Term Glossary

Metrics, Models & Concepts

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 \(1-\beta\). \begin{equation} RACHEV_{\alpha, \beta}=\frac{CVaR_{\beta}(r_{f}-r)}{CVaR_{\alpha}(r-r_{f})} \end{equation}

\(r\)
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: \begin{equation} RACHEV_{\alpha, \beta}=\frac{CVaR_{\beta}(-r)}{CVaR_{\alpha}(r)} \end{equation}

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