英文标题：
《A General Framework for Portfolio Theory. Part I: theory and various
models》
---
作者：
Stanislaus Maier-Paape and Qiji Jim Zhu
---
最新提交年份：
2017
---
英文摘要：
Utility and risk are two often competing measurements on the investment success. We show that efficient trade-off between these two measurements for investment portfolios happens, in general, on a convex curve in the two dimensional space of utility and risk. This is a rather general pattern. The modern portfolio theory of Markowitz [H. Markowitz, Portfolio Selection, 1959] and its natural generalization, the capital market pricing model, [W. F. Sharpe, Mutual fund performance , 1966] are special cases of our general framework when the risk measure is taken to be the standard deviation and the utility function is the identity mapping. Using our general framework, we also recover the results in [R. T. Rockafellar, S. Uryasev and M. Zabarankin, Master funds in portfolio analysis with general deviation measures, 2006] that extends the capital market pricing model to allow for the use of more general deviation measures. This generalized capital asset pricing model also applies to e.g. when an approximation of the maximum drawdown is considered as a risk measure. Furthermore, the consideration of a general utility function allows to go beyond the \"additive\" performance measure to a \"multiplicative\" one of cumulative returns by using the log utility. As a result, the growth optimal portfolio theory [J. Lintner, The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets, 1965] and the leverage space portfolio theory [R. Vince, The Leverage Space Trading Model, 2009] can also be understood under our general framework. Thus, this general framework allows a unification of several important existing portfolio theories and goes much beyond.
---
中文摘要：
效用和风险是衡量投资成功与否的两个相互竞争的指标。我们证明了这两种投资组合度量之间的有效权衡通常发生在效用和风险二维空间中的凸曲线上。这是一种相当普遍的模式。马科维茨的现代投资组合理论【H.Markowitz，portfolio Selection，1959年】及其自然推广，资本市场定价模型【W.F.Sharpe，共同基金绩效，1966年】是我们一般框架的特例，当风险度量被视为标准差，效用函数是身份映射。利用我们的一般框架，我们还恢复了[R.T.Rockafellar、S.Uryasev和M.Zabarankin，《利用一般偏差度量进行投资组合分析的母基金》，2006年]中的结果，该结果扩展了资本市场定价模型，允许使用更多的一般偏差度量。这种广义资本资产定价模型也适用于，例如，当最大提款的近似值被视为风险度量时。此外，考虑到一般效用函数，通过使用log效用，可以超越“加法”性能度量，而成为累积回报的“乘法”度量。因此，在我们的一般框架下，也可以理解增长最优投资组合理论【J.Lintner，《风险资产的估值与股票投资组合和资本预算中风险投资的选择》，1965年】和杠杆空间投资组合理论【R.Vince，《杠杆空间交易模型》，2009年】。因此，这一总体框架允许将几个重要的现有投资组合理论统一起来，并且远远超出了这一范围。
---
分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Portfolio Management 项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
--

---
PDF下载：
-->