# 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?

## 2 Answers

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.

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.

• why can you interpret the empirical sharpe ratio as the number of stds that the mean return is from 0? – Trajan Jun 15 '20 at 9:34