Share portfolio on the Polish Capital Market in Conditions of Financial Crisis

Transcription

1 5. meziárodí koferece Řízeí a modelováí fiačích rizik Ostrava VŠB-TU Ostrava, Ekoomická fakulta, katedra Fiací září 00 Share portfolio o the Polish Capital Market i Coditios of Fiacial Crisis Adriaa Mastalerz-Kodzis, Ea Pośpiech Abstract Ivestig is oe of the basic activities i ecoomy. Selected elemets of ivestmet strategies are cosidered i the research. The ork cosists of to parts here the first oe focuses o brief descriptios of ivestmet strategies ad the other cocetrates o give data aalyses methods, methods hich may be useful i risk aalysis ad buildig ivestmet strategies. I the secod part, basig o data take from Stock Exchage i Warsa selected measures ad ivestmet portfolio compoets ere calculated ith the use of preseted formulae. There is a summary at the ed of article. Key ords Ivestmet strategies, portfolio theory, share risk measures, portfolio risk measures Itroductio Aalysis of fiacial data is oe of the fastest developig fields of ecoometrics ad theory of fiaces. The icrease of market risk ad the ecessity to protect agaist it are the mai stimuli developmet methods o fiacial data aalyses. The dyamic developmet of Polish fiacial market causes that there is a eed for better ad better tools for aalyses ad fiacial pheomea descriptios. More ad more efficiet class models are the result of lookig for combied modelig fiacial variables of time ros ad depedecies betee them. Recetly, capital markets have bee exposed to big risk resultig from fiacial crisis. The questio is hether there is a chace to geerate some positive profit ivestig o the stock market durig crisis ad hat elemets should a portfolio share cosist of so that it ould geerate a positive rate of retur at least risk. Pesio scheme i Polad is based o 3 structures i hich the Poles gather moey for their pesios. The first oe is obligatory for everyoe ad the moey are collected i Social Isurace Board (ZUS) hich is admiistered by govermet. The secod oe is also obligatory, based o the capital market ad is admiistered by Ope Retiremet Fuds (OFE). The third oe is volutary, also based o the capital market ad admiistered by private ivestors (objects). Ope Retiremet Fuds (OFE), hich have bee ivestig /amog others/ o the Polish market i recet years sho losses, hich ill result i little pesios for the Poles. The questio is hether the losses of OFE are due to decreasig stock prices, or hether the costs of ruig retiremet fuds are too high. Therefore, the aim of this research as to build a effective portfolio of shares based o data obtaied from Warsa Stock Exchage. It is obvious that there are may ivestmet strategies ad may ays of buildig up the compoets of portfolio. The article focuses o selected strategies. Adriaa Mastalerz-Kodzis, Ph.D., Uiversity of Ecoomics i Katoice, adamast@ae.katoice.pl Ea Pośpiech, Eg., Ph.D., Uiversity of Ecoomics i Katoice, posp@ae.katoice.pl

2 5. meziárodí koferece Řízeí a modelováí fiačích rizik Ostrava VŠB-TU Ostrava, Ekoomická fakulta, katedra Fiací září 00 Basic otio of portfolio theory I 965, Jack Hirshleifer stated that A ivestmet is actually a curret recatatio for future profit. Hoever, the preset is relatively ell ko hile the future is a mystery. Therefore, a ivestmet is a recatatio of the certai profit for the ucertai oe. Ivestmet strategy is a set of cocrete rules ad behavior patters used by the ivestor to realize their decisios o buyig ad sellig o a give market. Differet kids of ivestmet techiques are used for differet strategies. The idea of ivestmet pyramid ell reflects the folloig levels, goig doards: Ivestmet strategy Ivestmet system Ivestmet style (disciplie i ivestig) Koledge of market (educatio, koledge about the market) Ivestmet style ca be described as a idividual feature of each ivestor. Psychology of fiacial markets advises that the ivestor should ork o their developmet ad use a certai ivestmet style, hich ill help to elimiate the to crucial problems each ivestor faces: ucertaity ad icosistecy. I this article, e should like to cocetrate o the structure of portfolio basig o data from Warsa Stock Exchage. I the classical theory of portfolio created by Harry Markoitz, to characteristics of securities are used: expected rate of retur ad rate of retur variace. Let us mark share price as P t i period (momet) t (look [, 4]). Rate of retur from share durig period t is a value P P = t t R t () Pt By usig historical data like rates of retur realized i past periods, a estimated expected rate of retur ca be calculated as a arithmetic mea. The expected rate of retur from share is a value R = R t t= () If the distributio of rate of retur is uko but the value of R have bee observed i the past, it may be assumed that chages i rates of retur i the future ill be close to those i the past, ad ill be oscillatig aroud the expected rate of retur. The arithmetic mea of rate of retur o a sample is the best estimator of uko expected rate of retur. While usig historical data, oe should ask the questio about the umber of periods take ito accout to calculate the expected rate of retur. The higher the umber of periods, the more stable arithmetic mea is (stable ith regard to little sesitivity to extreme values i ro). Hoever, it is the curret value of rate of retur together ith recet values that have the biggest ifluece o the future rate of retur value. Therefore, too log historical periods should ot be take ito cosideratio. This research covers the period of fiacial crisis so data take from May, 008 up to August, 00. The value of expected rate of retur does ot iclude differetiatio of rates of retur i historical periods take ito accout. Iformatio o differetiatio ca be obtaied by calculatig rate of retur variace ad its root stadard deviatio. The bigger the value of expected rate of retur ad loer stadard deviatio is, the loer the risk of ivestig i shares is. The bigger the differetiatio of rate of retur is, the bigger the risk is. The measure

3 5. meziárodí koferece Řízeí a modelováí fiačích rizik Ostrava VŠB-TU Ostrava, Ekoomická fakulta, katedra Fiací září 00 of share risk is the rate of retur variace. With the use of historical rates of retur from - periods the value of variace ca be calculated. Rate of retur variace Var ( R) = ( R t R) t= (3) No-egative values are used for variace of rates of retur. Variace is equal to zero he, ad oly he all take ito accout rates of retur equal the values of expected R. The bigger the historical deviatio of rates of retur is from expected values R, the bigger the variace is. The measure that is more frequetly used i risk aalyses for securities is the square root of variace, called stadard deviatio. Stadard deviatio of rate of retur is the value ( ) ( ( )) / s R = Var R = ( R t R) (4) t= The stadard deviatio of rate of retur presets the average deviatio of possible rate of returs ith regard to expected rate of retur. Stadard deviatio uses o-egative values, therefore, the bigger deviatio value is, the bigger the risk is. The ivestor, bearig i mid the rule of maximal icome ad miimal risk should buy shares at highest expected icome rate ad the loest stadard deviatio. By aalogy, the preseted above characteristics ca be used to defie for share portfolio. Expected portfolio rate of retur has bee preseted as / p = i E i= r ( r ) here: r p expected portfolio rate of retur i participatio of i-compay i portfolio E(r i ) expected share rate of retur for i-compay Variace of portfolio rate of retur is preseted as i (5) V p = i i= σ i + i jσ iσ j ρij (6) i= j = i+ here: V p variace of portfolio rate of retur σ i stadard deviatio of share rate of retur for i-compay ρij correlatio coefficiet of share rate of retur for i-compay ad j-compay Portfolio stadard deviatio is preseted as σ p = i i = σ i + i jσ iσ j ρij (7) i= j = i + Portfolio risk depeds ot oly o the risks of portfolio compoets but also o correlatio coefficiets of portfolio compoet rates of retur, here the more egative or slightly positive correlatio coefficiets of rates of retur are, the loer the risk of portfolio is.

4 5. meziárodí koferece Řízeí a modelováí fiačích rizik Ostrava VŠB-TU Ostrava, Ekoomická fakulta, katedra Fiací září 00 I case of to compaies i portfolio, the portfolio of miimal variace risk (MVP) cosists of folloig shares: σ σσ ρ =, σ + σ σ σ ρ σ σσ ρ = (8) σ + σ σ σ ρ The efficiet portfolio is such a portfolio hich: For the give expected rate of retur (but higher tha expected portfolio rate of retur a miimal risk) miimizes risk (stadard deviatio). For give risk (stadard deviatio) maximizes expected rate of retur. Efficiet portfolios are attractive for ivestor ho follos the rule of obtaiig the highest possible expected rate of retur ad loest stadard deviatio of rate of retur. Other portfolios are domiated by efficiet portfolios.. Workig out portfolio of miimal risk Participatio of shares i a portfolio of miimal risk ca be preseted as: = C I (9) here: vector of + compoets hose first -compoets are shares i a portfolio of miimal risk I vector of + compoets hose first -compoets are zeros ad the last oe is C a matrix hich is reverse to matrix C C a matrix of dimesios (+) (+) hose elemets are marked as: c ii c ij = σ i, i = K,, ; = σ σ ρ, i, j =, K,, i j ; i j ij c i, + = c+, i =, i = K,, ; c +, + = 0.. Workig out a efficiecy portfolio of a iflicted rate of retur Participatio of shares i a efficiet portfolio (miimal risk at a give rate of retur) is preseted as: D = I0 (0) here: vector of + compoets i hich first -compoets are participatio of shares i a efficiet portfolio I 0 vector of + compoets hose first -compoets are zeros, the oe before the last is, ad the last equals the iflicted expected the portfolio rate of retur D matrix reverse to matrix D D matrix of dimesios (+) (+) hose elemets are marked as: d ii = σ i, i = K,, ; dij = σ iσ j ρij, i, j =, K,, i j ; d i, + = d+, i =, i = K,, ;

5 5. meziárodí koferece Řízeí a modelováí fiačích rizik Ostrava VŠB-TU Ostrava, Ekoomická fakulta, katedra Fiací září 00 ( r ) d i, + = d+, i = E i, i = K,, ; d +, + = d+, + = d+, + = d+, + = d+, + = 0. 3 Empiric aalysis based o Stock Exchage i Warsa Empiric aalysis as carried out o the basis of data obtaied from selected compaies that are i WIG 0 idex group (0 biggest compaies i Warsa Stock Exchage) ad covered the period from 0 th May 008 to 3 th August 00 (575 observatios). Durig that period 7 out of 0 compaies shoed complete data. Graph No. presets WIG 0 idex values i the research period. Figure : WIG 0 idex graph i the research period (source: o ork) Idex values WIG t Table presets basic characteristics of rate of returs for selected shares. Coefficiet β as additioally calculated by the use of Sharp`s sigle idex model [look, 5], hich shos approximately by ho may uits ill the share rate of retur icrease if the market rate of retur idex gros by a uit. The model is preseted as: R α + β R + ε () = M here : R rate of retur of compay share R M rate of retur of market idex (i our ork WIG 0 idex) α free elemet β coefficiet β ε radom compoet Compay ame Expected rate of retur Stadard deviatio of Coefficiet β rate of retur ASSECOPOL BIOTON BRE -7.8E BZWBK CEZ -.4E GETIN 4.46E GTC KGHM LOTOS PBG PEKAO PGNIG PKNORLEN

6 5. meziárodí koferece Řízeí a modelováí fiačích rizik Ostrava VŠB-TU Ostrava, Ekoomická fakulta, katedra Fiací září 00 PKOBP 6.09E POLIMEXMS TPSA TVN 4.4E Table No. : Specificatio of expected rate of retur, stadard deviatio of rate of retur ad β coefficiet for selected compaies (source- o ork) Figure shos a clear decrease of idex values i the first period, ad ext due to β coefficiet higher tha zero there is also a decrease of share prices o the stock. Coefficiet β iforms that amog cosidered compaies there are aggressive shares (β>) ad defesive oes (β<). Oly 8 out of 7 cosidered compaies obtaied positive expected rate of retur. Figure : Risk profit depedece amog rates of retur i selected compaies (source: o ork) Depedece betee risk ad profit for give shares Values of expected retur rates 0,00 0, ,05-0,0005 0,0 0,05 0,03 0,035 0,04 0,045-0,00-0,005 Stadard deviatios of share rates of retur Depedece betee ros of rates of retur for give compaies ere examied. Correlatio coefficiets betee compaies of positive expected rates of retur are preseted i table No.. BZWBK GETIN KGHM LOTOS PEKAO PKN ORLEN PKOBP TVN BZWBK GETIN KGHM LOTOS PEKAO PKNORLEN PKOBP 0.5 TVN Table No. : Correlatio coefficiets betee compaies ( source: o ork) The aalysis of data preseted i the above table allos to dra the coclusio that share rates of retur are positively correlated ad the depedece is eak, moderate or sigificat. Next, a share portfolio cosistig of ad later 3 selected from above shoed shares ill be created. For these portfolios the folloig characteristics ill be calculated: expected rate of retur from portfolio ad portfolio variace. Next, obtaied data ill be compared. Durig the aalysis of obtaied characteristics ad correlatios betee rates of retur (oly

7 5. meziárodí koferece Řízeí a modelováí fiačích rizik Ostrava VŠB-TU Ostrava, Ekoomická fakulta, katedra Fiací září 00 compaies that had a positive expected rate of retur ad those hose correlatio as belo 0.5 ere take ito cosideratio), portfolios cosistig of to or three compoets ca be examied (Table No. 3). Portfolio compositio Participatio of give compaies i portfolio Expected value of portfolio Stadard deviatio of portfolio β coefficiet of porfolio BZWBK, LOTOS KGHM, TVN TVN, GETIN E TVN, LOTOS LOTOS, KGHM LOTOS, GETIN LOTOS, PEKAO LOTOS, GETIN, TVN LOTOS, KGHM, TVN LOTOS, GETIN, TVN LOTOS, KGHM, TVN Table No. 3: Presetatio of selected characteristics of efficiet share portfolios ( source: o ork) Data preseted i Table 3 idicate that from the selected compaies it is impossible to build a portfolio at a expected value of over Stadard deviatios are ot loer tha.7% ad ot higher tha 3%. Therefore, eve durig fiacial crisis ad basig o portfolios cosistig oly of shares it is possible to build a portfolio of positive rate of retur ad little stadard deviatio. Figure 3: Profit- risk depedece of rates of retur i selected portfolios (source: o ork) Profit-risk depedece for portfolios Expected values for portfolio 0,0005 0,0004 0,0003 0,000 0, ,05 0,07 0,09 0,0 0,03 0,05 0,07 0,09 0,03 Stadard deviatio of portfolio Moreover, sesitivity measures ca be for example used to protect portfolio value (look [3]). The strategy cosists i modifyig the portfolio i such a ay that the proper sesitivity measure takes the earlier accepted value. For example, it as decided that the cosidered portfolios had the coefficiet β equal to. Letter meas participatio of KGHM share i the ely established portfolio built up from most profitable efficiet portfolios preseted i Table 3, ad compay shares of BZWBK ad KGHM (of positive rate of retur ad β>). For example, for the first pair the folloig equatio is to be solved

8 5. meziárodí koferece Řízeí a modelováí fiačích rizik Ostrava VŠB-TU Ostrava, Ekoomická fakulta, katedra Fiací září ( ) = here is a additioal share of BZWBK compay i the portfolio. Solvig the equatio gives = X compay ad its β Share portfolio ad its β Participatio of share i Compay X Portfolio share BZWBK BZWBK+LOTOS BZWBK LOTOS+KGHM BZWBK LOTOS+KGHM+TVN KGHM BZWBK+LOTOS KGHM LOTOS+KGHM KGHM LOTOS+KGHM+TVN Table No. 4: Presetatio of shares of selected efficiet portfolios ad compay shares givig β equal to (source: o ork) 4 Summary I coclusio, it may be stated that eve i a period of recet big fluctuatios ad drops o Warsa Stock Exchage, there is a simple ay to build up a portfolio strategy geeratig positive profit at a relatively lo risk. Hoever, it should be stressed that i the research the strategy of buildig a portfolio as based oly o Warsa Stock Exchage shares. Obviously, a portfolio may also iclude other stock values like portfolio compoets free from risk, bods, optios, hich additioally differetiate the portfolio ad loers its risk. Nevertheless, as oe ca clearly see, eve a portfolio cosistig of oly shares brigs positive profit. Fiacial istitutios participatig i Stock Exchage i a efficiet ay have a chace for profit. If they, hoever, geerate losses it is probably due to bad ivestmet strategies, icorrect maagemet or too high maiteace costs of coductig fiacials activities. Referece [] HAUGEN ROBERT A. Teoria ooczesego iestoaia. Obszery podręczik aalizy portfeloej. WigPress, Warszaa 996 [] JAJUGA K. JAJUGA T. Iestycje, istrumety fiasoe, aktya iefiasoe, ryzyko fiasoe, iŝyieria fiasoa. Wydaicto Naukoe PWN, Warszaa 006 [3] JAJUGA K. Zarządzaie ryzykiem., Wydaicto Naukoe PWN, Warszaa 009 [4] MARKOWITZ H.M. Portfolio selectio-efficiet diversificatio of ivestmets. Yale Uiversity Press, Ne Have 959 [5] SHARPE W.F. A simplified model for portfolio aalysis. Maagemet Sciece, vol. 9, 963