Advanced Statistics: robson_sys
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
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| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.165 | ||||
| SD | 0.215 | ||||
| Sharpe ratio (Glass type estimate) | -0.767 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.748 | ||||
| df | 31.000 | ||||
| t | -1.252 | ||||
| p | 0.890 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.976 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.455 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.962 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.467 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.905 | ||||
| Upside Potential Ratio | 1.138 | ||||
| Upside part of mean | 0.207 | ||||
| Downside part of mean | -0.372 | ||||
| Upside SD | 0.118 | ||||
| Downside SD | 0.182 | ||||
| N nonnegative terms | 14.000 | ||||
| N negative terms | 18.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.596 | ||||
| Mean of criterion | -0.165 | ||||
| SD of predictor | 0.283 | ||||
| SD of criterion | 0.215 | ||||
| Covariance | -0.005 | ||||
| r | -0.086 | ||||
| b (slope, estimate of beta) | -0.066 | ||||
| a (intercept, estimate of alpha) | -0.126 | ||||
| Mean Square Error | 0.047 | ||||
| DF error | 30.000 | ||||
| t(b) | -0.475 | ||||
| p(b) | 0.681 | ||||
| t(a) | -0.802 | ||||
| p(a) | 0.786 | ||||
| Lowerbound of 95% confidence interval for beta | -0.347 | ||||
| Upperbound of 95% confidence interval for beta | 0.216 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.445 | ||||
| Upperbound of 95% confidence interval for alpha | 0.194 | ||||
| Treynor index (mean / b) | 2.510 | ||||
| Jensen alpha (a) | -0.126 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.188 | ||||
| SD | 0.219 | ||||
| Sharpe ratio (Glass type estimate) | -0.861 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.840 | ||||
| df | 31.000 | ||||
| t | -1.406 | ||||
| p | 0.915 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.073 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.365 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.058 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.379 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.982 | ||||
| Upside Potential Ratio | 1.043 | ||||
| Upside part of mean | 0.200 | ||||
| Downside part of mean | -0.388 | ||||
| Upside SD | 0.112 | ||||
| Downside SD | 0.192 | ||||
| N nonnegative terms | 14.000 | ||||
| N negative terms | 18.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.546 | ||||
| Mean of criterion | -0.188 | ||||
| SD of predictor | 0.262 | ||||
| SD of criterion | 0.219 | ||||
| Covariance | -0.005 | ||||
| r | -0.093 | ||||
| b (slope, estimate of beta) | -0.078 | ||||
| a (intercept, estimate of alpha) | -0.146 | ||||
| Mean Square Error | 0.049 | ||||
| DF error | 30.000 | ||||
| t(b) | -0.513 | ||||
| p(b) | 0.694 | ||||
| t(a) | -0.917 | ||||
| p(a) | 0.817 | ||||
| Lowerbound of 95% confidence interval for beta | -0.388 | ||||
| Upperbound of 95% confidence interval for beta | 0.232 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.470 | ||||
| Upperbound of 95% confidence interval for alpha | 0.179 | ||||
| Treynor index (mean / b) | 2.416 | ||||
| Jensen alpha (a) | -0.146 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.113 | ||||
| Expected Shortfall on VaR | 0.135 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.077 | ||||
| Expected Shortfall on VaR | 0.132 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 32.000 | ||||
| Minimum | 0.863 | ||||
| Quartile 1 | 0.952 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.032 | ||||
| Maximum | 1.140 | ||||
| Mean of quarter 1 | 0.907 | ||||
| Mean of quarter 2 | 0.977 | ||||
| Mean of quarter 3 | 1.016 | ||||
| Mean of quarter 4 | 1.060 | ||||
| Inter Quartile Range | 0.079 | ||||
| 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) | -0.427 | ||||
| VaR(95%) (moments method) | 0.102 | ||||
| Expected Shortfall (moments method) | 0.116 | ||||
| Extreme Value Index (regression method) | -0.042 | ||||
| VaR(95%) (regression method) | 0.085 | ||||
| Expected Shortfall (regression method) | 0.100 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.373 | ||||
| Quartile 1 | 0.373 | ||||
| Median | 0.373 | ||||
| Quartile 3 | 0.373 | ||||
| Maximum | 0.373 | ||||
| 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 | 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 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) | -0.120 | ||||
| Compounded annual return (geometric extrapolation) | -0.134 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.360 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.991 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.165 | ||||
| SD | 0.237 | ||||
| Sharpe ratio (Glass type estimate) | -0.699 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.698 | ||||
| df | 716.000 | ||||
| t | -1.156 | ||||
| p | 0.876 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.884 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.487 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.883 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.488 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.940 | ||||
| Upside Potential Ratio | 7.410 | ||||
| Upside part of mean | 1.302 | ||||
| Downside part of mean | -1.468 | ||||
| Upside SD | 0.158 | ||||
| Downside SD | 0.176 | ||||
| N nonnegative terms | 348.000 | ||||
| N negative terms | 369.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 717.000 | ||||
| Mean of predictor | 0.648 | ||||
| Mean of criterion | -0.165 | ||||
| SD of predictor | 0.353 | ||||
| SD of criterion | 0.237 | ||||
| Covariance | 0.028 | ||||
| r | 0.341 | ||||
| b (slope, estimate of beta) | 0.229 | ||||
| a (intercept, estimate of alpha) | -0.314 | ||||
| Mean Square Error | 0.050 | ||||
| DF error | 715.000 | ||||
| t(b) | 9.711 | ||||
| p(b) | -0.000 | ||||
| t(a) | -2.316 | ||||
| p(a) | 0.990 | ||||
| Lowerbound of 95% confidence interval for beta | 0.183 | ||||
| Upperbound of 95% confidence interval for beta | 0.275 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.579 | ||||
| Upperbound of 95% confidence interval for alpha | -0.048 | ||||
| Treynor index (mean / b) | -0.722 | ||||
| Jensen alpha (a) | -0.314 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.193 | ||||
| SD | 0.237 | ||||
| Sharpe ratio (Glass type estimate) | -0.815 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.815 | ||||
| df | 716.000 | ||||
| t | -1.349 | ||||
| p | 0.911 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.001 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.370 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.371 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.082 | ||||
| Upside Potential Ratio | 7.221 | ||||
| Upside part of mean | 1.290 | ||||
| Downside part of mean | -1.483 | ||||
| Upside SD | 0.156 | ||||
| Downside SD | 0.179 | ||||
| N nonnegative terms | 348.000 | ||||
| N negative terms | 369.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 717.000 | ||||
| Mean of predictor | 0.585 | ||||
| Mean of criterion | -0.193 | ||||
| SD of predictor | 0.354 | ||||
| SD of criterion | 0.237 | ||||
| Covariance | 0.029 | ||||
| r | 0.341 | ||||
| b (slope, estimate of beta) | 0.229 | ||||
| a (intercept, estimate of alpha) | -0.327 | ||||
| Mean Square Error | 0.050 | ||||
| DF error | 715.000 | ||||
| t(b) | 9.701 | ||||
| p(b) | -0.000 | ||||
| t(a) | -2.413 | ||||
| p(a) | 0.992 | ||||
| Lowerbound of 95% confidence interval for beta | 0.182 | ||||
| Upperbound of 95% confidence interval for beta | 0.275 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.593 | ||||
| Upperbound of 95% confidence interval for alpha | -0.061 | ||||
| Treynor index (mean / b) | -0.846 | ||||
| Jensen alpha (a) | -0.327 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.025 | ||||
| Expected Shortfall on VaR | 0.030 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.013 | ||||
| Expected Shortfall on VaR | 0.025 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 717.000 | ||||
| Minimum | 0.918 | ||||
| Quartile 1 | 0.991 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.008 | ||||
| Maximum | 1.082 | ||||
| Mean of quarter 1 | 0.982 | ||||
| Mean of quarter 2 | 0.996 | ||||
| Mean of quarter 3 | 1.003 | ||||
| Mean of quarter 4 | 1.017 | ||||
| Inter Quartile Range | 0.016 | ||||
| Number outliers low | 14.000 | ||||
| Percentage of outliers low | 0.020 | ||||
| Mean of outliers low | 0.956 | ||||
| Number of outliers high | 10.000 | ||||
| Percentage of outliers high | 0.014 | ||||
| Mean of outliers high | 1.044 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.053 | ||||
| VaR(95%) (moments method) | 0.018 | ||||
| Expected Shortfall (moments method) | 0.025 | ||||
| Extreme Value Index (regression method) | 0.014 | ||||
| VaR(95%) (regression method) | 0.018 | ||||
| Expected Shortfall (regression method) | 0.024 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.003 | ||||
| Median | 0.008 | ||||
| Quartile 3 | 0.011 | ||||
| Maximum | 0.414 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.005 | ||||
| Mean of quarter 3 | 0.010 | ||||
| Mean of quarter 4 | 0.213 | ||||
| Inter Quartile Range | 0.008 | ||||
| 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 | 0.125 | ||||
| Mean of outliers high | 0.414 | ||||
| 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) | -0.123 | ||||
| Compounded annual return (geometric extrapolation) | -0.139 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.335 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.651 | ||||
| Compounded annual return / Expected Shortfall lognormal | -4.553 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.386 | ||||
| SD | 0.264 | ||||
| Sharpe ratio (Glass type estimate) | -1.460 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.451 | ||||
| df | 130.000 | ||||
| t | -1.032 | ||||
| p | 0.545 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.234 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.321 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.229 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.326 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.847 | ||||
| Upside Potential Ratio | 5.820 | ||||
| Upside part of mean | 1.215 | ||||
| Downside part of mean | -1.600 | ||||
| Upside SD | 0.162 | ||||
| Downside SD | 0.209 | ||||
| N nonnegative terms | 53.000 | ||||
| N negative terms | 78.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.967 | ||||
| Mean of criterion | -0.386 | ||||
| SD of predictor | 0.522 | ||||
| SD of criterion | 0.264 | ||||
| Covariance | 0.036 | ||||
| r | 0.260 | ||||
| b (slope, estimate of beta) | 0.132 | ||||
| a (intercept, estimate of alpha) | -0.513 | ||||
| Mean Square Error | 0.066 | ||||
| DF error | 129.000 | ||||
| t(b) | 3.055 | ||||
| p(b) | 0.337 | ||||
| t(a) | -1.407 | ||||
| p(a) | 0.578 | ||||
| Lowerbound of 95% confidence interval for beta | 0.046 | ||||
| Upperbound of 95% confidence interval for beta | 0.217 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.234 | ||||
| Upperbound of 95% confidence interval for alpha | 0.208 | ||||
| Treynor index (mean / b) | -2.931 | ||||
| Jensen alpha (a) | -0.513 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.421 | ||||
| SD | 0.266 | ||||
| Sharpe ratio (Glass type estimate) | -1.579 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.570 | ||||
| df | 130.000 | ||||
| t | -1.117 | ||||
| p | 0.549 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.355 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.202 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.349 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.208 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.970 | ||||
| Upside Potential Ratio | 5.625 | ||||
| Upside part of mean | 1.202 | ||||
| Downside part of mean | -1.622 | ||||
| Upside SD | 0.160 | ||||
| Downside SD | 0.214 | ||||
| N nonnegative terms | 53.000 | ||||
| N negative terms | 78.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.831 | ||||
| Mean of criterion | -0.421 | ||||
| SD of predictor | 0.520 | ||||
| SD of criterion | 0.266 | ||||
| Covariance | 0.036 | ||||
| r | 0.262 | ||||
| b (slope, estimate of beta) | 0.135 | ||||
| a (intercept, estimate of alpha) | -0.533 | ||||
| Mean Square Error | 0.067 | ||||
| DF error | 129.000 | ||||
| t(b) | 3.089 | ||||
| p(b) | 0.335 | ||||
| t(a) | -1.452 | ||||
| p(a) | 0.581 | ||||
| Lowerbound of 95% confidence interval for beta | 0.048 | ||||
| Upperbound of 95% confidence interval for beta | 0.221 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.258 | ||||
| Upperbound of 95% confidence interval for alpha | 0.193 | ||||
| Treynor index (mean / b) | -3.128 | ||||
| Jensen alpha (a) | -0.533 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.030 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.918 | ||||
| Quartile 1 | 0.991 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.004 | ||||
| Maximum | 1.051 | ||||
| Mean of quarter 1 | 0.979 | ||||
| Mean of quarter 2 | 0.997 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.017 | ||||
| Inter Quartile Range | 0.013 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.046 | ||||
| Mean of outliers low | 0.956 | ||||
| Number of outliers high | 8.000 | ||||
| Percentage of outliers high | 0.061 | ||||
| Mean of outliers high | 1.032 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.250 | ||||
| VaR(95%) (moments method) | 0.021 | ||||
| Expected Shortfall (moments method) | 0.034 | ||||
| Extreme Value Index (regression method) | 0.377 | ||||
| VaR(95%) (regression method) | 0.020 | ||||
| Expected Shortfall (regression method) | 0.036 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.011 | ||||
| Median | 0.023 | ||||
| Quartile 3 | 0.037 | ||||
| Maximum | 0.260 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | 0.022 | ||||
| Mean of quarter 3 | 0.023 | ||||
| Mean of quarter 4 | 0.151 | ||||
| Inter Quartile Range | 0.027 | ||||
| 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 | 0.167 | ||||
| Mean of outliers high | 0.260 | ||||
| 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) | -0.343 | ||||
| Compounded annual return (geometric extrapolation) | -0.314 | ||||
| Calmar ratio (compounded annual return / max draw down) | -1.208 | ||||
| Compounded annual return / average of 25% largest draw downs | -2.079 | ||||
| Compounded annual return / Expected Shortfall lognormal | -8.991 | ||||