Portfolio selection and skewness: Evidence from international stock markets

This paper finds that the returns of the world's 14 major stock markets are not normally distributed, and that the correlation matrix of these stock markets was stable during the January 1988–December 1993 time period. Polynomial goal programming, in which investor preferences for skewness can be incorporated, is utilized to determine the optimal portfolio consisting of the choices of 14 international stock indexes. The empirical findings suggest that the incorporation of skewness into an investor's portfolio decision causes a major change in the construction of the optimal portfolio. The evidence also indicate that investors trade expected return of the portfolio for skewness.     

Portfolio selection with skewness: A multiple-objective approach

In the presence of skewness, the portfolio selection entails considering competing and conflicting objectives, such as maximizing both its expected returns and skewness, and minimizing its risk for decreasing absolute risk-aversion investors. Since it is unlikely that a portfolio can solve the multiple-objectives problem simultaneously, a portfolio selection must depend on the investor's preference among objectives. This article shows that investor preference can be incorporated into a polynomial goal programming problem from which a portfolio selection with skewness is determined. An inefficient mean-variance portfolio may be optimal in the mean-variance-skewness content. The features of applying polynomial goal programming in portfolio selection are 1) the existence of an optimal solution, 2) the flexibility of the incorporation of investor preference, and 3) the relative simplicity of computational requirements.     

The Effect of Shortfall as a Risk Measure for Portfolios with Hedge Funds

Abstract:  Current research suggests that the large downside risk in hedge fund returns disqualifies the variance as an appropriate risk measure. For example, one can easily construct portfolios with nonlinear pay-offs that have both a high Sharpe ratio and a high downside risk. This paper examines the consequences of shortfall-based risk measures in the context of portfolio optimization. In contrast to popular belief, we show that negative skewness for optimal mean-shortfall portfolios can be much greater than for mean-variance portfolios. Using empirical hedge fund return data we show that the optimal mean-shortfall portfolio substantially reduces the probability of small shortfalls at the expense of an increased extreme crash probability. We explain this by proving analytically under what conditions short-put payoffs are optimal for a mean-shortfall investor. Finally, we show that quadratic shortfall or semivariance is less prone to these problems. This suggests that the precise choice of the downside risk measure is highly relevant for optimal portfolio construction under loss averse preferences.     

Performance Evaluation,Portfolio Selection,and HARA Utility

Absract

The main goal of this work is the generalization of the approach of Jobson and Korkie for funds performance evaluation. Therefore, the paper considers the portfolio selection problem of an investor who faces short sales restrictions when choosing among F different investment funds and assumes the investor’s utility function to be of the HARA type. A performance measure is developed and its relationship to previously proposed measures is discussed. Particular attention is given to the special case of cubic utility implying skewness preferences. Findings are illustrated by an empirical example.     

Portfolio choice with skewness preference and wealth-dependent risk aversion

This paper studies a dynamic portfolio choice problem for an investor with both wealth-dependent risk aversion and wealth-dependent skewness preferences. In a general economic setting, the solution is characterized in terms of a system of extended Hamilton-Jacobi-Bellman (EHJB) equations and the solution is given in closed form in some special cases. We demonstrate the effects of higher order risk preferences and state-dependent risk aversion on the optimal asset allocation decisions. We find that wealth-dependent risk aversion facilitates risk taking and the skewness preference leads to a more positively skewed portfolio in certain circumstances.     

“KLICing” there and back again: Portfolio selection using the empirical likelihood divergence and Hellinger distance

Stutzer (2000, 2003) proposes the decay-rate maximizing portfolio selection rule wherein the investor selects the asset mix that maximizes the rate at which the probability of shortfall decays to zero. A close examination of this rule reveals that it ranks portfolios by computing the divergence, in the Kullback-Leibler sense, between the unweighted portfolio return distribution and a tilted distribution meaned at the predetermined target or benchmark rate of return selected by or imposed upon the investor. This result implies, in the IID case, that Stutzer's rules can be written as a benchmark constrained Kullback-Leibler-based optimization problem with an endogenous utility interpretation. Here we expand on this idea by introducing two closely related portfolio selection rules based on the empirical likelihood divergence and the Hellinger-Matusita distance. The first of these is the reversed Kullback-Leibler divergence and the second is proportional to the average of the two divergences. The theoretical and in-sample properties of the new criteria suggest them to be competitive with and in some cases better than existing methods, especially in terms of skewness preference.     

Multivariate Shrinkage for Optimal Portfolio Weights

Abstract

This paper proposes a multivariate shrinkage estimator for the optimal portfolio weights. The estimated classical Markowitz weights are shrunk to the deterministic target portfolio weights. Assuming log asset returns to be i.i.d. Gaussian, explicit solutions are derived for the optimal shrinkage factors. The properties of the estimated shrinkage weights are investigated both analytically and using Monte Carlo simulations. The empirical study compares the competing portfolio selection approaches. Both simulation and empirical studies show that the proposed shrinkage estimator is robust and provides significant gains to the investor compared to benchmark procedures.     

Performance analysis of a collateralized fund obligation (CFO) equity tranche

This article examines the performance of the junior tranche of a collateralized fund obligation (CFO), i.e. the residual claim (equity) on a securitized portfolio of hedge funds. We use a polynomial goal programming model to create optimal portfolios of hedge funds, conditional to investor preferences and diversification constraints (maximum allocation per strategy). For each portfolio, we build CFO structures that have different levels of leverage, and analyze both the stand-alone performance as well as potential diversification benefits (low systematic risk exposures) of investing in the equity tranche of these structures. We find that the unconstrained mean-variance portfolio yields a high performance, but greater exposure to systematic risk. We observe the exact opposite picture in the case of unconstrained optimization, where a skewness bias is added, thus proving the existence of a trade-off between stand-alone performance and low exposure to systematic risk factors. We provide evidence that leveraged exposure to these hedge fund portfolios through the structuring of CFOs creates value for the equity tranche investor, even during the recent financial crisis.     

Robustness of the inference procedures for the global minimum variance portfolio weights in a skew-normal model

In this paper, we study the influence of skewness on the distributional properties of the estimated weights of optimal portfolios and on the corresponding inference procedures derived for the optimal portfolio weights assuming that the asset returns are normally distributed. It is shown that even a simple form of skewness in the asset returns can dramatically influence the performance of the test on the structure of the global minimum variance portfolio. The results obtained can be applied in the small sample case as well. Moreover, we introduce an estimation procedure for the parameters of the skew-normal distribution that is based on the modified method of moments. A goodness-of-fit test for the matrix variate closed skew-normal distribution has also been derived. In the empirical study, we apply our results to real data of several stocks included in the Dow Jones index.     

Investment decisions when utility depends on wealth and other attributes

The problem of optimal investment under a multivariate utility function allows for an investor to obtain utility not only from wealth, but other (possibly correlated) attributes. In this paper we implement multivariate mixtures of exponential (mixex) utility to address this problem. These utility functions allow for stochastic risk aversions to differing states of the world. We derive some new results for certainty equivalence in this context. By specifying different distributions for stochastic risk aversions, we are able to derive many known, plus several new utility functions, including models of conditional certainty equivalence and multivariate generalisations of HARA utility, which we call dependent HARA utility. Focusing on the case of asset returns and attributes being multivariate normal, we optimise the asset portfolio, and find that the optimal portfolio consists of the Markowitz portfolio and hedging portfolios. We provide an empirical illustration for an investor with a mixex utility function of wealth and sentiment.     

On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation

Recent studies in the empirical finance literature have reportedevidence of two types of asymmetries in the joint distributionof stock returns. The first is skewness in the distributionof individual stock returns. The second is an asymmetry in thedependence between stocks: stock returns appear to be more highlycorrelated during market downturns than during market upturns.In this article we examine the economic and statistical significanceof these asymmetries for asset allocation decisions in an out-of-samplesetting. We consider the problem of a constant relative riskaversion (CRRA) investor allocating wealth between the risk-freeasset, a small-cap portfolio, and a large-cap portfolio. Weuse models that can capture time-varying moments up to the fourthorder, and we use copula theory to construct models of the time-varyingdependence structure that allow for different dependence duringbear markets than bull markets. The importance of these twoasymmetries for asset allocation is assessed by comparing theperformance of a portfolio based on a normal distribution modelwith a portfolio based on a more flexible distribution model.For investors with no short-sales constraints, we find thatknowledge of higher moments and asymmetric dependence leadsto gains that are economically significant and statisticallysignificant in some cases. For short sales-constrained investorsthe gains are limited.     

Optimal Bond Portfolio for Investors with Long Time Horizons

We study the optimal bond portfolio for an investor with long time horizonusing Japanese interest rate data. A simple one-factor term structure modelis used for our numerical example. The optimal portfolio is computed using thetechnique of stochastic flows and Monte Carlo simulation. The hedgingportfolio is not negligible and the mean variance portfolio is very sensitiveto parameter values. The optimal portfolio is highly leveraged for a typicalparameter value. The investor holds a zero-coupon bond because of the lowerbound restriction on investor's wealth. The lower bound constraint may makethe optimal portfolio more realistic.     

m-Double Poisson Lévy markets

We develop novel mispricing of markets under asymmetric information and jumps for informed and uninformed investors, called m-Double Poisson markets, driven by independent Double Poisson processes. In the special case m?=?1, called the Double Poisson pure-jump Lévy market, both types of investors hold the same optimal portfolio and expected utility, and hence, the informed investor has no utility advantage over the uninformed. For the general market, instantaneous centralized moments of returns are used to compute optimal portfolios and utilities. The mean, variance, skewness and kurtosis of instantaneous returns are reported using jump amplitudes and frequencies.     

IPO first‐day returns: Skewness preference,investor sentiment and uncertainty underlying factors

In this paper, we investigate the initial public offering (IPO) first-day returns. Our focus is to examine the irrational component of the agent behavior towards IPO lotteries. Based on 234 French IPOs performed between 2002 and 2012, we find that IPOs with high initial returns have higher idiosyncratic skewness, turnover and momentum. This finding provides empirical evidence for investors' preference for stocks with lottery-like features and investor sentiment. In addition, we show that the skewness preference and the investor sentiment effect are stronger during periods of favorable market conditions. Our results are robust to the integration of uncertainty underlying factors.     

International asset allocation under regime switching, skew, and kurtosis preferences

This paper investigates the international asset allocation effectsof time-variations in higher-order moments of stock returnssuch as skewness and kurtosis. In the context of a four-momentInternational Capital Asset Pricing Model (ICAPM) specificationthat relates stock returns in five regions to returns on a globalmarket portfolio and allows for time-varying prices of covariance,co-skewness, and co-kurtosis risk, we find evidence of distinctbull and bear regimes. Ignoring such regimes, an unhedged USinvestor's optimal portfolio is strongly diversified internationally.The presence of regimes in the return distribution leads toa substantial increase in the investor's optimal holdings ofUS stocks, as does the introduction of skewness and kurtosispreferences.     

An Empirical Analysis on Log-Utility Asset Management

In this paper, we empirically verify the optimal portfolio schemes for the log-utility investor under incomplete information which converge to the optimal portfolio maximizing the expected log-utility under complete information. That is, our main interest lies in examining whether these schemes really attain the above desired properties, in the NYSE/AMEX stock market. With these properties regarded as performance measures, our empirical research is executed through a sensitivity analysis with transaction costs. Moreover, we show the interesting character of the U.S. stock market exhibited through the analysis.     

Portfolio management with stochastic interest rates and inflation ambiguity

We solve, in closed form, a stock-bond-cash portfolio problem of a risk- and ambiguity-averse investor when interest rates and the inflation rate are stochastic. The expected inflation rate is unobservable, but the investor can learn about it from observing realized inflation and stock and bond prices. The investor is ambiguous about the inflation model and prefers a portfolio strategy which is robust to model misspecification. Ambiguity about the inflation dynamics is shown to affect the optimal portfolio fundamentally different than ambiguity about the price dynamics of traded assets, for example the optimal portfolio weights can be increasing in the degree of ambiguity aversion. In a numerical example, the optimal portfolio is significantly affected by the learning about expected inflation and somewhat affected by ambiguity aversion. The welfare loss from ignoring learning or ambiguity can be considerable.     

Monthly Pattern and Portfolio Effect on Higher Moments of Stock Returns: Empirical Evidence from Hong Kong

Using a direct test, this paper studies the month-of-the-year effect on the higher moments of six industrial stock indices of the Hong Kong market. We also examine the portfolio effect on skewness and kurtosis across month of the year to see if such an anomaly exists. The empirical results support a weak month-of-the-year effect in higher moments of stock returns. Using a complete sample of all possible combinations for each portfolio size, we show that portfolio effect varies across month of the year for both skewness and kurtosis. In particular, our results show that diversification does not necessarily provide benefits to rational investors when the stock return distribution is non-normal, even though portfolio formation can reduce standard deviation. In June, August and October, diversification across industrial sectors results in a more negatively skewed and leptokurtic return distribution, which is not preferred by investors with risk-aversion. Two (one) possible explanations for the portfolio effect on skewness (kurtosis) are also provided. Our empirical results add new evidence to the existence of anomalies in the Hong Kong stock market. This revised version was published online in August 2006 with corrections to the Cover Date.     

OPTIMAL PORTFOLIO SELECTION WITH A SHORTFALL PROBABILITY CONSTRAINT: EVIDENCE FROM ALTERNATIVE DISTRIBUTION FUNCTIONS

We propose a new approach to optimal portfolio selection in a downside risk framework that allocates assets by maximizing expected return subject to a shortfall probability constraint, reflecting the typical desire of a risk-averse investor to limit the maximum likely loss. Our empirical results indicate that the loss-averse portfolio outperforms the widely used mean-variance approach based on the cumulative cash values, geometric mean returns, and average risk-adjusted returns. We also evaluate the relative performance of the loss-averse portfolio with normal, symmetric thin-tailed, symmetric fat-tailed, and skewed fat-tailed return distributions in terms of average return, risk, and average risk-adjusted return.     

A Benchmark Approach to Portfolio Optimization under Partial Information

This paper proposes a filtering methodology for portfolio optimization when some factors of the underlying model are only partially observed. The level of information is given by the observed quantities that are here supposed to be the primary securities and empirical log-price covariations. For a given level of information we determine the growth optimal portfolio, identify locally optimal portfolios that are located on a corresponding Markowitz efficient frontier and present an approach for expected utility maximization. We also present an expected utility indifference pricing approach under partial information for the pricing of nonreplicable contracts. This results in a real world pricing formula under partial information that turns out to be independent of the subjective utility of the investor and for which an equivalent risk neutral probability measure need not exist.