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Negative returns resulted positive Sharpe and positive Sortino

Negative returns resulted positive Sharpe and positive Sortino.
Can somebody explain this?

Clone Algorithm
9
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Backtest from to with initial capital
Total Returns
--
Alpha
--
Beta
--
Sharpe
--
Sortino
--
Max Drawdown
--
Benchmark Returns
--
Volatility
--
Returns 1 Month 3 Month 6 Month 12 Month
Alpha 1 Month 3 Month 6 Month 12 Month
Beta 1 Month 3 Month 6 Month 12 Month
Sharpe 1 Month 3 Month 6 Month 12 Month
Sortino 1 Month 3 Month 6 Month 12 Month
Volatility 1 Month 3 Month 6 Month 12 Month
Max Drawdown 1 Month 3 Month 6 Month 12 Month
# Backtest ID: 59dd2f7dedf30053b71dc873
There was a runtime error.
9 responses

Hi @Vladimir. I wrote up a short notebook explaining why the sign of Sharpe Ratio doesn't necessarily match the sign of cumulative returns. The TL;DR is that the sign of Sharpe Ratio is determined by the whether the arithmetic mean of (1 + daily_returns) is greater than 1, but the sign of cumulative returns is determined by whether the geometric mean of (1 + daily_returns) is greater than 1. Since arithmetic mean and geometric mean are both measures of central tendency, the sign of sharpe ratio and cumulative returns usually coincide, but they don't always.

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Disclaimer

The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.

Hi Scott,

Thank you for perfect research and brilliant explanation of what may be called Sharpe Ratio anomaly.

My 2 cents:

This apparent anomaly is the reason why academics generally use log returns rather than simple returns when calculating the Sharpe ratio of a standalone strategy.

However, in a constantly rebalanced diversified portfolio of multiple strategies (like the Q fund), it makes sense to judge each strategy using simple returns SRs, since the compounding is done at a portfolio level.

Since both Sharpe and Sortini require calculations of standard deviation and ROI, then if you have a neg. SD and a neg ROI, this is the same as multiplying two negatives. You'll get a positive number.

For anyone who might want to spend time examining that, this additional example might come in handy, pretty simple and only takes seconds to run, starting out with negative Sharpe & Sortino and ending at Sharpe +2.5, Sortino +9.5 with returns -130 ...

Does anyone know how to use the calculations here to be able to plot them in the custom chart?

Clone Algorithm
0
Loading...
Backtest from to with initial capital
Total Returns
--
Alpha
--
Beta
--
Sharpe
--
Sortino
--
Max Drawdown
--
Benchmark Returns
--
Volatility
--
Returns 1 Month 3 Month 6 Month 12 Month
Alpha 1 Month 3 Month 6 Month 12 Month
Beta 1 Month 3 Month 6 Month 12 Month
Sharpe 1 Month 3 Month 6 Month 12 Month
Sortino 1 Month 3 Month 6 Month 12 Month
Volatility 1 Month 3 Month 6 Month 12 Month
Max Drawdown 1 Month 3 Month 6 Month 12 Month
# Backtest ID: 59e663a8cb805441af336a92
There was a runtime error.

Walter deMilly,

Standard deviation by definition is always positive.

Vladimir

Sorry! I was thinking of another formula I use which involves STD. Has anyone yet solved this prob?

Walter - that notebook from Scott is an extensive explanation.

Disclaimer

The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.

Dan, thanks. I see now the prob in this case is related to a geometric mean of less than one.