> [!tldr] Sharpe Ratio
> The **Sharpe ratio** measures the risk-adjusted profitability of a strategy/portfolio: if the return is $R$ and volatility is $\sigma$ (over the same time horizon as the return), the Sharpe ratio is $\mathbb{E}[R] / \sigma$.
>
> If the portfolio contains no [[Factor Models|factor]] exposure, i.e. it only contains idiosyncratic returns, then its Sharpe is also called the **information ratio**.
For example, if $R,\sigma$ are annual, then that ratio is the annualized Sharpe. To convert that to the daily Sharpe, $R$ becomes $R/252$, and $\sigma$ becomes $\sigma / \sqrt{ 252 }$, so we divide the annualized Sharpe by $\sqrt{ 252 }$ to get the daily Sharpe.
Common criticism of using Sharpe ratios include:
- It doesn't differentiate between upside vol and downside vol, so a portfolio with a long upside tail is also penalized by a lower Sharpe.
- More generally, the denominator $\sigma$ is not exactly representative of all risks we want to adjust the returns for.