Portfolio Management: A Fuzzy Set Based Approach to Monitoring Size to Maximize Return and Minimize Risk
Fuzzy logic can be used when knowledge is
incomplete or when ambiguity of data exists. The purpose of
this paper is to propose a proactive fuzzy set- based model for
reacting to the risk inherent in investment activities relative to
a complete view of portfolio management. Fuzzy rules are
given where, depending on the antecedents, the portfolio size
may be slightly or significantly decreased or increased. The
decision maker considers acceptable bounds on the proportion
of acceptable risk and return. The Fuzzy Controller model
allows learning to be achieved as 1) the firing strength of each
rule is measured, 2) fuzzy output allows rules to be updated,
and 3) new actions are recommended as the system continues
to loop. An extension is given to the fuzzy controller that
evaluates potential financial loss before adjusting the
portfolio. An application is presented that illustrates the
algorithm and extension developed in the paper.
[1]. de Korvin, A., Strawser, J., and Siegel, P. (1995). "An
Application of Cost Control System to Cost Variance
Analysis". Managerial Finance 21 (3), pp. 17-35.
[2]. Ellsberg, Daniel. (1961) "Risk, Ambiguity and the Savage
Axioms". Quarterly Journal of Economics. 75(4), pp. 643-
669.
[3]. Slovic, P. and Tversky, A. (1974) "Who Accepts
Savage-s Axioms". Behavioral Science. 19, pp. 368-373.
[4]. Kahneman, Daniel and Tversky, Amos. (1979) "Prospect
Theory: An Analysis of Decisions under Risk".
Econometrica. 47 (2), pp. 263-291.
[5]. Einhorn, Hillel J. and Hogarth, Robin M. (1985)
"Ambuiguity and Uncertainty in Probabilistic Inference".
Psychological Review. 92. pp. 433-461.
[6]. Einhorn, Hillel J. and Hogarth, Robin M. (1986)
"Decision Making under Ambiguity". Journal of
Business. 59(4), pp. S225-S250.
[7]. Markowitz, H. M. (1952) "Portfolio Selection." Journal of
Finance. 7 (1). pp. 77-91.
[8]. Markowitz, H. M. (1959). Portfolio Selection, Efficient
Diversification of Investments. New York: John Wiley
and Sons, Inc.
[9]. Maller, R.A. and Turkington, D.A. (2003). "New Light on
the Portfolio Problem". Mathematical Methods of
Operations Research. 56(3), pp. 501-512.
[10]. Lim, Andrew and Zhou, Xun. (2002). "Mean-Variance
Portfolio Selection with Random Parameters in a
Complete Market". Mathematics of Operations Research.
27(1), pp. 101-120.
[11]. Kalyman, Basil. (1971) " Estimation Risk in Portfolio
Selection Model". Journal of Financial & Quantitative
Analysis. 6(1), pp. 559-582.
[12]. Gaivoronski, Alexei and De Lange, Petter. (2000). "An
Asset Liability Management Model for Casualty Insurers:
Complexity Reduction vs. Parameterized Decision Rules".
Annals of Operations Research. 99(1-4), pp. 227-250.
[13]. Goldfarb, D. and Iyengar, G. (2003). "Robust Portfolio
Selection Problems". Mathematics of Operations
Research. 28(1), pp. 1-39.
[14]. Pachamanova, Dessislava (2006). " Handling Parameter
Uncertainty in Portfolio Risk Minimization". Journal of
Portfolio Management 32(4), pp. 70-78.
[15].Faboozi, Frank, Kolm, Petter, Pachamanova, Dessislave,
Focardi, Sergio. (2007). "Robust Portfolio Optimization".
Journal of Portfolio Management, 33(3), pp. 40-48.
[16]. El Ghaoui, Laurent, Oks, Maksim, and Oustry, Francois.
(2003) "Worst-Case Value-At-Risk and Robust Portfolio
Optimization: A Conic Programming Approach".
Operations Research. 51(4) pp. 543-556.
[17]. Luciano, Elisa and Marena, Marina (2002) "Portfolio
Value at Risk Bounds". International Transactions in
Operational Research. 9, pp. 629-641.
[18]. Kozhan, Roman and Schmid, Wolfgang. (2009). "Asset
Allocation with Distorted Beliefs and Transaction Costs".
European Journal of Operational Research. 194 (1),
pp.236-249
[19]. Sharpe, W.F. (1963). "A Simplified Model for Portfolio
Analysis." Management Science. Pp. 277-293.
[20]. Grundke, Peter. (2009) "Importance Sampling for
Integrated Market and Credit Portfolio Models".
European Journal of Operational Research, 194 (1), pp.
206-226.
[21]. Balbás, Alejandro, Balbás, Raquel and Mayoral, Silvia
(2009). "Portfolio Choice and Optimal Hedging with
General Risk Functions: A Simplex-like algorithm".
European Journal of Operational Research. 192(2), pp.
603-620.
[22]. Teo, K.L. and Yang, X.Q. (2001). "Portfolio Selection
Problem with Minimax Type Risk Function". Annals of
Operations Research. 10(1-4), pp. 333-349.
[23]. Duval, Yann and Featherstone, Allen (2002).
"Interactivity and Soft Computing in Portfolio
Management: Should Farmers Own Food and
Agribusiness Stocks?" American Journal of Agriculture
Economics. 84 (1), pp. 120-133.
[24]. Khoshnevisan, Mohammad, Vimba, Edgars and
Bhattacharya, Sukanto (2007) "A Posited Fuzzy-
Evolutionary Computational Model to Minimize the
Tracking Error of an Option-Replicating Portfolio".
Journal of Derivations & Hedge Funds 13(3), pp. 214-219
[25]. Black, F. and Scholes, M. (1973). "The Pricing of
Options and Corporate Liabilities". Journal of Political
Economy 81(3), pp. 637-654.
[26]. Jain, R.(1977) "A Procedure for Multiple Aspects
Decision Making Using Fuzzy Sets." International Journal
of System Science, 8, pp. 1-7.
[27]. Dubois,D. and Prade, H. (1979) "Decision Making under
Fuzziness". Advances in Fuzzy Set Theory and
Applications.(M.Gupta, R.Ragade, R. Yager, eds.) North
Holland: Amsterdam.
[28]. Zebda, A. (1984) "The Investigation of Cost Variances:
A Fuzzy Set Theory Approach". Decision Sciences, 15,
pp. 359-388.
[29]. Zadeh, L. (1972). "A Rationale for Fuzzy Control".
ASME Journal of Dynamic Systems Measurement and
Control 94 Series G, pp. 3-4.
[30]. Mamdani, E. and Assilian, S. (1981). "An
Experimenting Linguistic Synthesis with A Fuzzy Logic
Controller". Fuzzy Reasoning and Its Applications,
E.Mamdani and B. Gaines, eds. (Academic Press), pp.
311-323.
[31]. Yasunobu, S. and Miyamoto, S. (1985). "Automatic
Train Operation System by Predictive Fuzzy Control".
Industrial Applications of Fuzzy Control, M. Sugeno, ed.
(North Holland), pp. 1-18.
[32]. Khoo, L., Yeong, H., and Tang, L. (1995).
"Application of Fuzzy Reasoning to A Surface Treatment
Process". Journal of Manufacturing Systems 14 (1), pp.
11-19.
[33]. Larkin, L. (1985). "A Fuzzy Logic Controller for
Aircraft Flight Control". Industrial Applications of Fuzzy
Control, M. Sugeno, ed. (North Holland), pp. 87-104.
[34]. Yagishta, O. Itoh, O., and Sugeno, M. (1990.
"Application of Fuzzy Reasoning to the Water
Purification Process". Industrial Applications of Fuzzy
Control, M. Sugeno, ed. (North Holland), pp. 19-40.
[35]. Sugeno, M. and Murakami, K. (1985). "An
Experimental Study on Fuzzy Parking Control Using A
Model Car". Industrial Applications of Fuzzy Control, M.
Sugeno, ed. (North Holland), pp. 19-40.
[36]. Yager, R. (1981). "A New Methodology for Ordinal
Multiobjective Decisions Based on Fuzzy Sets".
Decision Sciences . 12, pp. 589-600.
[37]. Shipley, M.F., Omer, K., and de Korvin, A. (1997) "A
Fuzzy Controller for Adjusting Sample Size to Meet
Quality Goals".Productivity and Quality Management
Frontiers. (C.G.Thor, J.A.Edosomwan, R. Poupart, D.J.
Sumanth, eds.), Norcross,Georgia: Engineering and
Management Press Institute of Industrial Engineers, VI,
501-513.
[1]. de Korvin, A., Strawser, J., and Siegel, P. (1995). "An
Application of Cost Control System to Cost Variance
Analysis". Managerial Finance 21 (3), pp. 17-35.
[2]. Ellsberg, Daniel. (1961) "Risk, Ambiguity and the Savage
Axioms". Quarterly Journal of Economics. 75(4), pp. 643-
669.
[3]. Slovic, P. and Tversky, A. (1974) "Who Accepts
Savage-s Axioms". Behavioral Science. 19, pp. 368-373.
[4]. Kahneman, Daniel and Tversky, Amos. (1979) "Prospect
Theory: An Analysis of Decisions under Risk".
Econometrica. 47 (2), pp. 263-291.
[5]. Einhorn, Hillel J. and Hogarth, Robin M. (1985)
"Ambuiguity and Uncertainty in Probabilistic Inference".
Psychological Review. 92. pp. 433-461.
[6]. Einhorn, Hillel J. and Hogarth, Robin M. (1986)
"Decision Making under Ambiguity". Journal of
Business. 59(4), pp. S225-S250.
[7]. Markowitz, H. M. (1952) "Portfolio Selection." Journal of
Finance. 7 (1). pp. 77-91.
[8]. Markowitz, H. M. (1959). Portfolio Selection, Efficient
Diversification of Investments. New York: John Wiley
and Sons, Inc.
[9]. Maller, R.A. and Turkington, D.A. (2003). "New Light on
the Portfolio Problem". Mathematical Methods of
Operations Research. 56(3), pp. 501-512.
[10]. Lim, Andrew and Zhou, Xun. (2002). "Mean-Variance
Portfolio Selection with Random Parameters in a
Complete Market". Mathematics of Operations Research.
27(1), pp. 101-120.
[11]. Kalyman, Basil. (1971) " Estimation Risk in Portfolio
Selection Model". Journal of Financial & Quantitative
Analysis. 6(1), pp. 559-582.
[12]. Gaivoronski, Alexei and De Lange, Petter. (2000). "An
Asset Liability Management Model for Casualty Insurers:
Complexity Reduction vs. Parameterized Decision Rules".
Annals of Operations Research. 99(1-4), pp. 227-250.
[13]. Goldfarb, D. and Iyengar, G. (2003). "Robust Portfolio
Selection Problems". Mathematics of Operations
Research. 28(1), pp. 1-39.
[14]. Pachamanova, Dessislava (2006). " Handling Parameter
Uncertainty in Portfolio Risk Minimization". Journal of
Portfolio Management 32(4), pp. 70-78.
[15].Faboozi, Frank, Kolm, Petter, Pachamanova, Dessislave,
Focardi, Sergio. (2007). "Robust Portfolio Optimization".
Journal of Portfolio Management, 33(3), pp. 40-48.
[16]. El Ghaoui, Laurent, Oks, Maksim, and Oustry, Francois.
(2003) "Worst-Case Value-At-Risk and Robust Portfolio
Optimization: A Conic Programming Approach".
Operations Research. 51(4) pp. 543-556.
[17]. Luciano, Elisa and Marena, Marina (2002) "Portfolio
Value at Risk Bounds". International Transactions in
Operational Research. 9, pp. 629-641.
[18]. Kozhan, Roman and Schmid, Wolfgang. (2009). "Asset
Allocation with Distorted Beliefs and Transaction Costs".
European Journal of Operational Research. 194 (1),
pp.236-249
[19]. Sharpe, W.F. (1963). "A Simplified Model for Portfolio
Analysis." Management Science. Pp. 277-293.
[20]. Grundke, Peter. (2009) "Importance Sampling for
Integrated Market and Credit Portfolio Models".
European Journal of Operational Research, 194 (1), pp.
206-226.
[21]. Balbás, Alejandro, Balbás, Raquel and Mayoral, Silvia
(2009). "Portfolio Choice and Optimal Hedging with
General Risk Functions: A Simplex-like algorithm".
European Journal of Operational Research. 192(2), pp.
603-620.
[22]. Teo, K.L. and Yang, X.Q. (2001). "Portfolio Selection
Problem with Minimax Type Risk Function". Annals of
Operations Research. 10(1-4), pp. 333-349.
[23]. Duval, Yann and Featherstone, Allen (2002).
"Interactivity and Soft Computing in Portfolio
Management: Should Farmers Own Food and
Agribusiness Stocks?" American Journal of Agriculture
Economics. 84 (1), pp. 120-133.
[24]. Khoshnevisan, Mohammad, Vimba, Edgars and
Bhattacharya, Sukanto (2007) "A Posited Fuzzy-
Evolutionary Computational Model to Minimize the
Tracking Error of an Option-Replicating Portfolio".
Journal of Derivations & Hedge Funds 13(3), pp. 214-219
[25]. Black, F. and Scholes, M. (1973). "The Pricing of
Options and Corporate Liabilities". Journal of Political
Economy 81(3), pp. 637-654.
[26]. Jain, R.(1977) "A Procedure for Multiple Aspects
Decision Making Using Fuzzy Sets." International Journal
of System Science, 8, pp. 1-7.
[27]. Dubois,D. and Prade, H. (1979) "Decision Making under
Fuzziness". Advances in Fuzzy Set Theory and
Applications.(M.Gupta, R.Ragade, R. Yager, eds.) North
Holland: Amsterdam.
[28]. Zebda, A. (1984) "The Investigation of Cost Variances:
A Fuzzy Set Theory Approach". Decision Sciences, 15,
pp. 359-388.
[29]. Zadeh, L. (1972). "A Rationale for Fuzzy Control".
ASME Journal of Dynamic Systems Measurement and
Control 94 Series G, pp. 3-4.
[30]. Mamdani, E. and Assilian, S. (1981). "An
Experimenting Linguistic Synthesis with A Fuzzy Logic
Controller". Fuzzy Reasoning and Its Applications,
E.Mamdani and B. Gaines, eds. (Academic Press), pp.
311-323.
[31]. Yasunobu, S. and Miyamoto, S. (1985). "Automatic
Train Operation System by Predictive Fuzzy Control".
Industrial Applications of Fuzzy Control, M. Sugeno, ed.
(North Holland), pp. 1-18.
[32]. Khoo, L., Yeong, H., and Tang, L. (1995).
"Application of Fuzzy Reasoning to A Surface Treatment
Process". Journal of Manufacturing Systems 14 (1), pp.
11-19.
[33]. Larkin, L. (1985). "A Fuzzy Logic Controller for
Aircraft Flight Control". Industrial Applications of Fuzzy
Control, M. Sugeno, ed. (North Holland), pp. 87-104.
[34]. Yagishta, O. Itoh, O., and Sugeno, M. (1990.
"Application of Fuzzy Reasoning to the Water
Purification Process". Industrial Applications of Fuzzy
Control, M. Sugeno, ed. (North Holland), pp. 19-40.
[35]. Sugeno, M. and Murakami, K. (1985). "An
Experimental Study on Fuzzy Parking Control Using A
Model Car". Industrial Applications of Fuzzy Control, M.
Sugeno, ed. (North Holland), pp. 19-40.
[36]. Yager, R. (1981). "A New Methodology for Ordinal
Multiobjective Decisions Based on Fuzzy Sets".
Decision Sciences . 12, pp. 589-600.
[37]. Shipley, M.F., Omer, K., and de Korvin, A. (1997) "A
Fuzzy Controller for Adjusting Sample Size to Meet
Quality Goals".Productivity and Quality Management
Frontiers. (C.G.Thor, J.A.Edosomwan, R. Poupart, D.J.
Sumanth, eds.), Norcross,Georgia: Engineering and
Management Press Institute of Industrial Engineers, VI,
501-513.
@article{"International Journal of Information, Control and Computer Sciences:58295", author = "Margaret F. Shipley", title = "Portfolio Management: A Fuzzy Set Based Approach to Monitoring Size to Maximize Return and Minimize Risk", abstract = "Fuzzy logic can be used when knowledge is
incomplete or when ambiguity of data exists. The purpose of
this paper is to propose a proactive fuzzy set- based model for
reacting to the risk inherent in investment activities relative to
a complete view of portfolio management. Fuzzy rules are
given where, depending on the antecedents, the portfolio size
may be slightly or significantly decreased or increased. The
decision maker considers acceptable bounds on the proportion
of acceptable risk and return. The Fuzzy Controller model
allows learning to be achieved as 1) the firing strength of each
rule is measured, 2) fuzzy output allows rules to be updated,
and 3) new actions are recommended as the system continues
to loop. An extension is given to the fuzzy controller that
evaluates potential financial loss before adjusting the
portfolio. An application is presented that illustrates the
algorithm and extension developed in the paper.", keywords = "Portfolio Management, Financial Market Monitoring,Fuzzy Controller, Fuzzy Logic,", volume = "3", number = "4", pages = "1098-8", }
