Financial and Technical Analysis of Insurance Sector with Goal Programming Model

Abstract

Keywords: Goal programming; management; decision making; insurance sector; multiple goals.

1. Introduction

There are many goals that companies have to set and achieve to be financially strong. It is important to set the right targets for an effective asset-liability management. These targets may be profit optimization, risk minimization, or reaching the desired liquidity ratio, for financial institutions. Goal programming is capable of handling decision problems involving multiple goals. A fourdecade-old concept, it began with the work of Charnes and Cooper [1] and was refined and extended by Ingnizio [2]. Since then, goal programming techniques has been applied to many areas such as agriculture planning [3], scheduling [4], tourism [5], plant nutrient management [6], healthcare planning [7], engineering [8], transportation problems [9] and many more. In the case of typical decision making, targets selected by management can be achieved by compromising other objectives. It is necessary to establish an order of importance among these targets. In this way, less important goals can be sought after achievement of more important goals. Since it is not always possible to achieve each goal, the goal programming will try to achieve as many multiple targets as possible. Banks need to create strategies to make efficient use of funds and analyze the various goals such as minimizing risk and ensure security for an efficient asset-liability management. In the *

Corresponding Author: e-mail: betul.zehra@hacettepe.edu.tr, tel: (312) 297 61 60

literature there are several examples that goal programming has been applied in banking and financial institutions area [10-15]. Rapid changes in the business environment have forced insurance agencies to re-examine their objectives and goal-programming has been used as an agency decision-making tool for these agencies [16]. It also has been used for optimum allocation of assets [17], capital budgeting [18], insurance agency management [19] and pension fund management [20]. Although goal programming is a well-known and useful technique to model multiple objective problems and applied to many different subject areas, in recent years there is relatively little literature published in actuarial / insurance field. One of them is the study of Heras et al in 2004 [21]. They used linear goal programming methodology to design Bonus-Malus premium scales with some interesting theoretical and practical attributes. In this study two different goal programming models are set up to conduct financial and technical analysis for the entire non-life insurance sector, not for a single company. Some of the financial and technical ratios are selected as goals. These ratios are thought to affect the sector and it is considered useful to include these constraints into the model. The goals suggested in these models are neither all-encompassing nor constant among agencies or among the other countries’ insurance sectors. The agencies can add different goals into the model in line with their own needs. “Republic Of Turkey Prime Ministry Under secretariat Of Treasury”, the regulatory and supervisory authority for insurance companies in Turkey, publishes annual reports on insurance and private pension activities each year. The data from these reports is used in this study. The purpose of this study is to make a financial and technical analysis in non-life insurance sector. The proposed models can be used as a guideline for life insurance sector or insurance agencies in making decisions and develop strategies to deal with various economic scenarios. This paper is organized as follows: Goal programming methodology is presented in section 2. Section 3 “Application”, consists of model formulations for financial analysis and technical analysis. In section 4, results for the models are presented. Section 5 concludes the study with the comments and certain suggestions for further research.

2. Methodology

Goal programming is an analytical approach devised to address decision-making problems where targets have been assigned to all the attributes and where the decision-maker is interested in minimizing the non-achievement of the corresponding goals. In other words, the decision maker seeks a Simonian satisficing solution (i.e., satisfactory and sufficient) with this strategy [22]. In typical decision making situations, the goals set by management can be achieved only at the expense of other goals. Since it is not always possible to achieve every goal to the extent the decision maker desires, goal programming attempts to reach a satisfactory level of multiple objectives [23]. The procedures for structuring a linear programming model are similar to those for a goal programming model. But the main difference between them is the objective function. While linear programming tries to find the best possible outcome for a single object and tries to maximize or minimize the objective function, goal programming minimizes the deviations between the target values of the objectives and the realized results.

min z    di  di  , subject to   aij x j  di  di   bi , x j , di , di  0 m

x j is the decision variable for j=1,…,m; aij represents the decision variable

coefficients; bi is the aspiration level; d i is the positive deviation variable from overachieving the ith goal and

di is the negative deviation variable from underachieving the ith goal for

i=1,…,n. If the management is unconcerned about whether there is an overachievement of the 

target, d i can be omitted from the object function, vice versa. In other words, bi the aspiration level which is needed to be achieved is chosen for each of the objectives thus the undesired deviations from the given set of goals are minimized by using the achievement function z (total deviation function/object function). In Table 1 for different acceptable situations such as overachievement or underachievement of

summarized. Table 1. General structure of goal programming model Goal

is the acceptable situation this implies anything below the 

aspiration level bi is acceptable so the overachievement of the target d i should be minimized to 0. For overachievement situation anything below the aspiration level bi should be driven to 

zero and if the management seeks to attain the aspiration level exactly both di and di must appear in the object function. As not all goals have the same importance, several variants have been conceived to weight goals differently [24]. There are two main variants/methods of goal programming; weighted goals programming and pre-emptive (lexicographic) goal programming. These two methods do not give the same results for the same problems and neither is one method is superior to the other method. They are designed to satisfy certain decision makers’ preferences. In weighted goal programming model, weights are assigned to the goals that measure their relative importance and then finds a solution that minimizes the weighted sum of the deviations from the targets. In pre-emptive (lexicographic) goal programming model, the decision maker ranks the goals in order of importance. He must rank his goals from the most important one to the least important. This method is used when decision maker has a clear preference order for satisfying the goals. These two variants of goal programming are studied in Charles et al [25] Schniederjans and Kwak [26], Tamiz and Jones [27], Crowder and Sposito [28], Tamiz et al. [29], and many others. Solving a problem by assigning weights to the deviational variables easy to implement but in practice it is not easy to come up with precise weight for each goal. Therefore, the pre-emptive method is used for this study. In this method priorities (P i’s) are assigned to each deviational variable in object function, with ranking that P1 is the most important goal, P 2 the next most important goal and so on. The model is given as;

min z   Pi  d  d  subject to  aij x j  di  di  bi , x j , di , di  0 . n

3. Application

Turkey non-life insurance data is used for the case study. The five years data is obtained from the annual reports about insurance and private pension activities that Republic of Turkey Prime Ministry Under secretariat of Treasury published between 2011 and 2015.

4. Results For The Models

The optimal solutions for these two goal programming models are found by LINGO software and results show all goals are fully achieved. Table 4. Results for Financial Ratios Goals Priority P1 P2 P3 P4 P5

Goals Achievement Fully Achieved Fully Achieved Fully Achieved Fully Achieved Fully Achieved

Table 4 shows from the first to fifth priority all goals are achieved for financial ratios since all negative deviations d1-, d2-, d3-, d4- are equal to zero. After fully achieving these goals first positive deviation d1+ is equal zero, meaning that we do not expect changes in the return of assets. For goal 2 (P2) the value of d2+ is 30.79735 so liquidity ratio can be increased by 30.79735 per year. For goal 3 (P3) the value of d3+ is 79.01530 and this indicates an increase in capital adequacy ratio by 79.01530. Similarly, for goal 4 (P 4) and for goal 5 (P5) we have overachievements of targets. We expect the increase in both shareholders’ equity/technical reserves ratio and premium/shareholders’ equity ratio by 42.65615 and 123.3794, respectively. Table 5. Results for Technical Ratios Goals Priority P1 P2 P3 P4

Goals Achievement Fully Achieved Fully Achieved Fully Achieved Fully Achieved

Table 5 shows from the first to the fourth priority all goals are achieved for technical ratios since the first two negative deviations d1-, d2- and last the two positive deviations d3+, d4+ are equal to zero. The first two positive deviations are also equal to zero, meaning that we do not expect changes in premium growth rate and technical profitability ratio. For goal 3 (P3), the value of d3- is 13.55034. This shows loss ratio can be decreased by 13.55034. Since the sector is only concerned with the overachievement of the loss ratio constraint and wants to minimize the d 3+ the

result is satisfactory. Besides, this is also satisfactory that the fourth negative deviation, d4- takes the value 2.323530 the expected value for expenses ratio for 2016 is 21.94647 with this model.

5. Conclusion

Decision-making helps decision-makers to improve systematic thinking and achieve results in the face of simple or complex problems. It is not always possible to reach the optimum result with the increase in goals. In this case, the decision-making process will be difficult and the decision maker will try to reach a solution with certain sacrifices. Multi-criteria decision methods which are developed to help decision making against multiple objectives or alternative problems have been started to be used in all systems over time. These methods, which are often used in the financial and insurance systems, provide optimum results for decision makers. In this study goal programming which is an important class of multi-criteria decision models is used to analyze financial and technical performance of Turkey’s non-life insurance sector. In the application we used five different financial ratios; premium/shareholders’ equity, shareholders’ equity/technical reserves, capital adequacy ratio, liquidity ratio, return on assets, that are important for financial analysis and four different technical ratios; premium growth rate, technical profitability ratio, loss ratio, expenses ratio, that are important for technical analysis of non-life insurance sector. All the goals that have been examined in the models are achieved by LINGO software. The results show there will be an improvement in the financial and technical performance of Turkey’s non-life insurance sector and we can reach our inspiration levels of our goals in two models with the priorities that we set. The proposed models can serve as a guideline for insurance agencies in making decisions and developing strategies to dial with various situations involving multiple, often conflicting goals. In order to use goal programming an insurance company first has to determine its goals or objectives. Different goals may be important to different companies. By regulatory and supervisory agencies and rating agencies in any country, additional goals can be added into the models in the line with their needs. Finally, these models with the same ratios or different ones will also be helpful for life insurance sector and the priorities of the goals can be changed and this leads to a change in the results.

Share and Cite