The Central Eposed to Risk as a Hedging Strategy: A Case Study of a Kenyan Pension Sheme Abstrat Titus Kipkoeh Rotih Shool of Siene, University of Eldoret, P.O BOX 1125-30100, Eldoret, Kenya. This study aims at estimating the CER 1 of the members of the pension sheme under study, and establishing how it an be used to determine whih mode of eit is more prevalent in the sheme, by analyzing their probabilities of ourrene at eat ages, of the members of the sheme. This shall assist the offie manage risks that ould be aused by suh unpreedented eits and inrease their returns. While the vast majority of ompanies have used CER in determining their vulnerability to running at a loss, this pratie is still a hallenge to many pension institutions in Kenya. Members of the pension sheme withdrew from the plan due to various reasons inluding death, retirement, termination/dismissal and resignation. The findings were presented in form of tables, harts and narratives. It is epeted that these findings shall assist the pension s offie to manage risks due to eits and inrease returns from the member s ontributions. Keywords: Central Eposed to Risk, Fore of Derement, Poisson Model, Defined Contribution, Defined Benefit 1. Introdution Every employed itizen of the ountry is required by law to register to a pension plan, designed to provide an inome upon retirement. The main types of plans are DC 2 (where members and employers ontributions are fied either as a perentage of pensionable earnings or as shilling amount. and DB 3 (where the benefits whih are ordinarily determined by the shemes rules are defined in advane. pension shemes, with the main objetive of saving now to provide an inome at retirement to the member. Inreased number of pension funds in the ountry saw the formation of an oversight authority, RBA 4, whose reation is part of an on-going finanial reform proess in the ountry s eonomy geared at mobilizing domesti saving, developing ountry s apital markets and enhaning eonomi development. The RBA governed by the Retirement Benefits At, is mandated with management and alleviation of old-age poverty through enhaned saving for the retirement. Pension funds have been lassified as the prinipal soure of retirement inome to millions of pensioners in the world (Sze 2008. These funds are also the most important to the GDP 5 of ountries and signifiant soure of apital in finanial markets (Omondi, 2008. A global pension risis has however emerged in the past two years owing to the depressed finanial markets. Earlier, Lindert (1994 and Curtler & Johnson (2004 had traed the earliest pension fund system to Germany, where they redited former German Chanellor Otto Von Bismark for enating a ompulsory savings program for workers in large firms who were eposed to the soialism ideologies. Perotti & Shwienbaher (2008 adds that the Bismark pension fund system was finaned through worker and employer ontributions, attrated taation inentives and paid retirement benefits one the worker reahed the age of 65. Lindert (1994 had earlier stated that the pension fund ontributions under this system were invested in finanial seurities. This system however had no provision for pension entitlement to personal representatives in ase of death, it was mainly restrited to the ivil servants and war veterans and many workers did not live to enjoy the retirement benefits as life epetany was 60 years (Lindert, 1994. Later, Perotti & Shwienbaher (2008 desribed the Bismark pension fund system as a soial seurity program defined as a omprehensive retirement program overing many prodution workers. The development of pension fund systems was a reation to the politial and eonomi shoks affeting the world during the Vitorian period (see Perotti & Shwienbaher 2008; Ambathsheer 2007a:12. The resultant loss of jobs, suspension of various urrenies and the stok market risis of 1929 prompted governments to reate poliies to ater for their working populations whih onsequently led to the formation of the modern pension fund systems (Perotti & Shwienbaher 2008. As pension fund systems developed, eonomi and politial shoks affeted their sustainability in different ountries (Meyer 2004; Newmann 2005 and so the only institutions that ould be trusted to seure retirement funds were the governments 1 Central Eposed to Risk 2 Defined Contribution 3 Defined Benefit 4 Retirement Benefit Authority 5 Gross Domesti Produt 154
Pension fund systems in Kenya were first put in plae after independene in 1963. The first post independent pension fund body, the NSSF 6, was established in 1965 (RBA, 2000. Prior to reforms, the pension fund system provided for benefits one a worker retired on attaining the mandatory retirement age of 55 (RBA, 2006. The guarantee was fied as the worker s full basi salary throughout his life or that of the widow as the law did not envisage a situation where the wife would support the husband. This law was embodied in the NSSF At and the Pensions At (Cap 189. The pension fund system in Kenya has been supervised by the independent Authority, RBA, sine 2000, whih oversees the 1997 RBA At that brought about regulation, protetion and struture to the pension fund industry. The RBA ontinues working to develop the industry and advise the government on pension poliy reforms. Kenya s pension fund system embraes four omponents namely the NSSF, CSPS 7, ORS 8 and IRS 9. Overally, the system is estimated to over 15% of the labor fore and to have aumulated assets of 18% of the GDP (Kakwani et al. 2006. The pension fund system overs an estimated 2 million workers leaving an estimated 5 million workers uninsured under any retirement sheme, of whih at least 10% are at or near the retirement age (Kakwani et al. 2006. The NSSF is a publi provident fund (pays benefits as a lump sum that overs an estimated 800 000 members in both the formal and informal setors (Stewart & Yermo 2009. The NSSF ontributions are mandatory for employees in firms with 5 or more employees, whereby members ontribute 5% of their monthly earnings subjet to a maimum of Ksh. 200 (US$ 2.7 that is mathed by an equal ontribution by the employer (Stewart & Yermo 2009. Aording to the Kenyan RBA, the employees are allowed to ontribute more on voluntary basis to a maimum of Ksh. 1,000 (US$ 13.3 per month. The old-age pension benefits are available to those aged 55 who have retired from ative employment (Stewart & Yermo 2009. The CSPS overs ivil servants, judiiary employees, military personnel, armed fores, teahers and parliamentarians (Kakwani et al. 2006. The sheme provides benefits inluding old age pension, injury and ompensation, survival benefits, dependeny pension for 5 years after death of a pensioner, disability pension (military only and gratuities in the form of lump sums. The CSPS had 125 000 members by Deember 2006 and the government ependiture amount to Ksh. 12.5 billion (US$ 178.6 million, about 4.7% of the government budget (Kakwani et al. 2006. ORS s were established by employers to at as vehiles for aumulation of retirement savings for the employees (RBA, 2000. The ORS an be operated on defined benefit or on defined ontribution ideologies but in Kenya the defined ontribution is the predominant design (RBA, 2008. Although there is no ompulsion for employers to set up the ORS, one established, the fund falls under the mandate of the Retirement Benefits Authority and must omply with the laid down regulations. The ORS are estimated to over an estimated 3% of the working population in Kenya (RBA, 2008 IRS s are run by finanial institutions mainly insurane ompanies whih provide an avenue for saving where employers do not have their own shemes, and for workers who wish to make additional voluntary ontributions (RBA, 2009. By the lose of 2009, RBA had registered 21 IRS that overed an estimated 2% of the working population. RBA (2009 points out the gap filled by the IRS where the number of employees is so small forming an ORS would not be finanially viable. The onepts and priniples of Central Eposed to Risk in Kenya are yet to be inorporated and adopted by most pension ompanies in management of risks and return inrements. There are notable appliations of Central Eposed to Risk in many ompanies all over the world, for instane a study by Sott (2000 showed that some motor vehile industries use the Central Eposed to Risk estimating the dependent probabilities of eit by either aidents or mehanial breakdown of vehiles at their eat ages in the industries. A researh by RBA indiates that most Kenyans who began their retirement as early as 1990 are outliving their savings. Moreover, early retirees barely get their ompensation due to inadequate atuarial framework (Kenya and UNESCO 2006. The 2004 pensioners survey arried out by RBA reveals that about 41% of retirees hanged their jobs but only 24.4% of them transferred their benefit to the new employer s sheme and only 7.1% deferred the benefit in the original sheme. A ase study arried out by CAPRA 10 only used the Central Eposed to Risk to develop a disaster risk information platform for raising risk management awareness in the region. The probabilisti tehniques were applied to the analysis of earthquakes, tsunamis, hurrianes, floods, landslides and volanoes. This study intensified in determining the regions with high vulnerability to a variety of natural hazards. Attention has not been given into eamining some other appliation areas of Central Eposed to Risk. For 6 National Soial Seurity Fund 7 Civil Servants Pension Sheme 8 Oupational Retirement Shemes 9 Individual Retirement Shemes 10 Central Amerian Risk Assessment 155
eample, little attention has been paid to its appliation in determining the probabilities of ourrene of different modes of derement in pension plans. Members of a pension sheme omprise of members present and ative only at a given alendar year. A member is deemed to have eited the sheme in ase of death, resignation from ative employment, when one is terminated/dismissed from ative employment and if he/she has retired. Pension shemes therefore have reords of its members from time of entry to time of eit. However, it s hypothesized that major mode of eit in pension shemes is through death or retirement even though it s not lear whih modes of eit is prevalent among the members. It s therefore essential to investigate whih mode of eit is more predominant and eamine whih agegroup these eits our. To establish this, a study of person years of eposure is neessary otherwise known as entral eposure to risk. Any pension offie is interested in minimizing risks assoiated with unpreedented eits of pensioners from the sheme. To asertain vulnerability to losses that may arise following these eits, pension offie require a well defined guideline or model whih aptures the probabilities of eits from the pension sheme at eat age or ohort. The Central eposed to risk is essentially a valid model in this area and provides a more elaborate framework for establishing the prevalent modes of eits from pension sheme and for determining the risk time between age-groups under observation. 1.1. Organization of the Paper The paper is split up into the following setions: In setion two, a review on some empirial models is done inluding presentations of their mathematial forms. Results are then presented in setion three, whih inludes the various tests done. The results are presented in figures and tables. Based on the results obtained in setion three, onlusions are made in the final setion, inluding reommendations. 2. Some Empirial Review 2.1. The Binomial Model Ideally, we observe n identially distributed, independent lives aged for eatly 1 year, we reord the numbers d who die. Using the notation set up for the disrete model, a life dies with probability q within the year. Hene D, the random variable the random variable representing the numbers dying in the year onditional on n alive at the beginning of the year, has distribution D B( n, q (1 ~ Giving a maimum likelihood estimator D qˆ = (2 n With variane Var( qˆ q (1 q n = (3 Where using usual notation we have set l = n. The trouble is of ourse that with real data we may observe the i th life in an interval (a i, b i, 0 < a i < b i < 1. In this ase Pr( (4 D X = 1 = bi a q+ a i i i 2.2. Poisson Model Poisson distribution is a lassi distribution normally used to model the number of rare events ourring during some period of time. In the study, it was assumed that N individuals were observed. Further, it was assumed that the fore mortality was µ and was used to denote the observed waiting time (entral eposed to risk. The Poisson model is then given by the assumption that D has Poisson distribution with parameter µ suh that P( D e d = ( E µe µ d = (1 d! This gave the distribution funtion of the rates of derement. 156
2.2 Estimation of fore of derement This was obtained by alulating the likelihood of observing the derements, d, if true value of hazard rate is µ. This yielded e L( µ = µ E ( µ E d d! Taking the natural logarithm of (2 gives; LogL( µ = d(logµ + log E µ E logd! (3 Differentiating (3 with respet to µ and equating to zero; L( µ = d E µ µ µ = d E Thus d µ = E = 0 The entral eposed to risk,, for a life aged is the time from date A to date B where date A is the latest of: The date of reahing age label, the start of the investigation and the date of entry, date B is the earliest of: The date of reahing age label +, the end of the investigation and the date of eit. (2 (4 (5 Empirial Results Data used in the analysis were obtained from a pension sheme in Kenya for different age groups over the years. R.gui was used to analyze the data. Figure (1 shows a omparison of eit modes at different ages. Figure 1: Bar graph showing different modes of eits at various age groups The most prevalent mode of eit is resignation as shown and was dominant at age groups 26-30, 36-40, 41-45 and 46-50. The age group 41-45 reorded the highest mode of eit through resignation. The mode of eit via retirement reorded lower numbers at lower age groups before 50 years and rose gradually towards normal retirement age of 60 years. At age group 51-55 there were a slightly higher reorded numbers of eits through retirement as individuals seek early retirement. The resignation eits are presented in figure (2. 157
Figure 2: Mode of eit through resignation at various age groups From a sample size of 148 observations, there were a total of 69 derements of whih 13 were due to retirement, 26 due to resignation, 11 deaths and 19 were termination/dismissal; resignation reporting the highest number. UDD assumption shall be made for the death eits, allowing the inlusion of all eits in the eposed to risk until the end of the year of age, whih shall oinide with the sample size. However, the eat population eposed to risk is of interest, whih is less than the sample size. The approah to this is to estimate the epeted waiting time, whose realization is the entral eposed to risk. An eamination of the entral eposed to risk yielded figure (3. Figure 3: Central eposed to risk verses age group The entral eposed to risk is low at the age group 26 to 30 and rises steadily to age group 36 to 40 whih is at peak. From the peak, it dereased gradually to retirement age at 60. This shows that the eposure of the members of this pension sheme to the risk of derement inreases steadily from age group 26-30 reahing maimum at age group 36-40, then dereases gradually to normal retirement at age 60. For a fund manager, this is an indiation that an hedging strategy needs to be developed for these groups of pensioners. A aussionary fund may be established to shield the fund from eposure to downside risk. To estimate the instanteneous eit rate, the fore of derement, estimated as µ, were alulated. The plot is presented in figure (4. The fore of derement was highest between age group 26-30 and relatively high between age groups 41-45, 51-55 and age group above 60 years and hene the rate of eit from the pension sheme was higher between these age groups. It was relatively lower between age groups 31-35, 46-50, 56-60 and lowest between age group 36-40 suggesting that this age groups eperiened a lower fore of derement, whih was lowest at age group 36-40. 158
Figure 4: Fore of derement at different age groups Conlusion Pension shemes are bedeviled with the problem of elaborate framework of establishing person years of eposure otherwise known as entral eposed to risk and the most prevalent mode of eits from the pension sheme. There may be failure by pension to antiipate major eit as and when they our at an appropriate time. This failure may lead to low alloation of finanes whih does not math the number of eits at given time and thus affet the running of the pension system. Pension systems require a well-grounded framework to be used to establish with a given degree of auray, the antiipated number of eits of pensioners and at what age. To be able to do so, pension sheme should adopt Central Eposed to risk method, whih aptures these projetion aspets of the pension system evidened by the study. To be able to make this method effiient in meeting this demand, further studies should be arried out to establish how to minimize the weaknesses of Poisson model, whih was the basis of the study. The binomial model an be tested for the same study. To establish how the Pension shemes returns are affeted, further studies should be arried out to establish the relationship between pensioners eits. This was not aptured in the study. Referenes Ambahtsheer, K. (2007a. Pension Revolution: A Solution to the Pension Crisis. Wiley. Curtler, D. & Johnson, R. (2004. The Birth and Growth of Soial Insurane State: Eplaining Old-age and medial insurane aross ountries. Publi Choie, (120:87-121. Kakwani et al (2006. Old-Age Poverty and Soial Pensions in Kenya, International Poverty Center, Working Paper No. 24. Lindert, P. H (1994. The Rise of Soial Spending, 1880 1930. Eplorations in Eonomi History, (31:1-37. Myers, M.D. (1997. Qualitative Researh in Information Systems. MIS Quarterly 21(2:241-242. Newman, M (2005. Soialism: A Very Short Introdution, Oford University Press. Njuguna G. A (2010. Strategies to improve pension fund effiieny in Kenya. PhD Thesis, Faulty of Business and Eonomi Sienes, Nelson Mandela Metropolitan University. Omondi, M. (2008. Value of pension assets drops after market orretion. Business Daily. May (16 13. Perroti, E. & Shwienbaher, A. (2008. The Politial Origin of Pension Funding. Available: http://www1.fee.uva.nl/fm/papers/perotti/the Politial Origin of Pension Reform 19 08 2008.pdf [Aessed April 09, 2015]. RBA ACT, (2000. Government Printers. Nairobi. RBA Quarterly Reports 2006, 2007, 2008, 2009, 2010. Available: http://www.rba. go.ke [Aessed 12 November 2014]. Sott, W.F. (2000. Mortality studies. University of Aberdeen, AB24 3UE U.K. Stewart, F. & Yermo J. (2009. Pensions in Afria. OECD Publishing. Sze M. 2008. Funding of Private Funds: Tehnial Assistane for Poliy Reforms. World Bank. 159
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