H. Konno and H. Yamazaki. Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Management Science, 37(5):519--531, May 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the portfolio optimization problem. This resulted in the consideration of various risk measures which were LP computable in the case of finite discrete random variables. Yitzhaki [27] introduced the mean risk model using the Gini s mean (absolute) difference as a risk measure. Konno and Yamazaki [11] analyzed the model where risk is measured by the (mean) absolute deviation. Young [28] considered the minimax approach (the worst case performances) to measure the risk. If the rates of return are multivariate normally distributed, then most of these models are equivalent to the Markowitz ....

H. Konno and H. Yamazaki, Mean--absolute deviation portfolio optimization model and its application to Tokyo stock market , Management Science, 37 (1991), pp. 519--531.

....is much harder to solve than a linearly constrained problem. As #(x) is the third moment #(x) divided by the variance # 2 (x) raised to the power 3 2 , maximizing the skewness tends to maximize the third moment while minimizing the variance. An alternative skewness model has been proposed [15, 16, 9] in which the absolute deviation of the return from the mean is used as a surrogate for the variance. Instead of maximizing the skewness their model maximizes the third moment, which simplifies the objective function. A quadratic constraint on the variance is replaced by a piecewise linear ....

Konno, H. and Yamazaki, H., Mean--Absolute Deviation Portfolio Optimization Model and its Application to Tokyo Stock Market, Management Science, 37, 1991, 519--531.

....Naert beslaegtet med: Chance constrained Programming : Laegger begraensninger pa risikoen (sandsynligheden) for uheldige haendelser [6] subject to Pf Tg ff hvor er for eksempel investeringstab. MAD modellen: Mean Absolute Deviation: Robust alternativ til varians som risikomal [13]. Min X i2U j r i Gamma E r j 1 Se http: www.jpmorgan.com RiskManagement 415.html Algoritmer for SP Direkte lsning: Mulig, men som regel ikke praktisk: SP er store og deres struktur er uvenlig for lsningsalgoritmer. Dekomposition: En oplagt mulighed, givet strukturen. Benders (eller ....

H. Konno and H. Yamazaki. Mean-absolute deviation portfolio optimization model and its applications to tokyo stock market. Mgmt. Sc., 37:519--531, 1991.

....mean 1 2 mean absolute deviation mean lower semi standard deviation 5 quantile Then we specify the investor s objective as max E (W ) E [jW E (W )j] where measures the degree of risk aversion. The mean absolute deviation is a good measure of the risk associated with the decision (see [18, 1, 29, 28, 31] for a review of properties of mean absolute deviation as a risk measure) The risk aversion factor allows to adapt the objective to the speci c views of the decision maker. Moreover, its preserves linearity: if the terminal wealth W is linear in the decision variables x, then the objective is a ....

H. Konno and H. Yamazaki. Mean absolute deviation portfolio optimization model and its applications to tokyo stock market. Management Science, 37:519531, 1991.

....contains expected wealth, but also takes into account the decision maker s risk aversion. We maximize E(W ) EjW E(W )j = X t2T p t W (t) X t2T p t W (t) X t2T p t W (t) 1) where 0 is a risk aversion factor to be determined by the decision maker (see [KY91] The whole problem is a large scale tree structured linear program. The terminal wealth E(W ) is a random variable. The objective (1) is only one of many possible statistical characteristics of it. The best way to get insight into this variable is to display its cumulative distribution function ....

H. Konno and H. Yamazaki. Mean absolute deviation portfolio optimization model and its applications to tokyo stock market. Management Science, 37:519531, 1991.

....In (5) 7) nonsmooth risk functions are used to guarantee a trade o# between profits and risks of underestimating losses and overestimating profits with substitution coe#cients # i , # j . These risk functions correspond to the Markovitz mean semivariance model [15] the Konno and Yamazaki model [13] with absolute deviations, and the S. Messner et al. dynamic energy model [16] In [19] it was shown that the use of absolute deviations with appropriate choice of risk coeeficients (similar to # i , # j ) is consistent with the stochastic dominance of random outcomes. The applicability of the ....

H.Konno, H.Yamazaki, Mean Absolute Deviation Portfolio Optimization Model and Its Application to Tokyo Stock Market, Management Science 37 (1991), 519-531.

....relations of degrees 1; k 1. Proof. By Theorem 1, x Gamma ffi (k) x y Gamma ffi (k) y ) y 6 (k 1) x: The implication y 6 (i 1) x ) y 6 (i) x, i = k; 1, completes the proof. 2 In the special case of k = 1 we conclude that the mean absolute deviation model of Konno and Yamazaki (1991) is 1 2 consistent with the first and second degree stochastic dominance. Indeed, the absolute deviation ffi (1) 2 ffi (1) and Theorem 2 implies the result. For k = 2 we see that the use of the central semideviation as the risk measure (instead of the variance in the Markowitz model) ....

Konno, H., H. Yamazaki (1991). Mean Absolute Deviation Portfolio Optimization Model and Its Application to Tokyo Stock Market, Management Science 37 519--531.

....the risk is measured by a variance from mean rate of return, thus resulting in a formulation of a quadratic programming model. Following Sharpe (1971) many 2 attempts have been made to linearize the portfolio optimization problem (c.f. Speranza, 1993 and references therein) Lately, Konno and Yamazaki (1991) proposed the MAD portfolio optimization model where risk is measured by (mean) absolute deviation instead of variance. The model is computationally attractive as (for discrete random variables) it results in solving linear programming (LP) problems. There is an argument that the variability of ....

....function. Despite the fact that problem (3) is seldom used as a tool for optimizing large portfolios, this model is widely recognized as a starting point for the MPT (c.f. Elton and Gruber, 1987) In an attempt to analyze reasons behind limited popularity of the Markowitz s model among investors, Konno and Yamazaki (1991) summarized its shortcomings as: a) a necessity to solve a large scale quadratic programming problem; 4 b) investor s reluctance to rely on variance as a measure of risk (Kroll at al. 1984) The Markowitz model is known to be valid (and consistent with the stochastic dominance) in the ....

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Konno, H., Yamazaki, H. (1991), "Mean--Absolute Deviation Portfolio Optimization Model and Its Application to Tokyo Stock Market", Management Science, 37, 519--531.

....of degrees 1; k 1. Proof. By Theorem 1, X Gamma ffi (k) X Y Gamma ffi (k) Y ) Y 6 (k 1) X: The implication Y 6 (i 1) X ) Y 6 (i) X, i = k; 1, completes the proof. 2 In the special case of k = 1 we conclude that the mean absolute deviation model of Konno and Yamazaki (1991) is 1 2 consistent with first and second degree stochastic dominance. Indeed, the absolute deviation satisfies ffi (1) 2 ffi (1) and Theorem 2 implies the result. For k = 2 we see that the use of the central semideviation as the risk measure (instead of the variance in the Markowitz ....

Konno, H., H. Yamazaki (1991). Mean Absolute Deviation Portfolio Optimization Model and Its Application to Tokyo Stock Market, Management Science 37 519--531.

....models using standard or absolute semideviations as risk measures are consistent with the stochastic dominance, if a bounded set of mean risk trade o#s is considered. In the portfolio selection context these models correspond to the Markowitz (1959,1987) mean semivariance model and the Konno and Yamazaki (1991) MAD model with absolute deviation. The paper is organized as follows. In the next section we recall the basics of the stochastic dominance and mean risk approaches. We also specify what we mean by consistency of these approaches. In Section 3 we introduce a convenient graphical tool for the ....

....distributions. For any # 0 there exist random variables x # SSD y such that x y and x (1 #) # x = y (1 #) # y . As an example one may consider two finite random variables: x defined as P x = 0 = 1 1 # , P x = 1 = # 1 # ; and y defined as P y = 0 = 1. Konno and Yamazaki (1991) introduced the portfolio selection model based on the # mean risk model. The model is very attractive computationally, since (for finite random variables) it leads to linear programming problems. Note that the absolute deviation # is a symmetric measure and the absolute semideviation # is ....

[Article contains additional citation context not shown here]

Konno, H., Yamazaki, H. (1991), "Mean Absolute Deviation Portfolio Optimization Model and Its Application to Tokyo Stock Market", Management Science, 37, 519--531.

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H. Konno and H. Yamazaki. Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Management Science, 37(5):519--531, May 1991.

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H. Konno and H. Yamazaki. Mean absolute deviation portfolio optimization model and its applications to tokyo stock market. Management Science, 37:519531, 1991.

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H. Konno and H. Yamazaki. Mean absolute deviation portfolio optimization model and its applications to tokyo stock market. Management Science, 37:519531, 1991.

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Konno, H., and H. Yamazaki (1991) "Mean Absolute Deviation Portfolio Optimization Model and Its Application to Tokyo Stock Market", Management Science, 37, 519--531.

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Konno, H., and A. Wijayanayake (1999) "Mean-Absolute Deviation Portfolio Optimization Model Under Transaction Costs", Journal of the Operations Research Society of Japan, 42 (4), 422--435.

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H. Konno and H. Yamazaki. Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Management Science, 37(5):519-531, 1991.

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Konno H., Yamazaki H. (1991): Mean Absolute Deviation Portfolio Optimization Model and its Applications to Tokyo Stock Market. Management Science 37, 519 -- 531 20

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Konno, H. and Yamazaki, H. (1991), Mean-absolute deviation portfolio optimization models and its applications to Tokyo stock market, Management Sciences, 37, pp.519-531.

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