非遍历性的最优杠杆

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摘要翻译：
在现代投资组合理论中，效用函数的使用有助于平衡投资的预期收益和这些收益中的不确定性。凯利准则提供了另一种方法，植根于信息论，它总是隐含着对数效用。这两种方法似乎不相容，从各自的角度来看，对投资者的风险偏好限制过松或过紧。这种冲突可以根据两种方法中使用的乘法模型是非遍历的来理解，这导致在单一实现中集合平均回报不同于时间平均回报。经典的处理，从概率论的一开始，就使用系综平均，而凯利结果是通过考虑时间平均得到的。最大化投资的时间平均增长率定义了一个最优杠杆，而从集合平均收益得到的增长率线性依赖于杠杆。因此，后一种措施可以激励投资者最大化杠杆，这不利于时间平均增长和整体市场稳定。夏普比率对杠杆不敏感。讨论了它与最优杠杆的关系。更好地理解时间不可逆性和非遍历性的重要性以及由此产生的杠杆界限可能有助于政策制定者重塑金融风险控制。
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英文标题：
《Optimal leverage from non-ergodicity》
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作者：
Ole Peters
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最新提交年份：
2010
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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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
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英文摘要：
  In modern portfolio theory, the balancing of expected returns on investments against uncertainties in those returns is aided by the use of utility functions. The Kelly criterion offers another approach, rooted in information theory, that always implies logarithmic utility. The two approaches seem incompatible, too loosely or too tightly constraining investors' risk preferences, from their respective perspectives. The conflict can be understood on the basis that the multiplicative models used in both approaches are non-ergodic which leads to ensemble-average returns differing from time-average returns in single realizations. The classic treatments, from the very beginning of probability theory, use ensemble-averages, whereas the Kelly-result is obtained by considering time-averages. Maximizing the time-average growth rates for an investment defines an optimal leverage, whereas growth rates derived from ensemble-average returns depend linearly on leverage. The latter measure can thus incentivize investors to maximize leverage, which is detrimental to time-average growth and overall market stability. The Sharpe ratio is insensitive to leverage. Its relation to optimal leverage is discussed. A better understanding of the significance of time-irreversibility and non-ergodicity and the resulting bounds on leverage may help policy makers in reshaping financial risk controls.
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PDF链接：
https://arxiv.org/pdf/0902.2965

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关键词：遍历性 Quantitative Applications Perspectives Optimization 方法 最优 投资者 收益 Kelly