# Is scaled Sharpe ratio a t-statistic?

I was just reading Quantitative Trading: How to Build Your Own Algorithmic Trading Business and it suggests annualizing Sharpe ratio in order to compare performance of strategies:

$$\text{Annualized Sharpe Ratio} = \sqrt{N_T} \frac{\bar{R_s} - R_{b}}{\sigma_{R_s}}$$

where $$\bar{R_s}$$ are strategy returns for a certain period, $$R_b$$ -- benchmark returns and $$N_T$$ is number of periods in a year (e.g. 12 if $$R_s$$ is computed monthly). This seems like a t-statistic?

$$t_{\bar{x}} = \sqrt{n}\frac{\bar{x} - \mu}{\text{s.e.}({\bar{x}})}$$

So Sharpe ratio can be interpreted as a number of standard deviations from a benchmark returns?

• @noob2 it divides std in denominator, so you can just move sqrt(n) in front. – spacemonkey Sep 21 '20 at 11:28

## 1 Answer

Yes, Sharpe follows a student's t distribution.

https://alo.mit.edu/wp-content/uploads/2017/06/The-Statistics-of-Sharpe-Ratios.pdf