## Term Glossary

### Rachev Ratio

Rachev Ratio Reward-to-risk measure and defined as the ratio between the CVaR of the opposite of the excess return at a given confidence level $1-\alpha$ and the CVaR of the excess return at another confidence level $1-\beta$. $$RACHEV_{\alpha, \beta}=\frac{CVaR_{\beta}(r_{f}-r)}{CVaR_{\alpha}(r-r_{f})}$$

$r$
asset return
$r_f$
risk free rate of return
$CVaR_{\alpha}$
Conditional Value-at-Risk at $\alpha$-quantile
$CVaR_{\beta}$
Conditional Value-at-Risk at $\beta$-quantile

An intraday version of the ratio could be reduced further by setting a risk-free rate equal to zero: $$RACHEV_{\alpha, \beta}=\frac{CVaR_{\beta}(-r)}{CVaR_{\alpha}(r)}$$

The STARR ratio is a special case of the Rachev ratio. For example, STARR(5%) = Rachev ratio with $(\alpha,\beta)$ = (1, 0.05).

###### Function Reference
portfolio_rachevRatio, position_rachevRatio