# Calmar Ratio – Definition

### Calmar Ratio Definition

The Calmar ratio refers to a formula used in measuring the performance of a fund by comparing the annual compounded rate of return and the maximum drawdown risk of the fund. The Calmar ratio is often used to evaluate hedge funds and Commodity Trading Advisors. This ratio assesses the performance of a fund as well as its risks.

The Calmar ratio calculates the average annual rate of return of a fund for a specified time and divides the figure realized by the maximum drawdown of the fund. When the ratio is low, it means the fund performed badly over a specific time based on its risk-adjusted basis. If the Calmar ratio is high, the fund performed better.

### A Little More on What is the Calmar Ratio

Terry W. Young developed the Calmar ratio in 1991, it is a performance measurement used to assess Commodity Trading Advisors and hedge funds. The Calmar ratio is an appellate for the California Managed Accounts Reports.

This performance measurement ratio helps investors determine the risks of investments before undertaking them. The Calmar ratio is not the same as the MAR ratio, while the former uses a short-term data (mostly a period of three years), MAR ratio considers data emanating from when the investment is initiated.

Risk-adjusted basis is crucial when assessing the performance of an investment using the Calmar ratio. Due to its consideration for risk-adjusted, the Calmar ratio has gained prominence amongst other performance measure ratios. When calculating the calmar ratio of funds, a time frame of three years is often used, although, the period can be more than three years or less in some cases. Investors are able to evaluate both the risks and returns of an investment as they contribute to the overall performance of the investment.

Examples of other performance measure ratios are the MAR ratio, Sortino ratio and Sharpe tration.

### Reference for “Calmer Ratio”

https://www.investopedia.com › Investing › Financial Analysis

https://en.wikipedia.org/wiki/Calmar_ratio

https://www.fool.com/knowledge-center/what-is-a-calmar-ratio.aspx

https://breakingdownfinance.com/finance-topics/performance…/calmar-ratio/

https://www.financialmarkets-abc.com/caia/CalmarRatio.pdf

### Academic research on “Calmer Ratio”

Robust evidence on the similarity of Sharpe ratio and drawdown-based hedge fund performance rankings, Auer, B. R., & Schuhmacher, F. (2013). Robust evidence on the similarity of Sharpe ratio and drawdown-based hedge fund performance rankings. Journal of international financial markets, institutions and money24, 153-165. In this article, we analyse whether the class of adequately defined drawdown-based performance measures produces hedge fund rankings similar to the one that can be obtained using the Sharpe ratio. Supported by a series of robustness checks, we find that the choice of performance measure does not matter if investors are simply interested in identifying the best hedge funds and if a sufficient return history is used to calculate performance measure estimates. In small time series sample sizes typically used to evaluate hedge funds, the rankings cannot be regarded as strictly identical. However, with an increasing time series dimension, the ranking differences fall considerably.

Maximum drawdownMagdon-Ismail, M., & Atiya, A. F. (2004). Maximum drawdown. The maximum loss from a market peak to a market nadir, commonly called the maximum drawdown (MDD), measures how sustained one’s losses can be. Malik Magron-Ismail and Amir Atiya present analytical results relating the MDD to the mean return and Sharpe ratio. The MDD factors into many risk- adjusted measures of performance, such as the Calmar ratio. Magdon-Ismail and Atiya propose new scaling laws for these ratios, which facilitates the comparison of funds with track records of different length. They also discuss the portfolio implications of their results.

Sufficient conditions for expected utility to imply drawdown-based performance rankings, Schuhmacher, F., & Eling, M. (2011). Sufficient conditions for expected utility to imply drawdown-based performance rankings. Journal of Banking & Finance35(9), 2311-2318. The least restrictive sufficient condition for expected utility to imply Sharpe ratio rankings is the location and scale (LS) property (see Sinn, 1983Meyer, 1987). The normal, the extreme value, and many other distributions commonly used in finance satisfy this property. We argue that the LS property is also sufficient for expected utility to imply drawdown-based performance measure rankings, because for investment funds satisfying the LS condition, the Sharpe ratio and drawdown-based performance measures result in identical rankings. Hence, the same conditions that provide an expected utility foundation for the Sharpe ratio also provide a foundation for drawdown-based performance measures. We conclude that from a decision-theoretic perspective, drawdown-based performance measures are as good as the Sharpe ratio.

The low return distortion of the Sharpe ratio, Auer, B. R. (2013). The low return distortion of the Sharpe ratio. Financial Markets and Portfolio Management27(3), 299-306. This article formalizes the undesirable property of the Sharpe ratio that a fund with a certain poor performance can increase its Sharpe ratio in a prospective period by generating a sufficiently negative excess return. Specifically, we set out the conditions that a fund must meet to be exposed to this kind of effect. Furthermore, we provide a formal statement of the excess return value that needs to be deceeded to obtain a higher Sharpe ratio. In an empirical application, we investigate the practical relevance of this kind of distortion. We find that an economically significant number of funds listed in the CISDM hedge fund database have at least once reported a sufficiently negative return, causing an increased Sharpe ratio fund performance.

Sufficient conditions for expected utility to imply drawdown-based performance rankings, Schuhmacher, F., & Eling, M. (2011). Sufficient conditions for expected utility to imply drawdown-based performance rankings. Journal of Banking & Finance35(9), 2311-2318. The least restrictive sufficient condition for expected utility to imply Sharpe ratio rankings is the location and scale (LS) property (see Sinn, 1983Meyer, 1987). The normal, the extreme value, and many other distributions commonly used in finance satisfy this property. We argue that the LS property is also sufficient for expected utility to imply drawdown-based performance measure rankings, because for investment funds satisfying the LS condition, the Sharpe ratio and drawdown-based performance measures result in identical rankings. Hence, the same conditions that provide an expected utility foundation for the Sharpe ratio also provide a foundation for drawdown-based performance measures. We conclude that from a decision-theoretic perspective, drawdown-based performance measures are as good as the Sharpe ratio.