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Why Sharpe Ratio Does Not Determine Drawdown Duration

Article Quant Q&A · Author: MarianP
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Summary

The document asks whether an annualized Sharpe ratio can predict how often or how long a strategy will lose money, and whether a striking record of few losing days implies a particular Sharpe ratio. The responses distinguish average excess return relative to volatility from path-dependent outcomes such as drawdowns. Because return paths and volatility patterns can differ, the Sharpe ratio alone does not specify drawdown size, duration, or frequency.

Under an assumption of normally distributed returns, the mean and standard deviation can be used to estimate the chance of a negative return, or of crossing a specified threshold. That inference depends on the distributional assumption; for other return distributions, further information is needed. The discussion therefore supports probability estimates under a model, not a direct conversion from Sharpe ratio to time spent losing. It offers no calculation for the cited firm’s record and does not address estimation uncertainty or serial dependence.

Key ideas

  • Sharpe ratio summarizes mean excess return relative to return volatility.
  • Drawdowns depend on the sequence of returns and cannot be inferred directly from Sharpe ratio alone.
  • Under normally distributed returns, mean and standard deviation can estimate the chance of a negative return.
  • Non-normal return distributions require additional information for precise loss probabilities.

Tags

StatisticsRisk managementBacktesting
Full text
# Sharpe Ratio and time spent in loss


# Sharpe Ratio and time spent in loss












Is it possible to express, given an annualized Sharpe Ratio value, what is an expected maximum/average time spent in a draw-down or something in this manner?

E.g. with SR of 10, you'd expect to spend e.g. about 1 day losing money every 2 weeks and not more than 3?

UPDATE: I was partly motivated to pose this question by reading about Virtu Financial Inc. going public and reporting it has only had 1 losing day in the last 5 years. What Sharpe Ratio would that imply?

## Answer by Richi Wa (score 3)

https://quant.stackexchange.com/a/10559

In my opinion: no. Looking at sharpe-ratio in an ex-post way you only divide average return (above risk free) by volatility.

Volatlity can have many patterns. A draw-down is something path dependent. There is no strict implication from draw-down to volatility. One can assume that having observed a large draw-down the asset has had rather large volatility. But there is no strict and direct connection. In fact it would be over-simplifying - don't do this.

## Answer by pbr142 (score 3)

https://quant.stackexchange.com/a/10566

You can interpret the empirical Sharpe Ratio (average return divided by standard deviation of returns) as the number of standard deviations that the mean return is from 0. Assuming a normal distribution for the returns, you can calculate how likely it is that the asset will have a negative return. If you know the mean and standard deviation themselves, you could also calculate the probability of having a return above/below any threshold (same logic applies to excess returns).

But this only works for normally distributed returns. For any other (more realistic) distribution, you would need to know more parameters to say anything precise.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.