Advanced Statistics: Parcours Reversal LT
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.066 | ||||
| SD | 0.216 | ||||
| Sharpe ratio (Glass type estimate) | 0.305 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.302 | ||||
| df | 92.000 | ||||
| t | 0.849 | ||||
| p | 0.199 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.401 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.009 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.403 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.008 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.646 | ||||
| Upside Potential Ratio | 2.322 | ||||
| Upside part of mean | 0.236 | ||||
| Downside part of mean | -0.171 | ||||
| Upside SD | 0.190 | ||||
| Downside SD | 0.102 | ||||
| N nonnegative terms | 27.000 | ||||
| N negative terms | 66.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 93.000 | ||||
| Mean of predictor | 0.205 | ||||
| Mean of criterion | 0.066 | ||||
| SD of predictor | 0.193 | ||||
| SD of criterion | 0.216 | ||||
| Covariance | -0.002 | ||||
| r | -0.054 | ||||
| b (slope, estimate of beta) | -0.060 | ||||
| a (intercept, estimate of alpha) | 0.078 | ||||
| Mean Square Error | 0.047 | ||||
| DF error | 91.000 | ||||
| t(b) | -0.515 | ||||
| p(b) | 0.696 | ||||
| t(a) | 0.960 | ||||
| p(a) | 0.170 | ||||
| Lowerbound of 95% confidence interval for beta | -0.293 | ||||
| Upperbound of 95% confidence interval for beta | 0.172 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.084 | ||||
| Upperbound of 95% confidence interval for alpha | 0.240 | ||||
| Treynor index (mean / b) | -1.090 | ||||
| Jensen alpha (a) | 0.078 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.044 | ||||
| SD | 0.204 | ||||
| Sharpe ratio (Glass type estimate) | 0.217 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.215 | ||||
| df | 92.000 | ||||
| t | 0.603 | ||||
| p | 0.274 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.489 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.921 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.490 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.920 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.416 | ||||
| Upside Potential Ratio | 2.068 | ||||
| Upside part of mean | 0.220 | ||||
| Downside part of mean | -0.175 | ||||
| Upside SD | 0.173 | ||||
| Downside SD | 0.106 | ||||
| N nonnegative terms | 27.000 | ||||
| N negative terms | 66.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 93.000 | ||||
| Mean of predictor | 0.186 | ||||
| Mean of criterion | 0.044 | ||||
| SD of predictor | 0.183 | ||||
| SD of criterion | 0.204 | ||||
| Covariance | -0.002 | ||||
| r | -0.043 | ||||
| b (slope, estimate of beta) | -0.048 | ||||
| a (intercept, estimate of alpha) | 0.053 | ||||
| Mean Square Error | 0.042 | ||||
| DF error | 91.000 | ||||
| t(b) | -0.412 | ||||
| p(b) | 0.659 | ||||
| t(a) | 0.692 | ||||
| p(a) | 0.245 | ||||
| Lowerbound of 95% confidence interval for beta | -0.280 | ||||
| Upperbound of 95% confidence interval for beta | 0.184 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.099 | ||||
| Upperbound of 95% confidence interval for alpha | 0.205 | ||||
| Treynor index (mean / b) | -0.920 | ||||
| Jensen alpha (a) | 0.053 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.089 | ||||
| Expected Shortfall on VaR | 0.111 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.040 | ||||
| Expected Shortfall on VaR | 0.076 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 93.000 | ||||
| Minimum | 0.876 | ||||
| Quartile 1 | 0.991 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.010 | ||||
| Maximum | 1.236 | ||||
| Mean of quarter 1 | 0.957 | ||||
| Mean of quarter 2 | 0.997 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.082 | ||||
| Inter Quartile Range | 0.020 | ||||
| Number outliers low | 11.000 | ||||
| Percentage of outliers low | 0.118 | ||||
| Mean of outliers low | 0.926 | ||||
| Number of outliers high | 12.000 | ||||
| Percentage of outliers high | 0.129 | ||||
| Mean of outliers high | 1.137 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.602 | ||||
| VaR(95%) (moments method) | 0.041 | ||||
| Expected Shortfall (moments method) | 0.117 | ||||
| Extreme Value Index (regression method) | 0.376 | ||||
| VaR(95%) (regression method) | 0.037 | ||||
| Expected Shortfall (regression method) | 0.074 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.018 | ||||
| Median | 0.044 | ||||
| Quartile 3 | 0.111 | ||||
| Maximum | 0.280 | ||||
| Mean of quarter 1 | 0.012 | ||||
| Mean of quarter 2 | 0.033 | ||||
| Mean of quarter 3 | 0.095 | ||||
| Mean of quarter 4 | 0.204 | ||||
| Inter Quartile Range | 0.093 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.111 | ||||
| Mean of outliers high | 0.280 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.131 | ||||
| VaR(95%) (moments method) | 0.208 | ||||
| Expected Shortfall (moments method) | 0.290 | ||||
| Extreme Value Index (regression method) | 2.250 | ||||
| VaR(95%) (regression method) | 0.430 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.127 | ||||
| Compounded annual return (geometric extrapolation) | 0.092 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.329 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.453 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.832 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.065 | ||||
| SD | 0.206 | ||||
| Sharpe ratio (Glass type estimate) | 0.313 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.313 | ||||
| df | 2043.000 | ||||
| t | 0.875 | ||||
| p | 0.191 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.389 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.015 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.389 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.015 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.488 | ||||
| Upside Potential Ratio | 4.701 | ||||
| Upside part of mean | 0.623 | ||||
| Downside part of mean | -0.558 | ||||
| Upside SD | 0.158 | ||||
| Downside SD | 0.132 | ||||
| N nonnegative terms | 553.000 | ||||
| N negative terms | 1491.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2044.000 | ||||
| Mean of predictor | 0.216 | ||||
| Mean of criterion | 0.065 | ||||
| SD of predictor | 0.233 | ||||
| SD of criterion | 0.206 | ||||
| Covariance | -0.004 | ||||
| r | -0.078 | ||||
| b (slope, estimate of beta) | -0.069 | ||||
| a (intercept, estimate of alpha) | 0.080 | ||||
| Mean Square Error | 0.042 | ||||
| DF error | 2042.000 | ||||
| t(b) | -3.528 | ||||
| p(b) | 1.000 | ||||
| t(a) | 1.078 | ||||
| p(a) | 0.140 | ||||
| Lowerbound of 95% confidence interval for beta | -0.107 | ||||
| Upperbound of 95% confidence interval for beta | -0.031 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.065 | ||||
| Upperbound of 95% confidence interval for alpha | 0.224 | ||||
| Treynor index (mean / b) | -0.936 | ||||
| Jensen alpha (a) | 0.080 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.044 | ||||
| SD | 0.205 | ||||
| Sharpe ratio (Glass type estimate) | 0.213 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.213 | ||||
| df | 2043.000 | ||||
| t | 0.594 | ||||
| p | 0.276 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.489 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.914 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.489 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.914 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.318 | ||||
| Upside Potential Ratio | 4.458 | ||||
| Upside part of mean | 0.611 | ||||
| Downside part of mean | -0.567 | ||||
| Upside SD | 0.152 | ||||
| Downside SD | 0.137 | ||||
| N nonnegative terms | 553.000 | ||||
| N negative terms | 1491.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2044.000 | ||||
| Mean of predictor | 0.189 | ||||
| Mean of criterion | 0.044 | ||||
| SD of predictor | 0.234 | ||||
| SD of criterion | 0.205 | ||||
| Covariance | -0.004 | ||||
| r | -0.077 | ||||
| b (slope, estimate of beta) | -0.068 | ||||
| a (intercept, estimate of alpha) | 0.056 | ||||
| Mean Square Error | 0.042 | ||||
| DF error | 2042.000 | ||||
| t(b) | -3.491 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.769 | ||||
| p(a) | 0.221 | ||||
| Lowerbound of 95% confidence interval for beta | -0.106 | ||||
| Upperbound of 95% confidence interval for beta | -0.030 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.087 | ||||
| Upperbound of 95% confidence interval for alpha | 0.200 | ||||
| Treynor index (mean / b) | -0.645 | ||||
| Jensen alpha (a) | 0.056 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.020 | ||||
| Expected Shortfall on VaR | 0.026 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.013 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2044.000 | ||||
| Minimum | 0.860 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.181 | ||||
| Mean of quarter 1 | 0.992 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.010 | ||||
| Inter Quartile Range | 0.001 | ||||
| Number outliers low | 339.000 | ||||
| Percentage of outliers low | 0.166 | ||||
| Mean of outliers low | 0.988 | ||||
| Number of outliers high | 352.000 | ||||
| Percentage of outliers high | 0.172 | ||||
| Mean of outliers high | 1.014 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.095 | ||||
| VaR(95%) (moments method) | 0.006 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.634 | ||||
| VaR(95%) (regression method) | 0.006 | ||||
| Expected Shortfall (regression method) | 0.019 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 32.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.008 | ||||
| Median | 0.023 | ||||
| Quartile 3 | 0.084 | ||||
| Maximum | 0.300 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.015 | ||||
| Mean of quarter 3 | 0.040 | ||||
| Mean of quarter 4 | 0.147 | ||||
| Inter Quartile Range | 0.076 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.031 | ||||
| Mean of outliers high | 0.300 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.030 | ||||
| VaR(95%) (moments method) | 0.155 | ||||
| Expected Shortfall (moments method) | 0.200 | ||||
| Extreme Value Index (regression method) | 0.713 | ||||
| VaR(95%) (regression method) | 0.150 | ||||
| Expected Shortfall (regression method) | 0.362 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.126 | ||||
| Compounded annual return (geometric extrapolation) | 0.092 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.305 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.624 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.576 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | NA | ||||
| Sharpe ratio (Hedges UMVUE) | NA | ||||
| df | NA | ||||
| t | NA | ||||
| p | NA | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.338 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.403 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | NA | ||||
| b (slope, estimate of beta) | NA | ||||
| a (intercept, estimate of alpha) | NA | ||||
| Mean Square Error | NA | ||||
| DF error | NA | ||||
| t(b) | NA | ||||
| p(b) | NA | ||||
| t(a) | NA | ||||
| p(a) | NA | ||||
| Lowerbound of 95% confidence interval for beta | NA | ||||
| Upperbound of 95% confidence interval for beta | NA | ||||
| Lowerbound of 95% confidence interval for alpha | NA | ||||
| Upperbound of 95% confidence interval for alpha | NA | ||||
| Treynor index (mean / b) | NA | ||||
| Jensen alpha (a) | NA | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | -12492933348697024.000 | ||||
| Sharpe ratio (Hedges UMVUE) | -12420719861132300.000 | ||||
| df | 130.000 | ||||
| t | -8833837887775228.000 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -13930479873814932.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -10910959848449668.000 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.254 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.404 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | -0.000 | ||||
| r | -0.000 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | -0.000 | ||||
| p(b) | 0.500 | ||||
| t(a) | -8640778657124372.000 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.000 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.044 | ||||
| Upperbound of 95% confidence interval for alpha | -0.044 | ||||
| Treynor index (mean / b) | 92705824830151790539756537905152.000 | ||||
| Jensen alpha (a) | -0.044 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | 0.000 | ||||
| Mean of outliers high | NA | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 0.000 | ||||
| Minimum | NA | ||||
| Quartile 1 | NA | ||||
| Median | NA | ||||
| Quartile 3 | NA | ||||
| Maximum | NA | ||||
| Mean of quarter 1 | NA | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | NA | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | NA | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | NA | ||||
| Mean of outliers high | NA | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | NA | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||