Range Measures
The range measures add the size of the loss tail to the size of the gain tail. They measure how far apart the two ends of the daily return distribution are, at three levels of averaging.
Mathematical Formulation
Range
The best day minus the worst day.
CVaR range
The mean of the worst 5% of days, as a loss, plus the mean of the best 5% of days, on the fractional-tail estimator of CVaR (95%).
Tail Gini range
The same with tail Gini in place of CVaR.
Reading it
All three are daily. A large range with a small CVaR range means the extremes are isolated days rather than a fat tail.
They are symmetric: a large gain tail raises them as much as a large loss tail.
Like every metric on FolioLab, this value describes the run window. It is a measurement of past returns, not a forecast of future ones.
Where FolioLab reports it
results.<method>.performance.return_range: daily, over the run window.results.<method>.performance.cvar_range_95: daily, over the run window.results.<method>.performance.tail_gini_range_95: daily, over the run window.
Each value appears on the result page under Further Risk Measures, in the PDF and Excel reports, in the compare view and through the MCP explain_metric tool. A run stored before this measure existed does not carry it.
Only riskfolio-lib has these measures. FolioLab lifts its owa_rg, owa_cvrg and owa_tgrg weights under the BSD-3 licence and matches RG, CVRG and TGRG of riskfolio-lib 7.0.1 to rounding.
References
- Cajas, D. (2021). "OWA Portfolio Optimization: A Disciplined Convex Programming Framework." SSRN Working Paper.
Not investment advice. Past performance is not indicative of future results.