Advanced Statistics: gdes
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 | -0.048 | ||||
| SD | 0.174 | ||||
| Sharpe ratio (Glass type estimate) | -0.276 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.273 | ||||
| df | 68.000 | ||||
| t | -0.662 | ||||
| p | 0.745 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.094 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.544 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.092 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.546 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.373 | ||||
| Upside Potential Ratio | 0.375 | ||||
| Upside part of mean | 0.048 | ||||
| Downside part of mean | -0.096 | ||||
| Upside SD | 0.116 | ||||
| Downside SD | 0.129 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 68.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 69.000 | ||||
| Mean of predictor | 0.300 | ||||
| Mean of criterion | -0.048 | ||||
| SD of predictor | 0.217 | ||||
| SD of criterion | 0.174 | ||||
| Covariance | 0.006 | ||||
| r | 0.147 | ||||
| b (slope, estimate of beta) | 0.118 | ||||
| a (intercept, estimate of alpha) | -0.083 | ||||
| Mean Square Error | 0.030 | ||||
| DF error | 67.000 | ||||
| t(b) | 1.220 | ||||
| p(b) | 0.113 | ||||
| t(a) | -1.071 | ||||
| p(a) | 0.856 | ||||
| Lowerbound of 95% confidence interval for beta | -0.075 | ||||
| Upperbound of 95% confidence interval for beta | 0.311 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.239 | ||||
| Upperbound of 95% confidence interval for alpha | 0.072 | ||||
| Treynor index (mean / b) | -0.407 | ||||
| Jensen alpha (a) | -0.083 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.064 | ||||
| SD | 0.184 | ||||
| Sharpe ratio (Glass type estimate) | -0.347 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.343 | ||||
| df | 68.000 | ||||
| t | -0.832 | ||||
| p | 0.796 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.165 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.474 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.162 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.476 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.418 | ||||
| Upside Potential Ratio | 0.278 | ||||
| Upside part of mean | 0.042 | ||||
| Downside part of mean | -0.106 | ||||
| Upside SD | 0.102 | ||||
| Downside SD | 0.153 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 68.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 69.000 | ||||
| Mean of predictor | 0.274 | ||||
| Mean of criterion | -0.064 | ||||
| SD of predictor | 0.210 | ||||
| SD of criterion | 0.184 | ||||
| Covariance | 0.008 | ||||
| r | 0.196 | ||||
| b (slope, estimate of beta) | 0.172 | ||||
| a (intercept, estimate of alpha) | -0.111 | ||||
| Mean Square Error | 0.033 | ||||
| DF error | 67.000 | ||||
| t(b) | 1.638 | ||||
| p(b) | 0.053 | ||||
| t(a) | -1.368 | ||||
| p(a) | 0.912 | ||||
| Lowerbound of 95% confidence interval for beta | -0.038 | ||||
| Upperbound of 95% confidence interval for beta | 0.381 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.273 | ||||
| Upperbound of 95% confidence interval for alpha | 0.051 | ||||
| Treynor index (mean / b) | -0.371 | ||||
| Jensen alpha (a) | -0.111 | ||||
| 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 | 0.108 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.061 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 69.000 | ||||
| Minimum | 0.697 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.281 | ||||
| Mean of quarter 1 | 0.983 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.017 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.014 | ||||
| Mean of outliers low | 0.697 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.014 | ||||
| Mean of outliers high | 1.281 | ||||
| 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 | 1.000 | ||||
| Minimum | 0.303 | ||||
| Quartile 1 | 0.303 | ||||
| Median | 0.303 | ||||
| Quartile 3 | 0.303 | ||||
| Maximum | 0.303 | ||||
| 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) | -0.019 | ||||
| Compounded annual return (geometric extrapolation) | -0.020 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.065 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.181 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.054 | ||||
| SD | 0.133 | ||||
| Sharpe ratio (Glass type estimate) | -0.410 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.410 | ||||
| df | 1519.000 | ||||
| t | -0.987 | ||||
| p | 0.516 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.224 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.404 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.224 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.404 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.506 | ||||
| Upside Potential Ratio | 0.931 | ||||
| Upside part of mean | 0.100 | ||||
| Downside part of mean | -0.155 | ||||
| Upside SD | 0.078 | ||||
| Downside SD | 0.108 | ||||
| N nonnegative terms | 14.000 | ||||
| N negative terms | 1506.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1520.000 | ||||
| Mean of predictor | 0.327 | ||||
| Mean of criterion | -0.054 | ||||
| SD of predictor | 0.299 | ||||
| SD of criterion | 0.133 | ||||
| Covariance | 0.004 | ||||
| r | 0.111 | ||||
| b (slope, estimate of beta) | 0.049 | ||||
| a (intercept, estimate of alpha) | -0.071 | ||||
| Mean Square Error | 0.017 | ||||
| DF error | 1518.000 | ||||
| t(b) | 4.357 | ||||
| p(b) | 0.444 | ||||
| t(a) | -1.284 | ||||
| p(a) | 0.516 | ||||
| Lowerbound of 95% confidence interval for beta | 0.027 | ||||
| Upperbound of 95% confidence interval for beta | 0.071 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.178 | ||||
| Upperbound of 95% confidence interval for alpha | 0.037 | ||||
| Treynor index (mean / b) | -1.105 | ||||
| Jensen alpha (a) | -0.071 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.064 | ||||
| SD | 0.137 | ||||
| Sharpe ratio (Glass type estimate) | -0.464 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.464 | ||||
| df | 1519.000 | ||||
| t | -1.117 | ||||
| p | 0.518 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.278 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.350 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.277 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.350 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.555 | ||||
| Upside Potential Ratio | 0.847 | ||||
| Upside part of mean | 0.097 | ||||
| Downside part of mean | -0.161 | ||||
| Upside SD | 0.075 | ||||
| Downside SD | 0.115 | ||||
| N nonnegative terms | 14.000 | ||||
| N negative terms | 1506.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1520.000 | ||||
| Mean of predictor | 0.282 | ||||
| Mean of criterion | -0.064 | ||||
| SD of predictor | 0.298 | ||||
| SD of criterion | 0.137 | ||||
| Covariance | 0.005 | ||||
| r | 0.115 | ||||
| b (slope, estimate of beta) | 0.053 | ||||
| a (intercept, estimate of alpha) | -0.079 | ||||
| Mean Square Error | 0.019 | ||||
| DF error | 1518.000 | ||||
| t(b) | 4.517 | ||||
| p(b) | 0.442 | ||||
| t(a) | -1.386 | ||||
| p(a) | 0.518 | ||||
| Lowerbound of 95% confidence interval for beta | 0.030 | ||||
| Upperbound of 95% confidence interval for beta | 0.076 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.190 | ||||
| Upperbound of 95% confidence interval for alpha | 0.033 | ||||
| Treynor index (mean / b) | -1.200 | ||||
| Jensen alpha (a) | -0.079 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.018 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1520.000 | ||||
| Minimum | 0.835 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.099 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.002 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 9.000 | ||||
| Percentage of outliers low | 0.006 | ||||
| Mean of outliers low | 0.928 | ||||
| Number of outliers high | 14.000 | ||||
| Percentage of outliers high | 0.009 | ||||
| Mean of outliers high | 1.042 | ||||
| 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) | -0.347 | ||||
| VaR(95%) (regression method) | -0.234 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.366 | ||||
| Quartile 1 | 0.366 | ||||
| Median | 0.366 | ||||
| Quartile 3 | 0.366 | ||||
| Maximum | 0.366 | ||||
| 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) | -0.019 | ||||
| Compounded annual return (geometric extrapolation) | -0.019 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.053 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.105 | ||||
| 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 | 1.083 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.395 | ||||
| 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 | 1.003 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.399 | ||||
| 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) | -8694624991756914.000 | ||||
| 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) | -135728974094065125531125284864000.000 | ||||
| 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 | ||||