Octave Jokung

Mean-Variance-Skewness Portfolio Performance Gauging: A General Shortage Function and Dual Approach

This paper proposes a nonparametric efficiency measurement approach for the static portfolio selection problem in mean-variance-skewness space. A shortage function is defined that looks for possible increases in return and skewness and decreases in variance. Global optimality is guaranteed for the resulting optimal portfolios. We also establish a link to a proper indirect mean-variance-skewness utility function. For computational reasons, the optimal portfolios resulting from this dual approach are only locally optimal. This framework permits to differentiate between portfolio efficiency and allocative efficiency, and a convexity efficiency component related to the difference between the primal, nonconvex approach and the dual, convex approach. Furthermore, in principle, information can be retrieved about the revealed risk aversion and prudence of investors. An empirical section on a small sample of assets serves as an illustration.

Making inefficient market indices efficient

The concept of efficient portfolios plays an important role in modern financial theory and practice. Although there is an extensive and growing literature that focuses on testing portfolio efficiency, outside of mean-variance optimization, which has several serious shortcomings, no systematic methodology for building efficient portfolios from inefficient indices has been developed. This paper addresses this issue. It uses the concept of Marginal Conditional Stochastic Dominance and a generalization of the 50% Portfolio Rule to develop a tractable and parsimonious methodology for constructing an efficient portfolio from a given, inefficient index. Because the Stochastic Dominance (SD) approach considers the entire probability distributions of asset returns, the resulting portfolios are efficient with respect to all risk-averse, non-satiable investors regardless of the form of their utility functions or the distributions of asset returns.

Risk Apportionment Via Bivariate Stochastic Dominance

This paper extends to bivariate utility functions, Eeckhoudt et al.’s (2009) result for the combination of ‘bad’ and ‘good’. The decision-maker prefers to get some of the ‘good’ and some of the ‘bad’ to taking a chance on all the ‘good’ or all the ‘bad’ where ‘bad’ is defined via (N,M)-increasing concave order. We generalize the concept of bivariate risk aversion introduced by Richard (1975) to higher orders. Importantly, in the bivariate framework, preference for the lottery [(X,T);(Y,Z)] to the lottery [(X,Z);(Y,T)] when (X,Z) dominates (Y,T) via (N,M)-increasing concave order allows us to assert bivariate risk apportionment of order (N,M) and to extend the concept of risk apportionment defined by Eeckhoudt and Schlesinger (2006).

Risk Aversion, Wealth and International Capital Flows

This paper models capital flows in a rich-poor, two-country, two-asset, dual-risk economy with decreasing absolute risk aversion. The first risk is asset-specific. The second is political and dependent; i.e., related to particular asset outcomes. In this framework, the role of wealth in determining asset preferences is demonstrated, and the conditions for diversification are derived. The wealth effect and diversification conditions are applied to explain ongoing two-way capital flows in general as well as the apparent paradox of domestic capital flight with simultaneous inflows of foreign capital. Copyright 1998 by Blackwell Publishing Ltd.

Non-Differentiable Transformations Preserving Stochastic Dominance

In this paper, we solve the following problem: when does a stochastic improvement in one risk maintain itself under a non everywhere continuously differentiable transformation of this risk? Using the notion of divided differences, we show that stochastic dominance at the third (and higher) order, and sometimes at the second one, is not preserved after simple piecewise linear transformation of the initial risk. Our analysis complements the one that exists for everywhere continuously differentiable transformations.

Long-term health investment when people underestimate their adaptation to old age-related health problems

This paper explores in a two-period model the economic implications of people’s tendency to underestimate their ability to adapt to age-related health problems. We model this misperception by assuming that the individual underestimates his future subjective health. Under standard assumptions, we show that, when people allocate their resources during their youth between present consumption, savings, and health investment, they invest more in health as long as the magnitude of the cross-marginal utility of health and consumption is not too negative.

Change in Bivariate Risk and Asset Prices

This paper analyzes the effect on the price of the risky asset of both global and marginal changes in dependent or independent exogenous and endogenous risks. Global changes induce riskier behavior and decrease market price when the utility function exhibits generalized relative risk aversions less than their benchmark values. Marginal changes in the endogenous risk decrease the market price when all the coefficients of generalized relative risk aversion to the endogenous risk are less than their orders. Marginal changes in the exogenous risk decrease the price of the risky asset when all the coefficients of generalized risk aversion to the exogenous risk are less than one. Positive dependence induces a decrease in the market price whereas negative dependence causes an increase in the same price. Increasing the correlation of the two risks leads to the fall in the price of the risky asset when the utility function of the representative investor exhibits pair-wise risk aversion. We recover the results concerning the univariate framework with additive background risk.

The role of population and wealth in international capital flows

Purpose – Seeks to analyze the role of population and wealth in determining capital movements between countries. Design/methodology/approach – By applying the Clark-Jokung 50 percent portfolio theorem, considers the specific case of a two country world where the cumulative conditional expected outcome on the asset in one country is greater than or equal to that in the other country. Findings – Specifically, lower population and wealth ratios (poor/rich) increase net capital flows to the poor country. Originality/value – So far most of the literature on cross-border capital flows has generally neglected the role of population and underestimated the role of wealth. This study addresses the gaps left by these deficiencies.

Portfolio Rules for Conditional Stochastic Dominance: Applications to the Elliptical Distributions

In this paper we generalize the Clark-Jokung 50% portfolio theorem(Management Science, 1999) to an arbitrary threshold and we apply it to a wide and well-known family of distributions, the elliptical distributions (multivariate normal, Student t, multivariate exponential,...). We consider the specific case of a two-asset portfolio where the cumulative conditional expected outcome on one asset is greater or equal to the cumulative conditional expected outcome of the other asset.We show that when the joint distribution of the returns of the two assets follows an elliptical distribution, the conditions for 100alpha% portfolio theorem to hold are a higher expected return for the dominant asset and that the threshold 100alpha% is less than the percentage invested in the minimum-variance portfolio.