**Assignment**

**ICM 10****7****Securities, Futures and Options ( SFO )**

**Question A )**

**1.1 Datas**

To 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 IT****C****ompanies**

**Table****2****: List of****the Data Set**

**1.2 Efficient frontier building**

The 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.

**Table****3****:****Description of Assumptions and Constraints for Efficient Frontier**

As a consequence, the efficient frontier was created and plotted in Figure 1.

**1.3****Market****P****ortfolio****building**

The 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.

**Table****4****:****Description of Assumptions and Constraints for Market Portfolio**

Based on the computation, the market portfolio with the highest Sharpe ration of 1.19 was found. Figure 1 shows that the green trigon grade on the efficient frontier represents the market portfolio.

**Figure 1: Efficient Frontier and Market Portfolio**

**( 2004-2014, No Short Selling )**

**Question B )**

The market portfolio shown in Figure 1 is a desirable one in footings of both a portfolio theory and a public presentation rating. Under the theory, all portfolios lying on the efficient frontier are said to be efficient from the position of a risk-return feature as the efficient frontier represents the lower limit hazard for a given return and the maximal return for a given hazard. If the portfolio that does non lie on the efficient frontier, it could non be regarded as an optimum hazardous portfolio. Furthermore, the tangency portfolio of a consecutive line ( i.e. Capital Market Line ) from a hazard free rate to the efficient frontier is called the market portfolio, which has the highest Sharpe ratio ( Bodie, et al. , 2014 ) . As the Sharpe ratio represents a ratio to mensurate the investing efficiency, the market portfolio with the highest Sharpe ratio could be considered to be most efficient. Hence, all investors wish to keep the market portfolio.

Additionally, the public presentation rating confirms that the market portfolio is a practical 1. Based on the public presentation analysis between the market portfolio and CAC All-Tradable Index, the market portfolio outperformed the stock index significantly. Specifically, the return of the market portfolio ( 18.2 % ) was more than five times higher than that of the index ( 3.3 % ) . Furthermore, the Sharpe ratio of the market portfolio ( 1.19 ) was well better than that of the stock index ( 0.1 ) . On the other manus, the standard divergence, or hazard of the market portfolio ( 13.9 % ) was smaller than that of the index ( 16.6 % ) . Besides, as shown in Figure 2-a, the market portfolio experienced a comparatively moderate bead during the fiscal crisis in 2008 to 2009, while it saw a much stronger recovery after 2009 as compared to the index. In short, the market portfolio has a higher return and lower hazard feature. Therefore, it can be concluded that the market portfolio is a desirable one.

**Table****5****:****Performance Summary of Market Portfolio and Stock Index**

**( 2004-2014, No Short Selling )**

**Figure 2****-a****:****Accumulative****Tax return of****Market Portfolio and Stock Index**

**( 2004-2014, No Short Selling )**

**Figure 2****-b****:****Accumulative****Tax return of****Market Portfolio and Stock Index**

**( 2004-2014, No Short Selling )**

**Question C )**

**3.1 Minimum discrepancy portfolio building**

The 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.

**Table****6****:****Description of premises and restraints for minimal discrepancy portfolio**

As a consequence of the computation, the minimal discrepancy portfolio with the lowest discrepancy of 0.0159 was found, which corresponds to the standard divergence of 12.6 % . Figure 1 presents the ruddy square grade on the efficient frontier which represents the minimal discrepancy portfolio.

**3.2 Compositions of market portfolio**

As 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.

**Table****6****: Compositions of Market Portfolio**

**( 2004-2014, No Short Selling )**

**3.3 Compositions of minimal discrepancy portfolio**

The 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 % .

**Table****7****:****Compositions of****Minimum Variance Portfolio**

**( 2004-2014, No Short Selling )**

**Question D )**

**4.1 Efficient frontier building**

The 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.

**Table****8****:****Description of Assumptions and Constraints for Efficient Frontier**

Based on the computation, the efficient frontier was created and plotted in Figure 3.

It can be concluded that the form of the efficient frontier is dependent on the restraints. If the restraints are released, say a short merchandising is allowed, the efficient frontier moves to the left. Therefore, the efficient frontier that is wholly free of restraints remains at the most left. On the contrary, the efficient frontier moves more to the right and besides the form becomes smaller in size as the restraints are stricter.

**4.2****Market****P****ortfolio****building**

The 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.

**Table****9****:****Description of Assumptions and Constraints for Market Portfolio**

As a consequence of the computation, the market portfolio with the highest Sharpe ratio of 1.53 was found. As shown in Figure 3, the blue cross grade on the efficient frontier represents the market portfolio.

**Figure****3****: Efficient Frontier and Market Portfolio**

**( 2004-2014, Short Selling )**

**Figure****4****: Efficient Frontier****with No Short Selling and Short Selling**

**( 2004-2014 )**

**4.3 Minimum discrepancy portfolio building**

The 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.

**Table****10****:****Description of Assumptions and Constraints for Minimum Variance Portfolio**

Based on the computation, the minimal discrepancy portfolio with the lowest discrepancy of 0.0126 was found, which corresponds to the standard divergence of 11.2 % . As shown in Figure 3, the ruddy square grade on the efficient frontier represents the minimal discrepancy portfolio.

**4.4 Compositions of market portfolio**

The 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.

**Table****11****: Compositions of Market Portfolio**

**( 2004-2014, Short Selling )**

**4.5 Compositions of minimal discrepancy portfolio**

As 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.

**Table****12****: Performance****Statistic****of Market Portfolio****with Short Selling and No Short Selling**

**( 2004-2014 )**

**Table****13****: Compositions of Minimum Variance Portfolio**

**( 2004-2014, Short Selling )**

**Table****14****: Performance****Statistic****of****Minimal Discrepancy****Portfolio**

**with Short Selling and No short Selling****( 2004-2014 )**

**Question****Tocopherol****)**

**5.1 Premise of clip separation**

**Formula 1: ( 2004+2014 ) /2=2009**

Because 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.

**5.2****Re-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.

**Table****1****5****: Performance****Statistic****of****Market Portfolio and****Minimal Discrepancy****Portfolio**

**( 2004-20****09****, Short Selling****)**

**Table****16****:****Portfolio Weight of Market Portfolio and Minimum Variance Portfolio**

**5.3 Performance comparing between m****arket****P****ortfolio****and m****inimum****V****ariance****P****ortfolio****utilizing the information****degree Fahrenheit****read-only memory****2009 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.

**Figure****5****-a****:****Accumulative****Tax return of****Market Portfolio and Minimum****Variance Portfolio**

**( 200****9****-2014,****Short Selling )**

**Figure****5****-b****:****Accumulative****Tax return of****Market Portfolio and Minimum****Variance Portfolio**

**( 200****9****-2014,****Short Selling )**

**Question****F****)**

**6.1 Equally leaden portfolio and market-capitalization leaden portfolio building**

Harmonizing 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.

**Figure****6****: Efficient Frontier and Market Portfolio**

**( 2004-20****09****, Short Selling )**

**6.2 Phosphorus****erformance****comparing****of the four portfolios****:****the market portfolio, the minimal discrepancy portfolio, the every bit leaden portfolio, and the market****–****cap****italization****weighted portfolio****( Portfolio weight such as****market portfolio****and****minimal discrepancy portfolio****is 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.

**Figure****7-a****:****Accumulative****Roentgen****eturn of****Meter****arket****Phosphorus****ortfolio,****Meter****inimum****Volt****ariance****Phosphorus****ortfolio,****Tocopherol****qually****Tungsten****eighted****Phosphorus****ortfolio, and****Meter****arket****-C****ap****italization****Tungsten****eighted****Phosphorus****ortfolio**

**( 200****9****-2014,****Short Selling )**

**Figure****7-b****:****Accumulative****Roentgen****eturn of****Meter****arket****Phosphorus****ortfolio,****Meter****inimum****Volt****ariance****Phosphorus****ortfolio,****Tocopherol****qually****Tungsten****eighted****Phosphorus****ortfolio, and****Meter****arket****-C****ap****italization****Tungsten****eighted****Phosphorus****ortfolio**

**( 200****9****-2014,****Short Selling )**

**Table****17****:****Portfolio Weight of Market Portfolio, Minimum Variance Portfolio, Equally Weighted Portfolio and Market-Capitalization Weighted Portfolio**

**Table****18****:****Performance Statistic of Market Portfolio, Minimum Variance Portfolio, Equally Weighted Portfolio and Market-Capitalization Weighted Portfolio**

**Mentions**

Archer, S. H. , Francis, J.C. ( 1971 ) .*Portfolio Analysis.*United statess: Prentice-Hall, Inc. ,

Bodie, Z. , Kane, A. , Marcus, A ( 2014 ) .*Investings.*United kingdom: McGraw-Hill Education

Levy, H. , Sarnat, M ( 1984 ) .*PORTFOLIO AND INVESTMENT SELECTION: Theory AND PRACTICE.*United statess: Prentice-Hall, Inc. ,

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