Advanced Statistics: ST TREND
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 | 0.270 | ||||
| SD | 0.527 | ||||
| Sharpe ratio (Glass type estimate) | 0.512 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.506 | ||||
| df | 63.000 | ||||
| t | 1.183 | ||||
| p | 0.121 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.343 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.363 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.347 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.359 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 7.485 | ||||
| Upside Potential Ratio | 9.358 | ||||
| Upside part of mean | 0.337 | ||||
| Downside part of mean | -0.068 | ||||
| Upside SD | 0.527 | ||||
| Downside SD | 0.036 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 56.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 64.000 | ||||
| Mean of predictor | 0.269 | ||||
| Mean of criterion | 0.270 | ||||
| SD of predictor | 0.362 | ||||
| SD of criterion | 0.527 | ||||
| Covariance | 0.002 | ||||
| r | 0.012 | ||||
| b (slope, estimate of beta) | 0.018 | ||||
| a (intercept, estimate of alpha) | 0.265 | ||||
| Mean Square Error | 0.282 | ||||
| DF error | 62.000 | ||||
| t(b) | 0.098 | ||||
| p(b) | 0.461 | ||||
| t(a) | 1.126 | ||||
| p(a) | 0.132 | ||||
| Lowerbound of 95% confidence interval for beta | -0.352 | ||||
| Upperbound of 95% confidence interval for beta | 0.388 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.206 | ||||
| Upperbound of 95% confidence interval for alpha | 0.735 | ||||
| Treynor index (mean / b) | 14.839 | ||||
| Jensen alpha (a) | 0.265 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.185 | ||||
| SD | 0.362 | ||||
| Sharpe ratio (Glass type estimate) | 0.510 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.504 | ||||
| df | 63.000 | ||||
| t | 1.178 | ||||
| p | 0.122 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.345 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.361 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.349 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.357 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 5.048 | ||||
| Upside Potential Ratio | 6.905 | ||||
| Upside part of mean | 0.253 | ||||
| Downside part of mean | -0.068 | ||||
| Upside SD | 0.361 | ||||
| Downside SD | 0.037 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 56.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 64.000 | ||||
| Mean of predictor | 0.201 | ||||
| Mean of criterion | 0.185 | ||||
| SD of predictor | 0.368 | ||||
| SD of criterion | 0.362 | ||||
| Covariance | 0.006 | ||||
| r | 0.045 | ||||
| b (slope, estimate of beta) | 0.044 | ||||
| a (intercept, estimate of alpha) | 0.176 | ||||
| Mean Square Error | 0.133 | ||||
| DF error | 62.000 | ||||
| t(b) | 0.355 | ||||
| p(b) | 0.362 | ||||
| t(a) | 1.099 | ||||
| p(a) | 0.138 | ||||
| Lowerbound of 95% confidence interval for beta | -0.205 | ||||
| Upperbound of 95% confidence interval for beta | 0.294 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.144 | ||||
| Upperbound of 95% confidence interval for alpha | 0.495 | ||||
| Treynor index (mean / b) | 4.162 | ||||
| Jensen alpha (a) | 0.176 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.145 | ||||
| Expected Shortfall on VaR | 0.181 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.018 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 64.000 | ||||
| Minimum | 0.955 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.167 | ||||
| Mean of quarter 1 | 0.990 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.114 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 9.000 | ||||
| Percentage of outliers low | 0.141 | ||||
| Mean of outliers low | 0.983 | ||||
| Number of outliers high | 11.000 | ||||
| Percentage of outliers high | 0.172 | ||||
| Mean of outliers high | 1.166 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -6.555 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.000 | ||||
| Extreme Value Index (regression method) | -0.329 | ||||
| VaR(95%) (regression method) | 0.016 | ||||
| Expected Shortfall (regression method) | 0.028 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.001 | ||||
| Median | 0.008 | ||||
| Quartile 3 | 0.037 | ||||
| Maximum | 0.069 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.005 | ||||
| Mean of quarter 3 | 0.030 | ||||
| Mean of quarter 4 | 0.057 | ||||
| Inter Quartile Range | 0.036 | ||||
| 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) | 0.447 | ||||
| Compounded annual return (geometric extrapolation) | 0.257 | ||||
| Calmar ratio (compounded annual return / max draw down) | 3.715 | ||||
| Compounded annual return / average of 25% largest draw downs | 4.502 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.421 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.373 | ||||
| SD | 0.703 | ||||
| Sharpe ratio (Glass type estimate) | 0.530 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.530 | ||||
| df | 1412.000 | ||||
| t | 1.231 | ||||
| p | 0.484 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.314 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.374 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.314 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.374 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.221 | ||||
| Upside Potential Ratio | 4.314 | ||||
| Upside part of mean | 1.318 | ||||
| Downside part of mean | -0.945 | ||||
| Upside SD | 0.634 | ||||
| Downside SD | 0.305 | ||||
| N nonnegative terms | 136.000 | ||||
| N negative terms | 1277.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1413.000 | ||||
| Mean of predictor | 0.461 | ||||
| Mean of criterion | 0.373 | ||||
| SD of predictor | 0.636 | ||||
| SD of criterion | 0.703 | ||||
| Covariance | -0.003 | ||||
| r | -0.007 | ||||
| b (slope, estimate of beta) | -0.008 | ||||
| a (intercept, estimate of alpha) | 0.377 | ||||
| Mean Square Error | 0.495 | ||||
| DF error | 1411.000 | ||||
| t(b) | -0.272 | ||||
| p(b) | 0.505 | ||||
| t(a) | 1.241 | ||||
| p(a) | 0.479 | ||||
| Lowerbound of 95% confidence interval for beta | -0.066 | ||||
| Upperbound of 95% confidence interval for beta | 0.050 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.218 | ||||
| Upperbound of 95% confidence interval for alpha | 0.972 | ||||
| Treynor index (mean / b) | -46.626 | ||||
| Jensen alpha (a) | 0.377 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.182 | ||||
| SD | 0.587 | ||||
| Sharpe ratio (Glass type estimate) | 0.311 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.310 | ||||
| df | 1412.000 | ||||
| t | 0.721 | ||||
| p | 0.490 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.534 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.155 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.534 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.154 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.553 | ||||
| Upside Potential Ratio | 3.580 | ||||
| Upside part of mean | 1.178 | ||||
| Downside part of mean | -0.996 | ||||
| Upside SD | 0.485 | ||||
| Downside SD | 0.329 | ||||
| N nonnegative terms | 136.000 | ||||
| N negative terms | 1277.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1413.000 | ||||
| Mean of predictor | 0.263 | ||||
| Mean of criterion | 0.182 | ||||
| SD of predictor | 0.627 | ||||
| SD of criterion | 0.587 | ||||
| Covariance | -0.006 | ||||
| r | -0.017 | ||||
| b (slope, estimate of beta) | -0.016 | ||||
| a (intercept, estimate of alpha) | 0.186 | ||||
| Mean Square Error | 0.344 | ||||
| DF error | 1411.000 | ||||
| t(b) | -0.631 | ||||
| p(b) | 0.511 | ||||
| t(a) | 0.737 | ||||
| p(a) | 0.488 | ||||
| Lowerbound of 95% confidence interval for beta | -0.065 | ||||
| Upperbound of 95% confidence interval for beta | 0.033 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.309 | ||||
| Upperbound of 95% confidence interval for alpha | 0.682 | ||||
| Treynor index (mean / b) | -11.593 | ||||
| Jensen alpha (a) | 0.186 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.057 | ||||
| Expected Shortfall on VaR | 0.071 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.026 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1413.000 | ||||
| Minimum | 0.780 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.167 | ||||
| Mean of quarter 1 | 0.986 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.020 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 116.000 | ||||
| Percentage of outliers low | 0.082 | ||||
| Mean of outliers low | 0.958 | ||||
| Number of outliers high | 148.000 | ||||
| Percentage of outliers high | 0.105 | ||||
| Mean of outliers high | 1.048 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.626 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.011 | ||||
| Extreme Value Index (regression method) | 0.138 | ||||
| VaR(95%) (regression method) | 0.008 | ||||
| Expected Shortfall (regression method) | 0.033 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 23.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.023 | ||||
| Quartile 3 | 0.141 | ||||
| Maximum | 0.271 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.006 | ||||
| Mean of quarter 3 | 0.093 | ||||
| Mean of quarter 4 | 0.207 | ||||
| Inter Quartile Range | 0.140 | ||||
| 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) | -2.053 | ||||
| VaR(95%) (moments method) | 0.228 | ||||
| Expected Shortfall (moments method) | 0.230 | ||||
| Extreme Value Index (regression method) | -1.132 | ||||
| VaR(95%) (regression method) | 0.248 | ||||
| Expected Shortfall (regression method) | 0.259 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.442 | ||||
| Compounded annual return (geometric extrapolation) | 0.254 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.935 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.223 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.560 | ||||
| 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 | 2.222 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.691 | ||||
| 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 | 1.981 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.682 | ||||
| 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) | -8660303154527020.000 | ||||
| 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) | 146665931900714638228346883801088.000 | ||||
| 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 | ||||