Comparison of performance indicators for tau variations
| Portfolio | Return | Standard deviation | Sharpe ratio | Beta | Treynor ratio | Omega ratio | Tracking error | Turnover |
|---|---|---|---|---|---|---|---|---|
| τ = 0.1625 X τ = 0.025 | ||||||||
| Tang_Eq 8% | – | – | – | – | – | – | – | – |
| MinV_Eq 8% | – | – | – | – | – | – | – | – |
| VolT_Eq 8% | – | – | – | – | – | – | – | – |
| ParR_Eq 8% | – | – | – | – | – | – | – | – |
| Tang_BL 8% | – | – | 0.001 | −0.001 | – | – | – | – |
| MinV_BL 8% | – | – | −0.001 | 0.001 | – | – | – | – |
| VolT_BL 8% | – | – | – | – | – | – | – | – |
| ParR_BL 8% | – | – | – | – | – | – | – | – |
| NP 8% | – | – | – | – | – | – | – | – |
| Market 8% | – | – | – | – | – | – | – | – |
| Tang_Eq 15% | −0.001 | – | −0.003 | – | −0.001 | −0.001 | – | – |
| MinV_Eq 15% | – | – | – | – | – | – | – | – |
| VolT_Eq 15% | – | – | – | – | – | – | – | – |
| ParR_Eq 15% | – | – | – | – | – | – | – | – |
| Tang_BL 15% | −0.004 | – | −0.013 | – | −0.003 | −0.004 | – | 0.002 |
| MinV_BL 15% | 0.001 | – | 0.001 | – | – | – | – | – |
| VolT_BL 15% | 0.001 | – | 0.004 | – | – | – | – | – |
| ParR_BL 15% | – | – | 0.002 | – | – | – | – | – |
| NP 15% | – | – | – | – | – | – | – | – |
| Market 15% | – | – | – | – | – | – | – | – |
| Tang_Eq 20% | −0.001 | – | −0.003 | – | −0.001 | – | – | – |
| MinV_Eq 20% | – | – | – | – | – | – | – | – |
| VolT_Eq 20% | – | – | – | – | – | – | – | – |
| ParR_Eq 20% | – | – | – | – | – | – | – | – |
| Tang_BL 20% | – | – | 0.001 | – | – | – | – | – |
| MinV_BL 20% | 0.001 | – | 0.001 | – | – | 0.001 | −0.001 | – |
| VolT_BL 20% | 0.001 | – | 0.003 | 0.001 | 0.001 | – | – | – |
| ParR_BL 20% | – | – | – | – | – | – | – | – |
| NP 20% | – | – | – | – | – | – | – | – |
| Market 20% | – | – | – | – | – | – | – | – |
| τ = 0.3 X τ = 0.1625 | ||||||||
| Tang_Eq 8% | – | – | – | – | – | – | – | – |
| MinV_Eq 8% | – | – | – | – | – | – | – | – |
| VolT_Eq 8% | – | – | – | – | – | – | – | – |
| ParR_Eq 8% | – | – | – | – | – | – | – | – |
| Tang_BL 8% | – | – | 0.001 | – | 0.001 | – | – | – |
| MinV_BL 8% | 0.001 | – | 0.004 | – | 0.001 | 0.001 | – | – |
| VolT_BL 8% | 0.001 | – | 0.003 | 0.001 | – | 0.001 | – | – |
| ParR_BL 8% | – | – | – | – | – | – | – | – |
| NP 8% | – | – | – | – | – | – | – | – |
| Market 8% | – | – | – | – | – | – | – | – |
| Tang_Eq 15% | 0.001 | – | 0.001 | – | – | 0.001 | – | – |
| MinV_Eq 15% | – | – | – | – | – | – | – | – |
| VolT_Eq 15% | – | – | – | – | – | – | – | – |
| ParR_Eq 15% | – | – | – | – | – | – | – | – |
| Tang_BL 15% | – | – | 0.001 | – | – | – | – | – |
| MinV_BL 15% | – | – | – | – | – | – | – | – |
| VolT_BL 15% | – | – | – | – | – | 0.001 | – | – |
| ParR_BL 15% | – | – | −0.001 | – | – | – | – | – |
| NP 15% | – | – | – | – | – | – | – | – |
| Market 15% | – | – | – | – | – | – | – | – |
| Tang_Eq 20% | 0.001 | – | 0.003 | – | 0.001 | – | – | – |
| MinV_Eq 20% | – | – | – | – | – | – | – | – |
| VolT_Eq 20% | – | – | – | – | – | – | – | – |
| ParR_Eq 20% | – | – | – | – | – | – | – | – |
| Tang_BL 20% | – | – | 0.001 | – | – | 0.001 | – | – |
| MinV_BL 20% | – | – | – | – | – | −0.001 | – | – |
| VolT_BL 20% | – | – | – | – | −0.001 | – | – | – |
| ParR_BL 20% | – | – | – | – | −0.001 | – | – | – |
| NP 20% | – | – | – | – | – | – | – | – |
| Market 20% | – | – | – | – | – | – | – | – |
| Portfolio | Return | Standard deviation | Sharpe ratio | Beta | Treynor ratio | Omega ratio | Tracking error | Turnover |
|---|---|---|---|---|---|---|---|---|
| τ = 0.1625 X τ = 0.025 | ||||||||
| Tang_Eq 8% | – | – | – | – | – | – | – | – |
| MinV_Eq 8% | – | – | – | – | – | – | – | – |
| VolT_Eq 8% | – | – | – | – | – | – | – | – |
| ParR_Eq 8% | – | – | – | – | – | – | – | – |
| Tang_BL 8% | – | – | 0.001 | −0.001 | – | – | – | – |
| MinV_BL 8% | – | – | −0.001 | 0.001 | – | – | – | – |
| VolT_BL 8% | – | – | – | – | – | – | – | – |
| ParR_BL 8% | – | – | – | – | – | – | – | – |
| NP 8% | – | – | – | – | – | – | – | – |
| Market 8% | – | – | – | – | – | – | – | – |
| Tang_Eq 15% | −0.001 | – | −0.003 | – | −0.001 | −0.001 | – | – |
| MinV_Eq 15% | – | – | – | – | – | – | – | – |
| VolT_Eq 15% | – | – | – | – | – | – | – | – |
| ParR_Eq 15% | – | – | – | – | – | – | – | – |
| Tang_BL 15% | −0.004 | – | −0.013 | – | −0.003 | −0.004 | – | 0.002 |
| MinV_BL 15% | 0.001 | – | 0.001 | – | – | – | – | – |
| VolT_BL 15% | 0.001 | – | 0.004 | – | – | – | – | – |
| ParR_BL 15% | – | – | 0.002 | – | – | – | – | – |
| NP 15% | – | – | – | – | – | – | – | – |
| Market 15% | – | – | – | – | – | – | – | – |
| Tang_Eq 20% | −0.001 | – | −0.003 | – | −0.001 | – | – | – |
| MinV_Eq 20% | – | – | – | – | – | – | – | – |
| VolT_Eq 20% | – | – | – | – | – | – | – | – |
| ParR_Eq 20% | – | – | – | – | – | – | – | – |
| Tang_BL 20% | – | – | 0.001 | – | – | – | – | – |
| MinV_BL 20% | 0.001 | – | 0.001 | – | – | 0.001 | −0.001 | – |
| VolT_BL 20% | 0.001 | – | 0.003 | 0.001 | 0.001 | – | – | – |
| ParR_BL 20% | – | – | – | – | – | – | – | – |
| NP 20% | – | – | – | – | – | – | – | – |
| Market 20% | – | – | – | – | – | – | – | – |
| τ = 0.3 X τ = 0.1625 | ||||||||
| Tang_Eq 8% | – | – | – | – | – | – | – | – |
| MinV_Eq 8% | – | – | – | – | – | – | – | – |
| VolT_Eq 8% | – | – | – | – | – | – | – | – |
| ParR_Eq 8% | – | – | – | – | – | – | – | – |
| Tang_BL 8% | – | – | 0.001 | – | 0.001 | – | – | – |
| MinV_BL 8% | 0.001 | – | 0.004 | – | 0.001 | 0.001 | – | – |
| VolT_BL 8% | 0.001 | – | 0.003 | 0.001 | – | 0.001 | – | – |
| ParR_BL 8% | – | – | – | – | – | – | – | – |
| NP 8% | – | – | – | – | – | – | – | – |
| Market 8% | – | – | – | – | – | – | – | – |
| Tang_Eq 15% | 0.001 | – | 0.001 | – | – | 0.001 | – | – |
| MinV_Eq 15% | – | – | – | – | – | – | – | – |
| VolT_Eq 15% | – | – | – | – | – | – | – | – |
| ParR_Eq 15% | – | – | – | – | – | – | – | – |
| Tang_BL 15% | – | – | 0.001 | – | – | – | – | – |
| MinV_BL 15% | – | – | – | – | – | – | – | – |
| VolT_BL 15% | – | – | – | – | – | 0.001 | – | – |
| ParR_BL 15% | – | – | −0.001 | – | – | – | – | – |
| NP 15% | – | – | – | – | – | – | – | – |
| Market 15% | – | – | – | – | – | – | – | – |
| Tang_Eq 20% | 0.001 | – | 0.003 | – | 0.001 | – | – | – |
| MinV_Eq 20% | – | – | – | – | – | – | – | – |
| VolT_Eq 20% | – | – | – | – | – | – | – | – |
| ParR_Eq 20% | – | – | – | – | – | – | – | – |
| Tang_BL 20% | – | – | 0.001 | – | – | 0.001 | – | – |
| MinV_BL 20% | – | – | – | – | – | −0.001 | – | – |
| VolT_BL 20% | – | – | – | – | −0.001 | – | – | – |
| ParR_BL 20% | – | – | – | – | −0.001 | – | – | – |
| NP 20% | – | – | – | – | – | – | – | – |
| Market 20% | – | – | – | – | – | – | – | – |
Note(s): Eq: considers historical mean and sample covariance as inputs. BL: considers as inputs returns and covariances using views in the Black-Litterman model; Tang: tangent portfolio; MinV: minimum variance portfolio; ParR: portfolio with equal risk contribution; VolT: volatility timing portfolio; NP: naive weighted portfolio. Market is a portfolio consisting of Ibovespa, S&P500 and BTC. The percentages of 8%, 15% and 20% represent ex-ante market's risk levels. Data refer to the period from 11/18/2016 to 08/30/2022
Source(s): Elaborated by the authors
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