Financial Portfolio Optimization Methods - Revision history

Tkokotas at 15:22, 18 December 2018

2018-12-18T15:22:41Z

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			''Developed by Andreas Kampianakis''


	In today's globalized market, financial risk and treatment of it that has gained great importance, especially after the [[Wikipedia:Financial_Crisis_of_2008\|Financial crisis of 2008]], where factors which may affect the fragile global economy proved to be thousands and often unconnected to each other. [http://www.telegraph.co.uk/news/worldnews/europe/greece/11705720/European-debt-crisis-Its-not-just-Greece-thats-drowning-in-debt.html Nations fail to pay their debts] and [http://www.telegraph.co.uk/finance/financialcrisis/6173145/The-collapse-of-Lehman-Brothers.html giants of the finance industry bailed out] <ref> McNeil, A. J., Frey, R., & Embrechts, P. (2015). Quantitative Risk Management: Concepts, Techniques and Tools: Concepts, Techniques and Tools. Princeton university press. </ref>. These financial institutions have developed various quantitative methods which can give a prediction of this risk level in financial portfolios. A financial portfolio is considered the summary of investments owned by an investor ( company or individual )<ref>[http://www.investopedia.com/terms/p/portfolio.asp] Investopedia, Portfolio definition and explanation, Retrieved September 2015</ref>. The first step for the quantitative measurement of risk in portfolios was made by Harry Markowitz in 1952 <ref name="Harry1">Markowitz, H. (1952). Portfolio selection. The journal of finance, 7(1), 77-91.</ref>, with the development of the mean-variance model as risk measurement, which shows interest until today and it is used by investors. Thereafter, various other methods were developed, focusing on alternative risk measures that could lead to linearization of the portfolio optimization problem <ref>Sharpe, W. F. (1971). A linear programming approximation for the general portfolio analysis problem. Journal of Financial and Quantitative Analysis, 6(05), 1263-1275.</ref> . The main principles of risk handing and best profit can be applied in project management.		In today's globalized market, financial risk and treatment of it that has gained great importance, especially after the [[Wikipedia:Financial_Crisis_of_2008\|Financial crisis of 2008]], where factors which may affect the fragile global economy proved to be thousands and often unconnected to each other. [http://www.telegraph.co.uk/news/worldnews/europe/greece/11705720/European-debt-crisis-Its-not-just-Greece-thats-drowning-in-debt.html Nations fail to pay their debts] and [http://www.telegraph.co.uk/finance/financialcrisis/6173145/The-collapse-of-Lehman-Brothers.html giants of the finance industry bailed out] <ref> McNeil, A. J., Frey, R., & Embrechts, P. (2015). Quantitative Risk Management: Concepts, Techniques and Tools: Concepts, Techniques and Tools. Princeton university press. </ref>. These financial institutions have developed various quantitative methods which can give a prediction of this risk level in financial portfolios. A financial portfolio is considered the summary of investments owned by an investor ( company or individual )<ref>[http://www.investopedia.com/terms/p/portfolio.asp] Investopedia, Portfolio definition and explanation, Retrieved September 2015</ref>. The first step for the quantitative measurement of risk in portfolios was made by Harry Markowitz in 1952 <ref name="Harry1">Markowitz, H. (1952). Portfolio selection. The journal of finance, 7(1), 77-91.</ref>, with the development of the mean-variance model as risk measurement, which shows interest until today and it is used by investors. Thereafter, various other methods were developed, focusing on alternative risk measures that could lead to linearization of the portfolio optimization problem <ref>Sharpe, W. F. (1971). A linear programming approximation for the general portfolio analysis problem. Journal of Financial and Quantitative Analysis, 6(05), 1263-1275.</ref> . The main principles of risk handing and best profit can be applied in project management.
	= Financial Portfolio Optimization Methods in PPM =		= Financial Portfolio Optimization Methods in PPM =

Andkamp: /* Annotated Bibliography */

2015-10-04T16:07:28Z

Annotated Bibliography

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	Elton, E. J., Gruber, M. J., Brown, S. J., & Goetzmann, W. N. (2009). Modern portfolio theory and investment analysis. John Wiley & Sons.		Elton, E. J., Gruber, M. J., Brown, S. J., & Goetzmann, W. N. (2009). Modern portfolio theory and investment analysis. John Wiley & Sons.
	A book that examines the characteristics and analysis of individual securities as well as the theory and practice of optimally combining securities into portfolios. It stresses the economic intuition behind the subject matter while presenting advanced concepts of investment analysis and portfolio management. Readers will also discover the strengths and weaknesses of modern portfolio theory as well as the latest breakthroughs.		A book that examines the characteristics and analysis of individual securities as well as the theory and practice of optimally combining securities into portfolios. It stresses the economic intuition behind the subject matter while presenting advanced concepts of investment analysis and portfolio management. Readers will also discover the strengths and weaknesses of modern portfolio theory as well as the latest breakthroughs.

	Schwalbe, K. (2013). Information technology project management. Cengage Learning. This book demonstrates the principles distinctive to managing information technology (IT) projects that extend beyond standard project management requirements. The book weaves today's theory with successful practices for an understandable, integrated presentation that focuses on the concepts, tools, and techniques that are most effective today.		Schwalbe, K. (2013). Information technology project management. Cengage Learning. This book demonstrates the principles distinctive to managing information technology (IT) projects that extend beyond standard project management requirements. The book weaves today's theory with successful practices for an understandable, integrated presentation that focuses on the concepts, tools, and techniques that are most effective today.

	=References=		=References=
	<references/>		<references/>

Andkamp at 16:06, 4 October 2015

2015-10-04T16:06:56Z

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	*[[Wikipedia:Investment_strategy\|Investment Strategy]]		*[[Wikipedia:Investment_strategy\|Investment Strategy]]
	*[[Wikipedia:Arbitrage_pricing_theory\|Arbitrage Pricing Theory]]		*[[Wikipedia:Arbitrage_pricing_theory\|Arbitrage Pricing Theory]]
			=Annotated Bibliography=
			Elton, E. J., Gruber, M. J., Brown, S. J., & Goetzmann, W. N. (2009). Modern portfolio theory and investment analysis. John Wiley & Sons.
			A book that examines the characteristics and analysis of individual securities as well as the theory and practice of optimally combining securities into portfolios. It stresses the economic intuition behind the subject matter while presenting advanced concepts of investment analysis and portfolio management. Readers will also discover the strengths and weaknesses of modern portfolio theory as well as the latest breakthroughs.
			Schwalbe, K. (2013). Information technology project management. Cengage Learning. This book demonstrates the principles distinctive to managing information technology (IT) projects that extend beyond standard project management requirements. The book weaves today's theory with successful practices for an understandable, integrated presentation that focuses on the concepts, tools, and techniques that are most effective today.

	=References=		=References=
	<references/>		<references/>

Andkamp at 18:08, 28 September 2015

2015-09-28T18:08:06Z

← Older revision		Revision as of 18:08, 28 September 2015
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	In today's globalized market, financial risk and treatment of it that has gained great importance, especially after the [[Wikipedia:Financial_Crisis_of_2008\|Financial crisis of 2008]], where factors which may affect the fragile global economy proved to be thousands and often unconnected to each other. [http://www.telegraph.co.uk/news/worldnews/europe/greece/11705720/European-debt-crisis-Its-not-just-Greece-thats-drowning-in-debt.html Nations fail to pay their debts] and [http://www.telegraph.co.uk/finance/financialcrisis/6173145/The-collapse-of-Lehman-Brothers.html giants of the finance industry bailed out] <ref> McNeil, A. J., Frey, R., & Embrechts, P. (2015). Quantitative Risk Management: Concepts, Techniques and Tools: Concepts, Techniques and Tools. Princeton university press. </ref>. These financial institutions have developed various quantitative methods which can give a prediction of this risk level in financial portfolios. A financial portfolio is considered the summary of investments owned by an investor ( company or individual )<ref>[http://www.investopedia.com/terms/p/portfolio.asp] Investopedia, Portfolio definition and explanation, Retrieved September 2015</ref>. The first step for the quantitative measurement of risk in portfolios was made by Harry Markowitz in 1952 <ref name="Harry1">Markowitz, H. (1952). Portfolio selection. The journal of finance, 7(1), 77-91.</ref>, with the development of the mean-variance model as risk measurement, which shows interest until today and it is used by investors. Thereafter, various other methods were developed, focusing on alternative risk measures that could lead to linearization of the portfolio optimization problem <ref>Sharpe, W. F. (1971). A linear programming approximation for the general portfolio analysis problem. Journal of Financial and Quantitative Analysis, 6(05), 1263-1275.</ref> . The main principles of risk handing and best profit can be applied in project management		In today's globalized market, financial risk and treatment of it that has gained great importance, especially after the [[Wikipedia:Financial_Crisis_of_2008\|Financial crisis of 2008]], where factors which may affect the fragile global economy proved to be thousands and often unconnected to each other. [http://www.telegraph.co.uk/news/worldnews/europe/greece/11705720/European-debt-crisis-Its-not-just-Greece-thats-drowning-in-debt.html Nations fail to pay their debts] and [http://www.telegraph.co.uk/finance/financialcrisis/6173145/The-collapse-of-Lehman-Brothers.html giants of the finance industry bailed out] <ref> McNeil, A. J., Frey, R., & Embrechts, P. (2015). Quantitative Risk Management: Concepts, Techniques and Tools: Concepts, Techniques and Tools. Princeton university press. </ref>. These financial institutions have developed various quantitative methods which can give a prediction of this risk level in financial portfolios. A financial portfolio is considered the summary of investments owned by an investor ( company or individual )<ref>[http://www.investopedia.com/terms/p/portfolio.asp] Investopedia, Portfolio definition and explanation, Retrieved September 2015</ref>. The first step for the quantitative measurement of risk in portfolios was made by Harry Markowitz in 1952 <ref name="Harry1">Markowitz, H. (1952). Portfolio selection. The journal of finance, 7(1), 77-91.</ref>, with the development of the mean-variance model as risk measurement, which shows interest until today and it is used by investors. Thereafter, various other methods were developed, focusing on alternative risk measures that could lead to linearization of the portfolio optimization problem <ref>Sharpe, W. F. (1971). A linear programming approximation for the general portfolio analysis problem. Journal of Financial and Quantitative Analysis, 6(05), 1263-1275.</ref> . The main principles of risk handing and best profit can be applied in project management.
	= Financial Portfolio Optimization Methods in PPM =		= Financial Portfolio Optimization Methods in PPM =

Andkamp at 18:07, 28 September 2015

2015-09-28T18:07:52Z

← Older revision		Revision as of 18:07, 28 September 2015
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	In today's globalized market, financial risk and treatment of it that has gained great importance, especially after the [[Wikipedia:Financial_Crisis_of_2008\|Financial crisis of 2008]], where factors which may affect the fragile global economy proved to be thousands and often unconnected to each other. [http://www.telegraph.co.uk/news/worldnews/europe/greece/11705720/European-debt-crisis-Its-not-just-Greece-thats-drowning-in-debt.html Nations fail to pay their debts] and [http://www.telegraph.co.uk/finance/financialcrisis/6173145/The-collapse-of-Lehman-Brothers.html giants of the finance industry bailed out] <ref> McNeil, A. J., Frey, R., & Embrechts, P. (2015). Quantitative Risk Management: Concepts, Techniques and Tools: Concepts, Techniques and Tools. Princeton university press. </ref>. These financial institutions have developed various quantitative methods which can give a prediction of this risk level in financial portfolios. A financial portfolio is considered the summary of investments owned by an investor ( company or individual )<ref>[http://www.investopedia.com/terms/p/portfolio.asp] Investopedia, Portfolio definition and explanation, Retrieved September 2015</ref>. The first step for the quantitative measurement of risk in portfolios was made by Harry Markowitz in 1952 <ref name="Harry1">Markowitz, H. (1952). Portfolio selection. The journal of finance, 7(1), 77-91.</ref>, with the development of the mean-variance model as risk measurement, which shows interest until today and it is used by investors. Thereafter, various other methods were developed, focusing on alternative risk measures that could lead to linearization of the portfolio optimization problem <ref>Sharpe, W. F. (1971). A linear programming approximation for the general portfolio analysis problem. Journal of Financial and Quantitative Analysis, 6(05), 1263-1275.</ref> . The main principles of risk handing and best profit can be applied in project management.		In today's globalized market, financial risk and treatment of it that has gained great importance, especially after the [[Wikipedia:Financial_Crisis_of_2008\|Financial crisis of 2008]], where factors which may affect the fragile global economy proved to be thousands and often unconnected to each other. [http://www.telegraph.co.uk/news/worldnews/europe/greece/11705720/European-debt-crisis-Its-not-just-Greece-thats-drowning-in-debt.html Nations fail to pay their debts] and [http://www.telegraph.co.uk/finance/financialcrisis/6173145/The-collapse-of-Lehman-Brothers.html giants of the finance industry bailed out] <ref> McNeil, A. J., Frey, R., & Embrechts, P. (2015). Quantitative Risk Management: Concepts, Techniques and Tools: Concepts, Techniques and Tools. Princeton university press. </ref>. These financial institutions have developed various quantitative methods which can give a prediction of this risk level in financial portfolios. A financial portfolio is considered the summary of investments owned by an investor ( company or individual )<ref>[http://www.investopedia.com/terms/p/portfolio.asp] Investopedia, Portfolio definition and explanation, Retrieved September 2015</ref>. The first step for the quantitative measurement of risk in portfolios was made by Harry Markowitz in 1952 <ref name="Harry1">Markowitz, H. (1952). Portfolio selection. The journal of finance, 7(1), 77-91.</ref>, with the development of the mean-variance model as risk measurement, which shows interest until today and it is used by investors. Thereafter, various other methods were developed, focusing on alternative risk measures that could lead to linearization of the portfolio optimization problem <ref>Sharpe, W. F. (1971). A linear programming approximation for the general portfolio analysis problem. Journal of Financial and Quantitative Analysis, 6(05), 1263-1275.</ref> . The main principles of risk handing and best profit can be applied in project management
	= Financial Portfolio Optimization Methods in PPM =		= Financial Portfolio Optimization Methods in PPM =

Andkamp: /* Mean Absolute Deviation Model */

2015-09-27T19:14:05Z

Mean Absolute Deviation Model

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	==Mean Absolute Deviation Model==		==Mean Absolute Deviation Model==
	The difficulties of solving the model of Markowitz and variants <ref>A simplified model for portfolio analysis </ref> led Konno and Yamazaki in 1988 to present a model consisting exclusively of linear constraints <ref>Konno, H., & Yamazaki, H. (1991). Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Management science, 37(5), 519-531.</ref>, which utilizes as a measure of risk the [[Wikipedia:Average_absolute_deviation\|mean absolute deviation (MAD)]] . Mean absolute deviation is defined as the average of the absolute deviation from the mean of the data. So the following formula was proposed as risk measure:		The difficulties of solving the model of Markowitz and variants <ref> Sharpe, W. F. (1963). A simplified model for portfolio analysis. Management science, 9(2), 277-293. </ref> led Konno and Yamazaki in 1988 to present a model consisting exclusively of linear constraints <ref>Konno, H., & Yamazaki, H. (1991). Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Management science, 37(5), 519-531.</ref>, which utilizes as a measure of risk the [[Wikipedia:Average_absolute_deviation\|mean absolute deviation (MAD)]] . Mean absolute deviation is defined as the average of the absolute deviation from the mean of the data. So the following formula was proposed as risk measure:

	<math display="block">		<math display="block">

Andkamp: /* Disadvantages */

2015-09-25T08:12:22Z

Disadvantages

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	=Disadvantages=		=Disadvantages=
	In literature ~~there has been~~ reported that many of these assumptions do not seem realistic. Assumption of "reasonable investors" often seem to fall short as they generally prefer portfolios different from those resulting from analyzes <ref>Camerer, C., & Weber, M. (1992). Recent developments in modeling preferences: Uncertainty and ambiguity. Journal of risk and uncertainty, 5(4), 325-370.</ref> <ref>Kroll, Y., Levy, H., & Rapoport, A. (1988). Experimental tests of the separation theorem and the capital asset pricing model. The American Economic Review, 500-519.</ref>. Moreover, the grade of complexity becomes greater as the problem grows and its solution becomes extremely difficult or even impossible. Finally, the assumptions mentioned do not take into account the uniqueness of each investor and consider everyone as a unified body, ignoring the behavior that each of them may present. So the difference of institutional and non-institutional investors can lead to values much higher than actual, due to herd behavior in the second category of investors, leading to systematic overvaluation of stock prices <ref>Maringer, D. G. (2006). Portfolio management with heuristic optimization (Vol. 8). Springer Science & Business Media.</ref>. This kind of disadvantages seem to gave birth to various approaches in the problem of portfolio optimization. Fuzzy handling of the problem , seem to solve various of the issues made due to the assumptions such as the nonuniform character of the information among the investors<ref>Gupta, P., Mehlawat, M. K., & Saxena, A. (2008). Asset portfolio optimization using fuzzy mathematical programming. Information Sciences, 178(6), 1734-1755.</ref> <ref>Pandit, P. K. (2013, September). Portfolio optimization using fuzzy linear programming. In INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND STATISTICS 2013 (ICMSS2013): Proceedings of the International Conference on Mathematical Sciences and Statistics 2013 (Vol. 1557, No. 1, pp. 206-210). AIP Publishing.</ref> . Moreover multi-criteria analysis haw been implemented in order cope with the investor’s personal attitude towards risk and specific objectives he/she may have <ref>Xidonas, P., Mavrotas, G., & Psarras, J. (2010). Portfolio management within the frame of multiobjective mathematical programming: a categorised bibliographic study. International Journal of Operational Research, 8(1), 21-41.</ref> <ref>Xidonas, P., Mavrotas, G., & Psarras, J. (2009). A multicriteria methodology for equity selection using financial analysis. Computers & Operations Research, 36(12), 3187-3203.</ref>. Especially in the field of "non-financial" assets there has been a lot of concern in utilization of such models in order to optimize the project portfolio. First of all, the inability of non divisible allocation , makes the portfolio of projects far more inflexible. This inflexibility makes MPT almost useless. Projects either start or do not, but once they are started there should be an end too. A portfolio optimization method must consider this nature of projects in order to function properly. Also, assets of financial portfolios are liquid; assessment and re-assesement can be done at any point. However opportunity of starting a new project may be limited. Most of the projects that have already started cannot be ceased or sold without the loss of the sunk costs. More specifically, a semi-complete project seems to have no salvation "return", so all the cost of abandonment falls on the shoulders of the investor.<ref>Hubbard, D. W. (2014). How to measure anything: Finding the value of intangibles in business. John Wiley & Sons.</ref>		In literature, it is reported that many of these assumptions do not seem realistic. Assumption of "reasonable investors" often seem to fall short as they generally prefer portfolios different from those resulting from analyzes <ref>Camerer, C., & Weber, M. (1992). Recent developments in modeling preferences: Uncertainty and ambiguity. Journal of risk and uncertainty, 5(4), 325-370.</ref> <ref>Kroll, Y., Levy, H., & Rapoport, A. (1988). Experimental tests of the separation theorem and the capital asset pricing model. The American Economic Review, 500-519.</ref>. Moreover, the grade of complexity becomes greater as the problem grows and its solution becomes extremely difficult or even impossible. Finally, the assumptions mentioned do not take into account the uniqueness of each investor and consider everyone as a unified body, ignoring the behavior that each of them may present. So the difference of institutional and non-institutional investors can lead to values much higher than actual, due to herd behavior in the second category of investors, leading to systematic overvaluation of stock prices <ref>Maringer, D. G. (2006). Portfolio management with heuristic optimization (Vol. 8). Springer Science & Business Media.</ref>. This kind of disadvantages seem to gave birth to various approaches in the problem of portfolio optimization. Fuzzy handling of the problem , seem to solve various of the issues made due to the assumptions such as the nonuniform character of the information among the investors<ref>Gupta, P., Mehlawat, M. K., & Saxena, A. (2008). Asset portfolio optimization using fuzzy mathematical programming. Information Sciences, 178(6), 1734-1755.</ref> <ref>Pandit, P. K. (2013, September). Portfolio optimization using fuzzy linear programming. In INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND STATISTICS 2013 (ICMSS2013): Proceedings of the International Conference on Mathematical Sciences and Statistics 2013 (Vol. 1557, No. 1, pp. 206-210). AIP Publishing.</ref> . Moreover multi-criteria analysis haw been implemented in order cope with the investor’s personal attitude towards risk and specific objectives he/she may have <ref>Xidonas, P., Mavrotas, G., & Psarras, J. (2010). Portfolio management within the frame of multiobjective mathematical programming: a categorised bibliographic study. International Journal of Operational Research, 8(1), 21-41.</ref> <ref>Xidonas, P., Mavrotas, G., & Psarras, J. (2009). A multicriteria methodology for equity selection using financial analysis. Computers & Operations Research, 36(12), 3187-3203.</ref>. Especially in the field of "non-financial" assets there has been a lot of concern in utilization of such models in order to optimize the project portfolio. First of all, the inability of non divisible allocation , makes the portfolio of projects far more inflexible. This inflexibility makes MPT almost useless. Projects either start or do not, but once they are started there should be an end too. A portfolio optimization method must consider this nature of projects in order to function properly. Also, assets of financial portfolios are liquid; assessment and re-assesement can be done at any point. However opportunity of starting a new project may be limited. Most of the projects that have already started cannot be ceased or sold without the loss of the sunk costs. More specifically, a semi-complete project seems to have no salvation "return", so all the cost of abandonment falls on the shoulders of the investor.<ref>Hubbard, D. W. (2014). How to measure anything: Finding the value of intangibles in business. John Wiley & Sons.</ref>
	<ref>Sabbadini, Tony. "Manufacturing Portfolio Theory." International Institute for Advanced Studies in Systems Research and Cybernetics (2010): 120-160.</ref>. Finally, MPT mostly makes use of a mathematical defined risk measure, but portfolios consisting for example from major building projects do not have a firm one.		<ref>Sabbadini, Tony. "Manufacturing Portfolio Theory." International Institute for Advanced Studies in Systems Research and Cybernetics (2010): 120-160.</ref>. Finally, MPT mostly makes use of a mathematical defined risk measure, but portfolios consisting for example from major building projects do not have a firm one.

Andkamp: /* Additional Constraints */

2015-09-23T19:08:14Z

Additional Constraints

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	==Additional Constraints==		==Additional Constraints==
	In real situations where investors desire portfolios that meet different realistic features like minimum lots of transactions and transaction costs, solvability of linear models is a critical aspect.		In real situations where investors desire portfolios that meet different realistic features like minimum lots of transactions and transaction costs, solvability of linear models is a critical aspect.
	Even if the solution of quadratic models like Mean Variance and Semi-Variance has been treated for restrictions in the total number of shares and minimum transactions lots <ref>Chang, T. J., Meade, N., Beasley, J. E., & Sharaiha, Y. M. (2000). Heuristics for cardinality constrained portfolio optimisation. Computers & Operations Research, 27(13), 1271-1302.</ref> <ref name="Angelelli"/>, the computational challenge to solve the big and realistic portfolio problems justifies the long tradition in literature of [[Wikipedia:Integer_programming\|mixed integer programming]] for portfolio selection with pragmatic characteristics <ref>Bertsimas, D., Darnell, C., Soucy, R., & Darnellt, C. (1998). Portfolio construction through mixed integer programming.</ref> <ref>Chiodi, L., Mansini, R., & Speranza, M. G. (2003). Semi-absolute deviation rule for mutual funds portfolio selection. Annals of Operations Research, 124(1-4), 245-265.</ref> <ref>Kellerer, H., Mansini, R., & Speranza, M. G. (2000). Selecting portfolios with fixed costs and minimum transaction lots. Annals of Operations Research, 99(1-4), 287-304.</ref> <ref>Konno, H., & Wijayanayake, A. (2001). Portfolio optimization problem under concave transaction costs and minimal transaction unit constraints. Mathematical Programming, 89(2), 233-250.</ref> <ref>Mansini, R., & Speranza, M. G. (2005). An exact approach for portfolio selection with transaction costs and rounds. IIE transactions, 37(10), 919-929.</ref>. The models extend the basic portfolio optimization models and result to increased complexity and difficulty of solution. However, the analyzes carried out are closer to reality and the parameters can be adjusted depending on the stock market and investor requirements. Such restrictions can be:		Even if the solution of quadratic models like Mean Variance and Semi-Variance has been treated for restrictions in the total number of shares and minimum transactions lots <ref>Chang, T. J., Meade, N., Beasley, J. E., & Sharaiha, Y. M. (2000). Heuristics for cardinality constrained portfolio optimisation. Computers & Operations Research, 27(13), 1271-1302.</ref> <ref name="Angelelli"/>, the computational challenge to solve the big and realistic portfolio problems justifies the long tradition in literature of [[Wikipedia:Integer_programming\|mixed integer programming]] for portfolio selection with pragmatic characteristics <ref>Kellerer, H., Mansini, R., & Speranza, M. G. (2000). Selecting portfolios with fixed costs and minimum transaction lots. Annals of Operations Research, 99(1-4), 287-304.</ref> <ref>Konno, H., & Wijayanayake, A. (2001). Portfolio optimization problem under concave transaction costs and minimal transaction unit constraints. Mathematical Programming, 89(2), 233-250.</ref> <ref>Mansini, R., & Speranza, M. G. (2005). An exact approach for portfolio selection with transaction costs and rounds. IIE transactions, 37(10), 919-929.</ref>. The models extend the basic portfolio optimization models and result to increased complexity and difficulty of solution. However, the analyzes carried out are closer to reality and the parameters can be adjusted depending on the stock market and investor requirements. Such restrictions can be:
	* Restriction in total number of shares. The investor chooses the maximum number of shares they want to invest.		* Restriction in total number of shares. The investor chooses the maximum number of shares they want to invest.
	* Limitation of minimum trading lots. The investor virtually round the percentages invested, due to limitations of the financial market.		* Limitation of minimum trading lots. The investor virtually round the percentages invested, due to limitations of the financial market.

Andkamp: /* Financial Portfolio Optimization Methods in PPM */

2015-09-23T18:52:08Z

Financial Portfolio Optimization Methods in PPM

← Older revision		Revision as of 18:52, 23 September 2015
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	= Financial Portfolio Optimization Methods in PPM =		= Financial Portfolio Optimization Methods in PPM =

	In order for a business to minimize the danger of exposure to a failed project, financial portfolio methods can be applied. Consider "assets" to be financial, physical, or information that combined with other assets in a project will increase value. The "group" of assets is designed to achieve the growth of value at acceptable levels of risk over the longer term. The "investor" is a business manager whose job it is to put assets to function efficiently as a portfolio <ref>Nikonov, O.V, (2007). Efficient Project Portfolio as a tool for Enterprise Risk Management. ERM Symposia </ref>. Each of Markowitz’ principles in Modern Portfolio Theory (MPT ) were translated into a criterion for project prioritization that aids in the success of project portfolio management (PPM). In modern project portfolio management, other than risk and return, there are elements such as benefits maximization, balance, strategic alignment and resource leveling. Application of methods of financial portfolio optimization can help a project manager to evaluate projects taking in consideration the interaction and influence of other projects.<ref>Thorp, J. (2003). The information paradox: realizing the business benefits of information technology. McGraw-Hill Ryerson.</ref>		In order for a business to minimize the danger of exposure to a failed project, financial portfolio methods can be applied. Consider "assets" to be financial, physical, or information that combined with other assets in a project will increase value. The "group" of assets is designed to achieve the growth of value at acceptable levels of risk over the longer term. The "investor" is a business manager whose job it is to put assets to function efficiently as a portfolio <ref>Nikonov, O.V, (2007). Efficient Project Portfolio as a tool for Enterprise Risk Management. ERM Symposia </ref>. Each of Markowitz’ principles in Modern Portfolio Theory (MPT) were translated into a criterion for project prioritization that aids in the success of project portfolio management (PPM). In modern project portfolio management, other than risk and return, there are elements such as benefits maximization, balance, strategic alignment and resource leveling. Application of methods of financial portfolio optimization can help a project manager to evaluate projects taking in consideration the interaction and influence of other projects.<ref>Thorp, J. (2003). The information paradox: realizing the business benefits of information technology. McGraw-Hill Ryerson.</ref>
	[[File:Pm.png\|1000px\|center\|middle\|thumb\|'''Figure 1:''' Translation of MPT criterias to PPM criterias <ref>Bonham, S. S. (2005). IT project portfolio management. Artech House.</ref>]]		[[File:Pm.png\|1000px\|center\|middle\|thumb\|'''Figure 1:''' Translation of MPT criterias to PPM criterias <ref>Bonham, S. S. (2005). IT project portfolio management. Artech House.</ref>]]

Andkamp: /* Cardinality constraints */

2015-09-23T18:41:58Z

Cardinality constraints

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	===Cardinality constraints===		===Cardinality constraints===
	One of the basic assumptions of portfolio theory is that investors can hold well diversified portfolios. However, there are signs that investors typically hold only a small number of securities. Market imperfections such as fixed transaction costs, provide one possible explanation for the selection of undiversified portfolios~~[40]~~. Moreover, the need to avoid the costs of monitoring and re-weighting a portfolio leads investors to the common practice of limiting the number of investments (population portfolio securities) that can be selected in a portfolio. The restriction on the number of securities in a portfolio can be expressed either as a strict equality or inequality requiring that the number of selected titles can not be greater than a predetermined number. The addition of the above restriction in each of the [[#Mean Variance Model\|models]] can be done by adding a variable <math>x_{i}</math> subject to the following limitations:		One of the basic assumptions of portfolio theory is that investors can hold well diversified portfolios. However, there are signs that investors typically hold only a small number of securities. Market imperfections such as fixed transaction costs, provide one possible explanation for the selection of undiversified portfolios<ref>Wilding, T. (2003). Using genetic algorithms to construct portfolios. Advances in portfolio construction and implementation, 135-160.</ref>. Moreover, the need to avoid the costs of monitoring and re-weighting a portfolio leads investors to the common practice of limiting the number of investments (population portfolio securities) that can be selected in a portfolio. The restriction on the number of securities in a portfolio can be expressed either as a strict equality or inequality requiring that the number of selected titles can not be greater than a predetermined number. The addition of the above restriction in each of the [[#Mean Variance Model\|models]] can be done by adding a variable <math>x_{i}</math> subject to the following limitations:

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