Optimizing the shares of native tree species in forest plantations with biased financial parameters

Addressing uncertainty is a key requirement to follow the principle of precaution in sustainable ecosystem management. The maximization of worst-case outcomes according to the “maximin” decision rule, based on the two parameters mean and variance of a financial indicator, is a prominent approach to integrate uncertainty in decision-making. In forestry, the problem of selecting the optimum tree species combination for a forest plantation investment can be seen as a problem of optimal portfolio selection, to be solved according to the “maximin” decision rule. Yet, it is well known that portfolios computed from expected means and variances are highly sensitive to changes in the estimated parameters. The financial results may be poor if we rely too much on the historical data. This paper tests an extended worst-case model that considers a lower bound for the expected mean net present value (NPV) of a tree species portfolio and an upper bound for its variance. Biased expected mean NPVs, variances and correlations for the tree species Picea abies [L.] Karst. (Spruce) and Fagus sylvatica L. (Beech) were used to test the variability of the resulting tree species portfolios (27 scenarios). A comprehensive simulated data set, which was adopted from an existing study and defined as the independent reference, served to evaluate the financial performance of the tree species portfolios obtained from optimization with the biased data. Compared with the results of classical worst-case optimization instances, it was feasible to reduce the variability of tree species shares effectively when the optimization was carried out with the extended worst-case approach. Furthermore, the financial performance of this approach was better when tested with the independent data. The worst-case forest NPVs achieved with the extended approach were on average 10% (statistical confidence 0.95) or 147% (statistical confidence 0.99) greater in comparison to the results of the classical approach. The influence of the uncertainty parameter selection was tested and the results were discussed against the controversial viewpoints on the usefulness of the “information-gap decision theory”. Finally, the significance of our results for sustainable ecosystem management is pointed out.     

Interval portfolio selection models within the framework of uncertainty theory

The expected returns for securities are traditionally estimated as crisp values. Since the improper values may bring on an unsuccessful investment decision, portfolio experts generally prefer offering interval estimations for expected returns rather than crisp ones. The portfolio selection problem with interval expected returns is widely studied recently. In this paper, by considering the security returns with interval expected returns as uncertain variables, a mean-semiabsolute deviation model is proposed within the framework of uncertainty theory, which is a crisp nonlinear programming model and can be well solved by the classical optimization algorithms. In order to illustrate the method, some numerical experiments are given and solved.     

Controlling portfolio skewness and kurtosis without directly optimizing third and fourth moments

In spite of their importance, third or higher moments of portfolio returns are often neglected in portfolio construction problems due to the computational difficulties associated with them. In this paper, we propose a new robust mean–variance approach that can control portfolio skewness and kurtosis without imposing higher moment terms. The key idea is that, if the uncertainty sets are properly constructed, robust portfolios based on the worst-case approach within the mean–variance setting favor skewness and penalize kurtosis.     

On mean-variance portfolio selection under a hidden Markovian regime-switching model

We study a mean-variance portfolio selection problem under a hidden Markovian regime-switching Black–Scholes–Merton economy. Under this model, the appreciation rate of a risky share is modulated by a continuous-time, finite-state hidden Markov chain whose states represent different states of an economy. We consider the general situation where an economic agent cannot observe the “true” state of the underlying economy and wishes to minimize the variance of the terminal wealth for a fixed level of expected terminal wealth with access only to information about the price processes. By exploiting the separation principle, we discuss the mean-variance portfolio selection problem and the filtering-estimation problem separately. We determine an explicit solution to the mean-variance problem using the stochastic maximum principle so that we do not need the assumption of Markovian controls. We also provide robust estimates of the hidden state of the chain and develop a robust filter-based EM algorithm for online recursive estimates of the unknown parameters in the model. This simplifies the filtering-estimation problem.     

综合收益最优的贷款组合鲁棒优化模型

商业银行信贷经营的基本目标是资金来源与运用在效益性、安全性和流动性上的“三性”平衡,而贷款组合优化配置是商业银行维持或达到资金“三性”平衡的有效方式,也是商业银行信贷经营管理中的重要内容.而贷款的预期收益具有不确定性,如果简单地假设其预期收益率往往会出现与实际脱节的情况,因此需要考虑贷款期间可能出现的变化.针对这一特征,考虑构建风险调整后资本收益率(RAROC)最优的贷款组合鲁棒优化模型.根据某商业银行实际经营数据进行数值分析,结果表明该模型具有鲁棒性,不仅能够兼顾贷款组合综合收益以及未来收益的不确定性因素,同时还可以在贷款组合风险约束范围内获得最大收益,为商业银行贷款优化配置管理提供有效可行的决策依据.     

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.     

Multi-period portfolio optimization under possibility measures

A single-period portfolio selection theory provides optimal tradeoff between the mean and the variance of the portfolio return for a future period. However, in a real investment process, the investment horizon is usually multi-period and the investor needs to rebalance his position from time to time. Hence it is natural to extend the single-period fuzzy portfolio selection to the multi-period case based on the possibility theory. In this paper, we propose the possibilistic expected value and variance for the terminal wealth with fuzzy forms after T periods by using the central value operator. Classes of multi-period possibilistic mean-variance models are formulated originally under the assumption that the proceeds of risky assets are fuzzy variables. Besides, we apply a particle swarm optimization algorithm to solve the proposed multi-period fuzzy portfolio selection models. A numerical example is given to illustrate the performance of the proposed models and algorithm.     

Dynamic optimal capital growth with risk constraints

In this paper, risk metrics in capital growth and drawdown as a financial risk measure were considered. Moreover, we developed a dynamic portfolio management model with constraints on the maximal drawdown. Exact optimization algorithms run into difficulties in this framework and this motivates the investigation of simulated annealing optimized algorithm to solve the problem of maximizing long term growth of simultaneous risky investment. Empirical research indicates that the approach is inspiring for this class of portfolio optimization problems.     

Optimal portfolio positioning under ambiguity

This paper analyzes the optimality of financial portfolios when the investor has a utility with ambiguity aversion. It provides a general result about the optimal portfolio profile under ambiguity, in the Anscombe–Aumann framework, using the Maccheroni et al. (2006) approach which includes Gilboa and Schmeidler's (1989) multiple prior preferences and Hansen and Sargent's (2011) multiplier preferences. The paper then details the CRRA case with an ambiguity index based on relative entropy. Such findings have practical applications in structured portfolio management. Indeed, it is important to take account of uncertainty about the true values of financial parameters when determining the best portfolio profile.     

Individual preferences and the effect of uncertainty on irreversible investment

This paper considers a relationship between investment behavior and an agent’s preferences in a stochastic one-sector growth model with irreversible investment. Further, it explores the effect of uncertainty in investment policies by using a non-expected utility function. Since uncertainty has an impact on investment policies not only through an option value but also through a risk-adjusted time preference rate in a general equilibrium framework, it is significant to distinguish the two preference parameters of the agent. While the previous partial equilibrium models with irreversible investment have exhibited a negative relationship between the desired capital stock and uncertainty, this paper implies that it is possible to generate a positive relationship for the appropriate parameters. This shows that the results of Hartman and Abel have been robust even in a general equilibrium model.     

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.     

Labor income,borrowing constraints,and equilibrium asset prices

Summary We develop a duality approach to study an individual's optimal consumption and portfolio policy when the individual has limited opportunities to borrow against future labor income and cannot totally insure the risk of income fluctuations. The individual's intertemporal consumption and portfolio problem is cast in a continuous-time setting under uncertainty. We transform the individual's intertemporal problem into a dual shadow prices problem that solves the shadow prices for the individual's optimal consumption plan or equivalently the individual's intertemporal marginal rates of substitution. We show that the shadow prices process can be expressed as a product of a martingale and a decreasing process (normalized by the bond price). The existence of an optimal solution to the individual's intertemporal consumption and portfolio problem is established via duality. The duality approach also allows us to characterize in a sample way the individual's optimal consumption and portfolio policy in the presence of labor income and borrowing constraints. Equilibrium implications of borrowing constraints on asset prices are also discussed in the paper.This is a revised version of an earlier paper, entitled Consumption and Portfolio Decisions with Labor Income and Borrowing Constraints. We thank George Constandinides, Ayman Hindy, and Chi-fu Huang for helpful comments. We also thank two anonymous referees for their helpful comments and suggestions. Financial support from the Batterymarch Fellowship Program (for Hua He) is gratefully acknowledged.     

Real estate investment: Market volatility and optimal holding period under risk aversion

This paper deals with real estate portfolio optimization when investors are risk averse. In this framework, we examine an important decision making problem, namely the determination of the optimal time to sell a diversified real estate portfolio. The optimization problem corresponds to the maximization of a concave utility function defined on both the free cash flows and the terminal value of the portfolio. We determine several types of optimal times to sell and analyze their properties. We extend previous results, established for the quasi linear utility case, where investors are risk neutral. We consider four cases. In the first one, the investor knows the probability distribution of the real estate index. In the second one, the investor is perfectly informed about the real estate market dynamics. In the third case, the investor uses an intertemporal optimization approach which looks like an American option problem. Finally, the buy-and-hold strategy is considered. For these four cases, we analyze in particular how the solutions depend on the market volatility and we compare them with those of the quasi linear case. We show that the introduction of risk aversion allows to better account for the real estate market volatility. We also introduce the notion of compensating variation to better measure the impacts of both the risk aversion and the volatility.     

Portfolio optimization using dynamic factor and stochastic volatility: evidence on Fat‐tailed errors and leverage

The portfolio optimization problem is investigated using a multivariate stochastic volatility model with factor dynamics, fat‐tailed errors and leverage effects. The efficient Markov chain Monte Carlo method is used to estimate model parameters, and the Rao–Blackwellized auxiliary particle filter is used to compute the likelihood and to predict conditional means and covariances. The proposed models are applied to sector indices of the Tokyo Stock Price Index (TOPIX), which consists of 33 stock market indices classified by industrial sectors. The portfolio is dynamically optimized under several expected utilities and two additional static strategies are considered as benchmarks. An extensive empirical study indicates that our proposed dynamic factor model with leverage or fat‐tailed errors significantly improves the predictions of the conditional mean and covariances, as well as various measures of portfolio performance.     

基于AFAD方法的工程项目组合选择评价模型研究

通过分析工程项目组合选择评价的特点,遵循指标设置的基本原则,构建了工程项目组合选择评价指标体系;集成层次分析法、模糊综合评价法、精确值评价法、数据包络分析法,构建了基于AFAD方法的工程项目组合选择评价模型。最后,通过实例表明该方法在为企业进行工程项目组合选择决策提供有效参考方面的可行性。     

Portfolio choice,consumption and welfare when rates of return are related to prices of consumer goods

This paper generalizes the two period model of portfolio selection under uncertainty by decomposing the aggregate consumption in each period into several goods, the prices of some of which are positively related to rates of return on some assets. The effect of these relations on the choice of portfolio is analyzed. The effects on the chosen portfolio of a lateral translation and of a mean preserving increase in the risk of the distributions of the random variables are analyzed. A generalization of the Hicks compensation to the case where the prices of consumer goods are positively related to rates of return on assets is offered and welfare implications are drawn.     

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.     

A risk index to model uncertain portfolio investment with options

This paper models the portfolio investment performance with options by using a risk index, which is defined as the average loss below the risk-free interest rate. Using a risk-free interest rate as the uniform reference rate for all portfolios, the risk index offers an easier-to-compare loss value than the value-at-risk return, where portfolio specific references are used to calculate the average losses. Besides, uncertainty theory is used in the paper to derive the portfolio decision when stock prices are subject to experts' estimations. By analytical computation and empirical analysis, we find that portfolios considering options generate better return than the ones without options. The empirical analysis reveals that the options can effectively hedge the risk, and the call option with a higher exercise price offers higher return per unit of option premium. Furthermore, our proposed model produces higher expected return in most cases than the model where the risk is measured by the chance of the total return failing to reach the threshold level of return.     

Shortfall minimization and the Naive (1/N) portfolio: an out-of-sample comparison

Naive portfolio selection, wherein an investor allocates an equal portion of their wealth to the field of candidate assets, is a simple ad-hoc way to create a portfolio. Naive portfolio selection contrasts to the many sophisticated portfolio selection rules that are optimal with respect to a specific portfolio allocation objective and which often perform well in sample. However, some recent research finds that many of these ‘optimal’ portfolio allocation mechanisms perform no better than naive diversification in out-of-sample data. This paper extends this line of inquiry by comparing the out-of-sample performance of naive portfolio selection to several recently developed shortfall-minimizing portfolio selection methods. The results corroborate the prior findings that optimal portfolio methods struggle to beat the naive portfolio in out-of-sample environments.     

Exchange rate dynamics under gradual portfolio adjustment

This paper generalizes the asset market approach to exchange rate determination by introducing gradual adjustment of asset-holder portfolios. The influence of different speeds of portfolio adjustment on exchange rate dynamics is considered. Asset market models characterized by instantaneous portfolio equilibrium appear as a special case. The dynamics of exchange rate adjustment following an open-market operation are shown to be qualitatively similar to those of the orthodox instantaneous portfolio equilibrium models. Thus, gradual portfolio adjustment does not compromise the qualitative results derived with the help of those models. The speed of portfolio adjustment is however shown to influence the degree of exchange rate volatility. In particular, the phenomenon of exchange rate overshooting depends crucially on the speed of portfolio adjustment.