Implied Ambiguity: Mean-Variance Inefficiency and Pricing Errors

2021 ◽  
Author(s):  
Chiaki Hara ◽  
Toshiki Honda
Keyword(s):  
Portfolio Choice ◽  
Ambiguity Aversion ◽  
Sufficient Conditions ◽  
Asset Returns ◽  
Sharpe Ratio ◽  
Choice Problem ◽  
Pricing Errors ◽  
Necessary And Sufficient ◽  
Mean Variance ◽  
The U.S

We investigate the optimal portfolio choice problem for an investor who has a utility function of the smooth ambiguity model. We identify necessary and sufficient conditions for a given portfolio to be optimal for such an investor. We define the implied ambiguity of a portfolio as the smallest ambiguity aversion coefficient with which the portfolio is optimal, and the measure of ambiguity perception as the part of the variability in asset returns that can be attributed to the ambiguity. We show that there are one-to-one relations between the implied ambiguity, the Sharpe ratio, and the pricing errors when the portfolio is taken as the pricing portfolio, and that the measure of ambiguity perception is determined by the Sharpe ratio and the alpha. Based on the U.S. stock market data, we assess how ambiguity averse the representative investor is and what types of stocks the investor perceives as having more ambiguous returns than others. This paper was accepted by Manel Baucells, behavioral economics and decision analysis.

AMBIGUITY AND PORTFOLIO INERTIA

2002 ◽  
Vol 05 (08) ◽  
pp. 785-795
Author(s):  
MARCELLO BASILI ◽  
FULVIO FONTINI
Keyword(s):  
Portfolio Choice ◽  
Expected Utility ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Specific Structure ◽  
Choice Problem ◽  
Choquet Expected Utility ◽  
Necessary And Sufficient

In this paper the Portfolio Choice problem is studied under ambiguity, formalized by means of the Choquet Expected Utility. Agents are supposed to be Choquet Expected Utility maximizers and are split into two categories: optimists, who hold a concave capacity, and pessimists, who hold a convex one. Portfolio inertia is defined and analyzed. Necessary and sufficient conditions are established between a specific structure of agents' beliefs, namely belief commonality, and Portfolio Inertia.

Justifying Mean-Variance Portfolio Selection when Asset Returns Are Skewed

2021 ◽  
Author(s):  
Frank Schuhmacher ◽  
Hendrik Kohrs ◽  
Benjamin R. Auer
Keyword(s):  
Empirical Evidence ◽  
Sufficient Conditions ◽  
Asset Returns ◽  
Common Belief ◽  
Risky Assets ◽  
Common Stocks ◽  
Elliptical Model ◽  
Mean And Variance ◽  
Mean Variance Portfolio ◽  
Mean Variance

We show that, in the presence of a risk-free asset, the return distribution of every portfolio is determined by its mean and variance if and only if asset returns follow a specific skew-elliptical distribution. Thus, contrary to common belief among academics and practitioners, skewed returns do not allow a rejection of mean-variance analysis. Our work differs from Chamberlain's [Chamberlain G (1983) A characterization of the distributions that imply mean-variance utility functions. J. Econom. Theory 29(1):185–201.] by focusing on the returns of portfolios, where the weights over the risk-free asset and the risky assets sum to unity. Furthermore, it extends Meyer's [Meyer J, Rasche RH (1992) Sufficient conditions for expected utility to imply mean-standard deviation rankings: Empirical evidence concerning the location and scale condition. Econom. J. (London) 102(410):91–106.] by introducing elliptical noise into their generalized location-scale framework. To emphasize the relevance of our skew-elliptical model, we additionally provide empirical evidence that it cannot be rejected for the returns of typical portfolios of common stocks or popular alternative investments. This paper was accepted by Kay Giesecke, finance.

scholarly journals Influence Of Membership Function’s Shape On Portfolio Optimization Results

2016 ◽  
Vol 6 (1) ◽  
pp. 45-54 ◽  
Author(s):  
Aleksandra Rutkowska
Keyword(s):  
Portfolio Optimization ◽  
Value At Risk ◽  
Optimization Problems ◽  
Selection Process ◽  
Sufficient Conditions ◽  
Credibility Measure ◽  
Risk Minimization ◽  
Different Shapes ◽  
Necessary And Sufficient ◽  
Mean Variance

Abstract Portfolio optimization, one of the most rapidly growing field of modern finance, is selection process, by which investor chooses the proportion of different securities and other assets to held. This paper studies the influence of membership function’s shape on the result of fuzzy portfolio optimization and focused on portfolio selection problem based on credibility measure. Four different shapes of the membership function are examined in the context of the most popular optimization problems: mean-variance, mean-semivariance, entropy minimization, value-at-risk minimization. The analysis takes into account both: the study of necessary and sufficient conditions for the existence of extremes, as well as the statistical inference about the differences based on simulation.

Optimal Portfolio Choice with Estimation Risk: No Risk-Free Asset Case

2021 ◽  
Author(s):  
Raymond Kan ◽  
Xiaolu Wang ◽  
Guofu Zhou
Keyword(s):  
Portfolio Choice ◽  
Exact Distribution ◽  
Optimal Portfolio ◽  
Portfolio Construction ◽  
Estimation Risk ◽  
Choice Problem ◽  
Out Of Sample ◽  
Mean Variance Portfolio ◽  
Mean Variance ◽  
Explicit Expressions

We propose an optimal combining strategy to mitigate estimation risk for the popular mean-variance portfolio choice problem in the case without a risk-free asset. We find that our strategy performs well in general, and it can be applied to known estimated rules and the resulting new rules outperform the original ones. We further obtain the exact distribution of the out-of-sample returns and explicit expressions of the expected out-of-sample utilities of the combining strategy, providing not only a fast and accurate way of evaluating the performance, but also analytical insights into the portfolio construction. This paper was accepted by Tyler Shumway, finance.

scholarly journals Integral stochastic ordering of the multivariate normal mean-variance and the skew-normal scale-shape mixture models

2020 ◽  
Vol 8 (1) ◽  
pp. 1-16
Author(s):  
Dariush Jamali ◽  
Mehdi Amiri ◽  
Ahad Jamalizadeh ◽  
N. Balakrishnan
Keyword(s):  
Sufficient Conditions ◽  
Stochastic Ordering ◽  
Multivariate Normal ◽  
Multivariate Normal Mean ◽  
Normal Mean ◽  
Stop Loss ◽  
Necessary And Sufficient ◽  
Mean Variance ◽  
Normal Scale ◽  
Skew Normal

‎In this paper‎, ‎we introduce integral stochastic ordering of two‎ most important classes of distributions that are commonly used to fit data possessing high values of skewness and (or)‎ ‎kurtosis‎. ‎The first one is based on the selection distributions started by the univariate skew-normal distribution‎. ‎A broad‎, ‎flexible and newest class in this area is the scale and shape mixture of multivariate skew-normal distributions‎. ‎The second one is the general class of Normal Mean-Variance Mixture distributions‎. ‎We then derive necessary and sufficient conditions for comparing the random vectors from these two classes of distributions‎. ‎The integral orders considered here are the usual‎, ‎concordance‎, ‎supermodular‎, ‎convex‎, ‎increasing convex and directionally convex stochastic orders‎. ‎Moreover‎, ‎for bivariate random vectors‎, ‎in the sense of stop-loss and bivariate concordance stochastic orders‎, ‎the dependence strength of random portfolios is characterized in terms of order of correlations‎.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Budgeting in Socio-economic Development Strategies (Raising a Problem)

2008 ◽  
pp. 134-151
Author(s):  
A. Shastitko ◽  
M. Ovchinnikov
Keyword(s):  
Economic Policy ◽  
Economic Development ◽  
Social Change ◽  
Eastern Europe ◽  
Statistical Data ◽  
Sufficient Conditions ◽  
Transitional Period ◽  
Socio Economic Development ◽  
Necessary And Sufficient ◽  
Economic Development Strategies

The article proposes an approach to the analysis of social change and contributes to the clarification of concepts of economic policy. It deals in particular with the notion of "change of system". The author considers positive and normative aspects of the analysis of capitalist and socialist systems. The necessary and sufficient conditions for the system to be changed are introduced, their fulfillment is discussed drawing upon the historical and statistical data. The article describes both economic and political peculiarities of the transitional period in different countries, especially in Eastern Europe.

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