1 May 2018 CFA Institute Journal Review

# An Upper Bound for an Ex Post Sharpe Ratio with Application in Performance Measurement (Digest Summary)

The authors derive a relationship between the ex post Sharpe ratio and maximum drawdown using profit and loss data—two critical parameters for assessing investment risk. The relationship is meant to help users quickly assess whether the given claim for any investment evaluated with the ex post Sharpe ratio is credible.

## How Is This Research Useful to Practitioners?

For their initial assessment to shortlist investment opportunities, some investment managers rely on performance reports given by the universe of available companies. Although they can always make independent assessments, managers find it difficult to fully analyze the huge stream of information pouring in. The ex post Sharpe ratio and maximum drawdown are key variables analysts often use to screen the data. Maximum drawdown is defined as the maximum cumulative loss incurred from one peak to the following trough within a given time frame (i.e., the maximum loss that the investor can expect to bear).

These two measures, however, may be subject to miscalculation or misrepresentation by the target company. The authors propose a quick check to assess whether the given information is accurate. If the length of the time series, risk-free rate, and average rate of return are known and the maximum drawdown is provided, the upper bound for the ex post Sharpe ratio can be estimated, and vice versa, from the relationship provided by the authors. Furthermore, when the ex post Sharpe ratio and maximum drawdown are both provided, the lower bound for the average return can be estimated.

## How Did the Authors Conduct This Research?

The authors consider the mathematical relationship between the ex post Sharpe ratio and the maximum drawdown using profit and loss data from S&P 500 Index constituent stocks during 2015. They choose two groups of stocks with a specified range of returns each, composed of 86 and 42 stocks, respectively.

The distribution of returns is assumed to be stationary and ergodic, whereby every sample is equally representative of the whole. Returns may be calculated using logarithmic or holding period returns. The bounds are derived using assumptions that can usually be satisfied in real-life situations and are thus practically implementable.

## Abstractorâ€™s Viewpoint

The research appears to be relevant and well suited to alleviate the issue of assessing the significant amount of information coming in. The validity of results should be tested over a longer period and for different economic cycles. Furthermore, it is unclear whether the results hold true for the stocks whose returns do not fall within the range specified in the research.