An empirical analysis of marginal conditional stochastic dominance

Stochastic dominance is a more general approach to expected utility maximization than the widely accepted mean–variance analysis. However, when applied to portfolios of assets, stochastic dominance rules become too complicated for meaningful empirical analysis, and, thus, its practical relevance has been difficult to establish. This paper develops a framework based on the concept of Marginal Conditional Stochastic Dominance (MCSD), introduced by Shalit and Yitzhaki (1994), to test for the first time the relationship between second order stochastic dominance (SSD) and stock returns. We find evidence that MCSD is a significant determinant of stock returns. Our results are robust with respect to the most popular pricing models.     

How does beta explain stochastic dominance efficiency?

Stochastic dominance rules provide necessary and sufficient conditions for characterizing efficient portfolios that suit all expected utility maximizers. For the finance practitioner, though, these conditions are not easy to apply or interpret. Portfolio selection models like the mean–variance model offer intuitive investment rules that are easy to understand, as they are based on parameters of risk and return. We present stochastic dominance rules for portfolio choices that can be interpreted in terms of simple financial concepts of systematic risk and mean return. Stochastic dominance is expressed in terms of Lorenz curves, and systematic risk is expressed in terms of Gini. To accommodate for risk aversion differentials across investors, we expand the conditions using the extended Gini.     

The Impact of Sampling Errors on the Choice of Portfolio Efficiency Analysis Rules with Borrowing and Lending of a Riskless Asset

This paper evaluates the impact of sampling errors on portfolio decisions using mean-variance and stochastic dominance rules where riskless borrowing and lending opportunities exist. The paper establishes criteria for comparing the alternative decision rules (for example, mean variance versus stochastic dominance) according to their effectiveness and the cost (in sampling error terms). Normal distributions are simulated using various assumed means, standard deviations, correlations, and sample sizes. These simulations enable one to evaluate the impact of sampling errors on the potential effectiveness of the empirical stochastic dominance and mean variance rules that include borrowing and lending of a riskless asset.     

Almost marginal conditional stochastic dominance

Marginal Conditional Stochastic Dominance (MCSD) developed by Shalit and Yitzhaki (1994) gives the conditions under which all risk-averse individuals prefer to increase the share of one risky asset over another in a given portfolio. In this paper, we extend this concept to provide conditions under which most (and not all) risk-averse investors behave in this way. Instead of stochastic dominance rules, almost stochastic dominance is used to assess the superiority of one asset over another in a given portfolio. Switching from MCSD to Almost MCSD (AMCSD) helps to reconcile common practices in asset allocation and the decision rules supporting stochastic dominance relations. A financial application is further provided to demonstrate that using AMCSD can indeed improve investment efficiency.     

Portfolio Selection in Stochastic Environments

In this article, I explicitly solve dynamic portfolio choiceproblems, up to the solution of an ordinary differential equation(ODE), when the asset returns are quadratic and the agent hasa constant relative risk aversion (CRRA) coefficient. My solutionincludes as special cases many existing explicit solutions ofdynamic portfolio choice problems. I also present three applicationsthat are not in the literature. Application 1 is the bond portfolioselection problem when bond returns are described by "quadraticterm structure models." Application 2 is the stock portfolioselection problem when stock return volatility is stochasticas in Heston model. Application 3 is a bond and stock portfolioselection problem when the interest rate is stochastic and stockreturns display stochastic volatility. (JEL G11)     

Downside risk and asset pricing

We analyze if the value-weighted stock market portfolio is stochastic dominance (SD) efficient relative to benchmark portfolios formed on size, value, and momentum. In the process, we also develop several methodological improvements to the existing tests for SD efficiency. Interestingly, the market portfolio seems third-order SD (TSD) efficient relative to all benchmark sets. By contrast, the market portfolio is inefficient if we replace the TSD criterion with the traditional mean–variance criterion. Combined these results suggest that the mean–variance inefficiency of the market portfolio is caused by the omission of return moments other than variance. Especially downside risk seems to be important for explaining the high average returns of small/value/winner stocks.     

Mean–variance portfolio selection with ‘at-risk’ constraints and discrete distributions

We examine the impact of adding either a VaR or a CVaR constraint to the mean–variance model when security returns are assumed to have a discrete distribution with finitely many jump points. Three main results are obtained. First, portfolios on the VaR-constrained boundary exhibit (K + 2)-fund separation, where K is the number of states for which the portfolios suffer losses equal to the VaR bound. Second, portfolios on the CVaR-constrained boundary exhibit (K + 3)-fund separation, where K is the number of states for which the portfolios suffer losses equal to their VaRs. Third, an example illustrates that while the VaR of the CVaR-constrained optimal portfolio is close to that of the VaR-constrained optimal portfolio, the CVaR of the former is notably smaller than that of the latter. This result suggests that a CVaR constraint is more effective than a VaR constraint to curtail large losses in the mean–variance model.     

Bootstrapping a distance test for stochastic dominance analysis

A major impediment to measuring portfolio performance under stochastic dominance has been the lack of test statistics for orders of stochastic dominance above first degree. In this article, the Bootstrap method, introduced by Efron (1979), is used to estimate critical values for distance statistics in order to test the null hypothesis of no dominance, under second- and third-degree stochastic dominance, for several samples of stock returns. These test statistics, suggested by Whitmore (1978), are analogous to the Kolmogorov-Smirnov distance statistics that can be used to test for first-degree stochastic dominance. Stochastic dominance is shown to accurately assess portfolio performance of sample distributions when the population distributions are controlled and Bootstrap statistics are employed in the analysis. In addition, second- and third-degree stochastic dominance analysis of the smallfirm January anomaly indicates that, over the 23-year time period 1964 to 1986, small firms statistically dominate a diversified market index in only one calendar year.     

Portfolio selection with mental accounts and background risk

Das et al. (2010) develop a model where an investor divides his or her wealth among mental accounts with motives such as retirement and bequest. Nevertheless, the investor ends up selecting portfolios within mental accounts and an aggregate portfolio that lie on the mean–variance frontier. Importantly, they assume that the investor only faces portfolio risk. In practice, however, many individuals also face background risk. Accordingly, our paper expands upon theirs by considering the case where the investor faces background risk. Our contribution is threefold. First, we provide an analytical characterization of the existence and composition of the optimal portfolios within accounts and the aggregate portfolio. Second, we show that these portfolios lie away from the mean–variance frontier under fairly general conditions. Third, we find that the composition and location of such portfolios can differ notably from those of portfolios on the mean–variance frontier.     

Farmland Investment Under Conditions of Certainty and Uncertainty

This study investigates the potential for farmland to improve mixed-asset portfolio efficiency. Three major conclusions are drawn from the research. First, in a world with certainty, farmland can be shown to statistically improve mixed-asset portfolio efficiency. Second, with the introduction of uncertainty into the portfolio allocation model, investors can justify small or no allocations of farmland in a mixed-asset portfolio, although it appears that even with uncertainty prudent investors should evaluate the asset class. Third, with respect to farmland investment and geographic diversification, the results question the ability of an optimized mean–variance portfolio to provide substantial improvement in comparison to a naïve portfolio. The marginal improvement in portfolio efficiency of an optimized farmland portfolio versus a naïve farmland portfolio is not statistically significant.     

Is gold good for portfolio diversification? A stochastic dominance analysis of the Paris stock exchange

This paper aims to assess the role of gold quoted in Paris in the diversification of French portfolios from 1949 to 2012 using the stochastic dominance (SD) approach. The principal advantage of this method is that there is no restriction on the distribution of the returns. Our results show that stock portfolios including gold stochastically dominate those without gold at the second and third orders. This implies that risk-averse investors would be better off by including gold in their stock portfolios to maximize their expected utilities. The study on sub-periods shows that this result holds especially in unstable or crisis times. However, these results do not hold for bond or risk-free portfolios, for which the portfolios without gold dominate those with gold. To check the robustness of our results, our SD analysis of a mixed portfolio (50% stocks, 30% bonds and 20% the risk-free asset) provides results similar to those for portfolios with stocks only, except from 1971 to 1983. Portfolios including gold quoted in London show results similar to those from Paris. The results of mean–variance performance measures confirm the findings of previous studies that gold is good for the diversification of stock portfolios but not for bond portfolios.     

Optimal dealer pricing under transactions and return uncertainty

The paper examines the optimal behavior of a single dealer who is faced with a stochastic demand to trade (modeled by a continuous time Poisson jump process) and facing return risk on his stock and on the rest of his portfolio (modeled by diffusion processes). Using stochastic dynamic programming, we derive the optimal bid and ask prices that maximize the dealer's expected utility of terminal wealth as a function of the state in which he finds himself. The relationship of the bid and ask prices to inventory of the dealer, instantaneous variance of return, stochastic arrival of transactions and other variables is examined.     

International portfolio selection with exchange rate risk: A behavioural portfolio theory perspective

This paper analyzes international portfolio selection with exchange rate risk based on behavioural portfolio theory (BPT). We characterize the conditions under which the BPT problem with a single foreign market has an optimal solution, and show that the optimal portfolio contains the traditional mean–variance efficient portfolio without consideration of exchange rate risk, and an uncorrelated component constructed to hedge against exchange rate risk. We illustrate that the optimal portfolio must be mean–variance efficient with exchange rate risk, while the same is not true from the perspective of local investors unless certain conditions are satisfied. We further establish that international portfolio selection in the BPT with multiple foreign markets consists of two sequential decisions. Investors first select the optimal BPT portfolio in each market, overlooking covariances among markets, and then allocate funds across markets according to a specific rule to achieve mean–variance efficiency or to minimize the loss in efficiency.     

International portfolio selection and efficiency analysis

In the risk-return tradeoff, the traditional mean-variance analysis has been widely used for studies of international portfolio efficiency and diversification. Without prior knowledge about either the parametric structure of assets' return distributions or the form of investors' preference functions, the variance may no longer serve as a suitable risk proxy. This article examines international portfolio efficiency and diversification effects through mean-variance and various distribution-free (or less restrictive) risk-return measures. We show empirically that the mean-variance model is appropriate for large or well-diversified portfolios, but may provide biased results for single assets and less diversified portfolios. While stochastic dominance stands as theoretically the most appropriate method of international portfolio selection and efficiency analysis, the lack of optimal search algorithms reduces its practical usefulness. Very little gain is obtained by using the Gini-mean-difference risk measure as compared to the semivariance measure. The semivariance measure is a powerful and convenient discriminator of risky prospects, while stochastic dominance can serve as a benchmark to justify portfolio efficiency.     

Diversification in euro area stock markets: Country versus industry

The harmonization of fiscal and economic policy within the European Monetary Union (EMU) has had a considerable impact on the economies of member countries. In particular, several studies indicate that the proceeding economic integration among euro area countries has important consequences for the factors driving asset returns in financial markets. However, these studies rely on one specific methodology [Heston, S.L., Rouwenhorst, K.G., 1994. Does industrial structure explain the benefits of international diversification? Journal of Financial Economics 36, 3–27; Heston, S.L., Rouwenhorst, K.G., 1995. Industry and country effects in international stock returns. Journal of Portfolio Management Spring, 53–58], that has recently been criticized as too restrictive. This study adopts a mean–variance approach instead. Using recent euro area stock markets data, we find strong evidence that diversification over industries yields more efficient portfolios than diversification over countries.     

An analysis of portfolio selection with background risk

This paper investigates the impact of background risk on an investor’s portfolio choice in a mean–variance framework, and analyzes the properties of efficient portfolios as well as the investor’s hedging behaviour in the presence of background risk. Our model implies that the efficient portfolio with background risk can be separated into two independent components: the traditional mean–variance efficient portfolio, and a self-financing component constructed to hedge against background risk. Our analysis also shows that the presence of background risk shifts the efficient frontier of financial assets to the right with no changes in its shape. Moreover, both the composition of the hedge portfolio and the location of the efficient frontier are greatly affected by a number of background risk factors, including the proportion of background assets in total wealth and the correlation between background risk and financial risk.     

HARA utility maximization in a Markov-switching bond–stock market

We present a flexible multidimensional bond–stock model incorporating regime switching, a stochastic short rate and further stochastic factors, such as stochastic asset covariance. In this framework we consider an investor whose risk preferences are characterized by the hyperbolic absolute risk-aversion utility function and solve the problem of optimizing the expected utility from her terminal wealth. For the optimal portfolio we obtain a constant-proportion portfolio insurance-type strategy with a Markov-switching stochastic multiplier and prove that it assures a lower bound on the terminal wealth. Explicit and easy-to-use verification theorems are proven. Furthermore, we apply the results to a specific model. We estimate the model parameters and test the performance of the derived optimal strategy using real data. The influence of the investor’s risk preferences and the model parameters on the portfolio is studied in detail. A comparison to the results with the power utility function is also provided.     

Capital market equilibrium with heterogeneous investors

As a two-parameter model that satisfies stochastic dominance, the mean-extended Gini model is used to build efficient portfolios. The model quantifies risk aversion heterogeneity in capital markets. In a simple Edgeworth box framework, we show how capital market equilibrium is achieved for risky assets. This approach provides a richer basis for analysing the pricing of risky assets under heterogeneous preferences. Our main results are: (1) identical investors, who use the same statistic to represent risk, hold identical portfolios of risky assets equal to the market portfolio; and (2) heterogeneous investors as expressed by the variance or the extended Gini hold different risky assets in portfolios, and therefore no one holds the market portfolio.     

Strategic International Diversification and Monthly Seasonality

To the author's knowledge no other studies have dealt with the effect of international diversification on stock market monthly seasonality. The aim of this study is to investigate this effect in various ways: stock market monthly seasonality is analyzed by incorporating exchange rates and trading costs in international portfolio returns. The variance of the world portfolio is decomposed into six components. Stochastic dominance approach is used to show the robustness of the results. Five trading strategies are compared to help international investors be more informed. All the results show that monthly seasonality is clearly present in an economic sense and robust. Particularly, when exchange rates are incorporated into portfolio returns. January has the highest return and the lowest risk in the world portfolio.     

Refining the bootstrap method of stochastic dominance analysis: The case of the January effect

This study investigates the effect of sample size and population distribution on the bootstrap estimated sampling distributions for stochastic dominance (SD) test statistics. Bootstrap critical values for Whitmore's (1978) second- and third-degree stochastic dominance test statistics are found to vary with both data sample size and variance of the population distribution. The results indicate the parametric nature of the statistics and suggest that the bootstrap method should be used to estimate a sampling distribution each time a new data sample is drawn. As an application of the bootstrap method, the January small firm effect is examined. The results conflict with the SD results of others, and indicate that not all investors would prefer to hold just a portfolio of small capitalization firms in January.