Power mapping with dynamical adjustment for improved portfolio optimization

For financial risk management it is of vital interest to have good estimates for the correlations between the stocks. It has been found that the correlations obtained from historical data are covered by a considerable amount of noise, which leads to a substantial error in the estimation of the portfolio risk. A method to suppress this noise is power mapping. It raises the absolute value of each matrix element to a power q while preserving the sign. In this paper we use the Markowitz portfolio optimization as a criterion for the optimal value of q and find a K/T dependence, where K is the portfolio size and T the length of the time series. Both in numerical simulations and for real market data we find that power mapping leads to portfolios with considerably reduced risk. It compares well with another noise reduction method based on spectral filtering. A combination of both methods yields the best results.     

考虑基准资产的动态投资组合选取

职业基金经理的目标经常是希望自己的投资组合以稳定的表现能够超越所某一基准资产或组合。因此本文给出一个考虑基准资产的动态均值——方差投资组合选取模型。假设状态之间的转移遵循马氏过程,给定状态转移矩阵,可以得到对风险资产最优投入的解析表达式。此表达式表明对风险资产的投入由三项构成,前两项是不考虑基准资产时对风险资产的投入,最后一项与基准资产有关;在基准资产上的权重由基准资产收益的大小来决定,与积极投资组合管理者的风险厌恶程度无关;随着风险厌恶程度的增加,管理者会减少在风险资产上的投入。数值分析显示考虑基准资产的投资组合是一个积极的投资组合。     

Do ADRs enhance portfolio performance for a domestic portfolio? Evidence from the 1990s

American depository receipts (ADRs) represent an increasingly popular and convenient mechanism for international investing. We analyze ADRs traded throughout the 1990s and find that these securities offer a diversification and portfolio performance benefit when combined with a domestic portfolio (proxied by the S&P 500). While we find that emerging market ADRs are effective instruments for reducing portfolio risk, they do not improve portfolio performance as measured by the Sharpe ratio. Developed market ADRs do improve portfolio performance as measured by the Sharpe ratio. The asset allocation which maximizes the Sharpe ratio is 84 percent domestic stocks, 16 percent developed ADRs, and 0 percent emerging ADRs. Further, due to problems in defining an appropriate market index for ADRs, the Sharpe ratio is viewed to be the preferred performance measure. Other measures such as Jensen’s alpha and the Treynor measure are susceptible to being “gamed” to distort portfolio performance.     

信贷资产组合保险策略定价研究

本文探讨了信贷资产组合保险策略在信用风险管理领域的地位。基于CreditMetrics模型，提出了信贷资产组合保险策略的定价算法，这是对主流风险计量模型的一种全新尝试。处理的过程对CreditMetrics的VaR技术做了一些细节上的变换，通过蒙特卡洛模拟得到了较理想的运算结果。最后对模型的实施提出了合理的建议。     

Dynamic mean–VaR portfolio selection in continuous time

The value-at-risk (VaR) is one of the most well-known downside risk measures due to its intuitive meaning and wide spectra of applications in practice. In this paper, we investigate the dynamic mean–VaR portfolio selection formulation in continuous time, while the majority of the current literature on mean–VaR portfolio selection mainly focuses on its static versions. Our contributions are twofold, in both building up a tractable formulation and deriving the corresponding optimal portfolio policy. By imposing a limit funding level on the terminal wealth, we conquer the ill-posedness exhibited in the original dynamic mean–VaR portfolio formulation. To overcome the difficulties arising from the VaR constraint and no bankruptcy constraint, we have combined the martingale approach with the quantile optimization technique in our solution framework to derive the optimal portfolio policy. In particular, we have characterized the condition for the existence of the Lagrange multiplier. When the opportunity set of the market setting is deterministic, the portfolio policy becomes analytical. Furthermore, the limit funding level not only enables us to solve the dynamic mean–VaR portfolio selection problem, but also offers a flexibility to tame the aggressiveness of the portfolio policy.     

控制权冲突、资本配置决策与投资组合选择

本文以长期股权投资和固定资产的投资组合选择为研究对象,从控制权私利的视角探讨了大股东自利性动机对资本配置决策的作用机理,并进行了相应的数值模拟。研究发现：（1）固定资产投资规模与长期股权投资高状态收益存在负相关关系,而长期股权投资规模则与其高状态收益概率正相关;（2）大股东自利性动机驱使下的资本配置决策偏离了分散持股时的资本配置水平,偏离程度会随着现金流权与控制权分离度的增加而展现出非线性变化态势。上述研究结论为当前有关加强上市公司大股东财务决策监管的政策导向提供了重要的经验启示。     

Estimating a covariance matrix for market risk management and the case of credit default swaps

We analyze covariance matrix estimation from the perspective of market risk management, where the goal is to obtain accurate estimates of portfolio risk across essentially all portfolios—even those with small standard deviations. We propose a simple but effective visualisation tool to assess bias across a wide range of portfolios. We employ a portfolio perspective to determine covariance matrix loss functions particularly suitable for market risk management. Proper regularisation of the covariance matrix estimate significantly improves performance. These methods are applied to credit default swaps, for which covariance matrices are used to set portfolio margin requirements for central clearing. Among the methods we test, the graphical lasso estimator performs particularly well. The graphical lasso and a hierarchical clustering estimator also yield economically meaningful representations of market structure through a graphical model and a hierarchy, respectively.     

Optimal capital growth with convex shortfall penalties

The optimal capital growth strategy or Kelly strategy has many desirable properties such as maximizing the asymptotic long-run growth of capital. However, it has considerable short-run risk since the utility is logarithmic, with essentially zero Arrow–Pratt risk aversion. It is common to control risk with a Value-at-Risk (VaR) constraint defined on the end of horizon wealth. A more effective approach is to impose a VaR constraint at each time on the wealth path. In this paper, we provide a method to obtain the maximum growth while staying above an ex-ante discrete time wealth path with high probability, where shortfalls below the path are penalized with a convex function of the shortfall. The effect of the path VaR condition and shortfall penalties is a lower growth rate than the Kelly strategy, but the downside risk is under control. The asset price dynamics are defined by a model with Markov transitions between several market regimes and geometric Brownian motion for prices within a regime. The stochastic investment model is reformulated as a deterministic programme which allows the calculation of the optimal constrained growth wagers at discrete points in time.     

模糊机会约束规划下的投资组合模型研究

证券的历史数据和专家对证券未来表现的判断是证券收益率的两个重要信息，本文用基于上述两个信息的可能性分布描述证券收益率的不确定性，并结合可能性理论的三个测度——可能性测度、必要性测度、可信性测度，建立了基于模糊机会约束规划的乐观型、悲观型和折衷型投资组合模型，并且得到了各模型的最优解的解析式。最后给出算例予以说明。     

基于自由现金流的投资组合研究

本文运用我国股市1998～2006年间的财务报表数据,选择正自由现金流、低自由现金流乘数和低财务杠杆的大公司,对其以自由现金流为基础的投资组合进行了检验。结果显示,以自由现金流为基础的投资组合回报始终优于市场指数,说明在我国股市实行基于自由现金流的投资组合是积极可行的。