount summed to 80,000,000. 
Thus, on average, the severity cost of claims per policy could be represented as; 
Severity 
80,000,000 
10000 = 8'000 
3.4.3 Pure Premium 
Pure premium is the summation of the product of frequency and severity. 
n L (Frequencyi *Severity i)2 
i=l 
Where i represent the various risk classes. 
22 
(8) 
I 
I 
I 
f 
3.4.4 Total Premium Main Cover 
The pure premium is then adjusted to loadings such as expenses, commissions, profits 
plus any additional benefits an insurance company offers; 
Total Premium main cover (P) 
= [Pure premium+ (P • expense loading rate) 
+ (P • commission loading rate)] + (P * profit loading rate) 
Total Premium main cover (P) 
_ Pure premium/ 
- 1- expense loading rate- comission load rate - profit load rate 
3.4.5 Total Pt·emium Payable 
The total premium payable is adjusted to include the optional benefits provided by 
. . 
msurance compames. 
(9) 
(10) 
Total Premium Payable ( 11) 
=Total premium main cover+ optional benefits 
23 
4 RESULTS AND ANALYSIS 
4.0 Introduction 
This chapter provides an outline of the preliminary analysis, model rating factors , 
assumptions used, model description, analysis of the findings on each rating factor used, 
comparing the results with the current existing model and a sensitivity analysis. 
4.1 Preliminary Analysis 
The data was collected from a local general insurance company in Kenya from the year 
2006 to 2015 . The data received included the policy number, client names, effective 
dates, underwriting year, sum assured, premiums charged per policy, type of cover, 
registration number, make, body type, engine number, chassis number, engine rating 
(CC), color, year of manufacture, carry capacity, claims paid and claim date. 
Data on client name, ID number, KRA pin, registration number, chassis number and 
engine number have been used for claims verification process. 
For this analysis, the rating factors related to the vehicle used include Year of 
manufacture, CC, Body, Make, Color, Carry Capacity and Value. Rating factors related 
to the policyholder include age and profession. Rating factors related to the policy 
include type of cover. 
The above rating factors have been used for the analysis due to the fact that there is data 
on it and it is sufficient for performing an analysis. 
The overall statistics for the data collected can be shown below: 
Overview statistics from 2005-2016 
Cars Insured 
-- ----
Sums Assured (Sum Values of the cars) 
Premiums 
Average Rating 
Table 3 Overall Statistics from 2005-20 I 6 
24 
I 
65,003 
32,489,574,214 I 
1,435,208,226 
4.42% 
I 
I 
,, 
The percentage captured for each column by the data can be summarized in the table 
below; 
Data Requested Total Entries 1 
POLICY 65,003 I 
CLIENT -- I -- 6S,003 I 
UW YEAR 65,003 ' 
S UM INSURE~~-- 65,003 I 
PREMIUM 65,003 
_2_YPE OF COVER - J =--=- 6~003 1 
REGISTRATION - L 65,003 4 
MAKE [ 62,003 ! 
BODY TYPE 65,003 
ENGINE NO. -, 65,003 ., 
CHASIS NO. 65,003 
'-------
Non Blank I Blank IPer~;ntage 
I Captured 
65,002 1 100.00% 
6~ 03 I-~----
65,003 
-:: 1 1_?o.oo% j 
100.00% 
64,992 1 11] 
65,003 - I 
~- 65,603-, --- - ~ i 
64,970 33 
6_4,691]-_-_--312 ,-
65,003 
3,737 . 61,266-1 -
3,901 61,102 
99.98% J 
100.00% I 
100.00% j 
9~.~5% -1 
99.52% I 
100.00% ! 
5.75% 
6.00% 
cc I 65,003 I _____ 4_8_,_15_4-+ _____ 1_6_,8_4_9_,1_ -~08% 
COLOR 65,003 1,884 63,119 
YOM 65,003 1 47,844 c- -17,l 59 ] 
CARRY CAPACITY 65,003 52,505 12,498 
--- - --
65,003 ,- -VALUE -------~---6_1_,8_8_6_,1 _____ 3__ ,11~~ 
CLAIM NO 65,003 4,175 60,828 
CLAIM DATE 1 -=- ~5,003 f 
PAID 65,003 
-~, 175 J 60,828 1 
4,175 1 60,828 
TOTAL 1,625,075 1 1,138,363 1 486,712 1 
Table 4 Data Percentage Captured 
2.90% 
73.6o% 1 
80.77% 
95.20% l 
6.42% 
- ~42% 1 
6.42% 
70.05% 1 
From the summary it can be noted on average about 70% of the colunms are not blank. 
This justifies the use of the data for this analysis. Colu11U1s such as engine number, 
chassis number, claim number, date and paid capture 6.42% which is relatively low. 
However these information is required for claim verification and not used for computing 
premium amounts. Color captures only 2.9% but is used as a rating factor in the analysis 
because literature review indicates a high correlation between the claims experience and 
the color of the vehicle. However the results for the color will be biased and so not 
highly reliable. 
However for the analysis, data used was fro m 2009-2015 because only 2,010 policies 
were recorded from 5 years (that is 2005 to 2008 and 20 16) which on average represents 
25 
a very small number ( 402) of policies per year and therefore analysis on this would not 
be reliable and hence has been ignored for this analysis. 
------------- -------
Overview statistics from 2009-2015 
Cars Insured 
r--------
Sums Assured 
Premiums 
, Average Rating 
Table 5 Overview Statistics from 2009- 2015 
4.2 Model Rating factors 
62,993 
30,137.489.113 1 
1,355,080,995 
The rating factors used for this analysis include age, year of manufacture, engine rating, 
body, make color cany capacity value all of which are split by type of cover. The type 
of covers include Third party act only, third party fire and theft , comprehensive cover 
and standard cover. 
However the data received as shown below only had 1 standard cover policy which is 
insignificant and therefore has been excluded in the model. 
1 TYPE OF COVER 
Comprehensive 
Lstandard Cover 
Third Party Act Only 
r Third Party Fire And Theft 
Total Exposure 
Table 6 Number of policies per type of cover 
4.3 Assumptions 
Expense premium 
_I __ _ 
r---
Number of policies I 
38,312 
65 
60,092 J 
Expense premium rate assumed for this study is 15%. Previous study estimate the 
expense to lie between 5-20% and is very subjective to the company. This model 
therefore assumes a few scenarios for expense premium rate (such as 5%, 10%, 15% and 
20%). 
Commission 
Commission rate assumed for this study is 20%. Commission rates also vary from 
company to company. This model therefore assumes a few scenarios for the commission 
rates such as 5%, I 0%, 15% or 20%. 
26 
I-
I 
I 
Profit loading 
Profit loading rate is assumed to be 5%. Profit loading rates also vary from one company 
to another. This could range from as low as 0% to as high as 10%. The 0% profit loading 
applies to insurance companies who intend to attract more business by offering lower 
premiums, while 10% is mostly applied to unique products with no substitutes in the 
market. However, higher profit loading reflects high premiums, high profits but may 
affect marketability of the product negatively. 
Age distribution and factor 
Based on literature review, the age factor is nonnally U-shaped. But due to insufficient 
data, this was not possible fir this model. Therefore a factor of 1 for each age has been 
used. Although this is not a good representation of reality, therefore would recommend a 
further study that could justify factors based on research on policyholders' age and 
accident rate in Kenya 
Profession 
This assumption is also very subjective. Therefore for this study a factor of 1 is assigned 
to all professions. However, a further study needs to be done about analyzing the 
relation between profession and accident rate in Kenya. 
Windscreen replacement 
The maximum amount for windscreen is assumed to be approximately KES 20,000 with 
an incidence rate of 2%. Therefore the risk premium due to windscreen replacement is 
approximately KES 400. 
4.4 Model Description 
The model is detenninistic in nature in that it includes fixed inputs and when run, it 
results to a single premium value. The model is dynamic in the sense that the raw data 
worksheet could be altered or replaced by individual company' s claim experience. This 
means that different companies could use this model by incorporating their company 
experience and adjusting assumptions based on their perceptions or past expe1i ence. 
27 
The total pure premium payable that incorporates the various motor rating factors can be 
computed as shown below; 
n L (Frequencyi * Severity az 
i=l 
(8) 
Where i represents the different rating factors, such as Year of manufacture (YOM), 
Engine rating (CC), Body, Make, Color, CaJTy Capacity and the value of the vehicle. 
The table below summmizes the pure premium value using the data and the above 
fom1Ula; 
TYP~ Of covm 
RISK PREMIUM 
11,870 
4.19% 145,757 6,109 
4.57% 159,812 7,304 
6.50% 153,946 10,000 
COlOR.COMPR~H~NSIV~ BLACK 11.18% 236,758 26,480 
CARRY.COMPREHENSIVE 4.73% 16W9 7,617 
VAlUE.COMPREHENSIVE 5.80% 194,804 
ARiiHMEiiC RISK PREMIUM 80,673 
GEOMETR IC RISK PREMIUM 34,904 
Figure 3 Geometric Pure Premium 
The above geometric risk premium is thereafter adjusted to incorporate the policyholder 
related factors (such as age, gender, profession), expense premium, commission 
premium and profit loading premium and other optional benefits (such as windscreen 
replacement, radio and entertainment). 
28 
The total premium payable can be computed using geometric risk premium as shown 
below; 
Pu re Ris.k Pr em ium 
Age adjust ed Risk Prem ium 
Expense Pr emiu m 
Commis.s:ions 
Profit Loading 
Total Premium Main Cover 
Optional B·enefits: 
Windscreen Replacement 
Radio and Entertainment 
Total Premium Opt ional Benefit s 
Total Premium Payable 
Figure 4 Model Output 
4.5 Analysis of the findings 
34,904 
.34,9()4 
7 , 222 
4 ,.8 14 
1,204 
48,144 
49,294 
400 
750 
1,1.50 
This section provides an analysis of the results obtained from the model using the 
va1ious rating factors. 
4.5.1 Year of manufacture 
It was deduced from the model that the value of premium increased with the year of 
manufacture. This result was unexpected as the literature review showed that newer car 
models have increased safety record compared to the older car models. The converse 
could be true because newer car models have more expensive spare parts and thus the 
premiums will be expected to be higher. 
4.5.2 Engine Rating (CC) 
The results showed that the value of premium increased as the engine rating, (CC), 
increased up to 5100 CC and reduces thereafter. Literature review also showed that the 
29 
engine rating of a car is directly proportional to the speed and power output. Cars with 
very high engine ratings are likely to be expensive, have extra safety features and are 
likely to be purchased by owners who either have a driver or are experienced in driving, 
having owned another car. Therefore the premium is likely to increase in line with high 
engine rating. 
The results showed a decrease in premium for cars with an engine rating beyond 5500 
CC. This could be attributed to the fact that most of the insured cars in this data had a 
CC below 5100 CC as shown below: 
Engine Rating (cc) 
101-1100 
I 1101-2100 
2101-3100 
------- - -- --
: 3101-4100 -
4101-5100 
I 
~L~ 
j 
,'-5_1_o1_-_6_1_o_o_-_-______ ~ 1---
6101-7100 
I 7101-8100 --
9101-10100 
Table 7 Exposure of Engine Rating 
%Exposure I 
2.72% I 
------- ------1 
85.73% 
9.81% 
0.94% 
0 .75% 
0.02% 
------ ---------1 
0.01% 
0.02% 
0.00% 
The above justifies as to why the results reflected a very low incident rate for cars with 
CC greater than 5100. 
4.5.3 Color 
The results also deduced that darker colored cars such as black and maroon had higher 
premiums than light colored cars such as white. This result was expected as the literature 
review showed that vehicles with lower visibility colors tend to have a higher accident 
risk as compared to those with higher visibility colors . In addition, results showed that 
green colored cars are associated with low incidence rates. This could be attributed to · 
the fact that the data was skewed which means there were very few green cars in the data 
received and therefore low premium rate. 
30 
4.5.4 Body of the car 
Furthem1ore, it was deduced that vehicles with larger body are charged higher premiums 
than those with smaller bodies. This is because of the fact that large body vehicles tend 
to be more expensive and have more costly spares. 
4.5.5 Carry capacity 
For CaJTY capacity, the results were evenly spread and therefore no conclusion can be 
based from this data. Further analysis need to be done to prove whether there is a 
conelation between the claims experience and carry capacity. 
4.5.6 Make and model 
The results showed that expensive makes (such as ford) have a higher premium compared 
to cheaper makes such as Toyota. This could be attributed to the fact that there were very 
few such makes which either had a high incidence rate or high severity amount. 
Furthennore, it was also deduced that makes such as KIA had a low premium. This was 
because the data comprised of few insured KIA cars with a low incidence rate. This result 
was expected because the literature review stated that the claims experience associated 
with a car brand that has significant volumes like Toyota is expected to be more stable 
and less volatile compared to a brand that has fewer cars. In addition, the repair costs 
associated with a car brand that has few volumes is also higher than a car brand that has 
larger volumes due to lack of readily available spare parts. 
4.6 Scenario Analysis 
A premium rate for a particular car with a value of 1 million had been computed using 
the current existing model and the motor rating factor model. The current model 
assumes a minimum rate on the value of the car that is approximately 4.5%. 
31 
Assuming there are about 6 different scenarios which could be summarized in the 
following table; 
Value (in YOM cc Make Body Color Premium Premium 
KES) (rating (current 
factor model) 
model) 
I 1M 2006 1500 Toyota Station Black 50,149 45,000 
Wagon 
2 1M 1995 3000 Toyota Saloon Black 46,484 45,000 
3 1M 2001 3000 Toyota Saloon White 34,992 45 ,000 
4 1M 2006 1500 Ford Saloon Black 76,188 45,000 
5 1M 2005 5100 Toyota Saloon White 32,946 45,000 
6 1M 2006 1500 Toyota Saloon White 37,228 45,000 
Table 8 Scenario Analysis 
From the results above, it could be noted that the rating factor model leads to different 
premium rates for different combinations of rating factors for a car whose value is 1 
million. The existing model would charge a constant premium of 45,000 for all the 
above scenarios. This means that some policyholders have been overpriced (for instance 
scenario 3,5,6) and others have been underp1iced ( for instance scenario I ,2,4). This is 
consistent with any pricing model that charges an average rate. Therefore, the rating 
factor model provides a better estimate for premium rates . 
4.7 Sensitivity of analysis 
Spread of the premium effect on each rating factor had been computed and ranked so as 
to find out the most relevant rating factor for insurers that could be contributing to the 
losses. Based on the results, it was noted that color had an abnormal premium effect. 
This was because the data was skewed in that it included one maroon car that had 
claimed an amount approximately KES 453 ,000. Because of this entry the spread of 
premium effect of color was highly skewed and unreliable. The spread of the premium 
32 
effect was the highest for value followed by body type, make, carry capacity, year of 
manufacture and engine rating 
The results are illustrated below: 
Spread of premium effect 
500,000 
450,000 
400,000 
350,000 
300,000 
250,000 
200,000 
150,000 
100,000 
50,000 
COLOR 
Figure 5 Spread of Premium 
VALUE BODY TYPE --•-MAKE 
33 
-CARRY 
CAPACITY 
-
YOM cc 
5 DISCUSSIONS 
5.0 Introduction 
This chapter provides conclusions, limitations and recommendations for this study. 
5.1 Conclusions 
In overall , the model findings reflected different premiums for different rating factors 
which therefore showed a con·elation between the claims experience and the motor 
rating factors. The findings reflected an increase in premium rate in line with an increase 
year of manufacture, engine rating and dark colored cars. 
Based on the spread of the premium effect in the vmious sub-categories, color had the 
maximum effect followed by value of the car, body type, make and model, can-ying 
capacity, year of manufacture and lastly engine rating which had the least impact on 
premiums. On the above basis, the most relevant rating factors were value of the car, 
body type, make and model , year of manufacture and engine rating. 
The geometric risk premium model provides a simple and practical method to compute 
the risk premium using rating factors as the square root of sum of squares provides some 
diversification benefit between the rating factors. 
5.2 Limitations 
Developing an initial motor rating factor model could be very time consuming. 
It requires regular updates and modifications to the model due to changes in policies for 
which expertise are required. 
In order to conduct an effective analysis, a lot of data may be required which is difficult 
to obtain due to confidentiality and limited publicly available information. 
Past data may not be in the fom1at required. Therefore cleaning of the data may be 
required which could be very challenging. 
The assumptions made on age and profession factors were difficult to obtain because of 
privacy issues, limited data and information. 
34 
The motor private vehicle rating model demonstrated how rating factors can be 
incorporated in the calculation of premiums. However it fell shor1 because some values 
used, could not be obtained or estimated precisely. 
5.3 Recommendations 
The analysis assumes independence among the rating factors. However to minimize the 
con·elation between different rating factors the model uses square root of sum of squares 
approach. This may not be the case in reality and therefore a fur1her study could be done 
to identify the exact coiTelation between the various rating factors . 
The analysis assumes that all professions are likely to have similar claims experience 
and therefore a factor of I has been used all through. This is because of lack of data on 
the profession of the policyholder. But this is usually not the case in reality because 
some occupations are much riskier and tend to have higher frequency or severity of 
claims than others for example a car rally driver. Therefore, further analysis on different 
profession and the effect on claims experience could be studied. 
A further reconunendation is an analysis on how age affects the level of accidents in 
Kenya. This further research will make the model more realistic and accurate compared 
as it ctmently assumes that both old and young are equally likely to claim. 
For rating factors such as color of the vehicle, which had limited data (2 .9%) could be 
re-analyzed using different reliable and sufficient data so as to confirm the impact of 
color on claims experience. 
Further studies should seek to determine precise values for the assumptions that will be 
suitable for various insurance companies. 
The effect of other rating factors such as marital status, age of license, convictions, 
geographical location, alarm/ immobilizer, modifications, use of vehicle and excess on 
motor premium pricing could be studied. 
35 
6 REFERENCES 
Abraham, K. (1985). Efficiency and fairness in insurance risk classification. Va Lavv 
Rev, 403-451. 
Ajne, B. (1980). A Note on the Multiplicative Ratemaking Model. ASTIN Bulletin, 1-9. 
Akerlof, G. A. (1970). The maket for lemons: Quanlity Uncertainty and the Market 
Mechanism. Q. J Econ, 488-500. 
Almer, B. (1957). Risk Analysis in Theory and Practical Statistics. Transactions of the 
15th International Congress of Actuaries , 314-353. 
Anderson, J. B. (2005). Risk and Insurance. U.S .A. 
Bailey, R. ( 1963 ). Insurance Rates with Minimum Bias. Proceedings of the Casualty 
Actuarial Society , 4-11. 
Bailey, R., & Simon, L. (1960). Two Studies in Automobile Insurance Ratemaking. 
Proceedings of the Casualty of Actuaries, 1-19. 
Bailey, R., & Simon, L. (1960). Two Studies in Automobile Insurance Ratemaking. 
ASTIN Bulletin: The Journal of the fAA, 1-19. 
Bermet, C., Hilary, N., Lavelle, D., Michaels, 1., Mitchell, G., Morales, P., ... Williams, 
N. (2008). Free Market Pricing GIRO Working Party. UK. 
Braver, E. R., & Trempel, R. E. (2004). Are Older Drivers Actually at Higher Risk of 
Involvement in Collisions Resulting in Deaths or Non-fatal injuries among their 
passengers and other road users? Injury Prevention, 27-32. 
Brockman, M. J., & Wright, T. (1992). Statistical Motor Rating: Making Effective Use 
of Your Data. Journal of the Institute of Actuaries, 457-543. 
Butler, P., Butler, T., & Williams, L. (1988). Sex-Divided Mileage, Accident, and 
Insurance Data Show that Auto Insurers Overcharge Most WOMEN. Journal of 
Insurance Regulation, 243-284; 373-416. 
Carrie, W. (2007). Research Methods. Journal of Business & Economic Research . 
36 
Chang, L. &. ( 1979). Pricing Automobile Insurance under Multivarriate Classification of 
Risks: Additive versus Multiplicative. Journal of risk and insurance, 73-96. 
Coutts, S. (1984). Motor Premium Rating. Insurance: Mathematics and Economics, 3, 
73-96. 
Creswell, J. W. (2002). Educational research; Planning, conducting and evaluating 
quantitative and qualitative research. Merrill Prentice Hall. 
Dahlby, B. G. (1983). Adverse selection and statistical discrimination. An analysis of 
Canadian automobile insurance. J. Public Econ, 121-131. 
Dickie, A. (2011). On Risk Classification. Washington: American Academy of Actuaries 
Risk Classification Work Group. 
Di01me, G. G. (1998). Evidence of adverse selection in automobile insurance market. 
Automobile Insurance; Road Safety, New Drivers, Risks, Insurance Fraud and 
Regulation, 13-46. 
Di01me, G. G. (200 1 ). Testing for the evidence of adverse selcetion in automobile 
insurance market. J Political Econ, 444-453. 
Dionne, G. R. (2014). Economic Effects of Risk Classification Bans. The Geneva Risk 
and Insurance Review, 184-221. 
DuMouchel, A. (1983). The 1982 Massachusetts Auto Insurance Classification Scheme. 
The Statistician, 1-13. 
Fairley, W., Tomberlin, T., & Weisberg, H. (1981). Pricing automobile Insurance under 
a Cross-Classification of Risks : Evidence from New Jersey. Journal of Risk and 
Insurance, 505-514. 
Friedland, J. (2013). Fundamentals of General Insurance Actuarial Analysis. Society of 
Actuaries. 
Groupe Consultatif Actuariel Europeen. (2011). Use of age & disbility as ratingfactors 
in insurance. 
Harrington, S. ( 1986). Estimation and Testing for Functional Form in Pure Premium 
Regression Models. ASTIN Bulletin, 31-43. 
37 
Jee, B. (1989) . A Comparative Analysis of Alternative Pure Premium Models in the 
Automobile Risk Classification. The Journal of Risk and insurance, 434-459. 
Jung, J. (1968). On Automobile Insurance Ratemaking. ASTIN Bulletin, 41-48. 
Kelly, M., & Nielson, N. (2006) . Age as a variable in Insurance Pricing and Risk 
Classification. The Geneva Papers on Risk and Insurance, Issues and Pracctice, 
212-232. 
Leedy, P. &. (2001) . Practical research: Planning and design. Sage publications. 
Mata, A. (2010). Step by Step Guide To Designing insurance Rating Models. MatBlas 
Limited. 
McKnight, A. J. , & McKnight, A. (2003). Young novice drivers: careless or clueless. 
Accident Analysis and Prevention, 921-925 . 
National Highway Traffic Safety Administration. (2013) . How Vehicle Age and Model 
Year Relate Driver Injury Severity in Fatal Crashes. Washington: U.S. 
Department of Transportation. 
National Highway Traffic Safety Administration. (2013). How Vehicle Age and Model 
Year Relate to Driver Injury Severity in Fatal Crashes. Washington: NHTSA"s 
National Center for Statistics and Analysis. 
Newstead, S., & D'Elia, A. (2007) . An investigation into the relationship between 
vehicle colour and crash risk. Prevention, 47-56. 
Noriszura, I., & Abdul, A. J. (2005) . Generalized Poisson Regression: An altemative for 
Risk Classification. Jurnal Teknologi , 39-54. 
Ponini, D. (20 15). Risk Classification Efficiency and the Insurance Market Regulation. 
Risks , 1-10. 
Puelz, R., & Kemmsies, W. (1993) . Implications for Unisex Statutes and Risk-pooling: 
The Costs of Gender and Unde1writing Attributes in the Automobile Insurance 
Market. Journal of Regulatory Economics, 289-301. 
Sant, D. (1980) . Estimating Expected Losses in Auto Insurance. Journal of Risk and 
Insurance, 133-151. 
38 
Schwarzwe, R. &. (2005). Is the market classification of risk always efficient? Evidence 
from Gem1an third party motor insurance. German Risk lnsur. Rev, 173-202. 
Shavell, S. (1987). Economic Analysis of Accident Law. Cambridge: Harvard University 
Press. 
Shavell, S. e. (1979). On Moral Hazard and Insurance. Bell Journal of Economics, 74-
91. 
Skogh, G. (1991). Insurance and the Institutional Economics ofFinancial Intermediation 
. Geneva Papers on Risk and Insurance, 59-72. 
Smith, M. &. (1994). Insurance Risk Management and Public Policy. Netherlands: 1-27. 
Stmie, V. J. (1977). Male and Female Driver. Differences Observed in Accidents, 761. 
Sydlaske. (1975). Gender Classification in the Insurance Industry. Columbia Law 
Review, 1381-1403 . 
Teff, B. C. (2008). Risks Older Drivers Pose to themselves and to other Road Users. 
Journal of Safety Research, 577-582. 
Weisberg, H. I. (I 982). A Statistical Perspective on Actuarial Methods for Estimating 
Pure Premiums from Cross-Classified Data .. Journal of Risk and Insurance 
(pre-1986), 539. 
Wils, W. P. (1994) . Insurance Risk Classifications in the EC: Regulatory Outlook. 
Oxford Journal o_fLegal Studies, 449-467. 
39