Diversified Portfolio: Evidence from Bombay Stock Exchange (BSE) in India

Transcription

1 Dversfed Portfolo: Evdence from Bombay Stock Exchange (BSE) n Inda

2 Aro Internatonal Research Journal May, 2016 Volume VI, ISSN: Dversfed Portfolo: Evdence from Bombay Stock Exchange (BSE) n Inda Dr. Seema Shokeen Assstant Professor Department of Busness Admnstraton Maharaja Surajmal Insttute, New Delh Emal ID : seemashokeen@ms-ggsp.org ABSTRACT Ths paper studes the effect of dversfcaton wth the help of analyzng the Markowtz model. It hghlghts that how many securtes should nclude n a well dversfed portfolo. Keepng n vew of present study, the man data used n the study s secondary n nature and the data related for ths study has been collected from the Centre for Montorng of Indan Economy (CMIE) prowess database software. The present study s for eleven years startng from 1 January, 2005 to 31 December, The sample sze ncludes a total number of 225 securtes and populaton conssts of all securtes lsted on BSE-500. The study used daly adjusted closng prces of lsted 225 securtes of BSE-500. The BSE Sensex s taken as the market proxy. The results of the present study suggested that a well dversfed portfolo should nclude securtes. The results of the study are consstent wth the prevous studes such as Evan and Archer (1968) and Irala and Patl (2007). As far as ths type of research s essental due to the nterest of nvestors, researchers and fnancal analysts. Therefore, ths research wll be valuable for nterested partes, nvestors, researchers that contrbute towards the perceptve of the Indan stock market. Keywords: Bombay Stock Exchange, Dversfcaton, Investors, Portfolo INTRODUCTION A well-desgned portfolo wll combne nvestment assets that have dfferent attrbutes. The core dea here s expressed n the classc advce Don t put all your eggs n one basket. If you drop the basket, you re toast. (Techncally you would be egged, but you get the pont). By dversfyng across varous unrelated nvestment assets, your portfolo should be less susceptble to large losses. And f we can avod or mnmze large losses, our overall nvestment experence should be better (Israelsen 2010, p. 63). It s not surprsng that ths problem

3 Dversfed Portfolo: Evdence from Bombay Stock Exchange (BSE) n Inda has receved a great deal of attenton. It has major mplcatons for the structure and very exstence of fnancal ntermedares, as well as for the behavor of all nvestors (Elton and Gruber, 1977). Dversfcaton s one of the mportant concepts of fnance. Smply t says, Dversfcaton s the technque of reducng rsk. Moreover, to determne the exact sze of a well dversfed portfolo s the core of the feld of fnance. There have been so many securtes avalable for nvestors for nvestng and due to the uncertanty most of the securtes are rsky. A portfolo selecton s a bg problem and dversfed portfolo how t makes, also a doubtful ssue. Much of the early lterature on dversfcaton effect n the captal market showed that there s a sgnfcant effect of dversfcaton. The study gven by Statman (1987) concluded that a well dversfed portfolo must nclude 30 securtes. Surprsngly, the study of Gupta and Khoon (2001) concluded that a well dversfed portfolo must nclude up to 27 securtes and Evan and Archer (1968) concluded that a well dversfed portfolo must nclude 10 stocks. However, a well dversfed portfolo concept s found controversal ssue n dfferent markets. Theoretcal Perspectve of Markowtz Model Markowtz poneered n developng a well defned theoretcal structure for portfolo analyss that can be summarzed as follows. Frst, the two relevant characterstcs of a portfolo are ts expected return and some measure of the dsperson of possble returns around the expected return, the varance beng analytcally the most tractable. Second, ratonal nvestors wll choose to hold effcent portfolos, whch are those that maxmze expected returns for a gven degree of rsk or, alternatvely and equvalently, mnmze rsk for a gven expected return. Thrd, t s theoretcally possble to dentfy effcent portfolos by the proper analyss of nformaton for each securty on expected return, the varance n that return, and the covarance of return for each securty and that for every other securty (Farrell, 1976). In the 2008, Hryappa n hs book nvestment management explaned the dversfcaton concept as A portfolo that s nvested n multple statements whose returns are uncorrelated wll have an expected smple return whch s weghted average of the ndvdual nstruments returns. Its volatlty wll be less than the 3

4 Aro Internatonal Research Journal May, 2016 Volume VI, ISSN: weghted average of the ndvdual nstruments volatltes. Ths s dversfcaton. The present paper formulate a well dversfed portfolo selecton problem, so as to fnd out how many securtes wll suffcent for a well dversfed portfolo. In the context, the man objectve of the present paper s to study that how many securtes are enough for a well dversfed portfolo. The paper also hghlghted that whether the results of the present study are consstent wth he results of past studes or not. Revew of Lterature The two artcles whch were authored by Markowtz and Roy publshed n 1952 about the behavoural bass. There s no depth of lterature on the ssue of dversfcaton effect. The revew of lterature shows that there are some studes on dversfcaton effect. But most of the studes showed dfferent results. In the Indan context, very few studes have explaned the concept of a well dversfed portfolo. Therefore, ths present research work has attempted to study a well dversfed portfolo concept. A bref revew n the context of dversfcaton effect s presented as follows: Evans and Archer (1968) estmated the relatonshp between dversfcaton and the level of varatons of portfolo returns. The study used 470 of the securtes lsted on Standard and Poor s Index. The results of the study suggested that a somewhat stable and predctable relatonshp exsted between the number of securtes ncluded n a portfolo and portfolo dsperson. The study also explaned that for the purpose of concludng portfolo accordng to ther methodology, there s a need to perform on margnal analyss. Wagner and Lau (1971) conducted a study on the effect of dversfcaton on rsk and n ther study showed that the rate of return on well dversfed low rsk portfolos was sgnfcantly lower than the return on well dversfed hgher rsk portfolos. The study suggested that the nvestment performance can often be mproved by expandng the lst of qualfed securtes to nclude hgher return, hgher rsk stocks, whle offsettng the ncrease n market rsk through more effectve dversfcaton. Elton and Gruber (1977) presented the formula for determnng the effect of dversfcaton on rsk and showed that estmatng expected varance and total rsk

5 Dversfed Portfolo: Evdence from Bombay Stock Exchange (BSE) n Inda seems to be very good but much cruder n estmatng varance n varance. Statman (1987) conducted a study on how many stocks make a dversfed portfolo. The study showed that for borrowng nvestors, a well dversfed portfolo must nclude 30 stocks and for lendng nvestors there must be at least 40 stocks. The concluson of ths study was that the extensvely accepted dea that the benefts of dversfcaton are practcally exhausted when the number of stocks reaches 10 to 15. A study of dversfcaton n the Johannesburg Stock Exchange by Neu-Ner and Frer (1997) questoned how many randomly selected Johannesburg Stock Exchange (JSE) s shares are requred to acheve a well dversfed portfolo. The populaton studed ncluded all securtes lsted on the man board of the Johannesburg Stock Exchange (JSE) durng the perod June 1993 to June The study concurred wth the study of Statman (1987) s fndngs that a welldversfed portfolo of randomly chosen shares on the Johannesburg Stock Exchange (JSE) must nclude at least 30 shares. It also concluded that sgnfcant benefts of dversfcaton could be acheved by holdng smaller portfolo. Another study conducted by Gupta and Khoon (2001) examned the relatonshp between the portfolo rsk and the number of stocks n a portfolo n the perod of September 1988 to June 1997 to determne the optmum sze of portfolo of stocks. In the study a sample of 213 stocks traded on Kuala Lumpur Stock Exchange (KLSE) were used. The results of the study revealed that the dversfcaton benefts are avalable up to the 27 securtes. Statman (2004) expressed that the benefts and costs of dversfcaton under the rules of mean varance portfolo theory are dfferent from those under the rules of behavoral portfolo theory. The study concluded that the reducton of rsk was not always a beneft n behavoral portfolo theory. It explaned that the optmal number of ndvdual stocks under the rules of behavoral portfolo theory was the number that balances the chance for uplft nto rches aganst the chance of a descent nto poverty. The rules of optmal dversfcaton n behavoral portfolo theory were smlar to the rules of sutablty that govern brokers and fnancal advsors. Sutablty regulatons requre brokers to make sure that an nvestor s desre for upsde potental dd not breach the nvestor s need for downsde 5

6 Aro Internatonal Research Journal May, 2016 Volume VI, ISSN: protecton. It also suggested that the rules of dversfcaton n behavoral portfolo theory were not as precse as the rules n mean varance portfolo theory, they were clear enough. It expressed that nvestors, fnancal advsors, and companes sponsorng 401(k) plans must be careful to draw a lne between upsde potental and downsde protecton n such a way that dreams of rches dd not plunge nvestors nto poverty. On the other hand, Irala and Patl (2007) also studed the concept of portfolo sze and dversfcaton by usng a monthly data durng the study perod of January 1999 to January The study suggested that a very hgh degree of dversfcaton was possble n Inda and also concluded that a portfolo sze of stocks was found to be approprate as the reducton n rsk was only margnal thereafter. Goetzmann and Kumar (2008) examned the dversfcaton choces of ndvdual nvestors durng a sx-year perod n the U.S. captal market hstory. The present study used a data from U.S. dscount brokerage house and found that the sample was underdversfed. Al Suqaer and Al Zyud (2011) examned the effect of dversfcaton on Amman Stock Exchange durng the study perod of 2/12/2005 to 13/3/2010. In the study, for the purpose of testng the hypothess, a sample of 100 companes was used. The results of the study revealed that dversfcaton ncrease wth a decrease rate. In a nutshell, on the bass of above mentoned studes, the present study concluded that there s a contnuous need of undertakng the study on dversfcaton effect. Based on these studes, the present study made an attempt to nvestgate that how many securtes make a well dversfed portfolo. Data Base and Research Methodology The present study s emprcal n nature whch ams to examne the dversfcaton effect wth the help of selected securtes of BSE-500. Keepng n vew of present study, the man data used n the study s secondary n nature. The present study s for eleven years startng from 1 January, 2005 to 31 December, The sample sze ncludes a total number of 225 securtes and populaton conssts of all securtes lsted on BSE-500. The study used daly adjusted closng prces of lsted 225 securtes of BSE-500. The selecton of securtes vares on the bass of the lstng n BSE-500,

7 Dversfed Portfolo: Evdence from Bombay Stock Exchange (BSE) n Inda market captalzaton, tradng volume and the avalablty of data. The securtes were selected from dfferent ndustry groups. The and the Centre for Montorng of Indan Economy (CMIE) data for the selected securtes were prowess database. extracted from the varous webstes such as Daly return: Daly returns on securtes are calculated by applyng the followng formula: - R t Pt ln *100 P t 1 Where R t s return on securty n tme perod t, P t s securtes prce at the tme t, P t 1 s securtes prce at the tme perod t-1 Market return: Market returns on securtes are calculated by applyng the followng formula: - X t It ln *100 I t 1 X t s the return on ndex, I t s the closng value and It 1 s the openng value Portfolo return: Portfolo return has been calculated by usng ths formula: N R w ( R ) P m 1 Where R P s the portfolo return and w s the weght gve to securty. Portfolo Varance: Portfolo varance has been calculated by usng ths formula: N N P ( w ) m w e 1 1 Where 2 P s varance of the portfolo, weghted average of error term of each securty n the portfolo. 2 s the expected varance of the ndex, 2 2 m w e s the 7

8 Aro Internatonal Research Journal May, 2016 Volume VI, ISSN: Portfolo Beta: Portfolo beta has been calculated by usng ths formula: N w P 1 Where P s the portfolo beta and s the beta of ndvdual securtes. Rsk Reducton: Markowtz (1952) n ther study explaned that the varance of a portfolo of N assets s gven by: N N N p w w wj j j 1 1 j 1 j Where 2 P = the portfolo varance j = correlaton between asset and j 2 = varance of the asset N = number of assets In other case where σ equals the and j equals the. After t the equaton becomes: N N N p w w wj 1 1 j 1 j Here that be noted for any gven w, the sum of all w j for j That wll be equal to (1- w ):

9 Dversfed Portfolo: Evdence from Bombay Stock Exchange (BSE) n Inda 2 p 2 2 (1 p) N 1 w In ths equaton assumng equal weghts, after that the equaton becomes to: p (1 ) p N Results and Analyss Results of Portfolo sze and portfolo rsk (Effect of dversfcaton) Table 1 presents the result of the dversfcaton effect. Usng data for 225 securtes over the perod of January 2005 to December 2015 showed that as more and more securtes ncrease n the portfolo, the portfolo rsk declnes. In the current study to examne the dversfcaton effect, securtes are randomly selected assumng equally weghted portfolos. The results of the dversfcaton effect have been measured by usng the Markowtz model. Table 1 shows that as the number of securtes n portfolo ncreases, the portfolos rsk as measured by the standard devaton decreases, whch ndcates the exstence of a negatve relatonshp between portfolo sze and portfolo rsk. The rsk of frst randomly selected securty came out to be percent. After addng one more securty, the rsk fell to 13.2 percent. The overall rsk reduces from percent to 7.22 percent. It also concluded that portfolo dversfcaton s applcable n Indan stock market. It s also very nterestng to note that a well dversfed portfolo should nclude 10 to 15 securtes. The results are also supported the results of Evan and Archer (1968) and Irala and Patl (2007) but n contrast to the study of Gupta and Khoon (2001). 9

10 Aro Internatonal Research Journal May, 2016 Volume VI, ISSN: Table 1 Results of Portfolo sze and portfolo rsk (January 2001-December 2011) (Effect of dversfcaton wth the help of daly data) No. of Securtes n Portfolos Portfolos Standard Devaton (Portfolos Rsk) Unque Rsk Proporton of unque rsk n total rsk (percent) Note: results are based on selected 225 securtes of Bombay Stock Exchange (BSE) Concluson and Scope for further research The study appled the applcatons of Markowtz model to examne the dversfcaton effect. It s very nterestng to note that a well dversfed portfolo should nclude 10 to 15 securtes. The results are also supported the results of Evan and Archer (1968) and Irala and Patl (2007) but n contrast to the study of Gupta and Khoon (2001). The present study concluded that portfolo dversfcaton s applcable n the Inda stock exchange. It revealed that as the number of securtes n portfolo ncreases, the portfolos rsk as measured by the

11 Dversfed Portfolo: Evdence from Bombay Stock Exchange (BSE) n Inda standard devaton decreases, whch ndcates the exstence of a negatve relatonshp between portfolo sze and portfolo rsk. The lmtaton of ths study s that t was carred out n only the Indan stock exchange and the results of the study may not be replcable to other countres stock exchange. The further study may be attempted to focus on other stock exchanges. Moreover, further research could be made to analyzed the rsk and return of dfferent securtes on the bass of daly, weekly, monthly, quarterly, half yearly data, yearly data and can check that the mean return and rsk of dfferent ntervals are equal or not. The effect of dversfcaton on r-square values deserves the further analyss. There s a need to carry out more research regardng ths study. References 1. Al Suqaer, Faten Shukr., & Al Zyud, Hussen (2011). The Effect of Dversfcaton on Achevng Optmal Portfolo. European Journal of Economcs, Fnance and Admnstratve Scences, 32, Elton, Edwn J., & Gruber, Martn J. (1977). Rsk Reducton and Portfolo Sze: An Analytcal Soluton. The Journal of Busness, 50(4), Evans, John L., & Archer, Stephen, H. (1968). Dversfcaton and the Reducton of Dsperson: An Emprcal Analyss. The Journal of Fnance, 23(5), Farrell, James L. (1976). The Mult-Index Model and Practcal Portfolo Analyss. Vrgna: The Fnancal Analysts Research Foundaton Charlottesvlle. 5. Goetzmann, Wllam N., & Kumar, Alok (2008). Equty Portfolo Dversfcaton. Revew of Fnance, 12, Gupta, G., & Khoon, Ch ng Huck (2001). How Many Securtes Make a Dversfed Portfolo n KLSE Stocks. Asan Academy of Management Journal, 6(1), Hryappa, B. (2008). Investment Management. New Delh: Publshed by New Age Internatonal (P) Ltd. 8. Irala, Lokanandha Reddy., & Patl, Prakash (2007). Portfolo Sze and Dversfcaton. SCMS Journal of Management, 4(1),

12 Aro Internatonal Research Journal May, 2016 Volume VI, ISSN: Israelsen, Crag L. (2010). 7 Twelve: A Dversfed Investment Portfolo Wth a Plan. New Jersey: Publshed by John Wley & Sons, Inc. 10. Neu-Ner, MA., & Frer, C. (1997). The benefts of dversfcaton on the JSE. Investment Analysts Journal, 46, Statman, Mer (1987). How Many Stocks Make a Dversfed Portfolo. Journal of Fnancal and Quanttatve Analyss, 22(3), Statman, Mer (2004). The Dversfcaton Puzzle. Fnancal Analyst Journal, 60(4), Wagner, W. H., & Lau, S. C. (1971). The Effect of Dversfcaton on Rsk. Fnancal Analysts Journal, 27(6), Webstes: