英文标题：
《The implied Sharpe ratio》
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作者：
Ankush Agarwal, Matthew Lorig
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最新提交年份：
2019
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英文摘要：
  In an incomplete market, including liquidly-traded European options in an investment portfolio could potentially improve the expected terminal utility for a risk-averse investor. However, unlike the Sharpe ratio, which provides a concise measure of the relative investment attractiveness of different underlying risky assets, there is no such measure available to help investors choose among the different European options. We introduce a new concept -- the implied Sharpe ratio -- which allows investors to make such a comparison in an incomplete financial market. Specifically, when comparing various European options, it is the option with the highest implied Sharpe ratio that, if included in an investor\'s portfolio, will improve his expected utility the most. Through the method of Taylor series expansion of the state-dependent coefficients in a nonlinear partial differential equation, we also establish the behaviour of the implied Sharpe ratio with respect to an investor\'s risk-aversion parameter. In a series of numerical studies, we compare the investment attractiveness of different European options by studying their implied Sharpe ratio.
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中文摘要：
在不完全市场中，将流动交易的欧洲期权纳入投资组合可能会提高风险厌恶投资者的预期终端效用。然而，与夏普比率（Sharpe ratio）不同的是，夏普比率提供了不同基础风险资产相对投资吸引力的简明衡量标准，没有此类衡量标准可帮助投资者在不同的欧洲选项中进行选择。我们引入了一个新概念——隐含夏普比率，它允许投资者在一个不完整的金融市场中进行这样的比较。具体而言，在比较各种欧洲期权时，如果将隐含夏普比率最高的期权包括在投资者的投资组合中，将最大程度地提高其预期效用。通过对非线性偏微分方程中状态相关系数的泰勒级数展开，我们还建立了隐含夏普比率相对于投资者风险厌恶参数的行为。在一系列的数值研究中，我们通过研究不同欧洲期权的隐含夏普比率来比较其投资吸引力。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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