Formation of the Optimal Investment Portfolio as a Precondition for the Bank s Financial Security

Transcription

1 Journal of Economcs and Busness Research, ISSN: , E ISSN (onlne) , ISSN L = Volume XXI, No. 2, 2015, pp Formaton of the Optmal Investment Portfolo as a Precondton for the Bank s Fnancal Securty A. S. Shapovalova, S. M. Shapovalova Anna Shapovalova, Svetlana Shapovalova Insttute of Economcs and Management, Vladmr Dahl East-Ukranan Unversty, Severodonetsk, Ukrane Abstract Ths artcle analyses the defnton of the bank s fnancal securty and nvestment actvtes. It descrbes a few types of models of bank s rsks management and the method CAPM, whch s chosen for use. In support for the chosen CAPM method, we ncluded the mathematcal model that allows elaboratng an optmal nvestment portfolo. The model stands at the bass of ths method and a case study of one of Ukranan banks. Keywords: fnancal securty, nvestment portfolo, rsk, return on nvestment, varance, securtes, covarance, yeld. Introducton The experence of the developed states proves that the fnancal securty of a bank s largely defned by approaches and forms of ts nvestment actvty. The practce of nvestment actvty n modern Ukranan banks, even n the condton of hgh share of foregn captal, and therefore the possblty of leadng world experence, unfortunately does not demonstrate the desred nvestment results. Such crcumstances may be

2 A. S. Shapovalova, S. M. Shapovalova explaned by objectve natonal realtes. However, gnorng advanced technques to buld attractve nvestment portfolos s able to both deepen mperfectons of nvestment actvtes of a bank and prevent effectve rsk management, threatenng the fnancal securty of the bank. Rsk takng s the bass of bankng. Banks do well when rsks taken by them are reasonable, under control and wthn ther fnancal capabltes and competences. Rsk n nvestng actvtes occurs as a result of devatons of actual data on the evaluaton of the current state and future development. These devatons can be both postve and negatve. In the frst case t goes about chance of recevng ncome, n the second about the rsk of loss. The relaton between bank proftablty and ts rsk (n smplfed form) can be expressed as lnear dependence. However, f a bank seeks to ensure ther fnancal securty n general, and executng securtes transactons, n partcular, t s necessary to use rsk management tools. A lot of research has been dedcated to the ssue of rsk management and rsk management of nvestment actvty n partcular [5, 2, 3], but those studes whch examned rsk measured t prmarly n terms of ntegral component of the nvestment. If we consder rsk as a factor that threatens the fnancal securty of the bankng actvtes, these studes have not dedcated attenton to the management of nvestment rsk for the banks fnancal securty. Therefore, the purpose of the artcle s to study the possblty and necessty of rsk management that occurs n the process of nvestng to ensure the fnancal securty of a bank, as well as demonstratng the theoretcal and methodologcal steps of constructng the optmal nvestment portfolo of modern bank securtes based on the approach of H. Markowtz, allowng to mnmze the rsk mentoned. Case Study The fnancal securty of a bank s a state of that nsttuton, whch s characterzed by a balance and resstance to external and nternal threats (rsks), ts ablty to acheve ther goals and generate suffcent fnancal resources for sustanable development. Based on ths defnton, the bank's fnancal securty can be ensured only n case of

3 Formaton of the optmal nvestment portfolo the balance of ts fnancal resources n the mplementaton of ts actvtes (operatng, fnancal or nvestment). The artcle studes the nvestment actvty of a bank as one of the most rsky, but at the same tme the most proftable bankng actvty. Therefore, the key to success n ths busness are effectve rsk management. There are many bank rsk management methods, lke: analyss and control gap, analyss and control duratons. The prmary method of analyss s modelng. The man control methods are: neutralzaton of clams and labltes; hedge of nterest rate rsk; the effectve border; optmzaton of the portfolo structure by mathematcal programmng. Gven that almost all methods have been suffcently studed and wdely used n bankng practce, the method of effectve border has been studed n the artcle. Ths method s based on an applcaton of defnng the nvestment portfolo prcng model CAPM (Captal Asset Prcng Model) to the problem of nterest rate rsk analyss. Another name for ths method s the method of average and devaton sample. Wthn the method there s consdered the effectveness of strateges dependng on the assocated rsk. Under the strategy, n ths case, t s necessary to understand the future cash flows generated by the current structure requrements and oblgatons and possble changes n the structure. As an ndcator of the strategy effcency there has been set mathematcal expectaton of the current or future value of cash flows, or other fnancal ndcators, related to ncome and net worth. Standard devaton of expected performance s taken as an ndcator of rsk assocated wth a gven strategy. Prehstory occurrence of CAPM method was the dscovery of H. Markowtz, who proposed a mathematcal model of optmal nvestment portfolo, as well as methods of constructon of such portfolos under certan condtons. For the role of the faclty to demonstrate the theoretcal and methodologcal steps to construct the optmal modern bank securtes nvestment portfolo, based on the approach of H. Markowtz, would best ft a bank that s actually engaged n nvestment actvtes (more or less successfully). Such bank s, for example, JSC "UkrSbbank". H. Markowtz approach for JSC "UkrSbbank" wll be treated as dscrete, n whch the begnnng of the nvestment perod s denoted as t = 0, and the end as t = 1. In ths case, at the tme t = 0, the nvestor must

4 A. S. Shapovalova, S. M. Shapovalova make a decson to purchase specfc fnancal nstruments that wll stay n ts portfolo by the tme t = 1. As the portfolo of JSC "UkrSbbank" s a set of ts partcular varety, ts decson s equvalent to selectng the optmal portfolo from the set of possble portfolos. The approach of H. Markowtz as for portfolo choce mples that JSC "UkrSbbank" tres to solve two problems: to maxmze expected yeld for a gven level of rsk and mnmze the uncertanty (rsk) for a gven level of expected yeld. As the nvestment portfolo s a collecton of varous assets (fnancal nstruments), ts yeld can be calculated as follows: r p W W W 1 0 (1) where: W 0 s the aggregate purchase prce of all assets ncluded n the portfolo at tme t = 0; W 1 - the total market value of the assets at the tme t = 1 and, n addton, the total cash ncome from ownershp of the asset from the moment t = 0 untl t = 1. It s necessary to note that JSC "UkrSbbank" has to decde on whch portfolo to buy at the tme t = 0. In dong so, t does not know what the ntended fgure of proftablty for most dverse alternatve portfolos wll be. Thus, JSC "UkrSbbank" must consder yeld, assocated wth any of these portfolos, a random varable. These portfolos have ther characterstcs, one of them - the expected (or average) yeld, and the other - the standard devaton. Wth a portfolo of JSC "UkrSbbank" wth a large number of assets n the future, t s expected that the number of companes whch wll be known any good news about wll be equal to the number of companes whch wll be announced any bad news. Ths means that the more dversfed the portfolo s, the less the unsystematc (own) rsk wll be. Thus, dversfcaton sgnfcantly reduces unsystematc rsk. Systemc rsk s manfested n another stuaton. Thus, wth the number of assets ncluded n the portfolo, systematc (market) rsk converges to the mean for all pars of assets ncluded n the portfolo. Thus, dversfcaton allows averagng the systematc rsk. Ths fndng s mportant, as n the case of adverse or favorable economc outlook, most securtes wll not be pad or, respectvely, pad. Despte 0

5 Formaton of the optmal nvestment portfolo the dversfcaton of the portfolo, you can always expect that such market phenomena affect the proftablty of the portfolo, especally as the market rsk can not be elmnated through dversfcaton. For example, f you know only statstcs on quoted yeld securtes, the further you can dentfy forward yeld value by usng varous functons (logarthmc, lnear or hyperbolc). Expected values are not determned as the average, but as predcted extrapolaton methods. Estmated and actual value of the average return on assets for complng a portfolo of securtes of JSC UkrSbbank s shown n Fgure no.1. Fg. no. 1. Dynamcs of sx quoted yeld securtes (the forecast and actual values, drawn up accordng to the offcal webste of JSC "UkrSbbank")

6 A. S. Shapovalova, S. M. Shapovalova However, as noted above, any nvestment actvty s related to rsk. Therefore, there rses the queston of assessng the rsk level of JSC "UkrSbbank" securtes. To assess the rsk of nvestments n securtes there have been used ndcators such as standard devaton and varance. The standard devaton used as a rsk assessment of the project, s also defned as a devaton from accepted values for trend forecastng. Varance s a measure of devaton of the values of random varable dstrbuton center. Larger values ndcate greater dsperson devaton values of the random varable from dstrbuton center. Varance or dstrbuton s the mathematc expectaton or mathematc expectaton of a value rased to the second degree of devaton from ts expected value (ts expectaton). So, varance s the measurement value of dsperson values of ths varable, takng nto account all ts mportance and ther probablty or weght. Varance of dscrete random varable s as follows: Where s called the standard devaton value of ts average value; D the operatorofa random varable varance. Let X, Y be two random varables defned on the same probablty space. Then ther covarance s defned as follows: (2) assumng that all expectatons E on the rght sde are defned. Yeld ndces values, values of varance, covarance rsk and two portfolos are shown n table no.1. (3)

7 Yeld Varence (σ 2 ) Covarence σ (rsk) Formaton of the optmal nvestment portfolo Table no. 1. Evaluaton of the rsk of avalable securtes At JSC "UkrSbbank" A couple of portfolos under consderaton CJSC "Kyvoblenergo" CJSC "Frst Ukranan Bureau of Credt Hstores" JSC "Ukranan Securtes Depostory" CJSC "Frst Ukranan Bureau of Credt Hstores" JSC "Ukranan Securtes Depostory" 59, ,88 7,53 48, ,54 5,17 CJSC "Kyvoblenergo" 23, ,41 5,67 Thus, f we know the portfolo yeld and can calculate ther rskness, t becomes possble to determne an effcent set of portfolos (.e. the set of not domnant portfolos that would let create the optmal structure). Under optmal nvestment portfolo structure n ths case we can understand a set of fnancal nstruments (securtes) that would ensure such level of rsk that would not create sgnfcant threats to the fnancal securty of the bank. The set of non-domnant portfolos, called effectve soluton, can be constructed by the soluton of the general problem to mnmze the rsk, was frst consdered by H. Markowtz: n n 2 jj mn (4) j1 1 where search ndex of the frst par of securtes n the pared multplcaton of the securtes share and the covarance of securtes ncluded n the par that are multpled; j search ndex for the second n a par of securtes n doubles by multplyng the share of securtes and the covarance of assets belongng to the couple multpled; n number of securtes n a portfolo; α share of portfolo securtes n fractons of a unt; σ j covarance of securtes ncluded n the par multpled when j, of securtes varance f = j, under two constrants. The frst constrant captures the desred rate of yeld, and the second constrant

8 A. S. Shapovalova, S. M. Shapovalova normalzes the weghts of the portfolo (wthout constrants on short poston): E r E ; The Lagrange objectve functon for the problem of mnmzng rsk at a fxed level of return s wrtten as: L (5) j jj 1 E r E 2 1 j The portfolo that mnmzes the rsk s, f we put L/ =L/λ j =0 for all and shares for j = 1,2. These frst order condtons defne a system of equatons, lnear weghtng factor for portfolo and Lagrange multplers and therefore t can be solved usng matrx methods (wth the possblty of usng standard software packages). Thus, the objectve functon for the problem wth three types of shares s wrtten as: L E E E E (6) After solvng the Lagrange equaton n the standard package of Mcrosoft Offce Excel, you can fnd a set n whch the coeffcent of correlaton are the number of securtes lsted n the nvestment portfolo of the company JSC "UkrSbbank". Ths soluton determnes the optmal portfolo of three companes securtes that mplements the requred yeld wth mnmum varance. The structure of the portfolo JSC "UkrSbbank" can be represented graphcally through fg. no. 2. The ntal value for determnng the optmal structure of the nvestment portfolo s to search for a break-even pont (wthout rsky

9 45,1 45,5 45,9 46,3 46,6 47,0 47,4 47,8 48,2 48,6 48,9 49,3 49,7 50,1 50,5 50,9 51,2 51,6 52,0 3,865 3,864 3,864 3,865 3,868 3,872 3,877 3,883 3,891 3,900 3,910 3,922 3,935 3,949 3,964 3,980 3,998 4,017 4,037 Portfolo structure 0,251 0,238 0,225 0,212 0,199 0,187 0,174 0,161 0,148 0,135 0,122 0,109 0,096 0,083 0,070 0,057 0,044 0,031 0,018 0,486 0,493 0,501 0,509 0,517 0,525 0,532 0,540 0,548 0,556 0,564 0,572 0,579 0,587 0,595 0,603 0,611 0,619 0,626 0,263 0,268 0,273 0,279 0,284 0,289 0,294 0,299 0,304 0,309 0,314 0,320 0,325 0,330 0,335 0,340 0,345 0,350 0,355 Formaton of the optmal nvestment portfolo yeld). The rsk-free rate of yeld makes 45.1%. The rsk for such yeld s the smallest (Table no. 2). Fg. no. 2. Structure-yeld of JSC "UkrSbbank" portfolo Table no. 2. Structure, rsk and yeld effectve set portfolo JSC "UkrSbbank" CJSC "Kyvoblenergo" CJSC "Frst Ukranan Bureau of Credt Hstores" JSC "Ukranan Securtes Depostory" Σ Portfolo rsk σ Yeld

10 A. S. Shapovalova, S. M. Shapovalova Varyng the desred yeld, we can buld an affordable and effcent set of portfolos JSC "UkrSbbank". Graphcally determned wthout rsk portfolo yeld, affordable and effectve set of securtes JSC "UkrSbbank" s shown n the dagram (Fg. no. 3). Fg. no. 3. Value of return and portfolo rsk n dfferent portfolos of JSC "UkrSbbank" securtes Followng the outstandng securtes effectve set of JSC "UkrSbbank" the optmal structure can be chosen. Moreover, there s a choce as more rsky and more proftable portfolo, and less rsky, but also less proftable. The choce depends on the propensty management of JSC "UkrSbbank" to rsk. When choosng the optmal structure of the nvestment portfolo t should not be forgotten that rsk management s not the only component that provdes fnancal securty of the bank. It should not be forgotten about the prncple of comprehensveness and consstency n provdng fnancal securty, because rsk factors that threaten t may not only reduce the nvestment yeld unpredctably, but also reduce the lqudty of the securtes.

11 Formaton of the optmal nvestment portfolo Conclusons Fnancal securty s a complex concept and ts mantenance s only possble n complex analyss and control of the bank n order to prevent crses. Investment actvty, thus, should be made only on the condton of fnancal securty. It s therefore advsable to use dfferent methods of managng nvestment rsk of commercal banks, to whch further research wll be devoted to. References [1]. Antpov, A. N., Kozachenko, A. V., Dbns, G. I. (1999). Управление инвестиционным процессом, Lugansk. [2]. Blank, I. (2001). Инвестиционнй менеджмент: Учебный курс. Kyv: Jel'ga-N. Nka-Centr. [3]. Casu, B., Molyneux, P., Grardone, C. (2006). Introducton to bankng. London: Prentce Hall Fnancal Tmes. [4]. Davdsson, M. (2013). Portfolo Theory forward Testng. Advances n Management & Appled Economcs, 3(3), p [5]. Informaton from offcal webste of JSC «UkrSbbank», [6]. Krchenko, O. A., Gіlenko, І. V., Rogol, S., Srotjan, S. V., Nєmoj, O. (2002). Банківський менеджмент: Навчальний посібник. Kyv: Znannja-Pres. [7]. Markowtz, H. (1952). Portfolo Selecton, The Journal of Fnance, vol. 7, No. 1., p [8]. O'Bren, J., Srvastava, S. (1995). Modern Portfolo Theory. Cncnnat, Oho: South-Western College Pub. [9]. Zaytseva, I., Kotsyuba, O. (2013). Banks as man Subjects of Investment Actvty. Busness Inform, (10), p