Black-Litterman model with multiple experts’ linguistic views. (English) Zbl 1422.62013
Ferraro, Maria Brigida (ed.) et al., Soft methods for data science. Selected papers based on the presentations at the 8th international conference on soft methods in probability and statistics, SMPS 2016, Rome, Italy, September 12–14, 2016. Cham: Springer. Adv. Intell. Syst. Comput. 456, 35-43 (2017).
Summary: This paper presents fuzzy extensions of the Black-Litterman portfolio selection model. Black and Litterman identified two sources of information about expected returns and combined these two sources of information into one expected return formula. The first source of information is the expected returns that follow from the capital asset pricing model and thus should hold if the market is in equilibrium. The second source of information is comprised of the views held by investors. The presented extension, owing to the use of fuzzy random variables, includes two elements that are important from the point of view of practice: linguistic information and the views of multiple experts. The paper introduces the model extension step-by-step and presents an empirical example.
For the entire collection see [Zbl 1355.62005].
For the entire collection see [Zbl 1355.62005].
MSC:
| 62-07 | Data analysis (statistics) (MSC2010) |
| 62B86 | Statistical aspects of fuzziness, sufficiency, and information |
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
| 62P20 | Applications of statistics to economics |
Keywords:
Black-Litterman model; fuzzy extensions; portfolio selection model; capital asset pricing model; market; random variables; model extensionReferences:
| [1] | Bevan A, Winkelmann K (1998) Using the Black-Litterman global asset allocation model: three years of practical experience, Goldman, Sachs & Company |
| [2] | Black F (1972) Capital market equilibrium with restricted borrowing. J Bus 45(3):444–455 · doi:10.1086/295472 |
| [3] | Black F, Litterman R (1990) Asset allocation: combining investors views with market equilibrium. Fixed Income Research, Goldman, Sachs & Company |
| [4] | Black F, Litterman R (1991) Global asset allocation with equities, bonds and currencies, Goldman, Sachs & Company |
| [5] | Black F, Litterman R (1992) Global portfolio optimization. Financ Anal J, 28–43 · doi:10.2469/faj.v48.n5.28 |
| [6] | Couso I, Dubois D (2009) On the variability of the concept of variance for fuzzy random variables. IEEE Trans Fuzzy Syst 5(17):1070–1080 · doi:10.1109/TFUZZ.2009.2021617 |
| [7] | Feng Y, Hu L, Shu H (2001) The variance and covariance of fuzzy random variables and their applications. Fuzzy Sets Syst 120:487–497 · Zbl 0984.60029 · doi:10.1016/S0165-0114(99)00060-3 |
| [8] | Gharakhani M, Sadjadi S (2013) A fuzzy compromise programming approach for the Black-Litterman portfolio selection model. Decis Sci Lett 1(2):11–22 · doi:10.5267/j.dsl.2012.12.001 |
| [9] | Gil M, Lopex-Diz M, Ralescu D (2006) Overview on the development of fuzzy random variables. Fuzzy Sets Syst 157:2546–2557 · Zbl 1108.60006 · doi:10.1016/j.fss.2006.05.002 |
| [10] | He G, Litterman R (1999) The intuition behind Black-Litterman model portfolios, Goldman, Sachs & Company |
| [11] | Huynh V-N, Nakamori Y (2005) Multi-expert decision-making with linguistic information: a probabilistic-based model. IEEE, Hawaii |
| [12] | Kacprzyk J, Orlovski S (2013) Optimization models using fuzzy sets and possibility theory. Springer, Netherlands · Zbl 0619.00013 |
| [13] | Krätschmer V (2001) A unified approach to fuzzy variables. Fuzzy Sets Syst 123:1–9 · Zbl 1004.60003 · doi:10.1016/S0165-0114(00)00038-5 |
| [14] | Kruse R, Meyer KD (1987) Statistic with vague data. Reidel Publishing Company · doi:10.1007/978-94-009-3943-1 |
| [15] | Kwakernaak H (1989) Fuzzy random variables. definition and theorems. Inf Sci 15:1–29 · Zbl 0438.60004 · doi:10.1016/0020-0255(78)90019-1 |
| [16] | Lawrence K, Pai DR, Klimberg RK, Lawrence SM (2009) A fuzzy programming approach to financial portfolio model. Financial Modeling Applications and Data Envelopment Applications 53 · doi:10.1108/S0276-8976(2009)0000013005 |
| [17] | Lintner J (1965) The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Rev Econ Stat 47(1):12–37 · doi:10.2307/1924119 |
| [18] | Litterman R, the Quantitative Resources Group (2003) Modern investment management: an equilibrium approach. John Wiley & Sons, New Jersey |
| [19] | Markowitz HM (1952) Portfolio selection. J Financ 7(1):77–91 |
| [20] | Meucci A (2008) The Black-Litterman approach: original model and extensions. http://ssrn.com/abstract=1117574 · doi:10.2139/ssrn.1117574 |
| [21] | Noor-E-Alama M, Ferdousi Lipi T, Ahsan Akhtar Hasin M, Ullah A (2011) Algorithms for fuzzy multi expert multi criteria decision making (ME-MCDM). Knowledge-Based Systems, April, 367–377 · doi:10.1016/j.knosys.2010.10.006 |
| [22] | Puri ML (1986) Fuzzy random variables. J Math Anal Appl 114:409–422 · Zbl 0592.60004 · doi:10.1016/0022-247X(86)90093-4 |
| [23] | Sharpe W (1964) Capital asset prices: a theory of market equilibrium under conditions of risk. J Financ 19(3):425–442 |
| [24] | Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning–I. Inf Sci 8:199–249 · Zbl 0397.68071 · doi:10.1016/0020-0255(75)90036-5 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
