New concepts and algorithms for portfolio choice

The paper studies the design of optimal (bond) portfolios taking into account various possible utility functions of an investor. The most prominent model for portfolio optimization was introduced by Markowitz. A real solution in this model can be achieved by quadratic programming routines for mean-variance analysis. Of course, there are many reasons for an investor to prefer other utility criteria than return/variance of return in the Markowitz model. In the last few years, many efficient multiple purpose optimization heuristics have been invented for the needs in optimizing telephone nets, chip layouts, job shop scheduling etc. Some of these heuristics have essential advantages: they are extremely flexible and very easy to implement on computers. One example of such an algorithm is the threshold-accepting algorithm (TA). TA is able to optimize portfolios under nearby arbitrary constraints and subject to nearly every utility function. In particular, the utility functions need neither to be convex, differentiable nor ‘smooth’ in any sense. We implemented TA for bond portfolio optimization with different utility criteria. The algorithms and computational results are presented. Under various utility functions, the ‘best’ portfolios look surprisingly different and have quite different qualities. Thus, for a portfolio manager it might be useful to provide himself with such a ‘multiple-taste’ optimizer in order to be able easily to readjust it according to his own personal utility considerations.     

The opportunity cost of mean–variance choice under estimation risk

Mean–variance portfolio choice is often criticized as sub-optimal in the more general expected utility framework. It is argued that the expected utility framework takes into consideration higher moments ignored by mean variance analysis. A body of research suggests that mean–variance choice, though arguably sub-optimal, provides very close-to-expected utility maximizing portfolios and their expected utilities, basing its evaluation on in-sample analysis where mean–variance choice is sub-optimal by definition. In order to clarify this existing research, this study provides a framework that allows comparing in-sample and out-of-sample performance of the mean variance portfolios against expected utility maximizing portfolios. Our in-sample results confirm the results of earlier studies. On the other hand, our out-of-sample results show that the expected utility model performs worse. The out-of-sample inferiority of the expected utility model is more pronounced for preferences and constraints under which in-sample mean variance approximations are weakest. We argue that, in addition to its elegance and simplicity, the mean–variance model extracts more information from sample data because it uses the covariance matrix of returns. The expected utility model may reach its optimal solution without using information from the covariance matrix.     

Portfolio optimization based on downside risk: a mean-semivariance efficient frontier from Dow Jones blue chips

To create efficient funds appealing to a sector of bank clients, the objective of minimizing downside risk is relevant to managers of funds offered by the banks. In this paper, a case focusing on this objective is developed. More precisely, the scope and purpose of the paper is to apply the mean-semivariance efficient frontier model, which is a recent approach to portfolio selection of stocks when the investor is especially interested in the constrained minimization of downside risk measured by the portfolio semivariance. Concerning the opportunity set and observation period, the mean-semivariance efficient frontier model is applied to an actual case of portfolio choice from Dow Jones stocks with daily prices observed over the period 2005–2009. From these daily prices, time series of returns (capital gains weekly computed) are obtained as a piece of basic information. Diversification constraints are established so that each portfolio weight cannot exceed 5 per cent. The results show significant differences between the portfolios obtained by mean-semivariance efficient frontier model and those portfolios of equal expected returns obtained by classical Markowitz mean-variance efficient frontier model. Precise comparisons between them are made, leading to the conclusion that the results are consistent with the objective of reflecting downside risk.     

Optimal portfolio strategies benchmarking the stock market

The paper investigates the impact of adding a shortfall risk constraint to the problem of a portfolio manager who wishes to maximize his utility from the portfolios terminal wealth. Since portfolio managers are often evaluated relative to benchmarks which depend on the stock market we capture risk management considerations by allowing a prespecified risk of falling short such a benchmark. This risk is measured by the expected loss in utility. Using the Black–Scholes model of a complete financial market and applying martingale methods, explicit analytic expressions for the optimal terminal wealth and the optimal portfolio strategies are given. Numerical examples illustrate the analytic results.     

均值-CVaR零售商的供应链服务决策及协调契约

研究零售商具有风险偏好行为下,同时考虑价格、质量和服务水平的供应链联合决策问题。运用均值-CVaR准则来刻画零售商风险偏好行为,它包括风险厌恶、风险中性和风险追求,同时具有损失规避的特性。首先得到供应链集中系统、制造商提供服务（模型$\mbox{I}$）和零售商提供服务（模型$\mbox{II}$）下的最优决策和最优利润（期望效用）。其次,证明了成本共担契约在零售商风险厌恶时可以实现供应链协调.第三,对模型$\mbox{I}$和模型$\mbox{II}$协调后的最优利润（期望效用）进行比较,证明两种模型下制造商利润相同,而与模型$\mbox{I}$相比,模型$\mbox{II}$下零售商获得更多的期望效用。最后,数值例子证明了得到的研究结果。     

Regulatory capital decisions in the Context of consumer loan portfolios

A topic of interest in recent literature is regulatory capital requirements for consumer loan portfolios. Banks are required to hold regulatory capital for unexpected losses, while expected losses are to be covered by either provisions or future income. In this paper, we show the set of efficient operating points in the market share and profit space for a portfolio manager operating under Basel II capital requirement and under capital constraints are a union of single-cutoff-score and double-cutoff-score operating points. For a portfolio manager to increase market-share beyond the maximum allowable under a single-cutoff score policy (eg, with binding capital constraints) requires granting loans to higher than optimal risk applicants. We show this result in greater portfolio risk but without an increase in regulatory capital requirement amount. The increase in forecasted losses is assumed to be absorbed by provisions or future margin income. Given portfolio managers take on higher risk under the same regulatory capital amount, our findings call for greater focus on provision amounts and future margin income under the supervisory review pillar of Basel II. This research raises the issue of whether the design of the regulatory formula for consumer loan portfolios is flawed.     

随机模糊的等比例-最小方差投资组合优化研究

Markowitz的均值-方差模型在投资组合优化中得到了广泛的运用和拓展,其中多数拓展模型仅局限于对随机投资组合或模糊投资组合的研究,而忽略了实际问题同时包含了随机信息和模糊信息两个方面。本文首先定义随机模糊变量的方差用以度量投资组合的风险,提出具有阀值约束的最小方差随机模糊投资组合模型,基于随机模糊理论,将该模型转化为具有线性等式和不等式约束的凸二次规划问题。为了提高上述模型的有效性,本文以投资者期望效用最大化为压缩目标对投资组合权重进行压缩,构建等比例-最小方差混合的随机模糊投资组合模型,并求解该模型的最优解。最后,运用滚动实际数据的方法,比较上述两个模型的夏普比率以验证其有效性。     

Effects of risk aversion and decision preference on equilibriums in supply chain finance incorporating bank credit with credit guarantee

We constructed a Stackelberg game in a supply chain finance (SCF) system including a manufacturer, a capital‐constrained retailer, and a bank that provides loans on the basis of the manufacturer's credit guarantee. To emphasize the financial service providers' risks, we assumed that both the bank and the manufacturer are risk‐averse and formulated trade‐off objective functions for both of them as the convex combination of the expected profit and conditional value‐at‐risk. To explore the effects of the risk preferences and decision preferences on SCF equilibriums, we mathematically analyzed the optimal order quantities, wholesale prices, and interest rates under different risk preference scenarios and performed numerical analyses to quantify the effects. We found that incorporating bank credit with a credit guarantee can effectively balance the retailer's financing risk between the bank and the manufacturer through interest rate charging and wholesale pricing. Moreover, SCF equilibriums with risk aversion are highly affected by the degree of both the lender's and guarantor's risk tolerance in regard to the borrower's default probability and will be more conservative than those in the risk‐neutral cases that only maximize expected profit.     

Optimal Investment in a Levy Market

In this paper we consider the optimal investment problem in a market where the stock price process is modeled by a geometric Levy process (taking into account jumps). Except for the geometric Brownian model and the geometric Poissonian model, the resulting models are incomplete and there are many equivalent martingale measures. However, the model can be completed by the so-called power-jump assets. By doing this we allow investment in these new assets and we can try to maximize the expected utility of these portfolios. As particular cases we obtain the optimal portfolios based in stocks and bonds, showing that the new assets are superfluous for certain martingale measures that depend on the utility function we use.     

改进的期望效用-熵模型在沪市股票选择中的应用研究

用Arrow-Pratt风险厌恶度来度量期望效用-熵平衡系数以改进风险型决策的期望效用-熵模型;根据改进的期望效用-熵模型以及期望效用准则,分别从上证50指数样本股中选取7只股票构造投资组合,进行比较.研究结果表明,用改进的期望效用-熵模型得到的股票组合效果更优.     

Multiple criteria linear programming model for portfolio selection

The portfolio selection problem is usually considered as a bicriteria optimization problem where a reasonable trade-off between expected rate of return and risk is sought. In the classical Markowitz model the risk is measured with variance, thus generating a quadratic programming model. The Markowitz model is frequently criticized as not consistent with axiomatic models of preferences for choice under risk. Models consistent with the preference axioms are based on the relation of stochastic dominance or on expected utility theory. The former is quite easy to implement for pairwise comparisons of given portfolios whereas it does not offer any computational tool to analyze the portfolio selection problem. The latter, when used for the portfolio selection problem, is restrictive in modeling preferences of investors. In this paper, a multiple criteria linear programming model of the portfolio selection problem is developed. The model is based on the preference axioms for choice under risk. Nevertheless, it allows one to employ the standard multiple criteria procedures to analyze the portfolio selection problem. It is shown that the classical mean-risk approaches resulting in linear programming models correspond to specific solution techniques applied to our multiple criteria model. This revised version was published online in June 2006 with corrections to the Cover Date.     

企业资本预算中的风险补偿与资本配置效率研究

在分权化企业的资本预算中，由于存在着分部管理者的道德风险与风险规避偏好，总部管理者必须对包含风险补偿的激励成本与激励努力带来的预期收益两者进行权衡。当努力导致的收益介于最优激励成本与风险规避偏好导致的次优激励成本之间时，风险补偿的存在将会导致总部管理者降低激励努力水平，从而减少了投资的期望收益，降低了资本的配置效率。     

Integrated portfolio management with options

In this paper we examine the problem of managing portfolios consisting of both, stocks and options. For the simultaneous optimization of stock and option positions we base our analysis on the generally accepted mean–variance framework. First, we analyze the effects of options on the mean–variance efficient frontier if they are considered as separate investment alternatives. Due to the resulting asymmetric portfolio return distribution mean–variance analysis will be not sufficient to identify optimal optioned portfolios. Additional investor preferences which are expressed in terms of shortfall constraints allow a more detailed portfolio specification. Under a mean–variance and shortfall preference structure we then derive optioned portfolios with a maximum expected return. To circumvent the technical optimization problems arising from stochastic constraints we use an approximation of the return distribution and develop economically meaningful conditions under which the complex optimization problem can be transformed into a linear problem being comparably easy to solve. Empirical results based on both, empirical market data and Monte Carlo simulations, illustrate the portfolio optimization procedure with options.     

A utility maximization approach to hedging in incomplete markets

In this paper we introduce the notion of portfolio optimization by maximizing expected local utility. This concept is related to maximization of expected utility of consumption but, contrary to this common approach, the discounted financial gains are consumed immediately. In a general continuous-time market optimal portfolios are obtained by pointwise solution of equations involving the semimartingale characteristics of the underlying securities price process. The new concept is applied to hedging problems in frictionless, incomplete markets.     

需求可变性降低对均值CVaR约束销售努力决策库存系统的影响

本文运用Levy提出的变换研究需求可变性降低对风险偏好零售商的库存决策、销售努力决策和期望效用的影响,用均值CVaR刻画零售商的风险偏好特性,它包括风险厌恶、风险追求,也具有损失规避的特性。首先,运用该变换定量刻画需求可变性的降低,证明该变换蕴含经典随机占优中的割准则序和二阶随机占优等。其次,给出系统的最优订货量、最优期望效用和最优销售努力水平,得到它们关于风险偏好系数的单调性,并给出降低需求可变性对期望效用的影响。第三,针对风险中性、风险厌恶(最大化CVaR)和风险追求(最小化CVaR)这三种特殊情况得到相应的结果,并给出企业在库存决策和促销决策的管理启示。最后,通过数值例子验证了得到的研究结果并给出相应的管理启示。     

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.     

Optimal contracts in portfolio delegation

The optimal contracts in portfolio delegation under general preferences are characterized when the underlying state variable is not contractible, and the principal must rely on the final returns of portfolios to design the compensation schemes for the fund manager. We show that the optimal contracts satisfy a second-order nonlinear ordinary differential equation that depends on the utility functions and the distribution of state price density. In general, there is an efficiency loss for the optimal contracts unless the utility functions of both the principal and the agent exhibit linear risk tolerance with identical cautiousness. Additional contractible observables, like stock indexes, can be used to improve the efficiency of the second-best contracts, even if they are not perfectly correlated with the underlying state price. A continuous-time example with power utilities is presented to illustrate the features of the optimal contracts.     

具有不同效用函数的最优投资组合分析

The question of optimal portfolio is that finds the trading strategy satisfying the maximal expected utility function subject to some constraints. There is the optimal trading strategy under the risk neutral probability measure (martingale measure) if and only if there is no-arbitrage opportunity in the market. This paper argues the optimal wealth and the optimal value of expected utility with different utility function.     

Efficient portfolios in financial markets with proportional transaction costs

In this article, we characterize efficient portfolios, i.e. portfolios which are optimal for at least one rational agent, in a very general multi-currency financial market model with proportional transaction costs. In our setting, transaction costs may be random, time-dependent, have jumps and the preferences of the agents are modeled by multivariate expected utility functions. We provide a complete characterization of efficient portfolios, generalizing earlier results of Dybvig (Rev Financ Stud 1:67–88, 1988) and Jouini and Kallal (J Econ Theory 66: 178–197, 1995). We basically show that a portfolio is efficient if and only if it is cyclically anticomonotonic with respect to at least one consistent price system that prices it. Finally, we introduce the notion of utility price of a given contingent claim as the minimal amount of a given initial portfolio allowing any agent to reach the claim by trading, and give a dual representation of it as the largest proportion of the market price necessary for all agents to reach the same expected utility level.     

A general approach to Bayesian portfolio optimization

We develop a general approach to portfolio optimization taking account of estimation risk and stylized facts of empirical finance. This is done within a Bayesian framework. The approximation of the posterior distribution of the unknown model parameters is based on a parallel tempering algorithm. The portfolio optimization is done using the first two moments of the predictive discrete asset return distribution. For illustration purposes we apply our method to empirical stock market data where daily asset log-returns are assumed to follow an orthogonal MGARCH process with t-distributed perturbations. Our results are compared with other portfolios suggested by popular optimization strategies.