The statistics of Sharpe ratios
The statistics of Sharpe ratios
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DOI：
10.2469/faj.v58.n4.2453
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发表时间：
2002-07-01
影响因子：
2.8
通讯作者：
Lo, AW
中科院分区：
文献类型：
--
作者：
Lo, AW
夏普比率的组成部分--预期收益率和波动率是未知量，必须通过统计方法进行估计，因此会出现估计误差。这就引出了一个自然的问题：夏普比率的测量有多准确？为了解决这个问题，1导出明确的表达式的统计分布的夏普比率使用标准渐近理论的假设下的回报产生过程独立和同分布的回报，平稳回报，并与时间聚合。1表明，每月夏普比率不能乘以root 12年化，除非在非常特殊的情况下，我得出正确的转换方法，在一般情况下的固定回报。在一个关于共同基金和对冲基金的实证例子中，我发现对冲基金的年度夏普比率可能被夸大了65%，因为月度回报存在序列相关性，一旦适当考虑到这种序列相关性，基于夏普比率的对冲基金排名可能会发生巨大变化。
The building blocks of the Sharpe ratio-expected returns and volatilities are unknown quantities that must be estimated statistically and are, therefore, subject to estimation error. This raises the natural question: How accurately are Sharpe ratios measured? To address this question, 1 derive explicit expressions for the statistical distribution of the Sharpe ratio using standard asymptotic theory under several sets of assumptions for the return-generating process-independently and identically distributed returns, stationary returns, and with time aggregation. 1 show that monthly Sharpe ratios cannot be annualized by multiplying by root12 except under very special circumstances, and I derive the correct method of conversion in the general case of stationary returns. In an illustrative empirical example of mutual funds and hedge funds, I find that the annual Sharpe ratio for a hedge fund can be overstated by as much as 65 percent because of the presence of serial correlation in monthly returns, and once this serial correlation is properly taken into account, the rankings of hedge funds based on Sharpe ratios can change dramatically.