Securities, Futures and Options (SFO) Essay

AssignmentICM 107Securities, Futures and Options ( SFO )Question A )1.1 DatasTo implement the analysis, the information was downloaded from the Bloomberg. First, the 20 Gallic IT companies were selected from CAC All-Tradable Index in falling order of market capitalisation.

Second, the 121 dividend-adjusted monthly stock monetary values from 30/09/2004 to 30/09/2014 were collected per stock to obtain the 120 monthly entire return informations series from 29/10/2004 to 30/09/2014. Here, the entire return means a return that is comprised of the rate of capital gain/loss plus dividend output ( Bodie, et al. , 2014 ) . Rather than utilizing the monthly return, more precise analysis and public presentation measuring could be achieved by utilizing the monthly entire return. Last, 1 twelvemonth T-bill was selected as a riskless rate. As all monthly informations such as return and standard divergence were annualized, it should be justifiable to fiting the clip skyline of the hazard free rate with the annualized return and hazard.Table 1: List of 20 Gallic ITCompanies1.

2 Efficient frontier buildingThe efficient frontier is constructed by happening the minimal discrepancy for a given mark expected return. This can be done utilizing the Solver in Excel. Here, the premises and restraints for making the efficient frontier were made as follows.Table3:Description of Assumptions and Constraints for Efficient Frontier1.3MarketPortfoliobuildingThe market portfolio is found by taking the portfolio that maximizes the Sharpe ratio on the minimal discrepancy frontier. Here, the premises and restraints for happening the market portfolio were made as follows.Table4:Description of Assumptions and Constraints for Market PortfolioFigure 2-a:AccumulativeTax return ofMarket Portfolio and Stock Index( 2004-2014, No Short Selling )3.1 Minimum discrepancy portfolio buildingThe minimal discrepancy portfolio is obtained by happening the portfolio that minimizes the portfolio discrepancy among the minimal discrepancy frontier. Here, the below premises and restraints were made.Table6:Description of premises and restraints for minimal discrepancy portfolio3.2 Compositions of market portfolioAs shown in Table 6, the composing of the market portfolio was comprised of 6 out of 20 stocks. The largest weight of the portfolio was 30.3 % of PHARMAGEST INTERACTIVE, whilst the smallest 1 was 3.8 % of UBISOFT ENTERTAINMENT.

This portfolio was constructed by the stocks that have a comparatively high Sharpe ratio. Harmonizing to 0.55 of the 3rd quartile of the Sharpe ratio, about 96 % of the market portfolio can be explained by the top 25 % stocks with high Sharpe ratio.

In add-on, the two smallest weight stocks such as PHARMAGEST INTERACTIVE and DASSAULT SYSTEMS SA accounted for around 55 % of the full weights. Furthermore, the negative correlativity between those two stocks was found although it was a significantly little one. Therefore, it could be said that the definition of the market portfolio is met.Table6: Compositions of Market Portfolio( 2004-2014, No Short Selling )3.3 Compositions of minimal discrepancy portfolioThe minimal discrepancy portfolio was composed of 8 out of 20 stocks. The largest weight of the portfolio was 37 % of PHARMAGEST INTERACTIVE, while the smallest 1 was 1.3 % of LECTRA and UBISOFT ENTERTAINMENT. As the minimal discrepancy portfolio can be built by minimising the portfolio discrepancy, it is an acceptable consequence that the top two lowest hazard stocks, PHARMAGEST INTERACTIVE and DASSAULT SYSTEMS SA occupied about 67 % of the portfolio weights, lending to take downing the overall portfolio discrepancy. Furthermore, it is found out that approximately 99 % of the portfolio weights lied within the first quartile hazard of 37.

7 % .Table7:Compositions ofMinimum Variance Portfolio( 2004-2014, No Short Selling )4.1 Efficient frontier buildingThe efficient frontier is constructed by happening the minimal discrepancy for a given mark expected returns. This can be done utilizing the Solver in Excel. Here, the premises and restraints for happening the efficient frontier were made as follows.Table8:Description of Assumptions and Constraints for Efficient Frontier4.2MarketPortfoliobuildingThe market portfolio is found by taking the portfolio that maximizes the Sharpe ratio on the minimal discrepancy frontier. Here, the premises and restraints for happening the market portfolio were made as follows.

Table9:Description of Assumptions and Constraints for Market Portfolio4.3 Minimum discrepancy portfolio buildingThe minimal discrepancy portfolio is obtained by happening the portfolio that minimizes the portfolio discrepancy among the minimal discrepancy frontier.

Here, the below premises and restraints were made.Table10:Description of Assumptions and Constraints for Minimum Variance Portfolio4.4 Compositions of market portfolioThe market portfolio was composed of 11 long stocks and 9 short stocks ( see Table 11 ) . The entire long place of the portfolio was 159.

4 % , while the entire short place was -59.4 % , ensuing in the net 100 % long portfolio. The top long weight was 36 % of DASSAULT SYSTEMS SA, whilst the top short was of -16 % of CEGEDIM SA, which was the lone stock with a negative Sharpe ratio of -0.03. As compared with the public presentation between the market portfolio with short merchandising and no short merchandising, it is obvious that the former portfolio was a portfolio with higher return and lower hazard. Hence, it can be concluded that the market portfolio with short merchandising could profit more from the portfolio variegation.Table11: Compositions of Market Portfolio( 2004-2014, Short Selling )4.5 Compositions of minimal discrepancy portfolioAs shown in Table 13, the composing of minimal discrepancy portfolio was a combination of 11 long stocks and 9 short stocks.

The entire long place of the portfolio was 136.2 % , while the entire short place was -36.2 % , ensuing in the net 100 % long portfolio. The positively largest weight was 39 % of DASSAULT SYSTEMS SA, whilst the negatively largest weight was of -7.7 % of GFI INFORMATIQUE. The first quartile of hazard ( 28 % ) can explicate 100 % of the sum long place of 136.2 % . Similar to the market portfolio, the minimal discrepancy portfolio could bask the portfolio variegation by leting for a short merchandising.

Hence, the minimal discrepancy portfolio with short selling achieves a higher return and a lower hazard one.Table12: PerformanceStatisticof Market Portfoliowith Short Selling and No Short Selling( 2004-2014 )Table13: Compositions of Minimum Variance Portfolio( 2004-2014, Short Selling )5.1 Premise of clip separationFormula 1: ( 2004+2014 ) /2=2009Because the inquiry ( vitamin E ) required spliting the whole period into 2 parts which is the first half of old ages and the remaining, 2009 was found by the expression 1. In this instance, the whole period ( 2004-2014 ) was divided to 2 equal parts, which is from 2004 to 2009 and from 2009 to 2014.5.

2Re-estimate the market portfolio and minimal discrepancy portfolio utilizing the first half of the informations merely.The minimal discrepancy portfolio means the portfolio of hazardous assets with the lowest discrepancy. Based on the public presentation analysis of the market portfolio and minimal discrepancy portfolio in the first five old ages, it is clear that the market portfolio was a higher return and lower hazard portfolio with higher Sharpe ratio compared with the minimal discrepancy portfolio. Table 15 shows that the hazard of the market portfolio was 68.3 % , while that of the minimal discrepancy portfolio was 11.

3 % . Additionally, the return of the market portfolio ( 122.0 % ) was significantly higher than that of the minimal discrepancy portfolio, which was merely 5.

0 % . Furthermore, the Sharpe ratio of the market portfolio ( 1.74 ) was well better than that of the minimal discrepancy portfolio ( 0.19 ) . In decision, the market portfolio is a better risk-return tradeoff portfolio.Table15: PerformanceStatisticofMarket Portfolio andMinimal DiscrepancyPortfolio( 2004-2009, Short Selling)5.

3 Performance comparing between marketPortfolioand minimumVariancePortfolioutilizing the informationdegree Fahrenheitread-only memory2009 to 2014( Portfolio weight is indistinguishable to that of 2004-2009 )Figure 5-a shows that the minimal discrepancy portfolio performed better than the market portfolio during the 2nd five old ages. Specifically, the minimal discrepancy portfolio was about 0 % at the beginning and increased until the terminal period ( 125 % ) . Meanwhile, the market portfolio started from around -60 % at 30/10/2009 and reached the top at around 23 % at 28/2/2014 and at the terminal of this period. Additionally, the return volatility of the minimal discrepancy portfolio was really stable as the portfolio has the least discrepancy. On the other manus, the return of the market portfolio was well volatile. Furthermore, it underperformed although it was constructed by the portfolio weights with the highest Sharpe of 2004-09. In decision, it could be considered that the market portfolio was less efficient and riskier than the minimal discrepancy portfolio in footings of a risk-return feature.

Figure5-a:AccumulativeTax return ofMarket Portfolio and MinimumVariance Portfolio( 2009-2014,Short Selling )Figure5-b:AccumulativeTax return ofMarket Portfolio and MinimumVariance Portfolio( 2009-2014,Short Selling )6.1 Equally leaden portfolio and market-capitalization leaden portfolio buildingHarmonizing to the description of market-capitalization in Table 2, the weight of market-capitalization weighted portfolio is on the day of the month of 30/9/2009, while the weight of every bit leaden portfolio is 1/20 ( 5 % each stock ) .

Figure 6 illustrates the different public presentation of different leaden portfolio. The expected return of market-capitalization leaden portfolio was 8.74 % , which was merely 4.13 % lower than that of every bit weighted portfolio. Meanwhile, the hazard of market-capitalization weighted portfolio ( 23.79 % ) was besides lower than every bit weighted portfolio ( 24.68 % ) . Therefore, the every bit leaden portfolio could accomplish a higher return and higher hazard than the market-capitalization weighted portfolio.

However, the every bit leaden portfolio and market-capitalization leaden portfolio were inefficient as both portfolios were inside the efficient frontier.Figure6: Efficient Frontier and Market Portfolio( 2004-2009, Short Selling )6.2 Phosphoruserformancecomparingof the four portfolios:the market portfolio, the minimal discrepancy portfolio, the every bit leaden portfolio, and the marketcapitalizationweighted portfolio( Portfolio weight such asmarket portfolioandminimal discrepancy portfoliois indistinguishable to that of 2004-2009 )Figure 7-a shows the cumulative return of the market portfolio, minimal discrepancy portfolio, every bit leaden portfolio and market-capitalization weighted portfolio between 2009 and 2014.It is noticeable that the market portfolio was by far the lowest profitable of the four types of portfolio over the period, while the minimal discrepancy portfolio outperformed the most for the bulk of the period.

In add-on, the every bit leaden portfolio and market-capitalization weighted portfolio performed the same degree of return with similar hazard ( see in Table 18 ) .At 30/10/2009, the cumulative return of the market portfolio was -56.2 % while that of other three portfolios was about 0 % . During the following 2.5 old ages, the cumulative return of the market portfolio fluctuated from -38.3 % in 26/2/2010 to -149.

3 % in 31/5/2012. During the same period, the informations of minimal discrepancy portfolio increased steadily to around 61.1 % in 30/5/2012, while the cumulative return of the every bit leaden portfolio and the market capitalisation weighted portfolio rose to 35.51 % and 33.82 % at 31/5/2011. By 29/8/2014, the cumulative return of the minimal discrepancy portfolio increased to 122.

8 % , and the return of the market portfolio besides reached the top which was about 19.4 % . Furthermore, the cumulative return of the every bit leaden portfolio and the market cap weighted portfolio grew easy to 84.5 % and 87.5 % .In decision, the minimal discrepancy portfolio with the lowest hazard achieved the best public presentation, whilst the market portfolio with the highest hazard recorded the worst public presentation. In other words, the higher return the lower hazard. Hence, the consequence could non be consistent with the portfolio theory, which specifies taking a higher hazard for deriving a higher return.

Figure7-a:AccumulativeRoentgeneturn ofMeterarketPhosphorusortfolio,MeterinimumVoltariancePhosphorusortfolio,TocopherolquallyTungsteneightedPhosphorusortfolio, andMeterarket-CapitalizationTungsteneightedPhosphorusortfolio( 2009-2014,Short Selling )Figure7-b:AccumulativeRoentgeneturn ofMeterarketPhosphorusortfolio,MeterinimumVoltariancePhosphorusortfolio,TocopherolquallyTungsteneightedPhosphorusortfolio, andMeterarket-CapitalizationTungsteneightedPhosphorusortfolio( 2009-2014,Short Selling )MentionsArcher, S. H. , Francis, J.

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