Portfolio Selection and Transactions Costs

This paper deals with the portfolio selection problem of risky assets with a diagonal covariance matrix, upper bounds on all assets and transactions costs. An algorithm for its solution is formulated which terminates in a number of iterations that is at most three times the number of assets. The efficient portfolios, under appropriate assumptions, are shown to have the following structure. As the risk tolerance parameter increases, an asset's holdings increases to its target, then stays there for a while, then increases to its upper bound, reaches it and stays there. Then the holdings of the asset with the next highest expected return proceeds in a similar way and so on.     

Capital structure of real estate assets: Theory and empirical evidence

This paper presents a model which intends to explain the capital structure of real estate assets. The model is cast in classical portfolio choice framework, but special attention is paid to the liquidity constraint. The test of this model on two assets with different capital structures (new housing and old housing in France) revealed the importance of return indicators as well as liquidity constraint in the household's financing decisions.     

A Portfolio Approach to Capital Budgeting: An Application to the Expansion to Additional Product Lines

The importance of the covariance of returns between capital assets is one of the basic principles of modern portfolio theory. An investor should seek capital assets which have negative covariance of returns, or if such capital assets are not available, capital assets with low covariance should be sought for a portfolio. From the variance-covariance structure of returns of the capital assets and the expected returns for each capital asset, a risk-reward trade-off or efficient frontier can be generated. The trade-off represents the minimum risk, as measured by portfolio variance, that could be incurred to realize a desired rate of return for the portfolio. This concept applies to a portfolio of capital budgeting projects as well as to a portfolio of securities. This paper demonstrates how this concept of portfolio diversification can be applied to a capital budgeting problem. The problem involves an actual problem faced by a U.S. distributor who must decide whether to expand sales into one of two industries. Quadratic programming is used to generate the risk-reward relationships and it is shown that the entry into one industry clearly provides a superior risk-reward relationship than entry into the other industry and compared to the company's present sales policy.     

Prediction of financial distress: An empirical study of listed Chinese companies using data mining

The deterioration in profitability of listed companies not only threatens the interests of the enterprise and internal staff, but also makes investors face significant financial loss. It is important to establish an effective early warning system for prediction of financial crisis for better corporate governance. This paper studies the phenomenon of financial distress for 107 Chinese companies that received the label ‘special treatment’ from 2001 to 2008 by the Shanghai Stock Exchange and the Shenzhen Stock Exchange. We use data mining techniques to build financial distress warning models based on 31 financial indicators and three different time windows by comparing these 107 firms to a control group of firms. We observe that the performance of neural networks is more accurate than other classifiers, such as decision trees and support vector machines, as well as an ensemble of multiple classifiers combined using majority voting. An important contribution of the paper is to discover that financial indicators, such as net profit margin of total assets, return on total assets, earnings per share, and cash flow per share, play an important role in prediction of deterioration in profitability. This paper provides a suitable method for prediction of financial distress for listed companies in China.     

Stochastic control of funding systems

This paper is concerned with funding systems, i.e. systems which accumulate funds for the future payment of financial obligations. Commonly, such funding requires a balance between (1) the desire to minimise the contributions that need to be diverted from other use to the support of the Fund, and (2) the need to maintain reasonable solvency in the Fund.Such funding is discussed here in a general framework. Applications are numerous. The specific applications mentioned in the paper are:

• Defined benefit retirement funding,

• Maintenance of a prudential margin by a non-life insurer,

• Dividend payment strategy.

The paper applies stochastic optimal control theory to determine how rates of contribution to the Fund and allocation of its assets by asset sector should respond to changing solvency. These results are obtainable from a particular differential equation, which may be solved numerically. Detailed numerical examples are provided.     

Robust portfolio choice with CVaR and VaR under distribution and mean return ambiguity

We consider the problem of optimal portfolio choice using the Conditional Value-at-Risk (CVaR) and Value-at-Risk (VaR) measures for a market consisting of n risky assets and a riskless asset and where short positions are allowed. When the distribution of returns of risky assets is unknown but the mean return vector and variance/covariance matrix of the risky assets are fixed, we derive the distributionally robust portfolio rules. Then, we address uncertainty (ambiguity) in the mean return vector in addition to distribution ambiguity, and derive the optimal portfolio rules when the uncertainty in the return vector is modeled via an ellipsoidal uncertainty set. In the presence of a riskless asset, the robust CVaR and VaR measures, coupled with a minimum mean return constraint, yield simple, mean-variance efficient optimal portfolio rules. In a market without the riskless asset, we obtain a closed-form portfolio rule that generalizes earlier results, without a minimum mean return restriction.     

Novel approaches for portfolio construction using second order stochastic dominance

In the last decade, a few models of portfolio construction have been proposed which apply second order stochastic dominance (SSD) as a choice criterion. SSD approach requires the use of a reference distribution which acts as a benchmark. The return distribution of the computed portfolio dominates the benchmark by the SSD criterion. The benchmark distribution naturally plays an important role since different benchmarks lead to very different portfolio solutions. In this paper we describe a novel concept of reshaping the benchmark distribution with a view to obtaining portfolio solutions which have enhanced return distributions. The return distribution of the constructed portfolio is considered enhanced if the left tail is improved, the downside risk is reduced and the standard deviation remains within a specified range. We extend this approach from long only to long-short strategies which are used by many hedge fund and quant fund practitioners. We present computational results which illustrate (1) how this approach leads to superior portfolio performance (2) how significantly better performance is achieved for portfolios that include shorting of assets.     

Market neutral portfolios

In this paper we consider the problem of constructing a market neutral portfolio. This is a portfolio of financial assets that (ideally) exhibits performance independent from that of an underlying market as represented by a benchmark index. We formulate this problem as a mixed-integer nonlinear program, minimising the absolute value of the correlation between portfolio return and index return. Our model is a flexible one that incorporates decisions as to both long and short positions in assets. Computational results, obtained using the software package Minotaur, are given for constructing market neutral portfolios for eleven different problem instances derived from universes defined by S&P international equity indices. We also compare our approach against an alternative approach based on minimising the absolute value of regression slope (the zero-beta approach).     

Portfolio Improvement by Using the Sharpe Rule and Value-at-Risk

This study discusses the applications of the Sharpe rule in portfolio measurement and management. It proposes that a portion of the portfolio value should be invested in some other assets for portfolio improvement. By applying the Sharpe rule, it can be determined that new stocks are worthy of adding to the old portfolio if they satisfy a condition, in which the average return rate of these stocks is greater than the return rate of the old portfolio multiplied by the sum of the elasticity of the VaR and 1. One attraction of our approach is diversification. A numerical example in the Hong Kong stock market is presented for illustration. Some experimental results show that a new portfolio with the 'highest' Sharpe ratio can be obtained by adding only a few new assets. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A multicriteria optimization model of portfolio rebalancing with transaction costs in fuzzy environment

In this paper we propose multicriteria credibilistic framework for portfolio rebalancing (adjusting) problem with fuzzy parameters considering return, risk and liquidity as key financial criteria. The portfolio risk is characterized by a risk curve that represents each likely loss of the portfolio return and the corresponding chance of its occurrence rather than a single pre-set level of the loss. Furthermore, we consider an investment market scenario where, at the end of a typical time period, the investor would like to modify his existing portfolio by buying and/or selling assets in response to changing market conditions. We assume that the investor pays transaction costs based on incremental discount schemes associated with the buying and/or selling of assets, which are adjusted in the net return of the portfolio. A hybrid intelligent algorithm that integrates fuzzy simulation with a real-coded genetic algorithm is developed to solve the portfolio rebalancing (adjusting) problem. The proposed solution approach is useful particularly for the cases where fuzzy parameters of the problem are characterized by general functional forms.     

金融资产收益率尾概率估计研究

在对金融资产进行投资时,投资者所关注的问题往往是金融资产收益率发生大波动的概率,简称尾概率.本文利用大偏差定理对此概率如何进行估计进行深入研究.将收益率按其尾部的分布特征分成三类,分别对其进行研究,得到三种不同的估计公式.本文对收益率序列存在相关性、收益率是多元随机变量情况下的尾概率估计问题也进行了分析.     

Fuzzy turnover rate chance constraints portfolio model

One concern of many investors is to own the assets which can be liquidated easily. Thus, in this paper, we incorporate portfolio liquidity in our proposed model. Liquidity is measured by an index called turnover rate. Since the return of an asset is uncertain, we present it as a trapezoidal fuzzy number and its turnover rate is measured by fuzzy credibility theory. The desired portfolio turnover rate is controlled through a fuzzy chance constraint. Furthermore, to manage the portfolios with asymmetric investment return, other than mean and variance, we also utilize the third central moment, the skewness of portfolio return. In fact, we propose a fuzzy portfolio mean–variance–skewness model with cardinality constraint which combines assets limitations with liquidity requirement. To solve the model, we also develop a hybrid algorithm which is the combination of cardinality constraint, genetic algorithm, and fuzzy simulation, called FCTPM.     

Large deviations theorems for optimal investment problems with large portfolios

The thrust of this paper is to develop a new theoretical framework, based on large deviations theory, for the problem of optimal asset allocation in large portfolios. This problem is, apart from being theoretically interesting, also of practical relevance; examples include, inter alia, hedge funds where optimal strategies involve a large number of assets. In particular, we also prove the upper bound of the shortfall probability (or the risk bound) for the case where there is a finite number of assets. In the two-assets scenario, the effects of two types of asymmetries (i.e., asymmetry in the portfolio return distribution and asymmetric dependence among assets) on optimal portfolios and risk bounds are investigated. We calibrate our method with international equity data. In sum, both a theoretical analysis of the method and an empirical application indicate the feasibility and the significance of our approach.     

Asset-liability management for Czech pension funds using stochastic programming

It is possible to model a wide range of portfolio management problems using stochastic programming. This approach requires the generation of input scenarios and probabilities, which represent the evolution of the return on investment, the stream of liabilities and other random phenomena of the problem and respect the no-arbitrage properties. The quality of the recommended capital allocation depends on the quality of the input scenarios and a validation of results is necessary. Appropriate scenario generation techniques and output analysis methods are described in the context of defined contribution pension fund and applied to the specific model of a Czech pension fund. The numerical results indicate various components that influence the recommended investment decisions and the fund’s achievements. In particular, the initial balance sheet position of the pension fund is important for the optimal investment strategy because of the accounting rules embedded in the model and tracking of both the market and purchasing value of assets.     

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.     

Asymptotics in a time-dependent renewal risk model with stochastic return

In this paper we study the asymptotic tail behavior for a non-standard renewal risk model with a dependence structure and stochastic return. An insurance company is allowed to invest in financial assets such as risk-free bonds and risky stocks, and the price process of its portfolio is described by a geometric Lévy process. By restricting the claim-size distribution to the class of extended regular variation (ERV) and imposing a constraint on the Lévy process in terms of its Laplace exponent, we obtain for the tail probability of the stochastic present value of aggregate claims a precise asymptotic formula, which holds uniformly for all time horizons. We further prove that the corresponding ruin probability also satisfies the same asymptotic formula.     

Socially Responsible Investment: A multicriteria approach to portfolio selection combining ethical and financial objectives

In a context of Socially Responsible Investment (SRI), this paper deals with portfolio selection for investors interested in ethical policies. In the opportunity set there are ethical assets and other assets which are not characterized as ethical. Two goals are considered, the traditional financial goal in the classical utility theory under uncertainty and an ethical goal in the same utility framework. A new financial-ethical bi-criteria model is proposed with absolute risk aversion coefficients and targets depending on the investor’s ethical profile. This approach is relevant as an increasing number of mutual funds are becoming interested in SRI strategies. From the proposed model, an actual case on green investment is developed. Concerning this case (without generalizing to other contexts), an analysis of the numerical results shows that efficient portfolios obtained by the traditional E-V model outperform the strong green portfolios in terms of expected return and risk, but this does not significantly occur with weak green investment.     

Optimal time-consistent investment and reinsurance policies for mean-variance insurers

This paper investigates the optimal time-consistent policies of an investment-reinsurance problem and an investment-only problem under the mean-variance criterion for an insurer whose surplus process is approximated by a Brownian motion with drift. The financial market considered by the insurer consists of one risk-free asset and multiple risky assets whose price processes follow geometric Brownian motions. A general verification theorem is developed, and explicit closed-form expressions of the optimal polices and the optimal value functions are derived for the two problems. Economic implications and numerical sensitivity analysis are presented for our results. Our main findings are: (i) the optimal time-consistent policies of both problems are independent of their corresponding wealth processes; (ii) the two problems have the same optimal investment policies; (iii) the parameters of the risky assets (the insurance market) have no impact on the optimal reinsurance (investment) policy; (iv) the premium return rate of the insurer does not affect the optimal policies but affects the optimal value functions; (v) reinsurance can increase the mean-variance utility.     

A generalized square of the zeta function. The spectral decomposition. II

An estimate of the remainder in the spectral decomposition of the generalized ζ function is given, which is more precise than the known ones. This paper is a continuation of a previous paper published in one of the preceding issues. Bibliography: 1 title. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 330, 2006, pp. 77–92.