Tractable Almost Stochastic Dominance

LL-Almost Stochastic Dominance (LL-ASD) is a relaxation of the Stochastic Dominance (SD) concept proposed by Leshno and Levy that explains more of realistic preferences observed in practice than SD alone does. Unfortunately, numerical applications of this concept, such as identifying if a given portfolio is efficient or determining a marketed portfolio that dominates a given benchmark, are computationally prohibitive due to the structure of LL-ASD. We propose a new Almost Stochastic Dominance (ASD) concept that is computationally tractable. For instance, a marketed dominating portfolio can be identified by solving a simple linear programming problem. Moreover, the new concept performs well on all the intuitive examples from the literature, and in some cases leads to more realistic predictions than the earlier concept. We develop some properties of ASD, formulate efficient optimization models, and apply the concept to analyzing investors’ preferences between bonds and stocks for the long run.     

Enhanced indexation based on second-order stochastic dominance

Second order Stochastic Dominance (SSD) has a well recognised importance in portfolio selection, since it provides a natural interpretation of the theory of risk-averse investor behaviour. Recently, SSD-based models of portfolio choice have been proposed; these assume that a reference distribution is available and a portfolio is constructed, whose return distribution dominates the reference distribution with respect to SSD. We present an empirical study which analyses the effectiveness of such strategies in the context of enhanced indexation. Several datasets, drawn from FTSE 100, SP 500 and Nikkei 225 are investigated through portfolio rebalancing and backtesting. Three main conclusions are drawn. First, the portfolios chosen by the SSD based models consistently outperformed the indices and the traditional index trackers. Secondly, the SSD based models do not require imposition of cardinality constraints since naturally a small number of stocks are selected. Thus, they do not present the computational difficulty normally associated with index tracking models. Finally, the SSD based models are robust with respect to small changes in the scenario set and little or no rebalancing is necessary.     

基于不确定性期望效用模型的投资优化

针对资产的收益的分布不确切知道,并且所获得的矩信息也不是准确值的问题,提出了最大化最坏情形期望效用的鲁棒性方法.引入了凹凸类效用函数来度量模型不确定情形下投资者的效用,用一个不确定性结构来刻画资产收益的所有可能的分布和收益的矩信息,通过把具有不确定性结构的鲁棒性模型转化成参数二次规划问题,得到了最优投资策略、有效前沿和均衡价格的解析表示.方法为采用保守策略并且厌恶不确定性的投资者提供了一种有效的投资决策方案.     

Asset pricing and portfolio selection based on the multivariate extended skew-Student-<Emphasis Type="Italic">t</Emphasis> distribution

The returns on most financial assets exhibit kurtosis and many also have probability distributions that possess skewness as well. In this paper a general multivariate model for the probability distribution of assets returns, which incorporates both kurtosis and skewness, is described. It is based on the multivariate extended skew-Student-t distribution. Salient features of the distribution are described and these are applied to the task of asset pricing. The paper shows that the market model is non-linear in general and that the sensitivity of asset returns to return on the market portfolio is not the same as the conventional beta, although this measure does arise in special cases. It is shown that the variance of asset returns is time varying and depends on the squared deviation of market portfolio return from its location parameter. The first order conditions for portfolio selection are described. Expected utility maximisers will select portfolios from an efficient surface, which is an analogue of the familiar mean-variance frontier, and which may be implemented using quadratic programming.     

Almost Stochastic Dominance and stocks for the long run

The geometric-mean argument and the recently developed Almost Stochastic Dominance criterion have been employed to make the case for “stocks for the long run”. We show that Almost Stochastic Dominance and the geometric-mean argument do not necessarily support long-run investment in equities. In fact, for standard preferences bonds may be preferred to stocks for the long run while stocks are preferred for shorter horizons.     

Linear-quadratic efficient frontiers for portfolio optimization

Finding portfolios with given mean return and minimal lower partial mean or variance, two risk criteria of interest in the theory of optimal portfolio selection, is a stochastic linear-quadratic program that can be converted to a large-scale linear or quadratic program when the asset returns are finitely distributed. These efficient frontiers can be computed on presently available platforms for problems of reasonable size; we discuss our experience with a problem involving one thousand assets. Asymptotic statistics for stochastic programs can be applied to justify sampling as a means to approximate continuous distributions by finite distributions.     

Statistical modelling of asymmetric risk in asset returns

The purpose of this article is to provide a straightforward model for asset returns which captures the fundamental asymmetry in upward versus downward returns. We model this feature by using scale gamma distributions for the conditional distributions of positive and negative returns. By allowing the parameters for positive returns to differ from parameters for negative returns we can test the hypothesis of symmetry. Some applications of this process to expected utility and semi-variance calculations are considered. Finally we estimate the model using daily UK FT100 index and Futures data.     

CED model for asset returns and fractal market hypothesis

A new general model for asset returns is studied in the framework of the Fractal Market Hypothesis (FMH). To accommodate markets with arbitrage opportunities, it concerns capital market systems in which the Conditionally Exponential Dependence (CED) property can be attached to each investor on the market. Employing the limit theorem for the CED systems, the universal characteristics for the distribution of asset returns are derived. This explains the special role of the Weibull distribution in modeling of global asset returns for market with no arbitrage and the two-power laws property of the density of global returns, evident in the empirical data. Finally, the link with two-parameter Pareto distributions is established.     

An asset return model capturing stylized facts

In this paper, we seek a model for asset returns which reproduces several well-documented stylized facts:1. log returns are not Gaussian; 2. absolute log returns are serially correlated, but the log returns are not; 3. the Taylor effect. There are many attempts to deal with the first, using various log-Lévy models for the asset; some of these are successful in fitting the unconditional distribution of log returns, but cannot of course reproduce the second stylized fact. We propose to model the returns with a hidden two-state Markovian regime (as in J Appl Econ 13:217–244, 1998), conditional on the value of which the returns have different distributions. A key observation is that if the means of the returns in the different regimes are the same, then the log returns are automatically uncorrelated, so we fit to index data under this restriction. By choosing symmetric hyperbolic distributions for the conditional returns, we are able to fit well the unconditional distributions, the autocovariances of absolute returns and the Taylor effect. Moreover, we find that a common regime model explains simultaneously these statistics for the S&P500, FTSE, DAX, Nikkei and CAC40. Implications for investment and option pricing are discussed.     

Stable distributions and the term structure of interest rates

In an abundance of cases asset returns fit stable distributions better than normal distributions. We examine a model where the term structure of interest rates follows a subordinate process directed by a stable process and indicate how to fix the parameters of the model.     

Scaling issues for risky asset modelling

In this paper we investigate scaling properties of risky asset returns and make a strong case (1) against the need for multifractal models and (2) in favor of the requirement of heavy tailed distributions. Amongst the standard empirical properties of risky asset returns are an autocorrelation function for the returns which dies away rapidly and is statistically insignificant beyond a few lags, and also autocorrelation functions of squares and absolute values of returns which die away very slowly, persisting over years, or even decades. Together these indicate that, assuming returns come from a stationary process, they are not independent, but at most short-range dependent, while various functions of the returns are long-range dependent. These scaling properties are well known, although commonly ignored for modeling convenience. However, much more can be inferred from the scaling properties of the returns. It turns out that the empirical scaling functions are initially linear and ultimately concave, which is strongly suggestive of returns distributions with infinite low order moments or alternatively that multifractal behavior is a modeling requirement. Modifications of the commonly used models cannot readily meet these requirements. The evidence will be presented and its significance discussed, along with a class of models which can incorporate the empirically observed features.     

Robust portfolio optimization with derivative insurance guarantees

Robust portfolio optimization aims to maximize the worst-case portfolio return given that the asset returns are allowed to vary within a prescribed uncertainty set. If the uncertainty set is not too large, the resulting portfolio performs well under normal market conditions. However, its performance may substantially degrade in the presence of market crashes, that is, if the asset returns materialize far outside of the uncertainty set. We propose a novel robust optimization model for designing portfolios that include European-style options. This model trades off weak and strong guarantees on the worst-case portfolio return. The weak guarantee applies as long as the asset returns are realized within the prescribed uncertainty set, while the strong guarantee applies for all possible asset returns. The resulting model constitutes a convex second-order cone program, which is amenable to efficient numerical solution procedures. We evaluate the model using simulated and empirical backtests and analyze the impact of the insurance guarantees on the portfolio performance.     

Portfolio management with background risk under uncertain mean-variance utility

This paper studies comparative static effects in a portfolio selection problem when the investor has mean-variance preferences. Since the security market is complex, there exists the situation where security returns are given by experts’ estimates when they cannot be reflected by historical data. This paper discusses the problem in such a situation. Based on uncertainty theory, the paper first establishes an uncertain mean-variance utility model, in which security returns and background asset returns are uncertain variables and subject to normal uncertainty distributions. Then, the effects of changes in mean and standard deviation of uncertain background asset on capital allocation are discussed. Furthermore, the influence of initial proportion in background asset on portfolio investment decisions is analyzed when investors have quadratic mean-variance utility function. Finally, the economic analysis illustration of investment strategy is presented.

     

A tail-revisited Markowitz mean-variance approach and a portfolio network centrality

A measure for portfolio risk management is proposed by extending the Markowitz mean-variance approach to include the left-hand tail effects of asset returns. Two risk dimensions are captured: asset covariance risk along risk in left-hand tail similarity and volatility. The key ingredient is an informative set on the left-hand tail distributions of asset returns obtained by an adaptive clustering procedure. This set allows a left tail similarity and left tail volatility to be defined, thereby providing a definition for the left-tail-covariance-like matrix. The convex combination of the two covariance matrices generates a “two-dimensional” risk that, when applied to portfolio selection, provides a measure of its systemic vulnerability due to the asset centrality. This is done by simply associating a suitable node-weighted network with the portfolio. Higher values of this risk indicate an asset allocation suffering from too much exposure to volatile assets whose return dynamics behave too similarly in left-hand tail distributions and/or co-movements, as well as being too connected to each other. Minimizing these combined risks reduces losses and increases profits, with a low variability in the profit and loss distribution. The portfolio selection compares favorably with some competing approaches. An empirical analysis is made using exchange traded fund prices over the period January 2006–February 2018.

     

Esscher transforms and consumption-based models

The Esscher transform is an important tool in actuarial science. Since the pioneering work of Gerber and Shiu (1994), the use of the Esscher transform for option valuation has also been investigated extensively. However, the relationships between the asset pricing model based on the Esscher transform and some fundamental equilibrium-based asset pricing models, such as consumption-based models, have so far not been well-explored. In this paper, we attempt to bridge the gap between consumption-based models and asset pricing models based on Esscher-type transformations in a discrete-time setting. Based on certain assumptions for the distributions of asset returns, changes in aggregate consumptions and returns on the market portfolio, we construct pricing measures that are consistent with those arising from Esscher-type transformations. Explicit relationships between the market price of risk, and the risk preference parameters are derived for some particular cases.     

Representative Agent Pricing of Financial Assets Based on L��vy Processes with Normal Inverse Gaussian Marginals

The aim of the paper is to test the assumption of normal inverse Gaussian returns from speculative investments. We construct an asset pricing model where price processes are pure jump processes having associated returns with marginal distributions of this particular type. The resulting model is not complete, and we employ a partial equilibrium framework with a representative agent. The model is confronted with some stylized facts, like the equity premium puzzle, and the results seem promising.     

Fitting asset returns to skewed distributions: Are the skew-normal and skew-student good models?

Vernic (2006), Bolancé et al. (2008), and Eling (2012) identify the skew-normal and skew-student as promising models for describing actuarial loss data. In this paper, we change the focus from the liability to the asset side and ask whether these distributions are also useful for analyzing the investment returns of insurance companies. To answer this question, we fit various parametric distributions to capital market data which has been used to describe the investment set of insurance companies. Our results show that the skew-student is an especially promising distribution for modeling asset returns such as those of stocks, bonds, money market instruments, and hedge funds. Combining the results of Vernic (2006), Bolancé et al. (2008), Eling (2012), and this paper, it appears that the skew-student is a promising actuarial tool since it describes both sides of the insurer’s balance sheet reasonably well.     

Investment models based on clustered scenario trees

Stochastic programming is widely applied in financial decision problems. In particular, when we need to carry out the actual calculations for portfolio selection problems, we have to assign a value for each expected return and the associated conditional probability in advance. These estimated random parameters often rely on a scenario tree representing the distribution of the underlying asset returns. One of the drawbacks is that the estimated parameters may be deviated from the actual ones. Therefore, robustness is considered so as to cope with the issue of parameter inaccuracy. In view of this, we propose a clustered scenario-tree approach, which accommodates the parameter inaccuracy problem in the context of a scenario tree.     

Mean–variance asset–liability management with asset correlation risk and insurance liabilities

Consider an insurer who invests in the financial market where correlations among risky asset returns are randomly changing over time. The insurer who faces the risk of paying stochastic insurance claims needs to manage her asset and liability by taking into account of the correlation risk. This paper investigates the impact of correlation risk to the optimal asset–liability management (ALM) of an insurer. We employ the Wishart process to model the stochastic covariance matrix of risky asset returns. The insurer aims to minimize the variance of the terminal wealth given an expected terminal wealth subject to the risk of paying out random liabilities of compound Poisson process. This ALM problem then becomes a linear–quadratic stochastic optimal control problem with stochastic volatilities, stochastic correlations and jumps. The recognition of an affine form in the solution process enables us to derive the explicit closed-form solution to the optimal ALM portfolio policy, obtain the efficient frontier, and identify the condition that the solution is well behaved.     

选择资产组合的EP-MV模型及最优解的解析表示

本文提出了存在无风险资产贷出或借入时的有效投资组合模型(EP-MV模型)，研究了不允许卖空(投资比例非负)约束条件下，EP-MV优化模型的算法，给出了有效投资组合投资比例的解析表示．在资产收益由多因素模型产生的基础上，得到了资产与有效投资组合的期望收益及风险的估计，便于实际应用．