私募基金规模、申购赎回机制与动态道德风险

运用动态合约理论与实物期权理论研究了私募基金最优激励相容合约的一般特征,考察了基金规模与申购赎回机制对缓解道德风险的作用。结论表明,私募基金最优激励相容合约由投资人的最大预期收益与管理者的最大预期回报共同决定,且购买私募基金类似于做多一种特殊期权,该期权标的资产价格由管理者后续值度量;投资人为激励管理者努力工作而付出的激励成本随基金初始规模或再申购比例递增,而最优基金规模由其边际激励成本与预期边际业绩决定;赎回成本影响投资人的最大预期收益,但对缓解道德风险不具显著作用;适当的业绩抽成可降低道德风险,且业绩抽成与私募基金初始规模或再申购比例在缓解道德风险方面存在一定的替代性。     

The participation puzzle with reference-dependent expected utility preferences

Expected utility theory with a smooth utility function predicts that, when allocating wealth between a risky and a riskless asset, investors allocate a positive amount to the risky asset whenever its expected return exceeds the riskless rate of return. A large number of people invest none of their wealth in risky assets, though, leading to the ”participation puzzle.” This paper explores whether the participation puzzle can be addressed when the utility function has a kink at the reference wealth level. It shows that when the reference wealth level is initial wealth increased by the riskless rate of return, there exists a range of expected excess returns for the risky asset for which the investor takes no position. Moreover, this range of expected excess returns is described by comparing a common performance measure of stock returns, the Omega Function, to a function of preference parameters. However, if the reference wealth level is any other constant, the usual expected utility prediction holds and investors allocate at least some of their wealth to the risky asset whenever it has a positive expected excess return.     

关于无风险资产不存在时资产组合选择的研究

以往关于资产组合选择的研究大多假设市场上存在无风险资产,但无风险资产实际上是不存在的.当不存在无风险资产时,假设投资者的效用定义在消费上,消费一直是投资者财富的一个固定比例,投资者的最优资产组合由两部分组成:短视的资产组合和对冲组合.假设只有股票和债券两种风险资产,当股票和债券的风险具有负的相关性时,投资者现在会消费更多,同时也会在股票上投资更多;两者正相关时,投资者无法降低风险,会减持股票并降低当前消费;两者不相关时,投资者持有的股票权重和存在无风险资产时一样.最后,还推导出了多种资产情况下最优消费和资产组合的解析表达式.     

On managerial risk-taking incentives when compensation may be hedged against

We consider a continuous time principal-agent model where the principal/firm compensates an agent/manager who controls the output’s exposure to risk and its expected return. Both the firm and the manager have exponential utility and can trade in a frictionless market. When the firm observes the manager’s choice of effort and volatility, there is an optimal contract that induces the manager to not hedge. In a two factor specification of the model where an index and a bond are traded, the optimal contract is linear in output and the log return of the index. We also consider a manager who receives exogenous share or option compensation and illustrate how risk taking depends on the relative size of the systematic and firm-specific risk premia of the output and index. Whilst in most cases, options induce greater risk taking than shares, we find that there are also situations under which the hedging manager may take less risk than the non-hedging manager.     

跳扩散环境下考虑红利支付的动态资产配置问题研究

研究资产价格带跳环境下红利支付对投资者资产配置的影响,投资者将其财富在风险资产和无风险资产中进行分配,在终端财富预期效用最大化标准下,利用动态规划原理建立的HJB方程推导最优配置策略,并得到最优动态资产配置策略的近似解.最后通过数值模拟,分析了跳和红利支付对投资者最优配置策略的影响.结果表明在跳发生的情况下,不管跳的大小和方向如何,投资者都会减少其在风险资产中的配置头寸,同时带有红利支付的资产比不带红利支付的资产对投资者更具吸引力.     

长期投资者的战略资产配置选择

在股票期望收益率服从一个均值回复过程的假设下,推导出具有幂效用函数的投资者的资产配置函数,着重分析了投资期限对投资者资产配置结果的影响,发现长期投资者比短期投资者在股票上配置更大的资产比例.虽然不同投资期限的投资者具有相同的短视配置,但是战略配置随着投资期限的增大而增大.     

模型不确定和极端事件冲击下带通胀的最优投资组合选择问题研究

本文研究了投资者在极端事件冲击下带通胀的最优投资组合选择问题, 其中投资者不仅对损失风险是厌恶的而且对模型不确定也是厌恶的. 投资者在风险资产和无风险资产中进行投资. 首先, 利用Ito公式推导考虑通胀的消费篮子价格动力学方程, 其次由通胀折现的终端财富预期效用最大化, 对含糊厌恶投资者的最优期望效用进行刻画. 利用动态规划原理, 建立最优消费和投资策略所满足的HJB方程. 再次, 利用市场分解的方法解出HJB方程, 获得投资者最优消费和投资策略的显式解. 最后, 通过数值模拟, 分析了含糊厌恶、风险厌恶、跳和通胀因素对投资者最优资产配置策略的影响.     

Security design and firm dynamics under long‐term moral hazard

This paper addresses a moral hazard problem in which the agent's actions affect the future profits of the firm. The optimal contract can be implemented through the issuance of variable coupon debt and purchase of fixed‐coupon debt. Consequently, the resulting capital structure acts as a hedge for the firm, reducing underinvestment costs in bad states of nature and controlling overinvestment incentives in good ones. However, owing to asymmetric information between the firm's manager and investors, this hedge is only partial. The firm's investments vary with cash flows, disclosing the agent's asymmetric information to the principal. Copyright © 2016 John Wiley & Sons, Ltd.     

贝叶斯方法在养老基金资产负债管理中的应用

把一个静态资产负债管理模型———均值方差模型应用到定额给付养老金计划的资产负债管理中,在允许无风险借贷的条件下研究养老金在无风险资产和风险资产间的分配问题,用定量分析的方法求出了最优投资组合的一般形式;又针对投资收益率特征参数未知的情况,提出了矩估计和贝叶斯估计两种方法求解最优资本配置比例,将两种方法的结果与一般形式对比,分析了影响最优投资组合的因素,得知养老基金在风险资产中的投资比例与基金经理对风险的厌恶程度、风险资产的风险益酬、风险资产收益率的波动性成负相关关系;并且随决策者掌握的历史信息增加,在风险资产上的投资比例也随之增加,投资行为逐渐趋于理性化;对上述结果进行仿真,验证了结论的有效性。     

基金契约中代理问题存在性研究

基金投资与基金经理之间的关系是一种委托一代理关系，这种委托一代理关系集中体现在基金契约中。为了激励基金经理能按照最大化基金投资的效用行动，减少代理问题，人们设计了各种类型的基金契约。本以一个最常用的线性基金契约为例，讨论分析了其中代理问题的存在性。     

Hedge fund performance appraisal using data envelopment analysis

In this paper we apply data envelopment analysis (DEA) to evaluate the performance of hedge fund classifications. The purpose of alternative investment strategies such as hedge funds is to offer absolute returns, so using passive benchmarks to measure their performance could be ineffective. With the increasing number of hedge funds available, institutional investors, pension funds, and high net worth individuals urgently need a trustworthy efficiency appraisal method. DEA can achieve this. An important benefit of the DEA measure is that benchmarks are not required, thereby alleviating the problem of using traditional benchmarks to examine non-normal distribution of hedge fund returns. We suggest that DEA be used as a complimentary technique (or method) for the selection of efficient hedge funds and funds of hedge funds for investors. Using DEA can shed light and further validate hedge fund manager selection with other methodologies.     

Optimal portfolio strategies with a liability and random risk: The case of different lending and borrowing rates

This paper deals with two problems of optimal portfolio strategies in continuous time. The first one studies the optimal behavior of a firm who is forced to withdraw funds continuously at a fixed rate per unit time. The second one considers a firm that is faced with an uncontrollable stochastic cash flow, or random risk process. We assume the firm’s income can be obtained only from the investment in two assets: a risky asset (e.g., stock) and a riskless asset (e.g., bond). Therefore, the firm’s wealth follows a stochastic process. When the wealth is lower than certain legal level, the firm goes bankrupt. Thus how to invest in the fundamental problem of the firm in order to avoid bankruptcy. Under the case of different lending and borrowing rates, we obtain the optimal portfolio strategies for some reasonable objective functions that are the piecewise linear functions of the firm’s current wealth and present some interesting proofs for the conclusions. The optimal policies are easy to be operated for any relevant investor.     

基金经理过度自信对基金收益与风险的影响研究

本文扩展了以前的研究范围，考察了基金经理过度自信对基金收益与风险的影响。与以前研究不同的是。我们在模型中引进了基金经理的能力这一参数，并假设基金经理从接收到的信号中提取信息的多少依赖于其能力的大小。我们发现。过度自信导致基金经理交易较多数量的风险资产。结果使得基金获得了较高的收益。但同时基金的风险也较高。从不同的角度。我们进一步证实了以前的研究结论。     

Optimal portfolio‐consumption choice under stochastic inflation with nominal and indexed bonds

This research solves the intertemporal portfolio choice problems with and without interim consumption under stochastic inflation. We assume a one‐factor nominal interest rate and a one‐factor expected inflation rate, implying a two‐factor real interest rate in the economy. In contrast to other related research which adopts the one‐factor real interest rate model, the inflation‐indexed bond is not a redundant asset class even in a complete market. The infinitely risk‐averse investor would prefer to invest all her wealth in inflation‐indexed bonds maturing at the investment horizon. We also show that, with the two‐factor real interest rate model, the consumption‐wealth ratio is not determined by the real interest rate alone. The investor's consumption–wealth ratio is also affected by the nominal interest rate and expected inflation rate levels. The capital market is calibrated to U.S. stocks, bonds, and inflation data. The optimal weights show that aggressive investors hold more nominal bonds in order to earn the inflation risk premiums, while conservative investors concentrate on indexed bonds to hedge against the inflation risk. Copyright © 2011 John Wiley & Sons, Ltd.     

Pricing and hedging of variable annuities with state-dependent fees

We investigate the problem of pricing and hedging variable annuity contracts for which the fee deducted from the policyholder’s account depends on the account value. It is believed that state-dependent fees are beneficial to policyholders and insurers since they reduce policyholders’ incentives to lapse the policies and match the costs incurred by policyholders with the pay-offs received from embedded guarantees. We consider an incomplete financial market which consists of two risky assets modelled with a two-dimensional Lévy process. One of the assets is a security which can be traded by the insurer, and the second asset is a security which is the underlying fund for the variable annuity contract. In our model we derive an equation from which the fee for the guaranteed benefit can be calculated and we characterize a strategy which allows the insurer to hedge the benefit. To solve the pricing and hedging problem in an incomplete financial market we apply a quadratic objective.     

Portfolio optimization with serially correlated, skewed and fat tailed index returns

This paper finds that mean-variance portfolio optimization of stocks, bonds, hedge funds, real estate investment trusts and commodities is sufficiently exact to optimize the investor’s utility. We approximate the expected utility using a Taylor series expansion including terms involving third and fourth order moments. The empirical findings for monthly data from August 1994–August 2009 suggest that the incorporation of skewness and kurtosis cause no noticeable change in the optimal portfolio allocation. However, the serial correlations of smoothed returns of hedge funds and real estate investment trusts indeed cause major changes in optimal portfolio allocation. Consequently, attention needs to be drawn to significant serial correlation and not to potential deviations from normality due to skewed and fat-tailed return distributions. The out-of-sample analysis using a moving window gives evidence that the optimal portfolio weight differ significantly considering serial correlation. The optimization using smoothed returns leads to the highest terminal wealth after 10 years. The highest utility is reached with smoothed as well as shrinked returns, while using unsmoothed as well as shrinked returns leads to an out-of-sample disaster. These findings have practical implications for investors who are willing to diversify their portfolios with hedge funds and real estate investment trusts.     

The role of index bonds in universal currency hedging

This study examines the demand for index bonds and their role in hedging risky asset returns against currency risks in a complete market where equity is not hedged against inflation risk. Avellaneda's uncertain volatility model with non-constant coefficients to describe equity price variation, forward price variation, index bond price variation and rate of inflation, together with Merton's intertemporal portfolio choice model, are utilized to enable an investor to choose an optimal portfolio consisting of equity, nominal bonds and index bonds when the rate of inflation is uncertain. A hedge ratio is universal if investors in different countries hedge against currency risk to the same extent. Three universal hedge ratios (UHRs) are defined with respect to the investor's total demand for index bonds, hedging risky asset returns (i.e. equity and nominal bonds) against currency risk, which are not held for hedging purposes. These UHRs are hedge positions in foreign index bond portfolios, stated as a fraction of the national market portfolio. At equilibrium all the three UHRs are comparable to Black's corrected equilibrium hedging ratio. The Cameron-Martin-Girsanov theorem is applied to show that the Radon-Nikodym derivative given under a P -martingale, the investor's exchange rate (product of the two currencies) is a martingale. Therefore the investors can agree on a common hedging strategy to trade exchange rate risk irrespective of investor nationality. This makes the choice of the measurement currency irrelevant and the hedge ratio universal without affecting their values.     

Static portfolio choice under Cumulative Prospect Theory

We derive the optimal portfolio choice for an investor who behaves according to Cumulative Prospect Theory (CPT). The study is done in a one-period economy with one risk-free asset and one risky asset, and the reference point corresponds to the terminal wealth arising when the entire initial wealth is invested into the risk-free asset. When it exists, the optimal holding is a function of a generalized Omega measure of the distribution of the excess return on the risky asset over the risk-free rate. It conceptually resembles Merton’s optimal holding for a CRRA expected-utility maximizer. We derive some properties of the optimal holding and illustrate our results using a simple example where the excess return has a skew-normal distribution. In particular, we show how a CPT investor is highly sensitive to the skewness of the excess return on the risky asset. In the model we adopt, with a piecewise-power value function with different shape parameters, loss aversion might be violated for reasons that are now well-understood in the literature. Nevertheless, we argue that this violation is acceptable.     

投资者情绪对基金羊群效应的影响研究

大量研究表明我国证券投资基金存在羊群效应,然而却很少对影响基金羊群效应的因素展开进一步的实证研究。基于此,本文利用主成分分析法测量投资者情绪,利用前十大流通股东中证券投资基金的家数来测量基金羊群效应的程度,研究投资者情绪指标是否对基金羊群效应产生影响。研究结果表明,投资者情绪是证券投资基金形成羊群效应的重要因素之一,基金经理在观察到上一期投资者悲观情绪(乐观情绪)时会做出负反馈策略。