47 
 
 RESEARCH METHODOLOGY 
3.1 Introduction  
In this chapter, we will discuss how we retrieved and analyzed the data. Next, 
the process for each model and methods used to achieve the objectives will be explained 
in detail. First of all, we will compute the value of claim ratio, RBC level, intellectual 
capital scores, and profitability ratios in terms of ROA and ROE percentages using each 
models formula based on the financial indicators stated in the financial statement from 
the annual report of takaful operators from the year 2015 until 2019. Next, we will 
compare the financial performance of the selected takaful operators based on claim 
ratio, RBC, and VAIC using the panel data regression method along with the tests to be 
performed in order to choose the model. Then, the relationship between financial 
performance and intellectual capital will be tested. Lastly, from these outcomes, we will 
compare which approach can give better prediction and analysis on the financial 
performance of takaful operators according to each takaful fund and can also provide 
improvement for their future financial performances. 
 
3.2 Types and Sources of Data 
This study focuses primarily on the financial performance of insurance operators in 
Malaysia using rating systems like RBC, financial ratios such as claim ratios, ROA, 
ROE, and intellectual capital. Data regarding the takaful operators in Malaysia is 
obtained from the secondary information of the annual report provided on each 
company’s website. It consists of information such as financial statements, the 
48 
 
company’s policy, risk management framework, and corporate governance statement. 
From this report, we will use the data on the financial statement for a period of five 
years, which include from 2015 until 2019 in computing RBC, claim ratio, and 
intellectual capital methods accordingly. A total of 15 takaful operators were selected 
for the purpose of the study listed under licensed financial institutions by BNM. The 
selection process involves companies that have sufficient financial data throughout the 
study period. The following table displays list of selected takaful operators: 
Table 3.1: List of Takaful operators in Malaysia 
No Company’s Name 
1 AIA Takaful Berhad 
2 AmMetLife Takaful Berhad 
3 Etiqa Family Takaful Berhad 
4 Etiqa General Takaful Berhad 
5 FWD Takaful Berhad 
6 Great Eastern Takaful Berhad 
7 Hong Leong MSIG Takaful Berhad 
8 Prudential BSN Takaful Berhad 
9 Sun Life Malaysia Takaful Berhad 
10 Syarikat Takaful Malaysia Am Berhad 
11 Syarikat Takaful Malaysia Keluarga Berhad 
12 Takaful Ikhlas Family Berhad 
13 Takaful Ikhlas General Berhad 
14 Zurich General Takaful Malaysia Berhad 
15 Zurich Takaful Malaysia Berhad 
 
49 
 
3.3 Descriptive Statistics 
Yet, the most frequent metric of central tendency is the mean. It is calculated by 
dividing the number of observations in the data frame by the values corresponding. The 
formula of mean is defined as below:  
?̅? =  
∑ 𝑥
𝑛
.     (3.1) 
The standard deviation is a measurement of how much a collection of data 
deviates out of its average. It quantifies a distribution’s actual variation, with the bigger 
the dispersal or volatility, the larger the standard deviation as well as the size of the 
value’s dispersion over its average. Below is the formula for standard deviation: 
 𝜎 =  √
∑(𝑥−?̅?)2
𝑛−1
,     (3.2) 
where 
𝜎: value of standard deviation, 
𝑥: each value in the dataset, 
?̅?: mean of all values in the dataset, 
𝑛: number of values in the dataset. 
 
A data point that is lesser than or equivalent to other values in the dataset is called the 
minimum. If we arranged the whole of our data from smallest to largest, the very first 
digit on the ranking would be the minimum. Meanwhile, the data point which is larger 
than or similar to all the other values in the dataset is referred to as maximum. The 
maximum would seem to be the final figure identified when we sorted through all our 
values in increasing order. 
 
50 
 
3.4 Claim Ratio    
A claim ratio will analyze the number of real payments that insurers or takaful 
providers spend out of the total premiums or donations that they obtain from the 
policyholders. This ratio, proposed by Rusmita (2018), has become one of the 
diagnostic measures used within the Early Warning System study to analyze an 
insurer’s financial condition by identifying credit restructuring inefficiencies. In this 
situation, a high ratio will reflect a reduced risk profile and a more productive business. 
The claim ratio represents the proportion of claims over premium earned, and yet it 
defines the insurer’s net profit (Foong & Idris, 2012). The formula to calculate the claim 
ratio is stated as: 
𝐶𝑙𝑎𝑖𝑚 𝑟𝑎𝑡𝑖𝑜 = 𝑁𝑒𝑡 𝑐𝑙𝑎𝑖𝑚
𝑖𝑛𝑐𝑢𝑟𝑟𝑒𝑑
𝑁𝑒𝑡
𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛𝑠.  (3.3) 
The value of the net claim incurred and net contributions are provided in each 
company’s financial statement. Since the value of net claim incurred indicates the 
amount of claim that the company has paid throughout the financial year, thus the values 
stated in the financial statement are in bracket forms. In the meantime, the net 
contributions referred to the number of contributions received in terms of premiums 
paid by the policyholders. 
 
3.5 Risk-Based Capital (RBC) 
Within the RBC approach, a takaful operator’s financial stability is determined 
through company capacity to fulfill the minimum reserve obligations with regard to its 
exposures. To calculate the RBC ratio, every insurance operator will be sorted out on 
the basis of the formula CAR technique (Mohamad et al., 2017). Through CAR, the 
financial strength of the operator will be evaluated whether it fulfills the supervisory 
51 
 
requirement of capital level implemented by BNM, which is 130% (Bank Negara 
Malaysia, 2013a). The CAR formula that evaluates the sufficiency of available capital 
to cover the necessary capital needed, which comes in the form of companies and 
shareholder’s funds stated below: 
𝐶𝐴𝑅 =  
𝑇𝐶𝐴
𝑇𝐶𝑅
𝑥 100%,     (3.4) 
where 
𝑇𝐶𝐴: Total Capital Available, 
𝑇𝐶𝑅: Total Capital Required. 
 
3.5.1 CAR for Takaful Operator 
BNM makes few requirements in order for a takaful operator to regulate according to 
Shariah principles. In order for Participant’s Risk Fund (PRF) to fulfill its requirements, 
every takaful operator must offer a loan without interest based on Shareholders Fund 
(SHF) if there happens to be any shortage in PRF. The TCA comprises the aggregate of 
Tier 1 and Tier 2 capitals with the exclusion of several deductions from funds. The 
components in TCA are stated in Table 3.2 below: 
Table 3.2: Total Capital Available (TCA) Components 
Tier 1 Tier 2 
 Issued and fully paid-up shares 
 Share premiums 
 Paid-up non –cumulative 
irredeemable preference shares 
 Capital reserves 
 Aggregate irredeemable 
preference shares 
 Obligatory capital loan stocks 
and other associated capital 
instruments 
52 
 
 Retained profits 
 Surplus from the valuation of 
takaful funds 
 Irredeemable subordinated debts 
 Available-for-sale reserves 
 Revaluation reserves for self-
occupied and other assets 
 General reserves 
 Subordinated term debts 
 Card from shareholders’ funds 
 
The TCA for a licensed takaful operator will be evaluated as: 
𝑇𝐶𝐴 = 𝐶𝐴𝑆𝐹 + ∑ 𝑀𝑖𝑛[𝐶𝐴𝑖𝑎𝑙𝑙 𝑖 , 130% 𝑜𝑓 𝑀𝑎𝑥(𝑆𝑉𝐶𝐶𝑖, 𝐶𝑅𝑖)], (3.5) 
where 
𝑖: takaful fund, 
𝐶𝐴𝑆𝐹: Capital available in shareholder’s fund, 
𝐶𝐴𝑖: Capital available in takaful fund 𝑖, 
𝑆𝑉𝐶𝐶𝑖: Surrender value of capital charges in takaful fund 𝑖, 
𝐶𝑅𝑖: Capital required from takaful fund 𝑖. 
 
The TCA value on each takaful fund is well-provided in the financial statement of every 
takaful operator. Therefore, there is no calculation on TCA. The TCR for takaful will 
be calculated based on capital charges on both takaful funds and shareholder funds as: 
 
𝑇𝐶𝑅 = ∑ 𝑀𝑎𝑥[𝑆𝑉𝐶𝐶𝑖,𝑎𝑙𝑙 𝑖 𝐶𝑅𝑖] + 𝑀𝑎𝑥[𝑆𝑉𝐶𝐶𝑆𝐹, 𝐶𝑅𝑆𝐹],  (3.6) 
where 
𝑆𝑉𝐶𝐶𝑖:  Surrender value of capital charges in takaful fund 𝑖, 
53 
 
𝐶𝑅𝑖: a summation of capital charges for credit risk, market risk, and takaful 
liabilities for each fund 𝑖, 
𝑆𝑉𝐶𝐶𝑆𝐹: Surrender value of capital charges in the shareholder’s fund, 
𝐶𝑅𝑆𝐹: consists of four types of risk capital charges on behalf of the 
shareholder’s fund, which are credit, market, expense liabilities, and 
operational. 
 
To compute TCR, each risk capital charge is computed individually using the formula 
for components of capital required to mitigate major risks provided in BNM’s takaful 
framework. Below is the list of formulas for every capital charge. 
 
3.5.1.1 Credit Risk Capital Charges (CRCC) 
The purpose of the CRCC is to offset the possibility of damages arising from asset 
loss, associated financial difficulties, and the reluctance or refusal of a counterparty to 
completely comply with its agreed financial commitments by a licensed takaful 
operator. The CRCC formula expresses as follows: 
 
where 
𝑖: takaful fund, 
𝑐𝑟𝑒𝑑𝑖𝑡 𝑒𝑥𝑝𝑜𝑠𝑢𝑟𝑒𝑖: credit exposure for takaful 𝑖, 
𝑐𝑟𝑒𝑑𝑖𝑡 𝑟𝑖𝑠𝑘 𝑐ℎ𝑎𝑟𝑔𝑒𝑖: credit risk charge for takaful 𝑖. 
 
𝐶𝑅𝐶𝐶 =  ∑ [ 𝑐𝑟𝑒𝑑𝑖𝑡 𝑒𝑥𝑝𝑜𝑠𝑢𝑟𝑒𝑖𝑎𝑙𝑙 𝑖 x 𝑐𝑟𝑒𝑑𝑖𝑡 𝑟𝑖𝑠𝑘 𝑐ℎ𝑎𝑟𝑔𝑒𝑖],  (3.7) 
54 
 
3.5.1.2 Market Risk Capital Charges (MRCC) 
The goal of the MRCC is to alleviate the chances of financial damages resulting 
from the decline across the stock value of assets as a result of stock ownership, profit 
rate, commodity and currency risks, non-parallel fluctuations in between valuation of 
liabilities as well as the valuation of assets supporting obligations as a result of the 
accumulation of the profit rate and so its allocation of exposures to specific creditors or 
groups of resources, as defined in the BNM takaful context in paragraph 9 of Appendix 
II (Bank Negara Malaysia, 2013b) (see in Appendix K). Stated below is the formula: 
 
where 
𝑖: takaful fund, 
𝑚𝑎𝑟𝑘𝑒𝑡 𝑒𝑥𝑝𝑜𝑠𝑢𝑟𝑒𝑖: market exposure for takaful 𝑖, 
 𝑚𝑎𝑟𝑘𝑒𝑡 𝑟𝑖𝑠𝑘 𝑐ℎ𝑎𝑟𝑔𝑒𝑖: market risk for takaful 𝑖. 
 
3.5.1.3 General Takaful Liabilities Capital Charges (GCC) 
Further and beyond the degree of security previously accounted for at the 75 per 
cent level of confidence, the GCC seeks to mitigate the risks of under-estimation of 
general takaful liabilities and unfavorable claims record for a licensed takaful operator 
engaging in general takaful operations. The formula for GCC is: 
 
 
where 
𝑖: takaful fund, 
𝑀𝑅𝐶𝐶 =  ∑ [ 𝑚𝑎𝑟𝑘𝑒𝑡 𝑒𝑥𝑝𝑜𝑠𝑢𝑟𝑒𝑖𝑎𝑙𝑙 𝑖 x 𝑚𝑎𝑟𝑘𝑒𝑡 𝑟𝑖𝑠𝑘 𝑐ℎ𝑎𝑟𝑔𝑒𝑖], (3.8) 
𝐺𝐶𝐶 = ∑[𝐶𝐿𝑖 𝑥 𝑟𝑖𝑠𝑘 𝑐ℎ𝑎𝑟𝑔𝑒𝑖] + [𝑈𝑅𝑅𝑖 𝑥 𝑟𝑖𝑠𝑘 𝑐ℎ𝑎𝑟𝑔𝑒𝑖],
𝑎𝑙𝑙 𝑖
                      (3.9) 
55 
 
𝐶𝐿𝑖: claim liabilities for takaful 𝑖, 
𝑟𝑖𝑠𝑘 𝑐ℎ𝑎𝑟𝑔𝑒𝑖: risk charge for takaful 𝑖, 
𝑈𝑅𝑅𝑖: Unexpired risk for takaful 𝑖, 
Claims liabilities and provision for unexpired risk (URR): Values determined in 
accordance with paragraph 10.2 in Appendix IV of BNM’s takaful framework (Bank 
Negara Malaysia, 2013b) (see in Appendix K). 
 
3.5.1.4 Family Takaful Liabilities Capital Charges (FCC) 
The FCC intends to mitigate the risk of under-estimation of family takaful 
obligations and unfavorable claims record, in addition to the amount of provision 
already accounted for at the 75 percent confidence level, for a licensed takaful operator 
operating on family takaful operations. The Appointed Actuary must evaluate as well 
as certify whether every FCC and ECC is decrement-supported, including such lapse-
supported and mortality-supported, and utilize the proper direction of stress factors 
appropriately when generating each FCC and ECC. To avoid any negative FCC and 
ECC occurrences, the stress direction chosen must be the one that generates the highest 
liability value in each risk component. In the corresponding actuarial analysis, the 
reason for identifying the stress factors for each product and each fund must be stated. 
Below is the FCC formula: 
 
where 
𝑉∗: adjusted best estimate value of family takaful liabilities computed using the 
stress factors stipulated in Appendix V according to BNM’s takaful framework (see in 
Appendix M), 
𝐹𝐶𝐶 = (𝑉∗ − 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑓𝑎𝑚𝑖𝑙𝑦 𝑡𝑎𝑘𝑎𝑓𝑢𝑙 𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠),  (3.10) 
56 
 
𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑓𝑎𝑚𝑖𝑙𝑦 𝑡𝑎𝑘𝑎𝑓𝑢𝑙 𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠: Value determined based on paragraph 
10.3 according to BNM’s takaful framework at 75% confidence level (see in Appendix 
N). 
 
3.5.1.5 Shareholder’s Fund Expense Liabilities Capital Charges (ECC) 
Despite exceeding the number of provisions previously accounted for at the 75 per cent 
level of confidence, the ECC aims to mitigate the risk under expenditure obligations 
and unfavorable experience of the shareholders’ capital expenditures. The formula for 
ECC is such following: 
 
where 
𝑖: takaful fund, 
𝑉∗: adjusted best estimate value of expense liabilities computed using Appendix V 
according to BNM’s takaful framework (see in Appendix M), 
𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠𝑖: Value determined based on paragraph 10.3 
according to BNM’s takaful framework at 75% confidence level (see in Appendix N). 
 
3.5.1.6 Operational Risk Capital Charges (ORCC) 
The ORCC aims to reduce the risk of a licensed takaful operator losing money 
due to insufficient or failing internal procedures, people, and systems in monitoring 
takaful business. The ORCC also risks losses accounts resulting from Shariah’s non-
compliance and a licensed takaful operator’s inability to fulfill its fiduciary obligations. 
 
𝐸𝐶𝐶 (𝐹𝑎𝑚𝑖𝑙𝑦) = ∑ (𝑉𝑒∗𝑖 − 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠𝑖)𝑎𝑙𝑙 𝑖 ,  (3.11) 
𝑂𝑅𝐶𝐶 = 1% 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑜𝑡𝑎𝑙 𝑎𝑠𝑠𝑒𝑡𝑠 𝑜𝑓 𝑡𝑎𝑘𝑎𝑓𝑢𝑙 𝑏𝑢𝑠𝑖𝑛𝑒𝑠𝑠,  (3.12) 
57 
 
where 
total assets of takaful business: refers to assets in takaful and shareholder’s funds.   
 
3.5.1.7 Surrender Value Capital Charges (SVCC) 
 
where 
𝑖: takaful fund, 
𝐴𝑔𝑔 𝑠𝑢𝑟𝑟𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑏𝑢𝑠𝑖𝑛𝑒𝑠𝑠 𝑖𝑛 𝑓𝑜𝑟𝑐𝑒𝑖: refers to shareholder’s fund and each 
family takaful fund established by a licensed takaful operator as per the fund segregation 
requirement stipulated in Guidelines on Takaful Operational Framework, 
𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠𝑖: the value of family takaful fund liabilities and the value of expense 
liabilities is determined in accordance with paragraph 10.3 of the BNM’s takaful 
framework (see in Appendix N). 
 
3.6 Value Added Intellectual Capital (VAIC) 
The intellectual capital of an insurance firm is calculated by using VAIC that 
include three components of efficiency in terms of capital, which are human, structural, 
and capital employed (Lu et al., 2014). According to a study made by Pulic (2000), a 
list of steps will be applied to compute a VAIC score. The formula of VAIC and its 
components are: 
𝑉𝐴𝐼𝐶𝑇𝑀 = 𝑉𝐴𝐶𝐴 + 𝑉𝐴𝐻𝑈 − 𝑆𝐶𝑉𝐴,  (3.14) 
𝑉𝐴𝐶𝐴 = 𝑉𝐴/𝐶𝐴,     (3.15) 
𝑉𝐴𝐻𝑈 = 𝑉𝐴/𝐻𝑈,    (3.16) 
𝑆𝐶𝑉𝐴 = 𝑆𝐶/𝑉𝐴,     (3.17) 
𝑆𝑉𝐶𝐶𝑖 = 𝑀𝑎𝑥[0, (𝐴𝑔𝑔 𝑠𝑢𝑟𝑟𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑏𝑢𝑠𝑖𝑛𝑒𝑠𝑠 𝑖𝑛 𝑓𝑜𝑟𝑐𝑒𝑖 − 𝑙𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠𝑖)],    (3.13) 
58 
 
where 
𝑉𝐴𝐶𝐴: Value Added Capital Employed, 
𝑉𝐴: value-added, 
𝐶𝐴: capital employed, 
𝑉𝐴𝐻𝑈: Value Added Human Capital, 
𝐻𝑈: human capital, 
𝑆𝐶𝑉𝐴: Value Added Structural Capital, 
𝑆𝐶: structural capital, 
 
VACA is the value added to the capital employed, and CA is the capital employed that 
is equivalent to the gross asset book value minus the intangible asset. Thus, VA is the 
revenue generated by a company usually extracted from the two sources of human 
capital (HU) and structural capital (SC). Since wage is not considered as an expense 
because such forms of costs play a significant and important role in profit production 
and are known as capital, thus we may quantify value-added using the following 
expression: 
𝑉𝐴 = 𝑂𝑃 + 𝐸𝐶 + 𝐷 + 𝐴,   (3.18) 
where 
𝑉𝐴: value-added, 
OP: operational profit, 
EC: employee cost, 
D: depreciation, 
A: amortisation. 
 
59 
 
We will calculate VAHU, which is the calculation of the human resource cost 
summarizing the contribution of every dollar paid as a laborer’s wage by dividing value-
added over with the cost of human resources. Another component that needs to be added 
into the components of VAIC calculation is Value Added Structural Capital (SCVA) 
which means the efficiency of structural capital. The formula is as: 
𝑆𝐶 = 𝑉𝐴 − 𝐻𝑈,    (3.19) 
where 
𝑆𝐶: structural capital, 
𝐻𝑈: human capital. 
This method assumes that each increase in intangible asset value, such as intellectual 
capital, has a favorable impact on the financial performance of insurance companies 
(Iswati & Anshori, 2007). Thus, the intellectual capital will be tested in accordance with 
ROA and ROE as the profitability indicators of the takaful operator. When insurance 
firms receive a significant part of their profits from their wealth, such gains had already 
been spent on, impacting their efficiency. Therefore, we used the overall benefit on 
takaful operations, and that will not affect the result. 
 
60 
 
3.7 Profitability Ratios Measurement 
Profitability ratios seem to be a series of various calculations that are being used 
to assess a company’s capacity to generate profits. Since such proportions increase 
significantly as well as outperform rivals’ performance, they may deem positive. These 
ratios are calculated by comparing earnings to various expenditure groups upon that 
cash flow statement. The primary objective of such ratios is to assess how efficiently an 
organization may generate returns with proportion to the cost of invested equities as 
well as assets available. Unless the effects from these assessments are positive, this 
denotes that investment use may be reduced. In computing profitability, it may be ideal 
for contrasting a firm’s existing performance with the previous year’s similar time. The 
motive is because several firms provide temporary sales, thus driving the company’s 
profitability ratios to fluctuate significantly throughout the year. 
 
3.7.1 Return on Assets (ROA) 
ROA is a measure of how profitable a company is due to its total assets. In 1919, 
ROA was established by the DuPont system, which highlights the firm’s capacity by 
offering an insight to a manager, customer, or consultant as to how effectively they can 
utilize their resources to achieve profits (Burca & Batrinca, 2014). According to Mehari 
(2013), this profitability ratio is likely among the most relevant specific metrics in 
evaluating insurers’ profitability and overall success since it reflects the revenues earned 
from investments they hold. The higher the ROA value, the better, and with less 
spending, the organization earns more revenue. Ishtiaq (2019) defined the formula to 
calculate ROA as below: 
61 
 
𝑅𝑂𝐴 =
𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒
𝑇𝑜𝑡𝑎𝑙 𝐴𝑠𝑠𝑒𝑡𝑠
.     (3.20) 
 
3.7.2 Return on Equity (ROE) 
In essence, the ROE ratio calculates the amount of return that the shareholders of 
a company’s capital stock earn on their shares. Equity return means the business’s 
ability to produce gains from its owners on the money it got. Yazid (2012) and Abu 
Hussin (2014) claim this ratio is an indicator of a firm’s profitability derived from the 
utilization of stocks. Generally, clients favor companies with higher ROEs. This can, 
nevertheless, be seen as a baseline to choose stocks from the same market. Benefit and 
revenue ratios differ greatly across industries. If a business wishes to offer dividends 
within the same industry and not retain the profit produced as empty cash, the ROE 
levels can differ. A study by Mansor (2016) also employed ROE to examine the 
relationship between risk and return. The term net income denotes an organization’s 
earnings after taxes as well as expenditures that have been deducted. Once obligations 
are cleared, shareholders’ equity seems to be the company’s owners’ outstanding right 
upon assets. The ROE formula is stated per: 
𝑅𝑂𝐸 =
𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒
𝑆ℎ𝑎𝑟𝑒ℎ𝑜𝑙𝑑𝑒𝑟′𝑠 𝐸𝑞𝑢𝑖𝑡𝑦
.    (3.21) 
 
3.8 Analysis of Data 
Data analysis was done by multicollinearity analysis, selecting an appropriate 
panel data regression model, and running a few classical assumption tests. Panel data 
regression analysis, the importance of the coefficient 𝑅2, F test, Panel Corrected 
Standard Error Model, and Generalized Least Squares models and hypothesis testing 
62 
 
were additional treatment and tests conducted. Few steps will be run through in order 
to decide the best model estimation. 
 
3.8.1 Multicollinearity Test 
When two or more independent variables are strongly correlated in a regression 
model with another, multicollinearity occurs (Daoud, 2018). The Pearson correlation 
matrix and variance inflation factor (VIF) will be used to analyze whether the study has 
a multicollinearity test problem or not. Whenever the correlation coefficient in the 
correlation matrix-valued at 0.8 or above, there is a drawback of collinearity (Gujarati 
& Porter, 2013). 
 
3.8.2 Panel Data Regression Model Estimation 
Panel data regression is a composition between cross-sectional and time-series data in 
which such a unit cross-sectional area is assessed multiple times. This kind of regression 
offers larger pieces of information, greater degrees of freedom, as well as less, less 
multicollinearity amongst regressors, resulting in more accurate econometric 
estimations (Hsiao, 2002). Panel data is classified into two types which are balanced 
panel data and unbalanced panel data. The data is considered balanced if the cumulative 
unit length on every observation seems to be the same. However, when the amount of 
years is distinct, it is referred to as unbalanced (Zulfikar, 2018). A decent sample 
appears as a major advantage whenever employing unbalanced panel data. Yet, because 
each year’s performance varies depending on different amounts of data, the reliability 
of the estimations fluctuates with time. Despite balanced panel data, it is the opposite 
63 
 
because the accuracy of estimations rarely changes with time, but the disadvantage is 
that the sample size is much smaller (Kerstens, 2014). For regression analysis, a total 
of 17 takaful operators, which are made up of 11 family takaful operators and six general 
takaful operators, have been selected for a five years study period. However, three 
general takaful operators, which are Hong Leong MSIG Takaful Berhad, Prudential 
BSN Takaful Berhad and Zurich General Takaful Malaysia Berhad have been excluded 
based on the listwise deletion process due to containing missing data for the year 2017, 
2018 and 2019 which then resulted a final total of 14 takaful operators involved in panel 
data regression analysis due to having sufficient data for five years period. The list of 
selected family and general takaful operators are as follow: 
Table 3.3: Selected Family and General Takaful Operators 
No Takaful Operators 
1 AIA Public Takaful Berhad 
2 AmMetLife Takaful Berhad 
3 Etiqa Family Takaful Berhad 
4 FWD Takaful Berhad 
5 Great Eastern Takaful Berhad 
6 Hong Leong MSIG Takaful Berhad 
7 Prudential BSN Takaful Berhad 
8 Sun Life Malaysia Takaful Berhad 
9 Syarikat Takaful Malaysia Keluarga Berhad 
10 Takaful Ikhlas Family Berhad 
11 Zurich Takaful Malaysia Berhad 
12 Etiqa General Takaful Berhad 
64 
 
13 Syarikat Takaful Malaysia Am Berhad 
14 Takaful Ikhlas General Berhad 
 
There are few steps of the panel regression method that will be used to make 
comparisons on the result of financial performances of takaful operators. Below is the 
formula for panel data regression: 
𝑌𝑖𝑡 = 𝛼 + 𝛽′𝑋𝑖𝑡 + 𝜀𝑖𝑡,    (3.22) 
where 
𝑌𝑖𝑡: the value of each dependent variable for each takaful fund on a particular year, 
𝛼: Y-intercept, 
𝛽′: the slope of the independent variables, 
𝑋𝑖𝑡: the model of each independent variable for each takaful fund on a particular 
year, 
𝜀𝑖𝑡: error term for each takaful fund on the particular year. 
 
There are four panel data regression models that will be assessed in this study. Each 
model will be either on a general takaful fund or family takaful fund, which then will 
be paired up according to each study period from 2015 until 2019. Below are the panel 
data regression equations that will be derived out: 
Model 1: ROA model for family takaful fund 
𝑅𝑂𝐴𝑖𝑡 = 𝛽0 + 𝛽1𝐶𝑅𝑖𝑡 + 𝛽2𝑉𝐴𝐼𝐶𝑖𝑡 + 𝛽3𝑅𝐵𝐶𝑖𝑡 + 𝜀𝑖𝑡, (3.23) 
Model 2: ROE model for family takaful fund 
𝑅𝑂𝐸𝑖𝑡 = 𝛽0 + 𝛽1𝐶𝑅𝑖𝑡 + 𝛽2𝑉𝐴𝐼𝐶𝑖𝑡 + 𝛽3𝑅𝐵𝐶𝑖𝑡 + 𝜀𝑖𝑡,  (3.24) 
Model 3: ROA model for general takaful fund 
𝑅𝑂𝐴𝑖𝑡 = 𝛽0 + 𝛽1𝐶𝑅𝑖𝑡 + 𝛽2𝑉𝐴𝐼𝐶𝑖𝑡 + 𝛽3𝑅𝐵𝐶𝑖𝑡 + 𝜀𝑖𝑡, (3.25) 
65 
 
Model 4: ROE model for general takaful fund 
𝑅𝑂𝐸𝑖𝑡 = 𝛽0 + 𝛽1𝐶𝑅𝑖𝑡 + 𝛽2𝑉𝐴𝐼𝐶𝑖𝑡 + 𝛽3𝑅𝐵𝐶𝑖𝑡 + 𝜀𝑖𝑡,  (3.26) 
where 
𝐶𝑅: claim ratio, 
𝑉𝐴𝐼𝐶: value-added intellectual capital, 
𝑅𝐵𝐶: risk-based capital, 
𝑖:  type of takaful fund, 
𝑡: year, 
𝛽0: constant, 
𝛽1, … , 𝛽3: coefficient of independent variables, 
𝜀: error term. 
This panel data regression analysis will be analyzed using a statistical software called 
STATA. There are many models listed in the panel data method, which are the common 
effect model, fixed-effect model, and random effect model. Firstly, the Chow Test, 
Hausman Test, and Breusch-Pagan Lagrange Multiplier (LM) Test will be tested prior 
to choosing which models to use. 
 
3.8.2.1 Random Effect Model (REM) 
Another name for this model is Error Components Model (ECM), and it involves 
time-invariant factors. This model assumes the variance within the family, and general 
takaful funds are considered to be stochastic as well as uncorrelated with the regressor 
in this model, which results in the time-invariant parameters being able to fulfill the 
function of predictors. Since this model enables greater involvement of independent 
66 
 
factors, which leads all samples in the group to have the same magnitudes, it contains 
lesser inputs compared to the FEM model. 
 
3.8.2.2 Fixed Effect Model (FEM) 
This model is also called Least Squares Dummy Variable (LSDV). This model 
excludes time-invariant factors, and this model preserves heterogeneity as it enables 
both profitability ratios in family and general takaful funds to carry their own endpoint 
while keeping the slope unchanged. As a consequence, this technique can determine the 
independent variable’s overall influence on the dependent factor. 
 
3.8.2.3 Common Effect Model (CEM) 
This model uses the method of Ordinary Least Square (OLS) to integrate both 
data in terms of cross-section and time-series and, which is also the reason why it is 
known as pooled OLS model. This model is simpler compared to the other two previous 
models since it implies that all data have been combined. As such, the gradient and 
intercept are consistent throughout units as well as durations. In this study, this model 
indicated that both family and general takaful funds produced similar profitability 
outcomes from the perspective of using claim ratio, RBC, and VAIC approaches. 
Nevertheless, this model lacks inconsistency of being heterogeneous since it integrates 
both profitability ratios outcomes in family and general takaful funds, which leads to 
consideration of the other models in the best model selection for this study. 
 
67 
 
3.8.3 Statistical Tests for The Best Model Selection 
3.8.3.1 Hausman Test 
The Hausman test is used for a data analysis model selection panel between the 
fixed effect model and the random effect model. The Hausman test hypothesis statement 
is: 
𝐻0: 𝑅𝑎𝑛𝑑𝑜𝑚 𝐸𝑓𝑓𝑒𝑐𝑡 𝑀𝑜𝑑𝑒𝑙, 
𝐻𝑎: 𝐹𝑖𝑥𝑒𝑑 𝐸𝑓𝑓𝑒𝑐𝑡 𝑀𝑜𝑑𝑒𝑙. 
If the p-value is > 0.05, 𝐻0 would be approved. If there is a p-value < 0.05, then 𝐻0 will 
be rejected. Following is the formula for the Hausman test: 
𝐻𝑎𝑢𝑠𝑚𝑎𝑛 𝑡𝑒𝑠𝑡 =
(?̂?𝐹𝐸−?̂?𝑅𝐸)
2
𝑉𝑎𝑟(?̂?𝐹𝐸)−𝑉𝑎𝑟(?̂?𝑅𝐸)
,    (3.27) 
where 
?̂?𝐹𝐸: Actual estimated value of fixed effects model, 
?̂?𝑅𝐸: Actual estimated value of a random-effects model. 
 
3.8.3.2 Breusch-Pagan Lagrange Multiplier (LM) Test 
This Lagrange Multiplier Test (LM) will be used to determine which model is 
between the random effect model and the common effect model to be used. The chi-
square value will determine the acceptance of the common effect model. The hypothesis 
testing will be as follows: 
𝐻0: 𝐶𝑜𝑚𝑚𝑜𝑛 𝐸𝑓𝑓𝑒𝑐𝑡 𝑀𝑜𝑑𝑒𝑙, 
𝐻𝑎: 𝑅𝑎𝑛𝑑𝑜𝑚 𝐸𝑓𝑓𝑒𝑐𝑡 𝑀𝑜𝑑𝑒𝑙. 
If the p-value is > 0.05, 𝐻0 would be approved. If there is a p-value < 0.05, then 𝐻0 will 
be rejected. Below is the formula for the LM test: 
68 
 
𝐹 =
𝑅
?̂?2
/𝑘
1−𝑅?̂?2/(𝑛−𝑘−1)
,    (3.28) 
where 
𝑛: number of observations, 
𝑘: number of regressors, 
𝑅𝑢2: coefficient of determination regression. 
 
3.8.3.3 Chow Test 
The Chow Test is a test most often used appropriately in analyzing panel data to decide 
if the variable is a fixed effect or a common effect. The Chow Test hypothesis statement 
will be as follows: 
𝐻0: 𝐶𝑜𝑚𝑚𝑜𝑛 𝐸𝑓𝑓𝑒𝑐𝑡 𝑀𝑜𝑑𝑒𝑙, 
𝐻𝑎: 𝐹𝑖𝑥𝑒𝑑 𝐸𝑓𝑓𝑒𝑐𝑡 𝑀𝑜𝑑𝑒𝑙. 
If the p-value is > 0.05, 𝐻0 would be approved. If there is a p-value < 0.05, then 𝐻0 will 
be rejected. Following is the formula for the Chow test: 
𝐶ℎ𝑜𝑤 𝑡𝑒𝑠𝑡 =
(𝑅𝑆𝑆𝑃−(𝑅𝑆𝑆1+𝑅𝑆𝑆2))/𝑘
(𝑅𝑆𝑆1+𝑅𝑆𝑆2)/(𝑁1+𝑁2−2𝑘)
,   (3.29) 
where 
𝑅𝑆𝑆𝑃: combined regression line, 
𝑅𝑆𝑆1: regression line before break, 
𝑅𝑆𝑆2: regression line after break, 
𝑘: explanatory variable, 
𝑁: number of observations. 
 
69 
 
3.8.4 Classical Assumption Test 
3.8.4.1 Normality Test 
Normality tests are typically performed to assess if a data collection seems to 
have a normal distribution and to calculate the probability that a random variable 
underlying the collected data is dispersed uniformly. This assumption can be satisfied 
using two types of normality which are the Skewness and Kurtosis test and the Shapiro 
Wilk test. According to Kim (2013), Skewness and Kurtosis test is applicable to many 
ranges of sample sizes, and since the sample size is greater than 50, Skewness and 
Kurtosis is the appropriate one. Meanwhile, the Shapiro-Wilk test is suitable for a 
sample size lesser than 50 (Mishra et al., 2019). A variable is considered to be 
asymmetric distribution if the skewness is approaching 0. However, the model is likely 
to be skewed positively if the skewness value falls closer to 1, which seems to be 
normally distributed. Since the total observations for model 1 and model 2 are 55, which 
are greater than 50, it is preferable to use the Skewness and Kurtosis test. For models 3 
and 4 which the total observation of the general takaful fund for a 5-years period is 15, 
which falls below 50, the Shapiro-Wilk test will be applied. The hypothesis statement 
for both normality tests will be as following: 
𝐻0: 𝑇ℎ𝑒 𝑑𝑎𝑡𝑎 𝑖𝑠 𝑛𝑜𝑟𝑚𝑎𝑙𝑙𝑦 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑒𝑑, 
𝐻𝑎: 𝑇ℎ𝑒 𝑑𝑎𝑡𝑎 𝑖𝑠 𝑛𝑜𝑡 𝑛𝑜𝑟𝑚𝑎𝑙𝑙𝑦 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑒𝑑. 
If the p-value is greater than 0.05, the data is considered to have a normal distribution. 
Below is the formula for skewness and also excess kurtosis:  
𝑍 =
𝑆𝑘𝑒𝑤𝑛𝑒𝑠𝑠 𝑣𝑎𝑙𝑢𝑒
𝑆𝐸𝑠𝑘𝑒𝑤𝑛𝑒𝑠𝑠
,    (3.30) 
𝑍 =
𝐸𝑥𝑐𝑒𝑠𝑠 𝑘𝑢𝑟𝑡𝑜𝑠𝑖𝑠
𝑆𝐸𝐸𝑥𝑐𝑒𝑠𝑠 𝑘𝑢𝑟𝑡𝑜𝑠𝑖𝑠
.    (3.31) 
Meanwhile, the formula for the Shapiro Wilk test will be as follows: 
70 
 
𝑊 =
(∑ 𝑎𝑡𝑦𝑡
𝑛
𝑡=2 )
2
∑ (𝑥𝑡−𝑦
𝑛
𝑡=1 )
2,    (3.32) 
where 
𝑛: number of observations, 
𝑎𝑡: tabulated coefficients, 
𝑦𝑡: the value of the ordered sample, 
𝑦: mean of the ordered sample. 
 
3.8.4.2 Heteroscedasticity Test 
The issue of heteroscedasticity arises from uneven volatility. It goes contrary to 
the Classical Linear Regression Model (CLRM) assumption, which states that all 
disruption factors must have the same variation. It is indeed essential to ensure this 
model is adequate and does not contradict the linear regression assumption. The null 
hypothesis is homoscedasticity, which means that the variance, 𝜎2 of all disturbances, 
𝜀 is constant.  
𝐻0: 𝑉(𝜀𝑖) = 𝜎
2𝑓𝑜𝑟 𝑎𝑙𝑙 𝑖, 
𝐻𝑎: 𝑉(𝜀𝑖) ≠ 𝜎
2𝑓𝑜𝑟 𝑎𝑙𝑙 𝑖. 
When the p-value falls below the 5% significance level, the null hypothesis should be 
denied since the variance of error terms, 𝜎2 are not constant. This implies that the model 
has uneven dispersion and is heteroskedastic, which requires adjustment to the model. 
If the p-value is greater than 0.05, the estimated model does not deal with any 
heteroscedasticity issue. The Breusch-Pagan Cook-Weisberg test will fulfil the 
heteroscedasticity assumption if the appropriate model is a random effect model. 
Meanwhile, the Modified Wald test will be applied if the best model chosen is the fixed 
effect model. 
71 
 
 
3.8.4.3 Autocorrelation Test 
The issue of autocorrelation or serial correlation arises when the model violates 
anyone’s CLRM’s principles. According to Asteriou and Hall (2019), omitted variables, 
model misspecification, and systematic measurement errors are all factors that 
contribute to autocorrelation. The expected volatility of the regression analysis will be 
affected as a consequence of such a serial correlation issue. The criteria would be that 
relationships and covariance amongst various disturbances all seem to be zero, implying 
that 𝑢𝑡 and 𝑢𝑠 are individually scattered.  
𝐶𝑜𝑣(𝑢𝑡,𝑢𝑠) = 0 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑡 ≠ 𝑠. 
Once this criterion is invalidated, both error terms are not uniformly scattered, 
implying that periods 𝑡 and 𝑠 may be connected. This highlights the issue of 
autocorrelation. In conclusion, hypothesis testing seems to be not relevant. The 
Woolridge test is used in this research to detect autocorrelation problems in the model 
in order to prevent autocorrelation. The Woolridge test will fulfil the autocorrelation 
assumption. The hypothesis testing will be as follow: 
𝐻0: 𝑁𝑜 𝑓𝑖𝑟𝑠𝑡 𝑜𝑟𝑑𝑒𝑟 𝑎𝑢𝑡𝑜𝑐𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛, 
𝐻𝑎: 𝐻𝑎𝑣𝑒 𝑓𝑖𝑟𝑠𝑡 𝑜𝑟𝑑𝑒𝑟 𝑐𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛. 
The null hypothesis will be no autocorrelation. If the p-value is greater than 0.05, the 
estimated model does not deal with any autocorrelation issue. 
 
3.8.4.4 Cross-Sectional Dependence Test 
Contemporaneous correlation is another term for cross-sectional dependence. 
Cross-sectional dependency issues must be addressed since they cause inaccuracy in 
72 
 
regression results. Pesaran’s CD-test will test the cross-sectional dependence to check 
if the residuals are associated within units. It is appropriate for panel data regression 
with relatively short time periods and high cross-section entities. The null hypothesis 
will be that error terms are uncorrelated as below: 
𝐻0: 𝑇ℎ𝑒 𝑒𝑟𝑟𝑜𝑟 𝑡𝑒𝑟𝑚𝑠 𝑎𝑟𝑒 𝑢𝑛𝑐𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑒𝑑, 
𝐻𝑎: 𝑇ℎ𝑒 𝑒𝑟𝑟𝑜𝑟 𝑡𝑒𝑟𝑚𝑠 𝑎𝑟𝑒 𝑐𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑒𝑑. 
If the p-value is greater than 0.05, the estimated model does not have any cross-sectional 
dependence. This test statistic has a basic assumption of normality and may be used to 
analyze both balanced and unbalanced panel data. 
 
3.8.5 Panel-Corrected Standard Error (PCSE) Model 
There are two suitable models that are commonly used in resolving the 
heteroscedasticity, autocorrelation, cross-sectional dependence, and normality issues, 
which are Generalized Least Squares (GLS) and panel corrected standard errors model 
(PCSE) (Blackwell III, 2005). This PCSE is considered appropriate if the cross-section 
units, 𝑁, are greater than time-series 𝑡, otherwise GLS is suitable if the condition is the 
opposite (Hoechle, 2007). According to Beck (2008), since the standard errors need to 
be adjusted due to the presence of cross-sectional dependence and panel 
heteroscedasticity flaws, it is recommended to apply PCSE instead of OLS standard 
errors. 
 
73 
 
3.8.6 Generalized Least Square (GLS) Model 
According to Wooldridge (2002), GLS analysis seems to be more accurate than 
OLS estimation. It indicates that if the model encounters autocorrelation or 
heteroscedasticity issues, GLS estimation is significant to be used in this study. This is 
supported by Hsiao (2002), who stated that this estimation might be used to address the 
autocorrelation issue. The non-normality of the data resulting from the 
heteroscedasticity problem will be resolved within this approach (Gujarati & Porter, 
2013). As a result, GLS estimation can tackle most of the autocorrelation and 
heteroscedasticity issues. 
 
3.8.7 Coefficient of Determination (𝑹𝟐) 
The coefficient determination test is used to determine the total variability in 
explanatory factors as a result of the variability in predictor variables, as represented by 
the R-square value (𝑅2). The determination coefficient is between 0 and 1. A value close 
to 1 means that independent variables give most of the data required to forecast changes 
in the dependent variable. Following is the formula for computing coefficient 
determination, 𝑅2: 
𝑅2 =
∑ (?̂?𝑖−𝑦)
2
𝑖
∑ (𝑦𝑖−𝑦)
2
𝑖
,    (3.33) 
where 
𝑦𝑖: 𝑦 value for observation 𝑖, 
𝑦: mean of 𝑦 value, 
?̂?𝑖: the predicted value of 𝑦 for observation 𝑖. 
 
74 
 
3.8.8 F-test 
The F analysis is performed to determine the effect of independent variables on 
a dependent variable at the same time. The condition for such a judgement is that if the 
value of the F coefficient is greater than the value of the F table, it means that control 
variables have an impact on the dependent variable at the same time. Conversely, unless 
the F coefficient value is below the F table’s value, this means that there is really no 
parallel effect of the independent variables towards the dependent factors. The F-test 
formula is as follows: 
𝐹 =
𝑅2/𝑘
(1−𝑅2)/𝑛−𝑘−1
,     (3.34) 
where 
𝑅2: coefficient of determination, 
𝑘: number of regressors, 
𝑛: number of observations. 
 
3.8.9 Hypothesis Testing 
Hypothesis testing will be utilized in this study in order to fulfill objective three 
and to study the significance of the independent variables towards the financial 
performance of takaful operators in terms of profitability. The null hypothesis is rejected 
when the p-value is less than 1%, 5%, or 10%. Even though the significance level is at 
10%, there is still no proof of a substantial link between financial profitability. As a 
consequence, at a minimum of 5% significance level, the three approaches, which are 
claim ratio, VAIC, and RBC, will seem to have a substantial association with financial 
75 
 
profitability for both family and general takaful. Below is the list of hypotheses for 
family and general takaful. 
 
Hypothesis 1 
𝐻0: 𝐶𝑅 ℎ𝑎𝑠 𝑛𝑜 𝑠𝑖𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑛𝑡 𝑒𝑓𝑓𝑒𝑐𝑡 𝑜𝑛  𝑓𝑖𝑛𝑎𝑛𝑐𝑖𝑎𝑙 𝑝𝑟𝑜𝑓𝑖𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦  
𝐻𝑎: 𝐶𝑅 ℎ𝑎𝑠 𝑠𝑖𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑛𝑡 𝑒𝑓𝑓𝑒𝑐𝑡 𝑜𝑛  𝑓𝑖𝑛𝑎𝑛𝑐𝑖𝑎𝑙 𝑝𝑟𝑜𝑓𝑖𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦  
 
Hypothesis 2 
𝐻0: 𝑉𝐴𝐼𝐶 ℎ𝑎𝑠 𝑛𝑜 𝑠𝑖𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑛𝑡 𝑒𝑓𝑓𝑒𝑐𝑡 𝑜𝑛  𝑓𝑖𝑛𝑎𝑛𝑐𝑖𝑎𝑙 𝑝𝑟𝑜𝑓𝑖𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦  
𝐻𝑎: 𝑉𝐴𝐼𝐶 ℎ𝑎𝑠 𝑠𝑖𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑛𝑡 𝑒𝑓𝑓𝑒𝑐𝑡 𝑜𝑛  𝑓𝑖𝑛𝑎𝑛𝑐𝑖𝑎𝑙 𝑝𝑟𝑜𝑓𝑖𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦  
 
Hypothesis 3 
𝐻0: 𝑅𝐵𝐶 ℎ𝑎𝑠 𝑛𝑜 𝑠𝑖𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑛𝑡 𝑒𝑓𝑓𝑒𝑐𝑡 𝑜𝑛  𝑓𝑖𝑛𝑎𝑛𝑐𝑖𝑎𝑙 𝑝𝑟𝑜𝑓𝑖𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦  
𝐻𝑎: 𝑅𝐵𝐶 ℎ𝑎𝑠 𝑠𝑖𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑛𝑡 𝑒𝑓𝑓𝑒𝑐𝑡 𝑜𝑛  𝑓𝑖𝑛𝑎𝑛𝑐𝑖𝑎𝑙 𝑝𝑟𝑜𝑓𝑖𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦