Semimartingale theory of monotone mean–variance portfolio allocation

We study dynamic optimal portfolio allocation for monotone mean–variance preferences in a general semimartingale model. Armed with new results in this area, we revisit the work of Cui et al. and fully characterize the circumstances under which one can set aside a nonnegative cash flow while simultaneously improving the mean–variance efficiency of the left‐over wealth. The paper analyzes, for the first time, the monotone hull of the Sharpe ratio and highlights its relevance to the problem at hand.     

The demand for risky assets under uncertain inflation : An examination of some widely used assumptions

This paper examines the effect of the following commonly used methods of incorporating random inflation into discrete-time models of the demand for risky assets: 1) the use of a multivariate normal probability distribution for nominal asset returns and the random inflation rate, and 2) the approximation of real asset returns by the difference between nominal returns and the rate of inflation. The combination of these assumptions results in a deceptively simple version of the inflationary capital asset pricing model (CAPM). However, in an approximation-free version of this model the expected value of real wealth does not exist. While it is obvious that mean-variance analysis is not applicable in such models, we also find that the model does not satisfy Ohlson's weakened conditions for a quadratic approximation to the portfolio selection problem. Furthermore, this model is neither a member of the generalized Pareto-Levy nor log-stable class of portfolio models analyzed by Fama, Samuelson, Ohlson, and Struck.     

An alternative perspective on the relationship between downside beta and CAPM beta

In this paper we derive relationships between the CAPM beta and three measures of downside risk discussed in the literature. The relationships are derived assuming data generating processes in the mean-variance and mean-semivariance frameworks. In a sample of emerging market index returns we highlight that the association between the CAPM beta and downside beta depends on the standard deviation, skewness and kurtosis of the market portfolio return distribution. Therefore choice of risk measure may depend on the market being investigated. We argue that the derived relationships may also help explain anomalous results in empirical investigations.     

组合投资的系统风险与非系统风险——兼评王辉等人的《投资组合风险的分散化研究》

本文在指出王辉等人的《投资组合风险的分散化研究》一文中出现的错误的基础上,根据资本资产定价模型(CAPM)将组合投资的风险分离为系统风险与非系统风险,最后讨论了组合投资的均值-方差模型。     

资本资产定价扩展模型理论及其发展趋势

组合投资理论自从马柯维茨1952年建立以来,一直在迅速发展,特别是夏普(1962)、林特尔(1965)和摩森(1966)提出并发展了资本资产定价模型(CAPM)后,使纯粹的理论研究有机会应用于实际证券分析当中。但是,CAPM忽略了许多因素的影响,使CAPM理论与实际存在难以弥合的距离。为此,对CAPM进行修正和补充就成为后来学者研究的重点。     

保险资金投资管理中的风险分散问题研究

组合投资是利用投资组合内各个风险资产之间的相关性来分散风险的,而均值—方差投资组合模型采用的相关性度量—相关系数无法准确地度量风险资产之间的相关性,这必将对组合投资的风险分散效果产生不利影响。本文提出,用理论性质更好的相关性度量来度量风险资产之间的相关性,并建立基于Kendallτ的投资组合模型。通过实证研究发现,在保险资金投资管理中,采用基于Kendallτ的投资组合模型能够取得比均值—方差投资组合模型更好的风险分散效果。     

SOME REMARKS ON ARBITRAGE AND PREFERENCES IN SECURITIES MARKET MODELS

We introduce the notion of a market-free-lunch that depends on the preferences of all agents participating in the market. In semimartingale models of securities markets, we characterize no arbitrage (NA) and no-free-lunch-with-vanishing-risk (NFLVR) in terms of the market-free-lunch and show that the difference between NA and NFLVR consists in the selection of the class of monotone, respectively monotone and continuous, utility functions that determines the absence of the market-free-lunch. We also provide a direct proof of the equivalence between the absence of a market-free-lunch, with respect to monotone concave preferences, and the existence of an equivalent (local/sigma) martingale measure.     

Incorporating time-varying jump intensities in the mean-variance portfolio decisions

This paper examines the role of time-varying jump intensities in forming mean-variance portfolios. We find that compared with the no-jump or constant-jump models, the model which incorporates time-varying jump intensities better fits the dynamics of the assets returns, and yields mean-variance portfolios with higher Sharpe ratios. Our research suggests that using a better econometric model that captures non-normal features in the data has benefits for portfolio allocation even for a mean-variance investor.     

CONTINUOUS-TIME MEAN-VARIANCE PORTFOLIO SELECTION WITH BANKRUPTCY PROHIBITION

A continuous-time mean-variance portfolio selection problem is studied where all the market coefficients are random and the wealth process under any admissible trading strategy is not allowed to be below zero at any time. The trading strategy under consideration is defined in terms of the dollar amounts, rather than the proportions of wealth, allocated in individual stocks. The problem is completely solved using a decomposition approach. Specifically, a (constrained) variance minimizing problem is formulated and its feasibility is characterized. Then, after a system of equations for two Lagrange multipliers is solved, variance minimizing portfolios are derived as the replicating portfolios of some contingent claims, and the variance minimizing frontier is obtained. Finally, the efficient frontier is identified as an appropriate portion of the variance minimizing frontier after the monotonicity of the minimum variance on the expected terminal wealth over this portion is proved and all the efficient portfolios are found. In the special case where the market coefficients are deterministic, efficient portfolios are explicitly expressed as feedback of the current wealth, and the efficient frontier is represented by parameterized equations. Our results indicate that the efficient policy for a mean-variance investor is simply to purchase a European put option that is chosen, according to his or her risk preferences, from a particular class of options.     

Market integration in developed and emerging markets: Evidence from the CAPM

Beta, as measured by the Capital Asset Pricing Model (CAPM), is widely used for pricing stocks, determining the cost of capital, and gauging the extent to which markets are integrated. The CAPM model assumes that equilibrium conditions prevail. The choice of which market portfolio to use in the regression – the home country or global index – depends on the level of global market integration. We present several new empirical observations on the pricing of stocks and market integration. We provide guidance on how practitioners should calculate beta on securities in various developed and emerging markets.     

General equilibrium pricing of nonredundant forward contracts

We derive the general equilibrium of a dynamic financial market in which the investors' opportunity set includes nonredundant forward contracts. We show that Breeden's (1979) consumption‐based CAPM equation for forward contracts contains an extra term relative to that for cash assets. We name this term a strategy risk premium. It compensates investors for the (systematic) risk that stems from their very portfolio strategies when the latter involve nonredundant forward contracts. We also show that Merton's (1973) multibeta intertemporal CAPM must be amended for forward contracts to exhibit adjusted risk premia for the market portfolio and all relevant state variables, as opposed to the usual risk premia for cash assets. Our results are shown not to depend on the usual cash‐and‐carry relationship, which, in general, does not hold. We, nevertheless, provide a well‐known special case where it does hold, albeit not grounded on the usual no‐arbitrage argument. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:817–840, 2003     

LINKED RECURSIVE PREFERENCES AND OPTIMALITY

We study a class of optimization problems involving linked recursive preferences in a continuous‐time Brownian setting. Such links can arise when preferences depend directly on the level or volatility of wealth, in principal–agent (optimal compensation) problems with moral hazard, and when the impact of social influences on preferences is modeled via utility (and utility diffusion) externalities. We characterize the necessary first‐order conditions, which are also sufficient under additional conditions ensuring concavity. We also examine applications to optimal consumption and portfolio choice, and applications to Pareto optimal allocations.     

MEAN VARIANCE PREFERENCES, EXPECTATIONS FORMATION, AND THE DYNAMICS OF RANDOM ASSET PRICES

This paper analyzes the dynamics of an explicit random process of prices and price expectations of finitely many assets in an economy with overlapping generations of heterogeneous consumers. They maximize expected utility with respect to subjective transition probabilities defined by Markov kernels which describe the forecasting behavior of agents. Given such forecasting rules (predictors) and an exogenous process of dividends, the evolution of equilibrium asset prices and expectations is described by a random dynamical system in the sense of Arnold (1998) . The paper investigates the long-run behavior (stationary solutions) by proving the existence and stability of random fixed points for mean-variance preferences under various predictors, including unbiased predictions, and adaptive, as well as OLS forecasting. An explicit characterization of rational expectations solutions is given, providing a full dynamic characterization of asset price processes for the classical CAPM in the case of stationary OLG economies. Numerical simulations are used to compare the performance of the different predictors under an AR(1) dividend process.     

OPTIMAL LOT SOLUTION TO CARDINALITY CONSTRAINED MEAN–VARIANCE FORMULATION FOR PORTFOLIO SELECTION

The pioneering work of the mean–variance formulation proposed by Markowitz in the 1950s has provided a scientific foundation for modern portfolio selection. Although the trade practice often confines portfolio selection with certain discrete features, the existing theory and solution methodologies of portfolio selection have been primarily developed for the continuous solution of the portfolio policy that could be far away from the real integer optimum. We consider in this paper an exact solution algorithm in obtaining an optimal lot solution to cardinality constrained mean–variance formulation for portfolio selection under concave transaction costs. Specifically, a convergent Lagrangian and contour-domain cut method is proposed for solving this class of discrete-feature constrained portfolio selection problems by exploiting some prominent features of the mean–variance formulation and the portfolio model under consideration. Computational results are reported using data from the Hong Kong stock market.     

Learning equilibrium mean-variance strategy

We study a dynamic mean-variance portfolio optimization problem under the reinforcement learning framework, where an entropy regularizer is introduced to induce exploration. Due to the time–inconsistency involved in a mean-variance criterion, we aim to learn an equilibrium policy. Under an incomplete market setting, we obtain a semi-analytical, exploratory, equilibrium mean-variance policy that turns out to follow a Gaussian distribution. We then focus on a Gaussian mean return model and propose a reinforcement learning algorithm to find the equilibrium policy. Thanks to a thoroughly designed policy iteration procedure in our algorithm, we prove the convergence of our algorithm under mild conditions, despite that dynamic programming principle and the usual policy improvement theorem failing to hold for an equilibrium policy. Numerical experiments are given to demonstrate our algorithm. The design and implementation of our reinforcement learning algorithm apply to a general market setup.     

Value Preserving Strategies and a General Framework for Local Approaches to Optimal Portfolios

We present some new general results on the existence and form of value preserving portfolio strategies in a general semimartingale setting. The concept of value preservation is derived via a mean-variance argument. It is also embedded into a framework for local approaches to the problem of portfolio optimization.     

Optimal portfolio composition and the CAPM

It is commonly assumed that the CAPM implies that all investors hold a balanced portfolio, “the market portfolio,” and investors just determine the proportion of their wealth held in the market portfolio and the risk-free asset. That this is patently at odds with observed investor behavior is sometimes used to justify rejecting the CAPM. However, by assuming that substitute securities exist, in this paper we still obtain the CAPM, although investors neither hold all of the assets in the market nor a balanced shareholding in the assets they do hold.     

博弈论在投资组合选择中的应用

博弈论是研究竞争与合作的理论 ,二人零和博弈是局中人是两个人的情况下 ,一个人的所得为另一个人的所失。把该理论运用到投资组合的选择上 ,根据同一证券在不同经济状况下的BEAT值不同 ,构成一个由N种证券在M种不同经济状况下的BETA矩阵 ,再由CAPM模型 ,得到它的收益 (利润 )矩阵 ,再根据线性规划的方法求得最优解。由此能解决在下期不确定性情况下的最优投资组合。     

Foreign exchange market liberalization and the international diversification of borrowing by Italian firms

In this article we try to assess the relative importance of real and financial determinants in firm's foreign currency borrowing by extending a model earlier developed by Kawai. We use this framework to examine the behavior of Italian firms during the 1980s. The financial components of firm's decisions are studied by means of a repeated mean-variance portfolio model based on ex ante expectation. We show that (a) the invoice currencies seem to be a good indicator of firm's real exchange risk; and (b) even at times of capital controls, corporate debt policy was affected by financial variables. The latter will become increasingly important as European financial integration moves on.