Advanced Statistics: TRENDSETTER
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 | 11606.183 | ||||
| SD | 26804.257 | ||||
| Sharpe ratio (Glass type estimate) | 0.433 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.428 | ||||
| df | 63.000 | ||||
| t | 1.000 | ||||
| p | 0.161 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.421 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.283 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.424 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.280 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 18861.580 | ||||
| Upside Potential Ratio | 18862.278 | ||||
| Upside part of mean | 11606.612 | ||||
| Downside part of mean | -0.429 | ||||
| Upside SD | 26804.242 | ||||
| Downside SD | 0.615 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 60.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 64.000 | ||||
| Mean of predictor | 0.273 | ||||
| Mean of criterion | 11606.183 | ||||
| SD of predictor | 0.319 | ||||
| SD of criterion | 26804.257 | ||||
| Covariance | -1434.976 | ||||
| r | -0.168 | ||||
| b (slope, estimate of beta) | -14136.102 | ||||
| a (intercept, estimate of alpha) | 15465.527 | ||||
| Mean Square Error | 709444239.474 | ||||
| DF error | 62.000 | ||||
| t(b) | -1.342 | ||||
| p(b) | 0.908 | ||||
| t(a) | 1.301 | ||||
| p(a) | 0.099 | ||||
| Lowerbound of 95% confidence interval for beta | -35190.266 | ||||
| Upperbound of 95% confidence interval for beta | 6918.063 | ||||
| Lowerbound of 95% confidence interval for alpha | -8295.291 | ||||
| Upperbound of 95% confidence interval for alpha | 39226.345 | ||||
| Treynor index (mean / b) | -0.821 | ||||
| Jensen alpha (a) | 15465.527 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.232 | ||||
| SD | 8.511 | ||||
| Sharpe ratio (Glass type estimate) | -0.262 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.259 | ||||
| df | 63.000 | ||||
| t | -0.606 | ||||
| p | 0.727 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.111 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.589 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.109 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.591 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.319 | ||||
| Upside Potential Ratio | 0.301 | ||||
| Upside part of mean | 2.102 | ||||
| Downside part of mean | -4.334 | ||||
| Upside SD | 4.776 | ||||
| Downside SD | 6.993 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 60.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 64.000 | ||||
| Mean of predictor | 0.223 | ||||
| Mean of criterion | -2.232 | ||||
| SD of predictor | 0.303 | ||||
| SD of criterion | 8.511 | ||||
| Covariance | 0.496 | ||||
| r | 0.192 | ||||
| b (slope, estimate of beta) | 5.392 | ||||
| a (intercept, estimate of alpha) | -3.436 | ||||
| Mean Square Error | 70.890 | ||||
| DF error | 62.000 | ||||
| t(b) | 1.541 | ||||
| p(b) | 0.064 | ||||
| t(a) | -0.921 | ||||
| p(a) | 0.820 | ||||
| Lowerbound of 95% confidence interval for beta | -1.601 | ||||
| Upperbound of 95% confidence interval for beta | 12.386 | ||||
| Lowerbound of 95% confidence interval for alpha | -10.889 | ||||
| Upperbound of 95% confidence interval for alpha | 4.018 | ||||
| Treynor index (mean / b) | -0.414 | ||||
| Jensen alpha (a) | -3.436 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.985 | ||||
| Expected Shortfall on VaR | 0.993 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.120 | ||||
| Expected Shortfall on VaR | 0.265 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 64.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 61902.750 | ||||
| Mean of quarter 1 | 0.871 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 3869.872 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.062 | ||||
| Mean of outliers low | 0.483 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.062 | ||||
| Mean of outliers high | 15476.487 | ||||
| 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) | -6.304 | ||||
| VaR(95%) (regression method) | 0.459 | ||||
| Expected Shortfall (regression method) | 0.487 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.057 | ||||
| Quartile 1 | 0.293 | ||||
| Median | 0.529 | ||||
| Quartile 3 | 0.764 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.057 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.471 | ||||
| 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) | -0.187 | ||||
| Compounded annual return (geometric extrapolation) | -0.888 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.888 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.888 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.894 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 118413.173 | ||||
| SD | 107652.707 | ||||
| Sharpe ratio (Glass type estimate) | 1.100 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.099 | ||||
| df | 1408.000 | ||||
| t | 2.551 | ||||
| p | 0.466 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.254 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.946 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.253 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.946 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 89390.269 | ||||
| Upside Potential Ratio | 89392.204 | ||||
| Upside part of mean | 118415.737 | ||||
| Downside part of mean | -2.564 | ||||
| Upside SD | 107862.867 | ||||
| Downside SD | 1.325 | ||||
| N nonnegative terms | 78.000 | ||||
| N negative terms | 1331.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1409.000 | ||||
| Mean of predictor | 0.424 | ||||
| Mean of criterion | 118413.173 | ||||
| SD of predictor | 0.568 | ||||
| SD of criterion | 107652.707 | ||||
| Covariance | 23509.177 | ||||
| r | 0.384 | ||||
| b (slope, estimate of beta) | 72871.336 | ||||
| a (intercept, estimate of alpha) | 87547.621 | ||||
| Mean Square Error | 9882979271.669 | ||||
| DF error | 1407.000 | ||||
| t(b) | 15.623 | ||||
| p(b) | 0.261 | ||||
| t(a) | 2.040 | ||||
| p(a) | 0.465 | ||||
| Lowerbound of 95% confidence interval for beta | 63721.271 | ||||
| Upperbound of 95% confidence interval for beta | 82021.401 | ||||
| Lowerbound of 95% confidence interval for alpha | 3365.140 | ||||
| Upperbound of 95% confidence interval for alpha | 171730.101 | ||||
| Treynor index (mean / b) | 1.625 | ||||
| Jensen alpha (a) | 87547.621 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.214 | ||||
| SD | 18.724 | ||||
| Sharpe ratio (Glass type estimate) | -0.118 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.118 | ||||
| df | 1408.000 | ||||
| t | -0.274 | ||||
| p | 0.504 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.963 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.727 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.963 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.727 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.164 | ||||
| Upside Potential Ratio | 1.149 | ||||
| Upside part of mean | 15.477 | ||||
| Downside part of mean | -17.691 | ||||
| Upside SD | 12.992 | ||||
| Downside SD | 13.475 | ||||
| N nonnegative terms | 78.000 | ||||
| N negative terms | 1331.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1409.000 | ||||
| Mean of predictor | 0.264 | ||||
| Mean of criterion | -2.214 | ||||
| SD of predictor | 0.564 | ||||
| SD of criterion | 18.724 | ||||
| Covariance | 4.331 | ||||
| r | 0.410 | ||||
| b (slope, estimate of beta) | 13.616 | ||||
| a (intercept, estimate of alpha) | -5.811 | ||||
| Mean Square Error | 291.847 | ||||
| DF error | 1407.000 | ||||
| t(b) | 16.866 | ||||
| p(b) | 0.246 | ||||
| t(a) | -0.788 | ||||
| p(a) | 0.513 | ||||
| Lowerbound of 95% confidence interval for beta | 12.032 | ||||
| Upperbound of 95% confidence interval for beta | 15.199 | ||||
| Lowerbound of 95% confidence interval for alpha | -20.268 | ||||
| Upperbound of 95% confidence interval for alpha | 8.646 | ||||
| Treynor index (mean / b) | -0.163 | ||||
| Jensen alpha (a) | -5.811 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.852 | ||||
| Expected Shortfall on VaR | 0.902 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.033 | ||||
| Expected Shortfall on VaR | 0.074 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1409.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 139369.667 | ||||
| Mean of quarter 1 | 0.962 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1810.158 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 89.000 | ||||
| Percentage of outliers low | 0.063 | ||||
| Mean of outliers low | 0.848 | ||||
| Number of outliers high | 78.000 | ||||
| Percentage of outliers high | 0.055 | ||||
| Mean of outliers high | 8165.405 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.500 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -1.554 | ||||
| VaR(95%) (regression method) | 0.022 | ||||
| Expected Shortfall (regression method) | 0.057 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.026 | ||||
| Quartile 1 | 0.105 | ||||
| Median | 0.125 | ||||
| Quartile 3 | 0.266 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.074 | ||||
| Mean of quarter 2 | 0.125 | ||||
| Mean of quarter 3 | 0.203 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.161 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.222 | ||||
| Mean of outliers high | 1.000 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.000 | ||||
| VaR(95%) (moments method) | 0.792 | ||||
| Expected Shortfall (moments method) | 1.144 | ||||
| Extreme Value Index (regression method) | -26.946 | ||||
| VaR(95%) (regression method) | 3027.175 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.186 | ||||
| Compounded annual return (geometric extrapolation) | -0.886 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.886 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.886 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.983 | ||||
| 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 | 2.288 | ||||
| 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 | 2.046 | ||||
| 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) | -8651169010734649.000 | ||||
| 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) | 321250673747272746337310850678784.000 | ||||
| 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 | ||||