On minimizing drawdown risks of lifetime investments

Drawdown measures the decline of portfolio value from its historic high-water mark. In this paper, we study a lifetime investment problem aiming at minimizing the risk of drawdown occurrences. Under the Black–Scholes framework, we examine two financial market models: a market with two risky assets, and a market with a risk-free asset and a risky asset. Closed-form optimal trading strategies are derived under both models by utilizing a decomposition technique on the associated Hamilton–Jacobi–Bellman (HJB) equation. We show that it is optimal to minimize the portfolio variance when the fund value is at its historic high-water mark. Moreover, when the fund value drops, the proportion of wealth invested in the asset with a higher instantaneous rate of return should be increased. We find that the instantaneous return rate of the minimum lifetime drawdown probability (MLDP) portfolio is never less than the return rate of the minimum variance (MV) portfolio. This supports the practical use of drawdown-based performance measures in which the role of volatility is replaced by drawdown.     

随机利率及随机收益保证下的投资策略

考虑随机利率环境及随机收益保证下基金经理的投资组合问题。利用鞅方法,得到了最优投资策略的显性解。结论表明,最优投资策略包括三个部分：投机策略、利率套期保值策略以及随机收益保证的复制策略,且该最优策略等价于将一部分资金投资于确保终端时刻获得最低收益的基准组合,而剩余资金则依照无保证情况下的最优策略进行投资。     

条件风险下的两基金分离定理

鉴于条件风险价值CVaR具有风险度量的合理性以及两基金分离定理对证券投资的重要意义,以CVaR作为风险度量研究两基金分离定理.在组合收益率服从正态分布的假设下,分别就投资组合含有或没有无风险资产的情形提出并证明了两基金分离定理;放开方差-协方差矩阵为非奇异这一通常假设,证明了CVaR风险度量下的两基金分离定理依然成立.     

Uniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk model

Consider an insurer who is allowed to make risk-free and risky investments. The price process of the investment portfolio is described as a geometric Lévy process. We study the tail probability of the stochastic present value of future aggregate claims. When the claim-size distribution is of Pareto type, we obtain a simple asymptotic formula which holds uniformly for all time horizons. The same asymptotic formula holds for the finite-time and infinite-time ruin probabilities. Restricting our attention to the so-called constant investment strategy, we show how the insurer adjusts his investment portfolio to maximize the expected terminal wealth subject to a constraint on the ruin probability.     

Portfolio insurance under a risk-measure constraint

We study the problem of portfolio insurance from the point of view of a fund manager, who guarantees to the investor that the portfolio value at maturity will be above a fixed threshold. If, at maturity, the portfolio value is below the guaranteed level, a third party will refund the investor up to the guarantee. In exchange for this protection, the third party imposes a limit on the risk exposure of the fund manager, in the form of a convex monetary risk measure. The fund manager therefore tries to maximize the investor’s utility function subject to the risk-measure constraint. We give a full solution to this non-convex optimization problem in the complete market setting and show in particular that the choice of the risk measure is crucial for the optimal portfolio to exist. Explicit results are provided for the entropic risk measure (for which the optimal portfolio always exists) and for the class of spectral risk measures (for which the optimal portfolio may fail to exist in some cases).     

基于半参数多元Copula-GARCH模型的开放式基金投资组合风险分析

利用Copula技术对我国开放式基金市场的投资组合进行了风险分析。为克服传统Copula模型对金融尾部数据刻画能力的不足,建立了半参数的多元Copula-GARCH模型,灵活地对各支基金的边缘分布进行拟合,刻画了开放式基金投资组合的相依结构。并利用基于Copula技术的蒙特卡洛模拟,对投资组合进行了VaR分析,结果证实了所建立模型的可行性和有效性。     

Portfolio insurance under a risk-measure constraint

We study the problem of portfolio insurance from the point of view of a fund manager, who guarantees to the investor that the portfolio value at maturity will be above a fixed threshold. If, at maturity, the portfolio value is below the guaranteed level, a third party will refund the investor up to the guarantee. In exchange for this protection, the third party imposes a limit on the risk exposure of the fund manager, in the form of a convex monetary risk measure. The fund manager therefore tries to maximize the investor’s utility function subject to the risk-measure constraint. We give a full solution to this non-convex optimization problem in the complete market setting and show in particular that the choice of the risk measure is crucial for the optimal portfolio to exist. Explicit results are provided for the entropic risk measure (for which the optimal portfolio always exists) and for the class of spectral risk measures (for which the optimal portfolio may fail to exist in some cases).     

Mean-variance versus expected utility in dynamic investment analysis

Given the existence of a Markovian state price density process, this paper extends Merton??s continuous time (instantaneous) mean-variance analysis and the mutual fund separation theory in which the risky fund can be chosen to be the growth optimal portfolio. The CAPM obtains without the assumption of log-normality for prices. The optimal investment policies for the case of a hyperbolic absolute risk aversion (HARA) utility function are derived analytically. It is proved that only the quadratic utility exhibits the global mean-variance efficiency among the family of HARA utility functions. A numerical comparison is made between the growth optimal portfolio and the mean-variance analysis for the case of log-normal prices. The optimal choice of target return which maximizes the probability that the mean-variance analysis outperforms the expected utility portfolio is discussed. Mean variance analysis is better near the mean and the expected utility maximization is better in the tails.     

Stochastic optimal control of DC pension funds

In this paper, we study the portfolio problem of a pension fund manager who wants to maximize the expected utility of the terminal wealth in a complete financial market with the stochastic interest rate. Using the method of stochastic optimal control, we derive a non-linear second-order partial differential equation for the value function. As it is difficult to find a closed form solution, we transform the primary problem into a dual one by applying a Legendre transform and dual theory, and try to find an explicit solution for the optimal investment strategy under the logarithm utility function. Finally, a numerical simulation is presented to characterize the dynamic behavior of the optimal portfolio strategy.     

Portfolio symmetry and momentum

This paper presents a novel theoretical framework to model the evolution of a dynamic portfolio (i.e., a portfolio whose weights vary over time), considering a given investment policy. The framework is based on graph theory and the quantum probability. Embedding the dynamics of a portfolio into a graph, each node of the graph representing a plausible portfolio, we provide the probabilities for a dynamic portfolio to lie on different nodes of the graph, characterizing its optimality in terms of returns. The framework embeds cross-sectional phenomena, such as the momentum effect, in stochastic processes, using portfolios instead of individual stocks. We apply our methodology to an investment policy similar to the momentum strategy of Jegadeesh and Titman (1993). We find that the strategy symmetry is a source of momentum.     

模糊线性规划在社保基金投资组合优化中的应用

如何选择一个满意的投资组合，在既定条件下实现一个最有效率的风险-收益搭配，是社保基金投资的关键问题，本通过建立和求解社保基金的投资风险最小化模糊线性规划模型和投资收益最大化模糊线性规划模型，试图优化社保基金的投资组合，章最后给出应用示例。     

Simultaneous pursuit of out-of-sample performance and sparsity in index tracking portfolios

Index tracking is a passive investment strategy in which a fund (e.g., an ETF: exchange traded fund) manager purchases a set of assets to mimic a market index. The tracking error, i.e., the difference between the performances of the index and the portfolio, may be minimized by buying all the assets contained in the index. However, this strategy results in a considerable transaction cost and, accordingly, decreases the return of the constructed portfolio. On the other hand, a portfolio with a small cardinality may result in poor out-of-sample performance. Of interest is, thus, constructing a portfolio with good out-of-sample performance, while keeping the number of assets invested in small (i.e., sparse). In this paper, we develop a tracking portfolio model that addresses the above conflicting requirements by using a combination of L0- and L2-norms. The L2-norm regularizes the overdetermined system to impose smoothness (and hence has better out-of-sample performance), and it shrinks the solution to an equally-weighted dense portfolio. On the other hand, the L0-norm imposes a cardinality constraint that achieves sparsity (and hence a lower transaction cost). We propose a heuristic method for estimating portfolio weights, which combines a greedy search with an analytical formula embedded in it. We demonstrate that the resulting sparse portfolio has good tracking and generalization performance on historic data of weekly and monthly returns on the Nikkei 225 index and its constituent companies.     

Optimal investment of DC pension plan under short-selling constraints and portfolio insurance

In this paper we investigate an optimal investment problem under short-selling and portfolio insurance constraints faced by a defined contribution pension fund manager who is loss averse. The financial market consists of a cash bond, an indexed bond and a stock. The manager aims to maximize the expected S-shaped utility of the terminal wealth exceeding a minimum guarantee. We apply the dual control method to solve the problem and derive the representations of the optimal wealth process and trading strategies in terms of the dual controlled process and the dual value function. We also perform some numerical tests and show how the S-shaped utility, the short-selling constraints and the portfolio insurance impact the optimal terminal wealth.     

允许投资组合条件下概率准则

概率准则具有一定的现实意义，其投资决策是以期望贴现资产为导向的．本文讨论了完备标准动态金融市场中在允许投资组合条件下的概率准则问题，得到了准则函数，贴现资产过程以及最优允许投资组合过程的解析表达式．期望贴现资产越大，准则函数越小。     

一种基于区间数的证券组合投资模型与求解

提出了区间数的相对左偏度的定义.利用区间数的相对左偏度作为区间数下表达证券风险损失率的一种补充,能合理地反映风险损失率与预期收益率之间的相关关系.建立了一种新的证券组合投资区间数规划模型,将区间数规划模型转化为参数线性规划问题求解,使证券组合投资决策分析更加具有柔性.最后通过实例分析了该模型的应用价值.     

Accommodating diverse institutional investment objectives and constraints using non-linear goal programming

Institutional portfolio managers face a diverse mix of conflicting investment objectives and constraints such as risk and retum goals, institutional liability considerations, fund management legal restrictions, institutional cash flow requirments, and protfolio management performance targets. This paper argues that lexicographic goal programming can be used to keep track of an institution's complex investment goals and will provide a best possible solution for the institution's portfolio selection problem. Three examples illustrate the applicability of non-linear goal programming to institutions' differing investment requirements.     

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.     

Scenario optimization asset and liability modelling for individual investors

We develop a scenario optimization model for asset and liability management of individual investors. The individual has a given level of initial wealth and a target goal to be reached within some time horizon. The individual must determine an asset allocation strategy so that the portfolio growth rate will be sufficient to reach the target. A scenario optimization model is formulated which maximizes the upside potential of the portfolio, with limits on the downside risk. Both upside and downside are measured vis-à-vis the goal. The stochastic behavior of asset returns is captured through bootstrap simulation, and the simulation is embedded in the model to determine the optimal portfolio. Post-optimality analysis using out-of-sample scenarios measures the probability of success of a given portfolio. It also allows us to estimate the required increase in the initial endowment so that the probability of success is improved.     

Arithmetic returns for investment performance measurement

This paper introduces new money-weighted metrics for investment performance analysis, based on arithmetic means of holding period rates weighted by the investment’s market values. This approach generates rates of return which measure a fund’s or portfolio’s performance and a fund manager’s performance. It also enables to show that the Internal Rate of Return (IRR) is a weighted mean of holding period rates associated with interim values which differ from market values, so that value additivity is violated. The manager’s Arithmetic Internal Rate of Return (AIRR) is shown to be the true period equivalent of the cumulative Time Weighted Rate of Return (TWRR), whereas the period TWRR (a geometric return) provides a different ranking. The method is easily generalized for coping with varying benchmark rates. We also cope with the practical problem of estimating interim values whenever they are not available.     

Building an Optimal Portfolio in Discrete Time in the Presence of Transaction Costs

Abstract

Portfolio theory covers different approaches to the construction of a portfolio offering maximum expected returns for a given level of risk tolerance where the goal is to find the optimal investment rule. Each investor has a certain utility for money which is reflected by the choice of a utility function. In this article, a risk averse power utility function is studied in discrete time for a large class of underlying probability distribution of the returns of the asset prices. Each investor chooses, at the beginning of an investment period, the feasible portfolio allocation which maximizes the expected value of the utility function for terminal wealth. Effects of both large and small proportional transaction costs on the choice of an optimal portfolio are taken into account. The transaction regions are approximated by using asymptotic methods when the proportional transaction costs are small and by using expansions about critical points for large transaction costs.