Equity Asset Allocation Model for EUR-based Eastern Europe Pension Funds

Transcription

1 TUTWPE(BFE) No. 04/119 Equity Aet Allocation Model for EUR-baed Eatern Europe Penion Fund Robert Kitt Hana Invetment Fund Liivalaia 12/8, Tallinn, Etonia Telephone: ; Fax: Department of Mechanic and Applied Mathematic Intitute of Cybernetic at Tallinn Univerity of Technology Akadeemia tee 21, Tallinn, Etonia Abtract Thi paper i aimed to explain the choice of intrument mix for EUR-baed long-term equity invetor, like penion fund, in the Eatern Europe. It i aumed that invetment into local ecuritie are the invetor preferred choice. Markowitz meanvariance optimization wa ued for determining optimal portfolio. Exponentially weighted hitorical time -erie were ued for input data. After finding an efficient et of portfolio hypothetical 100 wa inveted (a of March 1993) into the portfolio and thi invetment wa benchmarked againt EUR-hedged MSCI World index. Different portfolio mixe with everal rebalancing frequencie were teted in the way decribed. Portfolio mix propoed for real invetment i the following: North America (40%); Europe (35%); MSCI Pacific (10%); MSCI Emerging Market Free (10%) and MSCI Eatern Europe (5%). Thi portfolio mix gave a poitive reult over the period compared to benchmark. Suggeted rebalancing frequency i 1 month. JEL Claification Number: C5, C6, G1 Keyword: Portfolio theory, mean-variance optimization Acknowledgement The author would like to thank Dr Jaan Kalda for fruitful dicuion and Hana Invetment Fund Ltd for upporting the reearch. The financial upport from the Etonian Science Foundation (grant No 5036) i greatly appreciated. 1. Introduction A lot of attention i paid to the aet allocation in economic literature. Aet allocation i conidered the key value driver of portfolio performance, according to many 245

2 author (Brinon et al., 1986, 1991; Hanel et al., 1991; Surz et al., 1999; Ibboton and Kaplan, 2000). Majority of uch paper are written from US invetor point of view: their home currency i dollar and their home region i United State etc. The mandate of US equity portfolio manager i more or le clear a well: they have to outperform Standard and Poor 500 or Wilhire 5000 index. For Wetern European countrie the ituation i imilar - portfolio tend to have a trong home bia. Invetor mandate given to fund manager i alo to outperform local tock market index. Uually there i an international component alo in portfolio, but it hare i not dominant. To ummarize, equity aet allocation in developed countrie tend to be a combination of local and international portfolio, latter being minor. If moving outide developed countrie, the invetment choice become unclear. There are no trong invetment tradition and people do not conider the local index a their benchmark. One of the reaon i low amount of companie lited in the exchange, but motly people jut have no invetment experience and know-how. The problem with low number of lited companie force portfolio manager to look foreign invetment opportunitie. It i obviou, that at firt neighbouring countrie are conidered. So, enlarged home i looked and then other countrie follow. Another difference with emerging countrie invetment compared to Wetern peer: portfolio are much more inveted outide developed world imply becaue the home i out ide developed world. The goal of thi paper i to develop an equity invetment model for developing countrie. More precie, former communit countrie that are now entering to the European Union (EU) are kept in mind. The main aim i to develop a model and propoe invetment trategy for long-term invetment vehicle like penion fund of uch countrie. Mot of thee countrie have recently reformed their penion ytem. The reformed penion ytem involve uually a penion fund that are managed by private ector. Invetment manager of new penion fund hould fix their invetment policy and aet allocation. In thi paper, the aet allocation model for Eatern Europe penion fund i derived. 2. Finding an Aet Allocation Model Input Data 1. Bae currency of the portfolio i EUR (EEK). All hitorical time erie are converted to DEM. 2. Aet clae (time erie) ued for Equity portfolio*: Aet Cla Data from Data to North America Europe Pacific Emerging Market Free EM Eatern Europe *All hitorical data i retrieved from Bloomberg or Calculation were alo carried out for World for the ame period a choen for Europe. 246

3 Etimating Markowitz characteritic Weighted hitorical return, tandard deviation and covariation were found for all indice. Monthly data point were ued. Note that weight ued were normalized, i.e. w =1 (1) i Average return and tandard deviation are calculated from maximum available hitorical data. Covariation are calculated from maximum overlapping data for each pair of aet clae. Value of w i were found by uing the following equation: g i ti T = e ; gi w i = ; (2) g i where T i the characteritic time. For a better overview, occaionally return or tandard deviation were annualied. Multiplying the return by 12 and tandard deviation by quare root of 12 did it. Calculation a of the 31t of March 2003 with T=30 are hown in the Table 1. Table 1. Markowitz characteritic a of March 2003 with T=30 year World Europe N.Am Pacific EM Free EM EE Avg. return p.a. 5.35% 5.56% 6.84% 5.36% 8.96% 9.14% Standard. Dev p.a % 16.77% 19.58% 21.51% 27.40% 38.20% Finding the optimal portfolio Covariation Europe N.Am Pacific EM Free EM EE Europe % % % % % N.Am % % % % % Pacific % % % % % EM Free % % % % % EM EE % % % % % The technique ued for determining the et of efficient portfolio i decribed in detail in appendix A. The return level wa increaed by 0.05% and the et of efficient portfolio wa found. In Figure 1, the mean-variance pace for aet allocation (hereafter abbreviation AA could be ued) for March 2003 with T=30 i hown. Next the quetion arie, what could be an optimal portfolio for invetor? We have defined that optimal portfolio ha the maximum available expected return and it atifie both of the following condition: 1. Portfolio i efficient i.e. it lie on an efficient frontier. 2. Standard deviation of the optimal portfolio i equal to the tandard deviation of World index. Optimal portfolio i marked with diamond in Figure 1. Stability of optimal-tatu of the portfolio According to Markowitz mean-variance theory the efficient portfolio i the bet choice for the invetor. Unfortunately, there are three major practical iue: 247

4 1. What i the uitable lime -lag to calculate the tatitical characteritic? Are the latet index value more important than ome year old index value? 2. Are the tatitical characteritic table? What happen when hitorical return (what i conidered to be expected return) and other hitorical figure change? Since they are ued in optimization proce the et of efficient portfolio i changing with time and ha to be recalculated. 3. Markowitz model i a ingle-period model. What hould be the frequency of rebalancing portfolio in order to maintain the ame portfolio characteritic? Mean-variance Space 9.50% 9.00% 8.50% 8.00% 7.50% 7.00% 6.50% 6.00% 5.50% 5.00% 15.00% 20.00% 25.00% 30.00% 35.00% 40.00% Efficient Frontier World Europe N.Am Pacific EM Free EM EE AA rik = MSCI Wrld rik Figure 1. Mean-variance pace a of March 2003, with T=30 year Weight of data point We have conidered that weighting iue i important but there i no common market practice what hould be the ditribution function of weight of hitorical price. We have choen exponential ditribution function (2). Still, the characteritic time T play important role: larger value of T give larger weight to the older data point. We have choen value T=30 and T=100 in our calculation. Figure 2 how the relative value of weight when T=30. Recalculation of optimal portfolio De facto calculation have hown that tatitical moment are not table. The lower the rank of the moment the le table the repective moment tend to be. For example, hitorical return i rather a changing variable and not a table one. It i clear that the maller characteritic time T i ued, the larger i volatility of moment. We have calculated the efficient frontier and therefore found optimal portfolio for period of a of the end of March. We have alo ued two different characteritic time: T=30, T=100. In Table 2 the reult of thee calculation are preented. In addition, return and tandard deviation of benchmark ( World) 248

5 are alo hown. A een from Table 2, the hitorical return of optimal portfolio found, are higher than the return of benchmarking World index Figure 2. Relative weight of data point; T=30. Table 2. Optimal portfolio calculated in the period of Date T Portf. t.dev Portf. return Europe N.Am Pacific EM Free EM EE World t.dev 31/03/ % 10.30% 48.99% 10.04% 23.60% 17.38% 0.00% 15.91% 5.22% 31/03/ % 10.95% 48.20% 13.10% 23.03% 15.67% 0.00% 15.91% 5.73% 31/03/ % 8.90% 44.92% 14.00% 26.14% 14.94% 0.00% 15.68% 4.93% 31/03/ % 10.80% 36.43% 5.35% 23.21% 17.78% 17.24% 15.53% 5.78% 31/03/ % 13.35% 40.84% 0.00% 22.83% 5.85% 30.48% 15.54% 6.44% 31/03/ % 11.85% 37.61% 7.36% 25.84% 6.87% 22.31% 15.78% 7.72% 31/03/ % 9.60% 47.03% 20.32% 19.49% 13.16% 0.00% 16.04% 7.87% 31/03/ % 10.85% 47.90% 18.51% 20.83% 12.76% 0.00% 16.09% 8.80% 31/03/ % 9.35% 48.08% 17.80% 20.76% 13.37% 0.00% 16.15% 7.73% 31/03/ % 8.90% 49.43% 19.69% 17.22% 13.65% 0.00% 16.20% 7.33% 31/03/ % 6.65% 37.61% 24.45% 26.91% 11.03% 0.00% 16.60% 5.36% World return 31/03/ % 10.75% 50.65% 9.33% 21.31% 18.71% 0.00% 16.11% 5.78% 31/03/ % 11.50% 49.97% 12.71% 20.87% 16.45% 0.00% 16.10% 6.40% 31/03/ % 9.00% 46.48% 13.98% 23.96% 15.57% 0.00% 15.79% 5.31% 31/03/ % 11.60% 36.20% 2.36% 18.19% 21.81% 21.44% 15.59% 6.40% 249

6 31/03/ % 14.40% 40.96% 0.00% 16.44% 13.55% 29.04% 15.60% 7.24% 31/03/ % 12.70% 43.92% 7.46% 16.34% 11.99% 20.29% 15.91% 8.90% 31/03/ % 10.45% 52.00% 29.16% 6.92% 11.92% 0.00% 16.25% 9.05% 31/03/ % 11.95% 50.69% 22.67% 13.35% 13.29% 0.00% 16.30% 10.25% 31/03/ % 10.00% 52.14% 26.68% 7.88% 13.30% 0.00% 16.38% 8.71% 31/03/ % 9.45% 54.91% 28.05% 4.48% 12.56% 0.00% 16.44% 8.12% 31/03/ % 6.35% 38.40% 40.95% 12.09% 8.56% 0.00% 16.96% 5.35% 3. Teting of the model The third problem from the previou chapter remained unolved: what i the right frequency of rebalancing the portfolio. We did not find any quantitative formula for thi frequency. It depend on market ituation and other factor uch a liquidity. In cae of long-term invetment vehicle, we ugget that aet rebalancing hould be in line with portfolio liquidity. In cae of penion fund, we ugget monthly rebalancing with overand underweight of purchae of intrument. Rebalancing of the portfolio i one iue, another and even more important i the frequency of rebalancing of the model portfolio or portfolio aet allocation. In order to tet AA we have inveted hypothetical 100 currency unit (100 EUR equivalent amount of DEM) to both: our portfolio and World index a of 31 t of March We ue I a an interval of rebalancing our model portfolio. When I=1 then portfolio ha fixed AA and if I=120 then portfolio i not rebalanced. Rebalancing i alway done with latet available AA. For example: if rebalancing i done in June 1996, then AA of 31 t of March 1996 i ued. Table 3 give the overview out- or underperformance of uing uch method of rebalancing of AA. Model A i model calculated uing T=30 (ee Table 2); Model B i calculated uing T=100. Table give the final value (a of 31 t March 2003) of inveted 100 EUR in March In bracket % of outperforming month i hown. Table 3. Final value and percentage of outperforming month of AA trategie I Model A Model B World 1 112(45) 112(44) (45) 116(46) (46) 115(46) (43) 108(54) (46) 142(47) (42) 136(42) 155 It appear that uch trategy offer no poibility of outperforming benchmark index. The cloet reult were uing low rebalancing frequency or in the other word uing the original AA. Oberving more cloely initial AA it appear that i quite imilar to MSCI World index conitence (A of May 2002; paper downloaded from it i hown in Table

7 Table 4. World a of May 31, 2002 North America 45.24% Pacific 20,11% Europe 34.65% World % 4. The final Aet Allocation In order to determine the AA outperforming World we took the bet-performed AA. Thi wa AA of Model A dated March It appear that it i the cloet to World index a well. We have rounded each weight to cloet five-fold number, with exception of Europe that wa rounded to 35% not 40%. Intead wa increaed hare of home market ( EM EE) from 0 to 5%. Thi mean in fact that hare of Eatern Europe hare wa increaed. Reaon for uch increae i due to fact that Eatern European hare have hitorically (ee Kitt, 2003) hown higher peritence of poitive memory. So, there i higher chance that the poitive alpha compared to World remain there. Another reaon could come from local legilation. Table 5 how initial and latter tructure of propoed portfolio. Table 5. Structure of AA of Model A a of March 93 and propoed model Model A AA propoed Europe 38% 35% N.Am 41% 40% Pacific 12% 10% EM Free 9% 10% EM EE 0 5% It appear that propoed model ha outperformed benchmark in every rebalancing frequency. It i clear, that propoed portfolio i not efficient. Still, it lie quit cloe to efficient frontier a een from Figure 3. Figure 4 how development of World and portfolio uggeted in (I=1) Table 6. Final value and percentage of outperforming month of propoed AA* I AA World 1 166(53) (53) (52) (50) (50) (52) 155 * In period of EM EE wa replaced with EM Free becaue index data wa available only from

8 Mean-variance Space 9.50% 9.00% 8.50% 8.00% 7.50% 7.00% 6.50% 6.00% 5.50% 5.00% 15.00% 20.00% 25.00% 30.00% 35.00% 40.00% Efficient Frontier World Europe N.Am Pacific EM Free EM EE Propoed portfolio Figure 3. Mean-variance pace with propoed AA a of March 2003; T=30; Value of 100 inveted Difference in märt-93 ept-93 märt-94 ept-94 märt-95 ept-95 märt-96 ept-96 märt-97 ept-97 märt-98 ept-98 märt-99 ept-99 märt-00 ept-00 märt-01 ept-01 märt-02 ept-02 märt Difference (%) Portfell-AA Portfell MW Figure 4. Development of hypothetical 100 EUR inveted 1993, March into uggeted portfolio and World. 5. Summary The main goal of the paper wa to determine the optimal invetment tructure into global equity market from emerging Europe long-term invetor point of view. Geographical region conidered were: North America, Europe and Pacific via MSCI indice. In addition Emerging Market and Emerging Market Eatern Europe indice were looked. Claical Markowitz mean-variance analyi wa ued to develop optimal portfolio. The analyi wa done to find portfolio with higher expected return than 252

9 MSCI World index on the rik level of MSCI World index. After teting a model it appeared that portfolio found generally under performed MSCI World in following period. The reaon for that could be intability of lower-ranked tatitical moment. To find the uitable invetment portfolio rebalancing analyi wa carried on. Portfolio wa recontructed in time by uing new aet allocation derived from data point between two rebalancing. Thi analyi allowed to elect an invetment model that outperformed MSCI index for the time period conidered. Finally, the bet-performed aet allocation wa choen and modified to have ome expoure in local market. Final aet allocation propoed outperformed World index and had following tructure: North America (40%); Europe (35%); MSCI Pacific (10%); MSCI Emerging Market Free (10%) and MSCI Eatern Europe (5%). Reference Brinon, Gary P., L. Randolph Hood, and Gilbert L. Beebower, Determinant of Portfolio Performance, Financial Analyt Journal, vol. 42, no. 4 (July/Augut 1986): Brinon, Gary P., Brian D. Singer, and Gilbert L. Beebower, Determinant of Portfolio Performance II: An Update, Financial Analyt Journal, vol. 47, no. 3 (May/June 1991): Henel, Chri R., D. Don Ezra, and John H. Ilkiw, The Importance of the Aet Allocation Deciion, Financial Analyt Journal, vol. 47, no. 4 (July/Augut 1991): Surz, Ronald, Dale Steven and Mark Wimer, The Importance of Invetment Policy, The Journal of Inveting, Winter 1999, vol. 8, no. 4, Ibboton, Roger G., and Paul D. Kaplan, Doe Aet Allocation Policy Explain 40, 90, or 100 Percent of Performance?, Financial Analyt Journal, vol. 56, no. 1 (January/February 2000): Kitt, Robert, The importance of the Hurt exponent in decribing financial time erie, Proc. Etonian Acad. Sci. Phy. Math, 2003, 52, 2, Markowitz, Harry, Portfolio Selection: efficient diverification of invetment. 2 nd ed. Blackwell Publiher Ltd, 1991, (originally publihed 1959) 253

10 Appendix Optimization Technique for determining et of efficient portfolio. Idea i pure Markowitz portfolio optimization exercie from Markowitz, Let u be R a return vector of aet clae r1 r2 R =... r n Let u be V a co-variation matrix of return of aet = N V (2) N N N... NN Let u X be the tructure of the portfolio: X = x x... (3) [ ] 1 2 x n with contraint of x i = 0 Portfolio return i therefore calculated a follow: R p = RX (4) Portfolio variance i minimized a follow: Z 2 p = X V X T -> min (5) After olving equation (5) vector (3) give portfolio with minimum variance on given return level R p. Thi proce can be repeated on certain range of Rp min to Rp max. Boundarie ued are equal to minimum and maximum component of R. Portfolio with minimum variance on given return level are called efficient. (1) 254