Risk, return and stock performance measures
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1 Rsk, return and stock performance measures MIRELA MOMCILOVIC Hgher School of Professonal Busness Studes Vladmra Perca-Valtera 4, Nov Sad JOVAN NJEGIC Hgher School of Professonal Busness Studes Vladmra Perca-Valtera 4, Nov Sad SLOBODANKA JOVIN Hgher School of Professonal Busness Studes Vladmra Perca-Valtera 4, Nov Sad Abstract: - Ths paper evaluates rsk, return and performance measures for twelve stocks traded at Belgrade Stock Exchange. Our fndngs ndcate that nvestments n four stocks provde postve returns wth the realzed returns exceedng the requred returns n the perod from January 2007 to December Eght remanng stocks have negatve realzed returns and negatve alphas durng the same perod. Treynor, Sharpe and Jansen performance measures have sgnfcant Pearson correlaton coeffcents. They result n almost the same rankng order of the stocks and lead to vrtually the same nvestment decson. Key-Words: - Realzed rate of return, requred rate of return, beta, performance measures 1 Introducton The Sharpe [1], Ltner [2] and Black [3] Captal Asset Prcng Model descrbes relatonshp between requred rate of return and beta coeffcent (systematc rsk) of a partcular asset. The key element of the model s beta and t represents a measure of tendency of the asset to move up or down wth the market as a whole. Accordng to the model, nvestor would expect that only assets that have hgh beta can earn a hgh average returns. Rsk and return of nvestments n partcular stocks at Belgrade Stock Exchange have not suffcently been studed, nor have dfferent performance measures of the stocks. For the purpose of ths paper we wll examne actual realzed rate of return, requred rate of return and beta of each stock that consttutes ndex BELEX 15 on Belgrade Stock Exchange and that exsts for at least fve years (January 2007-December 2011). CAPM model wll be used to calculate the requred rate of return for each stock on the bass of ts beta. Also, evaluaton of Treynor [4], Sharpe [5] and Jansen [6] performance measures of the stocks wll be done n order to compare rankngs of performance measures and dscover f dfferent performance measures could lead to dfferent nvestment decsons. 2 Lterature revew Fnancal analysts and ndvdual nvestors rely on performance measures to select among avalable nvestments. We wll revew here the recent research fndngs that show that choce of partcular performance measure has no sgnfcant nfluence on the rankng of an nvestment. A hgh rank correlaton between rankngs of the performance measures was found by Pedersen and Rudholm-Alfn [7] n ther study of rsk-adjusted performance measures for dfferent asset classes. Pfngsten, Wagner and Wolfernk [8] took a real world data from two tradng books and examned rank correlatons gven dfferent rsk measures. They concluded that choce of rsk measure mght ISBN:
2 not be crtcal, snce they observed hgh values of Spearman s coeffcent. Elng and Schuhmacher [9] conducted emprcal study based on return of 2763 hedge funds and compared Sharpe rato and twelve other performance measures. Ther comparson results n almost dentcal rank orderng of dfferent performance measures across hedge funds. Merc, Ratner and Merc [10] compared Treynor, Sharpe and Jansen performance measures for ten U.S. sector portfolos and concluded that correlaton coeffcents between performance measures are very hgh and lead to smlar rankngs. 3 Methodology and data CAPM descrbes the relatonshp between the expected return on a rsky asset and ts beta coeffcent (β). Accordng to ths model requred return on rsky asset R s: R = R + β R R ) (1) f ( m f where R f s the rsk-free rate of return, R m s the rate of return on the market and (R m -R f ) represents market rsk premum. In the paper, we wll use a monthly weghted average nterest rate on the Republc of Serba government blls [11] as a rsk free rate of return R f. Monthly realzed returns of ndex BELEXlne [12] wll be used as a proxy for the market return R m. Beta coeffcent of the rsky asset can be defned as a measure of senstvty of partcular securty on systematc or market rsk. It can be calculated as follows: cov( Rr, Rm ) β = (2) 2 σ m where cov( R r, R m ) s the covarance between actual realzed returns on a partcular stock and the return 2 on the market and σ m s the varance of the market return. Theory states that rsk avers nvestor requres a rsk premum for rsky nvestment and the level of rsk premum s based on the level of stock s systematc rsk β. That s, nvestor would expect the hgher rsk premum f the level of β would be hgher. Unsystematc rsk can be dversfed away and thus s not consdered. Beta of each examned securtes wll be calculated by regressng the actual realzed returns on the securty [13] aganst the returns of BELEXlne ndex. The slope of the regresson lne represents the beta of partcular securty. In calculatons of beta monthly returns wll be used, snce emprcal studes show that beta value can be nfluenced by data frequency. [14] In ths paper relatve performance of the securtes wll be compared on the bass of three wdely used performance measures (Treynor rato, Sharpe rato and Jansen s alfa). Treynor rato TR can be calculated as follows: ( R R f ) TR = (3) β The hgher Treynor rato ndcates better performance of the stock. The same can be sad for the Sharpe rato SR, whch can be calculated as follows: ( R R f ) SR = (4) σ where σ s the standard devaton of the returns of the securty. Thrd performance measure s Jansen s alfa α. It can be calculated as follows: α = R R + β R R ) (5) [ ] f ( m f It should be sad that Jansen s alfa ndcates weather realzed returns of the securty excde the requred returns of the securty. Hgher α speaks about better performance of the securty. On the bass of the calculated three performance measures for each securty, we wll determne rankngs of the securty s performance and revew f dfferences n rank orderng of securtes exst between securtes. Also, we wll determne Person correlaton coeffcents between Treynor, Sharpe and Jansen performance measures. 4 Emprcal results Regresson results of realzed returns for selected securtes for the perod from January 2007 to December 2011 aganst market returns durng the same perod are presented n the Table 1. Standard procedure requres determnaton of regresson lne coeffcents (ntercept and slope). Beta coeffcents of the selected companes range from for AIK banka to for Alfa plam Vranje. Percentage of varaton n realzed stock s returns that can be explaned wth varatons n returns of market ndex s shown wth R² of the regresson. ISBN:
3 Table 1. Regresson results of stock s returns on market returns Company Company Intercept Slope R² AIK banka a.d. Ns AIKB Veternarsk zavod Subotca a.d. Subotca VZAS Komercjalna banka a.d. Beograd KMBN Soja proten a.d. Bečej SJPT Energoprojekt holdng a.d. Beograd ENHL Jubmes banka a.d. Beograd JMBN Tgar a.d. Prot TIGR Galenka Ftofarmacja a.d. Zemun FITO Metalac a.d. Gornj Mlanovac MTLC Imlek a.d. Beograd IMLK Jednstvo Sevojno a.d. Sevojno JESV Alfa plam a.d. Vranje ALFA The rest of the varatons n securty s returns comes from factors specfc for partcular company. For example, for the frst securty n Table 1 R² s and 76.8% of varatons n AIK banka Ns returns can be explaned wth market sources and 23.2% comes from components characterstc for ths company. Table 2. presents beta coeffcents, realzed rate of returns and alphas of the selected companes. Accordng to the CAPM nvestor would expect that stocks wth hghest beta have the hghest return. From Table 2. t can be seen that the hghest realzed return has Jednstvo Sevojno stock whle ts beta has second smoolest rank. Stocks of AIK banka Ns have the hghest beta and ts average annual realzed rate of return for the perod of fve years s negatve and amounts -5.85%, whle CAPM predcts return of -0.84%. Also, from the Table 2. can be seen that the average annual rsk-free nterest rate s 10.16% and average annual market rate of return s 2.82% for the fveyear perod. Average annual rsk-free rate of return s sgnfcantly hgher than the market rate of return n the fve-year perod and thus, a market premum s negatve and amounts -7.35%. That can be explaned wth the fact that Serba experenced and stll s experencng severe crss and that fnancal market s undeveloped. Table 2. Betas, realzed rates of return, requred rates of return and alphas of the selected companes Realzed Rsk free Market Requred Market rsk Company Beta rate of rate of rate of rate of premum return return return return Alpha β R r R f R m R m -R f R α JESV % 10.16% 2.82% -7.35% 4.52% 33.74% IMLK % 10.16% 2.82% -7.35% 4.20% 21.01% VZAS % 10.16% 2.82% -7.35% -0.78% 17.04% FITO % 10.16% 2.82% -7.35% 3.18% 2.78% BELEXlne % 10.16% 2.82% -7.35% 2.82% 0.00% AIKB % 10.16% 2.82% -7.35% -0.84% -5.00% ENHL % 10.16% 2.82% -7.35% 1.24% % MTLC % 10.16% 2.82% -7.35% 3.25% % JMBN % 10.16% 2.82% -7.35% 1.68% % SJPT % 10.16% 2.82% -7.35% 0.86% % TIGR % 10.16% 2.82% -7.35% 2.51% % ALFA % 10.16% 2.82% -7.35% 6.44% % KMBN % 10.16% 2.82% -7.35% 0.49% % ISBN:
4 Table 3. Alpha, Treynor rato, Sharpe rato and ther rankngs Company Alpha Rank Treynor rato Rank Sharpe rato Rank JESV IMLK VZAS FITO AIKB ENHL MTLC JMBN SJPT TIGR ALFA KMBN Alphas are calculated as dfference between realzed rate of return and requred rate of return for each stock, where requred rate of return for stock s calculated on the bass of CAPM model. Table 2. shows that only four stocks from the sample have postve average annual realzed rate of return and alpha coeffcent for the fve-year perod. It should be ponted out that constructon company Jednstvo Sevojno has experenced the abnormal postve return and has the hghest postve alpha. Three remanng companes wth postve alphas are nvolved n manufacturng (Imlek Beograd, Veternarsk zavod Subotca, Galenka Ftofarmacja Zemun). In the sample we can fnd three banks (AIK banka Ns, Komercjalna banka Beograd, Jumbes banka Beograd) and all three have negatve average annual realzed rate of return and alpha for the observed perod. In the Table 3. can be seen Alpha, Treyor rato and Sharpe rato for the selected companes. Table 4. Pearson correlaton Alpha 1 Alpha Treyor Sharpe Treyor ** 1 Sharpe ** ** 1 **Correlaton s sgnfcant at the 0.01 level (2- taled). Also, ths table presents ranks of these three performance measures. Rankngs of the companes accordng to Treynor, Sharpe and Jansen performance measure are qute smlar. The Pearson correlaton coeffcents between Treynor, Sharpe and Jansen performance measures are calculated and presented n Table 4. All three correlaton coeffcents are statstcally sgnfcant at level 1%. 4 Concluson In ths paper, we examne the rsk, return and performance measures of nvestments n 12 stocks that consttute ndex BELEX 15 on Belgrade Stock Exchange. For each stock beta, as a measure of market rsk, s calculated for the perod from January 2007 to December We saw that for examned tme perod beta s of the stocks are rather low, but we have to take these results wth some reserve. Mumnovc and Pavlovc [15] clam that beta coeffcents on undeveloped fnancal markets, n whch Serban market can be ncluded, s not representatve and t does not represent adequate measure of return nor adequate measure of rsk. Average annual requred rate of return s determned for each stock on the bass of the CAPM model and compared wth average annual realzed rate of return for each stock. As a measure of the dfference between realzed and requred rate of return we used stock s alpha coeffcent. We saw that only four out of twelve companes have realzed returns hgher than requred returns. Ths s certanly result of the world fnancal crss n the past perod, recesson n Serba and the fact that Serban fnancal market s undeveloped. Also, we calculated Treynor, Sharpe and Jansen stock s performance measures and ranked them n order to fnd out could dfferent performance measures lead nvestor to dfferent nvestment decsons. We found out that Pearson correlaton coeffcents ndcate that all three performance ISBN:
5 measures are hghly correlated and thus lead to vrtually the same nvestment decsons. It has to be ponted out that we used only twelve shares whch do not have to make representatve sample. Therefore, more extensve study should be undertaken. References: [1] Sharpe, W.F., Captal asset prces A theory of market equlbrum under condton of rsk, Journal of fnance, Vol. 19, No. 3, 1964, pp [2] Ltner, J., The valuaton of rsk assets and the selecton of rsky nvestments n stock portfolos and captal budget, Revew of Economcs and statstcs, Vol. 47, No. 1, 1965, pp [3] Black, F., Jansen, M. C., Scholes, M., The captal asset model: some emprcal tests. In Jansen, M. C., Studes n the theory of captal markets, Praeger, New York, [4] Treynor, J.L., How to rate management of nvestment funds, Harvard busness revew, Vol. 43, No. 1, 1965, pp [5] Sharpe, W.F., Mutual fund performance, Journal of busness, Vol. 39, No. 1, 1966, pp [6] Jansen, M.C., The performance of mutual funds n the perod , Journal of fnance, Vol. 23, No.2, 1968, pp [7] Pedersen, C.S., Rudholm-Alfn, T., Selectng a rsk-adjusted shareholder performance measure, Journal of asset management, Vol. 4, No. 3, 2003, pp [8] Pfngsten, A., Wagner, P., Wolfernk, C., An emprcal nvestgaton of the rank correlaton between dfferent rsk measures, Journal of bankng and fnance, Vol. 6, No. 4, 2004, pp [9] Elng, M., Schuhmacher, F., Does the choce of performance measure nfluence the evaluaton of hedge funds, Journal of bankng and fnance, Vol. 31, No. 9, 2007, pp [10] Merc, I., Ratner M., Merc G., Rsks, returns, and portfolo dversfcaton benefts of sector nvestments, Journal of the northeastern assocaton of busness, economcs and technology, Fall 2010, pp [11] (data accessed ) [12] (data accessed ) [13] (data accessed ) [14] Draper, P., Paudyal, K., Emprcal rregulartes n the estmaton of beta: The mpact of alternatve estmaton assumptons and procedures, Journal of busness fnance and accountng, Vol. 22, No. 1, 1995, pp [15] Mumnovc, S., Pavlovc, V., Relatonshp between fnancal and market ndcators and beta coeffcent for partcular shares whch are traded at Belgrade stock exchange, Accountng, No. 5-6, 2007, pp ISBN:
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