Sharpe & Sortino Ratios

Sharpe & Sortino Ratios

Risk-adjusted return metrics let you compare strategies that have different risk profiles.

Sharpe Ratio — excess return per unit of total risk (annualized): $\text{Sharpe} = \frac{\bar{r} - r_f}{\sigma} \times \sqrt{252}$

where $\bar{r}$ is the mean daily return, $r_f$ is the daily risk-free rate, and $\sigma$ is the sample std of daily returns.

Sortino Ratio — penalizes only downside volatility: $\text{Sortino} = \frac{\bar{r} - r_f}{\sigma_{down}} \times \sqrt{252}$

where $\sigma_{down}$ is the sample std computed only over returns below $r_f$ (the "downside deviation").

The Sortino ratio is preferred when return distributions are asymmetric, because upside volatility is not a risk — it's a reward.

Your Task

Implement:

• sharpe_ratio(returns, rf=0.0) — annualized Sharpe ratio
• sortino_ratio(returns, rf=0.0) — annualized Sortino ratio using downside std