A multi-period portfolio selection optimization model by using interval analysis

Due to few historical data that can be obtained in an emerging securities market, the future returns, risk and liquidity of securities cannot be forecasted precisely. The investment environment is usually fuzzy and uncertain. To handle these imprecise data, this paper discusses a fuzzy multi-period portfolio optimization problem where the returns, risk, and liquidity of securities are represented by interval variables. By taking the return, risk, liquidity and diversification degree of portfolio into consideration, an interval multi-period portfolio selection optimization model is proposed with the objective of maximizing the terminal wealth under the constraints of the return, risk and diversification degree of portfolio at each period. In the proposed model, a proportion entropy is employed to measure the diversification degree of portfolio. Using the fuzzy decision-making theory and multi-objective programming approach, the proposed model is transformed into a crisp nonlinear programming. Then, we design an improved particle swarm optimization algorithm for solution. Finally, a numerical example is given to illustrate the application of our model and demonstrate the effectiveness of the designed algorithm.     

Fuzzy possibilistic portfolio selection model with VaR constraint and risk-free investment

We propose a possibilistic portfolio model with VaR constraint and risk-free investment based on the possibilistic mean and variance, while assuming that the expected rate of returns is a fuzzy number. The model shows more clearly that, in the financial market affected by several non-probabilistic factors, risk-averse investors wish not only to reach the expected rate of returns in their actual investment, but also to assure that the maximum of their possible future risk is lower than an expected loss. Under the condition that the expected rate of returns is a normal distribution fuzzy variable, we proposed a theorem as the solution, and derive a crisp equivalent form of the possibilistic portfolio under constraints of VaR and risk-free investment. This model is an expansion of the fuzzy possibilistic mean–variance model by Zhang (2007). Finally, an empirical study is carried out using the data concerning some stocks of various industries listed at the Shanghai Stock Exchange. A conclusion is reached that the investors are able to choose a portfolio more suitable to them under the VaR constraint.     

Risk index based models for portfolio adjusting problem with returns subject to experts' evaluations

This paper discusses a portfolio adjusting problem with additional risk assets and a riskless asset in the situation where security returns are given by experts' evaluations rather than historical data. Uncertain variables are employed to describe the security returns. Using expected value and risk index as measurements of portfolio return and risk respectively, we propose two portfolio optimization models for an existing portfolio in two cases, taking minimum transaction lot, transaction cost, and lower and upper bound constraints into account. In one case the riskless asset can be both borrowed and lent freely, and in another case the riskless asset can only be lent and the borrowing of riskless asset is not allowed. The adjusting models are converted into their crisp equivalents, enabling the users to solve them with currently available programming solvers. For the sake of illustration, numerical examples in two cases are also provided. The results show that under the same predetermined maximum tolerable risk level the expected return of the optimal portfolio is smaller when the riskless asset can only be lent than when the riskless asset can be both borrowed and lent freely.     

Equity risk premium and time horizon: What do the U.S. secular data say?

We consider a representative investor whose wealth is made up of the equity market portfolio and the riskless asset, and who maximizes the expected utility of his/her future wealth for a given horizon. The solution of this program shows that the equilibrium value of the equity risk premium – the latter being measured by the difference between the expected equity portfolio return and the risk-free interest rate – is given by the product of the price of risk by the expected variance of stock returns. When returns are predictable, these two magnitudes are both time-varying and horizon-dependent. In accordance with this theoretical framework, our paper presents an econometric model of the equity risk premia for two traditional horizons: the one-period-ahead horizon (i.e. the ‘short-term’ premium) and the infinite-time horizon (i.e. the ‘long-term’ premium). Using annual US secular data from 1871 to 2008, and representing the expected returns by mixing the three traditional adaptive, extrapolative and regressive processes, large disparities in the dynamics of the two premia are evidenced. Concerning the determination of the equilibrium values of the two premia, the expected variances depend on the past values of the centered squared returns while the prices of risk (unobservable variables) are estimated according to the Kalman filter methodology, which enables us to capture the influence of hidden variables and of non-directly measurable psychological effects. A spread of interest rates adds to this determination. Possibly due to risky arbitrage and transaction costs, the results show that observed premia gradually converge towards their equilibrium values, this process being described by an error correction model. Overall, our model provides a rather satisfactory representation of ‘short-term’ and ‘long-term’ premia.     

Single Beta Models and Currency Futures Prices

The conditional capital asset pricing model is applied to foreign currency futures prices, covariance risk being measured relative to excess returns from a broadly diversified international portfolio of equities. Positive time-varying risk premia are found in all five currencies tested when the difference between the US and the average foreign interest rates is used as an instrumental variable for the expected excess return from the common stock portfolio.     

Dynamic asset allocation with ambiguous return predictability

We study an investor's optimal consumption and portfolio choice problem when he is confronted with two possibly misspecified submodels of stock returns: one with IID returns and the other with predictability. We adopt a generalized recursive ambiguity model to accommodate the investor's aversion to model uncertainty. The investor deals with specification doubts by slanting his beliefs about submodels of returns pessimistically, causing his investment strategy to be more conservative than the Bayesian strategy. Unlike in the Bayesian framework, the hedging demand against model uncertainty may cause the investor's stock allocation to decrease sharply given a small doubt of return predictability, even though the expected return according to the VAR model is large. Over much of the parameter space, the robust strategy is very close to the Bayesian strategy with Epstein–Zin preferences and risk aversion chosen to match the same average portfolio holdings. This is true in particular when the IID model is unlikely and the dividend yield is low, as in recent years. However, differences in strategies can be substantial if the IID model is unlikely and the dividend yield is high.     

Portfolio style: Return-based attribution using quantile regression

Return-based classification identifies a portfolio's style signature in the time series of its returns. Detection is based on a regression of portfolio returns on returns of factor mimicking indices. The method is easy to apply and does not require information about portfolio composition. Classification using least squares means that style is determined by the way factor exposure influences expected returns. We introduce regression quantiles as a complement to the standard analysis. The regression quantiles extract additional information from the time series of returns by identifying the way style affects returns at places other than the expected value. This allows discrimination among portfolios that would be otherwise judged equivalent based on conditional expectations. It also provides direct information about the impact of style on the tails of the conditional return distribution. Simple examples are presented to illustrate regression quantile classification.     

Individual Decision Making and Investor Welfare

This article analyses and quantifies the costs of suboptimal decision making for an investor with a multi-period horizon. In light of the empirical evidence that investors are too conservative and hold portfolios that are insufficiently diversified, we evaluate the costs of suboptimal equity participation both analytically and using simulation, and also estimate the costs of suboptimal diversification using simulation. We find that suboptimal leverage imposes only modest costs on the investor for reasonable parameter values. While the costs of inadequate diversification can be very high, we find that, because of the higher returns on small firms, an equally weighted portfolio of as few as five randomly chosen firms can provide the same level of expected utility as the value weighted market portfolio.
(J.E.L.: G11, G18, G23).     

THE PRICE LEVEL, THE QUANTITY THEORY OF MONEY, AND THE FISCAL THEORY OF THE PRICE LEVEL

This paper examines price‐level determination from the perspective of portfolio choice. Arbitrages among money balances, bonds, and investment goods determine their relative demands. Returns to real balance holdings and after‐tax returns to investment goods determine the relative values of nominal and real assets. Because expectations of government policies ultimately determine the expected returns to both nominal and real assets, the price level depends on interactions among current and expected future monetary and fiscal policies. The quantity theory and the fiscal theory emerge as special cases produced by restricting both the margins and the policies considered.     

基于盖斯克模型与模糊数的综合模型在风险投资项目中的应用

风险投资项目具有高不确定性,因此将风险投资项目复合实物期权方法中的期望现金流现值和投资成本均假定为确定值是不现实的。因此本文运用了复合实物期权(Geske模型)与模糊数的综合模型。该综合模型较好地解决了风险投资项目中的期望现金流现值和投资成本不为确定值的情况,并结合实例证明了其有效性。     

社会地位、非期望效用函数、资产定价和经济增长

本文利用非期望偏好结构 ,讨论消费和资产收益的时间序列行为。在这种递归偏好结构中 ,投资者积累财富不仅仅为了消费 ,也为了财富所带来的社会地位 ,我们研究这一假设对消费、投资组合策略、证券市场价格以及经济增长的影响 ,并利用所得到的定价方程讨论风险溢金问题。     

Interval programming model for risk-based partner selection of virtual enterprise

The problem of risk-based partner selection of virtual enterprise is investigated. By choosing optimal partner for each project task, the project risk is minimized. The risk parameters are expressed in the form of interval numbers when the precise values are difficult to obtain, and the model is formulated into a 0-1 nonlinear programming with interval coefficients in its objective function. In order to solve the problem, the definition of order relation between interval numbers is given, and the original model is converted into an equivalent crisp bi-objective programming model. Because of the highly constrained nature and multiple objective of the model, a genetic algorithm is proposed to find the set of Pareto or near Pareto optimal solutions. The approach is demonstrated by some numerical examples, and the result shows that the suggested approach has high efficiency and the model has potential to practical applications.     

Portfolio Choice and Liquidity Constraints*

We study the infinite‐horizon model of household portfolio choice under liquidity constraints and revisit the portfolio specialization puzzle. We show why the puzzle is robust to several model variations, and argue that positive correlation between earnings shocks and stock returns is unlikely to provide an empirically plausible resolution. We find that relatively small fixed costs for stock market entry are sufficient to deter stockholding because, for a plausible range of parameter values, households can achieve desired consumption smoothing with small or zero holdings of stocks. Such costs could arise from informational considerations, sign‐up fees, and investor inertia.     

中国资本账户开放进程中跨境证券投资对国内金融市场的影响*

随着中国资本项目开放进程的推进,跨境证券投资对国内金融市场的冲击日益增强。在此背景下,本文首先通过构建考虑了资本市场收益率以及有管理浮动汇率制度的IS LM BP模型对跨境证券投资与中国国内金融市场的相互影响机理进行了理论探究,并基于中国2005年7月—2016年8月的月度数据,运用马尔科夫区制转移向量自回归模型对中国资本账户开放进程中跨境证券投资与人民币汇率、股票市场收益率、短期利率的联动关系进行了实证分析。研究结果表明：第一,四者的关联性存在明显的区制特征,区制1主要包括次贷危机时期（2007—2008年）、欧债危机时期（2010—2012年）以及后金融危机时期（2015—2016年）,经济呈现“股票市场收益率较低、跨境证券投资较少、短期利率较高、金融市场波动性大”的状态;区制2主要包括次贷危机前夕（2005—2006年）、次贷危机后的量化宽松时期（2009—2010年）以及欧债危机后的调整期（2013—2014年）,经济呈现“股票市场收益率较高、跨境证券投资较多、短期利率较低、金融市场波动性小”的状态。第二,当处于资本市场化进程较快、金融市场波动性较大的区制阶段（区制1）时,跨境证券投资与国内金融市场的联动关系更加明显。本文研究结论对于我国进一步开放资本市场具有借鉴价值和政策启示。     

Liquidity and equity returns in Borsa Istanbul

We investigate the relationship between expected returns and liquidity measures in Borsa Istanbul. To do so, we gather a wide range of illiquidity measures that can be applied to the market. Firm-level cross-sectional regressions indicate that there is a positive relationship between various illiquidity measures and one- to six-month ahead stock returns. Findings of the article are robust after using different sample periods and controlling for well-known priced factors, such as market beta, size, book-to-market ratio and momentum. The portfolio analysis reveals that stocks that are in the highest illiquidity quintile earn 7.2%–19.2% higher risk-adjusted annual returns than those in the lowest illiquidity quintile. The illiquidity premium is stronger for small stocks and stocks with higher return volatility and it increases (decreases) during periods of extremely low (high) market returns.     

Diversification across ASEAN-wide sectoral and national equity returns

This paper examines the effects of local and global shocks on the sector indices and national returns of the Association of Southeast Asian Nations (ASEAN) by using the univariate AR-GARCH model. We find that regional and global shocks have different influences on the ASEAN-wide sector and national equity indices. There is evidence that the ASEAN-wide sectoral returns are mostly driven by local shocks, except for the insurance and technology sectors. The volatility of Singapore's and Vietnam's national returns mostly results from their own shocks rather than local and global shocks. Applying the trend spillover model, this paper also shows that the effects of regional and global shocks on return volatility have been decreasing for almost all ASEAN-wide sectors' equity indices, while the trend for the volatility spillover effects of those shocks are positive and significant for the production and industries group sectors, as well as the food and beverage sector. Comparing the variance ratios of ASEAN sectoral and national returns, it is evident that the percentage of national equity returns belonging to their own shocks is higher than that of sectoral returns, indicating that investors might be better off diversifying their assets across countries rather than sectors in ASEAN area. This finding is consistent with the results of the mean–variance frontiers, as the portfolio composed purely of ASEAN national returns has a stronger efficiency frontier than a portfolio of all ASEAN-wide sector equity returns. By using the spanning and intersection tests, the paper also indicates that adding ASEAN national equity returns might improve the efficiency frontiers of investors' holding portfolios.     

The Role of Industry Effects in Simultaneous Reversal and Momentum Patterns in One-Month Stock Returns

When stocks are ranked by returns in one month, the portfolio of loser stocks tends to outperform the portfolio of winner stocks in the subsequent month. Yet industry portfolios tend to display momentum. We develop a model of information diffusion among agents with constrained information processing ability that reconciles these well-documented phenomena. We test whether this model or the overreaction hypothesis is consistent with the data. Additionally, a trading strategy based on the model outperforms strategies based on overreaction and on industry momentum. The strategy produces abnormal returns while controlling for market–risk and the size, book value, January, momentum, and liquidity effects.     

Stock return predictability: the role of inflation and threshold dynamics

This paper argues that the nature of stock return predictability varies with the level of inflation. We contend that the nature of relations between economic variables and returns differs according to the level of inflation, due to different economic risk implications. An increase in low level inflation may signal improving economic conditions and lower expected returns, while the opposite is true with an equal rise in high level inflation. Linear estimation provides contradictory coefficient values, which we argue arises from mixing coefficient values across regimes. We test for and estimate threshold models with inflation and the term structure as the threshold variable. These models reveal a change in either the sign or magnitude of the parameter values across the regimes such that the relation between stock returns and economic variables is not constant. Measures of in-sample fit and a forecast exercise support the threshold models. They produce a higher adjusted R², lower MAE and RMSE and higher trading related measures. These results help explain the lack of consistent empirical evidence in favour of stock return predictability and should be of interest to those engaged in stock market modelling as well as trading and portfolio management.     

Labor income and risky investments: can part-time farmers compete?

In the developed countries, a majority of farm households receive at least as much income from nonfarm sources as from the farm. Such part-time farms have survived inspite of lower returns than full-time farms. This paper considers when lower returns to part-time farming could be compensated by risk-reduction due to diversification of income sources. The paper uses a dynamic portfolio choice model with labor income. The model and results could be applied in other contexts as well.     

The Cross–section of Risk Premia in the Italian Stock Market

Our analysis compares multi–factor models with Italian stock market data for the period 1990–2000. The first, the simple CAPM, is the relevant benchmark because of its simplicity. The second, the extended Fama–French model (including the momentum portfolio), is the best candidate for substituting the one–factor model. The third is a multi–factor model including sectors; and the fourth is a multi–factor model including the change in short–term interest rates as an extra factor. The results of our research are mildly positive. The Fama–French multi–factor model behaves rather well in time series tests. However, in the cross–section, the average premia are not significantly different from zero, supporting the idea that they are not able to explain the cross–section of returns in the Italian market. Moreover, there is weak evidence that the factor portfolios have predictive power for macroeconomic variables characterizing the state of the economy. What may explain the results? There are two main components: first is the presumably large size of shocks to returns in the Italian case, which makes it difficult to explore the relation among expected returns; second is the presence of extra factors which are not accounted for in our analysis. (J.E.L.: G11, G12).