Ledoit and Wolf's test for annualized portfolio Sharpe ratio difference
| Portfolio 1 | Portfolio 2 | p-value | SR portfolio 1 | SR portfolio 2 | |
|---|---|---|---|---|---|
| Risk 8% p.y. | Tang_Eq 8% | ParR_Eq 8% | 0.0279 | 0.8315 | 1.0473 |
| Tang_Eq 8% | VolT_BL 8% | 0.0699 | 0.8315 | 1.1486 | |
| Tang_Eq 8% | ParR_BL 8% | 0.0559 | 0.8315 | 1.5510 | |
| MinV_Eq 8% | ParR_BL 8% | 0.0878 | 0.9072 | 1.5510 | |
| ParR_BL 8% | Mercado 8% | 0.0978 | 1.5510 | 0.7734 | |
| Risk 15% p.y. | MinV_Eq 15% | VolT_BL 15% | 0.0998 | 0.9072 | 1.1505 |
| Tang_Eq 15% | ParR_BL 15% | 0.0439 | 0.9223 | 1.5516 | |
| MinV_Eq 15% | ParR_BL 15% | 0.0878 | 0.9072 | 1.5516 | |
| Tang_BL 15% | ParR_BL 15% | 0.0898 | 1.0764 | 1.5516 | |
| Risk 20% p.y. | Tang_Eq 20% | VolT_Eq 20% | 0.0659 | 0.9790 | 1.3280 |
| Tang_Eq 20% | ParR_BL 20% | 0.0619 | 0.9790 | 1.5511 | |
| MinV_Eq 20% | ParR_BL 20% | 0.0878 | 0.9072 | 1.5511 | |
| Tang_BL 20% | ParR_BL 20% | 0.0818 | 1.0683 | 1.5511 | |
| Tang_Eq 20% | Mercado 20% | 0.0519 | 0.9790 | 1.3891 |
| Portfolio 1 | Portfolio 2 | SR portfolio 1 | SR portfolio 2 | ||
|---|---|---|---|---|---|
| Risk 8% p.y. | Tang_Eq 8% | ParR_Eq 8% | 0.0279 | 0.8315 | |
| Tang_Eq 8% | VolT_BL 8% | 0.0699 | 0.8315 | ||
| Tang_Eq 8% | ParR_BL 8% | 0.0559 | 0.8315 | ||
| MinV_Eq 8% | ParR_BL 8% | 0.0878 | 0.9072 | ||
| ParR_BL 8% | Mercado 8% | 0.0978 | 1.5510 | ||
| Risk 15% p.y. | MinV_Eq 15% | VolT_BL 15% | 0.0998 | 0.9072 | |
| Tang_Eq 15% | ParR_BL 15% | 0.0439 | 0.9223 | ||
| MinV_Eq 15% | ParR_BL 15% | 0.0878 | 0.9072 | ||
| Tang_BL 15% | ParR_BL 15% | 0.0898 | 1.0764 | ||
| Risk 20% p.y. | Tang_Eq 20% | VolT_Eq 20% | 0.0659 | 0.9790 | |
| Tang_Eq 20% | ParR_BL 20% | 0.0619 | 0.9790 | ||
| MinV_Eq 20% | ParR_BL 20% | 0.0878 | 0.9072 | ||
| Tang_BL 20% | ParR_BL 20% | 0.0818 | 1.0683 | ||
| Tang_Eq 20% | Mercado 20% | 0.0519 | 0.9790 |
Note(s): 1: Only the results of the tests with a p-Value lower than 10% are presented in the table; other comparisons were not significant
2: 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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