Topic 1 Essay financial

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MODERN PORTFOLIO THEORY: THE RISK AND RETURN OF

SHARES ON THE JSE

EMILY ADENDORFF, JANINE BRITS, DANIEL CHAPPEL, CHIPO RUSERE AND CATHERINE

ZIMBA

1. INTRODUCTION

THE RESEARCH CONSISTS OF a simple practical data application of Markowitzsportfolio theory to the South African equity trading sector (JSE listed companies)- analysing the investment implications, and risk-return characteristics of, sharesin the three production sectors of the South African economy- resource,industrial and financial sectors. Four companies were selected to applyMarkowitzs mean-variance analysis to; these companies included BritishAmerican Tobacco and Northam Platinum Limited for the resources sector,Supergroup Limited for the industrial sector and Investec for the financialsector (Rubinstein, 2002: 1043).

The data shall be applied and analysed so as to test whetherMarkowitzs deduction of investments- that higher return corresponds withhigher risk- holds, with respect to the sample of equities that were chosen torepresent the South African JSE; as well as offering comment on an appropriateinvestment portfolio for South Africans with respect to the shares analysed in theresearch. Markowitzs fundamental theorem, the mean-variance portfoliotheorem, is of critical importance to modern portfolio theory, and was developedwith the sole intention of determining the optimum portfolio for an investor whenan investor is concerned with its return distributions over a single period; whichis achieved by assessing the risk-return characteristics of each prospective

securities - in this respect, the four company shares analysed in the research(Elton and Gruber, 1997: 1755).

2. METHODOLOGY

The first step in the process was the collection of annual data ranging from theperiod 2000 to 2010. The data consisted of annual mean share prices ofcompanies in the resource sector, the industrial sector and the financial sector.

The second step was to calculate the risk in terms of the share prices.This was calculated through the use of the following formula; [(current

average share price previous years average share price) / previous yearsshare price] * 100 (Howells and Bain, 2005: 191). The results showed the

probability by which the actual return may differ from the expected return.These were the main points plotted on the graph. Next was the calculation of

the mean return from the 11 year period. This was the average of the shareprices divided by the amount of years under observation which was 11. Risk istherefore measured by the uncertainty of reaching this computed mean return(Howells and Bain, 2005: 191) which can be shown by looking at the individualpoints and how much they vary from the mean. The final step was to calculatethe standard deviation, which is found by calculating the square root of thevariance (Howells and Bain, 2005: 191).

The standard deviation shows the extent of the spread of the data pointsaround the mean, that is the low points and the high points of the yearly returnscompared to the overall mean return. Essentially, this shows the investor thecertainty of getting of getting the mean return. The higher the standarddeviation, the riskier a particular asset is.


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3. DATA

The data collected and consulted to conduct the empirical analysis was collectedfrom a host of sources- predominantly from the company website of each of theshares analysed. Four shares were collected and analysed - three of which were

companies in alternate sectors of production in South Africa. Northam PlatinumLimited and British American Tobacco Limited Pty shares represented theresource sector, Supergroup Limited shares represented the Industrial sector,and Investec shares represented the financial sector. The data was collectedfor each company for a period of 10 years: from January 2001 to December2010. Theshares were specifically chosen in alternate sectors of production so as toinvestigate the trends in the share prices- and thus, share returns- in each of thealternate sectors; with a specific interest in analysing the volatility and riskassociated with each share in the alternate sectors- resource, industrial andfinancial- of the South African economy.

3.1 RESOURCE SECTOR SHARE: NORTHAM PLATINUM LIMITED

Data on share prices for Northam Platinum Limited (2011: 2) was collected forthe period from 2000 to 2011. In order to calculate the changes in share pricesfor the ten year period from 2001 to 2010, a table was constructed with all therelevant data. Table 1 below illustrates the average share prices that werecollected and the percentage change in share price over the period, which canbe seen as the return on the share generated by the corresponding changes inthe share price.

Table 1: Share prices and the return on share prices for Northam PlatinumLimited

Year Share Price (in rands) % Share Return

2001 15.25 8.408408408

2002 16.65 -35.36585366

2003 12.30 -38.20224719

2004 8.90 29.36507937

2005 12.60 66.70190275

2006 37.84 21.16666667

2007 48.00 28.99408284

2008 67.60 -125.33333332009 30.00 34.06593407

2010 45.50 2.339557845

The figures calculated in the table were then used to determine the mean returnand the standard deviation of Northam Platinum Limited share prices. The meanreturn was estimated at 6.58, which is the average return on shares over theperiod from 2001 to 2010. The standard deviation, which was calculated at54.0054, indicates that the fluctuations in the share prices are very volatile, andthat even though there were some very high returns on the shares, it has to be

compared to some very significant losses in share price. The figures estimated


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for the period were then plotted on a graph which included the mean return, inorder to consider graphically the deviations of share prices around the mean.

Figure 1: Volatility of share returns for Northam Platinum Limited

3.2 RESOURCE SECTOR SHARE: BRITISH AMERICAN TOBACCO

Data on share prices for Britain American Tobacco Company Pty (2011: 4) wascollected for the period from 2000 to 2011. In order to calculate the changes inshare prices for the ten year period from 2001 to 2010, a table was constructedwith all the relevant data. Table 2 below illustrates the average share prices thatwere collected and the percentage change in share price over the period, whichcan be seen as the return on the share generated by changes in share price.

Table 2: Share prices and the return on share prices for British AmericanTobacco

Year Share Price (in rands) % Share Return

2001 45.227 28

2002 57.897 13

2003 65.307 6

2004 69.272 25

2005 86.253 37

2006 118.22 22

2007 144.777 20

2008 174.117 3

2009 179.4342 6

2010 190.39 21


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The figures calculated in the table were then used to determine the mean andthe standard deviation of British American Tobacco share prices. The meanreturn was estimated at 18.12, which is the average return on shares over theperiod from 2001 to 2010. The standard deviation, which was calculated at10.92049, indicates that annual changes in the companys the share prices are

not very volatile- and offers quite a certain return on the share- since there is arelatively low (approximately 11 percent) probability of not attaining/earning themean return on the British American Tobacco share. The point that is interestingabout the graph in the case of British American Tobacco is that it actually fails toreflect the crux of Modern Portfolio Theory that postulates that the higher thereturn, the higher is the expected corresponding standard deviation (risk). The

figures estimated for the period were then plotted on a graph which included themean return, in order to consider graphically the deviations of share returnsaround the mean (return).

Figure 2: Volatility of share returns for British American Tobacco

3.3 INDUSTRIAL SECTOR SHARE: SUPERGROUP LIMITED

Data on share prices for Supergroup Limited (Thompson Data Stream, 2010b: 3)was collected for the period from 2000 to 2011. In order to calculate the changesin share prices for the ten year period from 2001 to 2010, a table wasconstructed with all the relevant data. Table 1 below illustrates the averageshare prices that were collected and the percentage change in share price over

the period, which can be seen as the return on the share generated by theannual changes in share price.

Table 3: Share prices and the return on share prices for Supergroup

Year Share Price (in rands) % Share return

2001 3.61 -19.39

2002 2.91 -5.8419

2003 2.74 93.7956

2004 5.31 -3.01318

2005 5.15 18.05822006 6.08 7.2368


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2007 6.52 -50.1533

2008 3.25 -91.0769

2009 0.29 151.724

2010 0.73 -2.6954

The figures calculated in the table were then used to determine the mean andthe standard deviation of Supergroup Limited share returns. The mean returnwas estimated at 9.864, which is the average return on shares over the periodfrom 2001 to 2010. The standard deviation, which was calculated at 68.68615,indicates that the fluctuations in the share prices are extremely volatile and thateven though there were some very high returns on the shares (93.795 percentshare return in 2006 and 151.724 percent return for the 2010 period), it has tobe compared to the very significant losses experienced by the share price (the91.0769 loss in share return in 2009). The standard deviation (risk) estimate of68.686 for the company reflects the high risk associated with holding- and

yielded the mean return on- Supergroup shares. The figures estimated for theperiod were then plotted on a graph which included the mean return, in order toconsider graphically the deviations of share returns around the mean.

Figure 3: Volatility of share returns for Supergroup Limited

3.4 FINANCIAL SECTOR SHARE: INVESTEC

Data on share prices for Investec (Thompson Data Stream, 2010a: 2) wascollected for the period from 2000 to 2011. In order to calculate the changes inshare prices for the ten year period from 2001 to 2010, a table was constructedwith all the relevant data. Table 1 below illustrates the average share prices thatwere collected and the percentage change in share price over the period, whichcan be seen as the return on the share generated by the corresponding changesin the share price.

Table 4: Share prices and the return on share prices for Investec

Year Share Price (in cents) % Share Return


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2001 42.16 -27.04

2002 30.64 -42.39556

2003 17.65 52.9745

2004 27.01 32.5925

2005 35.81 79.88822006 64.47 49.84472

2007 96.51 -40.932

2008 57.01 -0.24526

2009 43.02 50.9762

2010 64.95 -18.0754

The figures calculated in the table were then used to determine the mean andthe standard deviation of Investec share prices. The mean was estimated at

13.7587, which is the average return on shares over the period from 2001 to2010. The standard deviation, which was calculated at 44.6859, indicates thatthe fluctuations in the share prices are volatile, and that even though there weresome very high returns on the shares (79.89 percent return in 2005), it has to becompared to some very significant losses in share price, and thus significantlosses in terms of share return and capitalisation (illustrated by the 42.396percentage loss in share return in 2002). The figures estimated for the periodwere then plotted on a graph which included the mean return, in order toconsider graphically the deviations of share prices around the mean.


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Figure 4: Volatility of share returns for Investec shares

Table 5: Summary of the Mean Returns and Standard Deviations

4. FINDINGS AND DISCUSSION

4.1 Resources Sector

The resource sector produced varied results: with a large standard deviationfrom the mean in the case of Northam Platinum Limited, and smaller standarddeviation in the case of British American Tobacco- with inverse mean returns,respectively. British American Tobacco (2011: 11) presented the unique caseacross the data of being the only company whose share price never declinedacross the 10 year period- thus, whose share returns were consistently positive-illustrating a relatively stable, and profitable share.

The case of Northam Platinum Limited was different- in that Northamsshare price exhibited volatility in terms of the share price- and thus, the sharereturns- across the 10 year period. The Northam share had a higher riskcomponent (54. 005) compared to the British American Tobacco share riskcomponent (10.921); and a lower return yield in comparison- 6. 58 and 18.121

mean return (percentage) on the shares, respectively.

Listed Company Sector Mean Return Standard Deviation

Northam Platinum

Limited

Resource 18.12055 10.92049

British AmericanTobacco Plc

Resource 8.17 53.37347589

Super GroupLimited

Industrial 9.864344901 68.6815092

Investec Financial 13.75872 44.686


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Thus, Northam Platinum (2011: 17) is a more unstable- and riskier- shareinvestment, especially in comparison to the British American Tobacco share thatoperates within the same (resource) sector. A potential reason cited to explainthe alternate volatility in the share price of the two resource shares is thatPlatinum is a primary resource and so is extremely sensitive to exchange rate

fluctuations- thus, its share return is dependent upon the strength of- and thus,the demand for platinum- on the rand exchange rate which has experiencedperiods of over and under valuation.

However, British American Tobacco- tobacco considered a staple goodby its target market: smokers doesnt experience as serious fluctuations in theshare price due to the nature of the good that it produces and markets which hasa low sensitivity to substitutes (British American Tobacco, 2011: 41).

4.2 Industrial Sector

The standard deviation for supergroup is around 68.6815 and this is a relativelyhigh number which means that the chance of getting the mean return fromSupergroup shares is quite low. From the graphical representation of thecompanys returns over the years; it can be shown that, except for a positivespike in 2004 and a dip in 2008/2009 (probably because of the global financialsector and the effect this had on the steel industry), Supergroups mean returnsare generally scattered close to the mean return- with a solid mean return at9.8643 percent (Thompson Data Stream, 2010b: 3). One can alsonote that the company has begun recovering from the financial crisis since themiddle of 2008- indicated by the return on Supergroup shares in 2010 whichstood at a high 150 percent.

4.3 Financial Sector

The data we have gathered suggests that the financial sector is not quite asvolatile as we had expected it to be. In fact, the resource sector is quiteconsiderably more volatile, and the industrial sector is the most volatileaccording to our findings (Thompson Data Stream, 2010a: 4). We see this from acomparison of the respective standard deviations.

Over the course of history equities have been prone to spectacularfluctuations, particularly within the financial sector. The fact that any news orevent taking place within a listed company is broadcast instantaneously andworldwide means that financial sector equities can gain and lose value extremely

quickly. Expected future returns being the primary cause of investor sentiment.

It will be noted from the graph showing returns on Investec shares in the lastten years that the down trend beginning in 2006 occurred before the financialcrisis, and by the time the crisis was in full swing, returns on Investec shareswere on a major upward trend (Du Plessis and Ward, 2009: 37).

It has been suggested that returns on Investec do not exhibit the same levelof volatility as other such financial equities abroad, because the South Africanfinancial sector and the banking sector in particular is highly regulated andtherefore protected to a certain extent from global down trends or crises.


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5. CONCLUSION

The main reason for investigating the alternate mean return and standarddeviation (risk) components of shares is so as to determine- and select- the mostprofitable shares so as to construct an efficient (share) portfolio (Markowitz,1999: 7). A suitably diversified portfolio should incorporate a combination ofshares- differing in terms of risk- so as to command an investment portfolio thatsatisfies both the profit-maximisation and non-satiety conditions inherent torational consumers (individuals). The investment implicationsthat stem from the research is to consider the return and risk components ofeach of the shares investigated, and the sectoral trends that explain themovements in each share price- and thus, the share return (Howells and Bain,2009: 187). In terms of constructing an investmentportfolio out of the shares analysed- the most efficient portfolio would include (asthe obvious choice) the British American Tobacco share due to its relatively highand stable return (18.12055 percent mean return); the Investec share whichoffers a suitable, but riskier mean return (13.758 percent) and the Supergroup

share- which is although the most risky of the shares considered- it offers veryhigh returns in certain periods (2003, 2005 and 2006) and is perhaps necessaryfor a proper diversified portfolio.

The results that emanated from the data investigation are ultimately notin (total) support of Markowitzs theory that higher return is accompanied byhigher risk however, the shares were not investigated in different portfoliocombinations which would perhaps explain the inconsistency with the theorysince Markowitzs portfolio theory was aimed at investigating the suitability ofshare combinations in a portfolio- and selecting the portfolio that appeared themost efficient; and not by simply analysing the risk-return component ofindividual shares (securities) and choosing the security that appeared the mostefficient (Rubinstein, 2002: 1041.

REFERENCES

BRITISH AMERICAN TOBACCO PLC (2011). Historical share price data. [Online]

Available: http://www.bat.com/servlet/PageMerge?mainurl=%2Fgroup%2Fsites

%2Fuk%5F%5F3mnfen %2Ensf%2FvwPagesWebLive

%2FDO6FKDX7%3Fopendocument%26amp%3BSKN%3D1 [Accessed 15 April

2011].

DU PLESSIS, A. J. and WARD, M. (2009) A note on applying the Markowitzportfolio selection model as a passive investment strategy on the JSE.Investment Analysts Journal. 69 (1): 39- 45.

ELTON, E.J and GRUBER, M.J. (1997).Modern portfolio theory, 1959 to date.The Journal of Banking and Finance.21 (1): 1743- 1759.

HOWELLS, P and BAIN, K. (2005). The Economics of Money and Banking (3e).England: Prentice Hall.

MARKOWITZ, H. M. (1999) The early history of portfolio theory: 1600- 1960.Financial Analysts Journal. 55 (4): 5- 16.
http://www.bat.com/servlet/PageMerge?mainurl=%2Fgroup%2Fsites%2Fuk__3mnfen%09.nsf%2FvwPagesWebLive%2FDO6FKDX7%3Fopendocument%26amp%3BSKN%3D1http://www.bat.com/servlet/PageMerge?mainurl=%2Fgroup%2Fsites%2Fuk__3mnfen%09.nsf%2FvwPagesWebLive%2FDO6FKDX7%3Fopendocument%26amp%3BSKN%3D1http://www.bat.com/servlet/PageMerge?mainurl=%2Fgroup%2Fsites%2Fuk__3mnfen%09.nsf%2FvwPagesWebLive%2FDO6FKDX7%3Fopendocument%26amp%3BSKN%3D1http://www.bat.com/servlet/PageMerge?mainurl=%2Fgroup%2Fsites%2Fuk__3mnfen%09.nsf%2FvwPagesWebLive%2FDO6FKDX7%3Fopendocument%26amp%3BSKN%3D1http://www.bat.com/servlet/PageMerge?mainurl=%2Fgroup%2Fsites%2Fuk__3mnfen%09.nsf%2FvwPagesWebLive%2FDO6FKDX7%3Fopendocument%26amp%3BSKN%3D1http://www.bat.com/servlet/PageMerge?mainurl=%2Fgroup%2Fsites%2Fuk__3mnfen%09.nsf%2FvwPagesWebLive%2FDO6FKDX7%3Fopendocument%26amp%3BSKN%3D1


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NORTHAM PLATINUM LIMITED (2011). Thirteen year statistical review. [Online]Available: http://www.northam.co.za/im/13yr_statistical_review.asp. [Accessed15 April 2011].

RUBINSTEIN, M. (2002). Markowitzs Portfolio Selection: A fifty-yearretrospective. The Journal of Finance. LVII (3): 1041- 1045.

THOMPSON DATA STREAM (2010a). Investec Company Share Profile: DataStream, 2010. [Online] Thompson Data Stream. Available:

http://www.ru/library.co.za//thomp_son_data_//investec.pdf [Accessed 13 April2011].

THOMPSON DATA STREAM (2010b). Supergroup Limited (Ltd.) Company ShareProfile: Data Stream, 2010. [Online] Thompson Data Stream, Rhodes UniversityLibrary. Available: http://www.ru/library.co.za//thomp_son_data_//investec.pdf[Accessed 17 April 2011].
http://www.northam.co.za/im/13yr_statistical_review.asphttp://www.ru/library.co.za//thomp_son_data_//investec.pdfhttp://www.ru/library.co.za//thomp_son_data_//investec.pdfhttp://www.northam.co.za/im/13yr_statistical_review.asphttp://www.ru/library.co.za//thomp_son_data_//investec.pdfhttp://www.ru/library.co.za//thomp_son_data_//investec.pdf

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Topic 1 Essay financial