Advanced Statistics: Super Moderate Trader
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 | -0.028 | ||||
| SD | 0.101 | ||||
| Sharpe ratio (Glass type estimate) | -0.279 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.273 | ||||
| df | 33.000 | ||||
| t | -0.470 | ||||
| p | 0.679 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.443 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.889 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.439 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.894 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.368 | ||||
| Upside Potential Ratio | 0.842 | ||||
| Upside part of mean | 0.065 | ||||
| Downside part of mean | -0.093 | ||||
| Upside SD | 0.064 | ||||
| Downside SD | 0.077 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.564 | ||||
| Mean of criterion | -0.028 | ||||
| SD of predictor | 0.322 | ||||
| SD of criterion | 0.101 | ||||
| Covariance | -0.004 | ||||
| r | -0.128 | ||||
| b (slope, estimate of beta) | -0.040 | ||||
| a (intercept, estimate of alpha) | -0.006 | ||||
| Mean Square Error | 0.010 | ||||
| DF error | 32.000 | ||||
| t(b) | -0.729 | ||||
| p(b) | 0.764 | ||||
| t(a) | -0.082 | ||||
| p(a) | 0.533 | ||||
| Lowerbound of 95% confidence interval for beta | -0.153 | ||||
| Upperbound of 95% confidence interval for beta | 0.072 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.145 | ||||
| Upperbound of 95% confidence interval for alpha | 0.133 | ||||
| Treynor index (mean / b) | 0.703 | ||||
| Jensen alpha (a) | -0.006 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.033 | ||||
| SD | 0.103 | ||||
| Sharpe ratio (Glass type estimate) | -0.323 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.315 | ||||
| df | 33.000 | ||||
| t | -0.543 | ||||
| p | 0.705 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.487 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.847 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.482 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.851 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.411 | ||||
| Upside Potential Ratio | 0.770 | ||||
| Upside part of mean | 0.063 | ||||
| Downside part of mean | -0.096 | ||||
| Upside SD | 0.062 | ||||
| Downside SD | 0.081 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.505 | ||||
| Mean of criterion | -0.033 | ||||
| SD of predictor | 0.296 | ||||
| SD of criterion | 0.103 | ||||
| Covariance | -0.004 | ||||
| r | -0.129 | ||||
| b (slope, estimate of beta) | -0.045 | ||||
| a (intercept, estimate of alpha) | -0.011 | ||||
| Mean Square Error | 0.011 | ||||
| DF error | 32.000 | ||||
| t(b) | -0.738 | ||||
| p(b) | 0.767 | ||||
| t(a) | -0.153 | ||||
| p(a) | 0.560 | ||||
| Lowerbound of 95% confidence interval for beta | -0.170 | ||||
| Upperbound of 95% confidence interval for beta | 0.079 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.151 | ||||
| Upperbound of 95% confidence interval for alpha | 0.130 | ||||
| Treynor index (mean / b) | 0.739 | ||||
| Jensen alpha (a) | -0.011 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.051 | ||||
| Expected Shortfall on VaR | 0.062 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.025 | ||||
| Expected Shortfall on VaR | 0.052 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 34.000 | ||||
| Minimum | 0.882 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.085 | ||||
| Mean of quarter 1 | 0.983 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.022 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.059 | ||||
| Mean of outliers low | 0.923 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.118 | ||||
| Mean of outliers high | 1.050 | ||||
| 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) | 0.230 | ||||
| VaR(95%) (regression method) | 0.037 | ||||
| Expected Shortfall (regression method) | 0.132 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.035 | ||||
| Quartile 1 | 0.056 | ||||
| Median | 0.077 | ||||
| Quartile 3 | 0.097 | ||||
| Maximum | 0.118 | ||||
| Mean of quarter 1 | 0.035 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.118 | ||||
| Inter Quartile Range | 0.041 | ||||
| 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) | 0.011 | ||||
| Compounded annual return (geometric extrapolation) | 0.011 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.091 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.091 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.172 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.030 | ||||
| SD | 0.085 | ||||
| Sharpe ratio (Glass type estimate) | -0.351 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.351 | ||||
| df | 746.000 | ||||
| t | -0.593 | ||||
| p | 0.723 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.512 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.810 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.512 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.810 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.470 | ||||
| Upside Potential Ratio | 2.834 | ||||
| Upside part of mean | 0.180 | ||||
| Downside part of mean | -0.210 | ||||
| Upside SD | 0.056 | ||||
| Downside SD | 0.063 | ||||
| N nonnegative terms | 56.000 | ||||
| N negative terms | 691.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 747.000 | ||||
| Mean of predictor | 0.596 | ||||
| Mean of criterion | -0.030 | ||||
| SD of predictor | 0.368 | ||||
| SD of criterion | 0.085 | ||||
| Covariance | 0.001 | ||||
| r | 0.016 | ||||
| b (slope, estimate of beta) | 0.004 | ||||
| a (intercept, estimate of alpha) | -0.032 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 745.000 | ||||
| t(b) | 0.443 | ||||
| p(b) | 0.329 | ||||
| t(a) | -0.634 | ||||
| p(a) | 0.737 | ||||
| Lowerbound of 95% confidence interval for beta | -0.013 | ||||
| Upperbound of 95% confidence interval for beta | 0.020 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.131 | ||||
| Upperbound of 95% confidence interval for alpha | 0.067 | ||||
| Treynor index (mean / b) | -7.979 | ||||
| Jensen alpha (a) | -0.032 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.033 | ||||
| SD | 0.085 | ||||
| Sharpe ratio (Glass type estimate) | -0.392 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.391 | ||||
| df | 746.000 | ||||
| t | -0.662 | ||||
| p | 0.746 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.553 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.769 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.552 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.769 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.518 | ||||
| Upside Potential Ratio | 2.760 | ||||
| Upside part of mean | 0.178 | ||||
| Downside part of mean | -0.212 | ||||
| Upside SD | 0.056 | ||||
| Downside SD | 0.065 | ||||
| N nonnegative terms | 56.000 | ||||
| N negative terms | 691.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 747.000 | ||||
| Mean of predictor | 0.529 | ||||
| Mean of criterion | -0.033 | ||||
| SD of predictor | 0.363 | ||||
| SD of criterion | 0.085 | ||||
| Covariance | 0.001 | ||||
| r | 0.017 | ||||
| b (slope, estimate of beta) | 0.004 | ||||
| a (intercept, estimate of alpha) | -0.035 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 745.000 | ||||
| t(b) | 0.455 | ||||
| p(b) | 0.325 | ||||
| t(a) | -0.699 | ||||
| p(a) | 0.758 | ||||
| Lowerbound of 95% confidence interval for beta | -0.013 | ||||
| Upperbound of 95% confidence interval for beta | 0.021 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.135 | ||||
| Upperbound of 95% confidence interval for alpha | 0.064 | ||||
| Treynor index (mean / b) | -8.534 | ||||
| Jensen alpha (a) | -0.035 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.011 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.006 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 747.000 | ||||
| Minimum | 0.946 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.038 | ||||
| Mean of quarter 1 | 0.997 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.003 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 51.000 | ||||
| Percentage of outliers low | 0.068 | ||||
| Mean of outliers low | 0.991 | ||||
| Number of outliers high | 57.000 | ||||
| Percentage of outliers high | 0.076 | ||||
| Mean of outliers high | 1.009 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.416 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.004 | ||||
| Extreme Value Index (regression method) | 0.282 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | 0.009 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.006 | ||||
| Median | 0.007 | ||||
| Quartile 3 | 0.016 | ||||
| Maximum | 0.149 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.007 | ||||
| Mean of quarter 3 | 0.012 | ||||
| Mean of quarter 4 | 0.125 | ||||
| Inter Quartile Range | 0.010 | ||||
| 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 | 0.125 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -53.157 | ||||
| VaR(95%) (moments method) | 0.049 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -1.834 | ||||
| VaR(95%) (regression method) | 0.204 | ||||
| Expected Shortfall (regression method) | 0.208 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.011 | ||||
| Compounded annual return (geometric extrapolation) | 0.011 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.072 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.085 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.974 | ||||
| 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 | 1.011 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.512 | ||||
| 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 | 0.881 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.505 | ||||
| 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) | -8748809988409702.000 | ||||
| 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) | 344926607603091390483351981785088.000 | ||||
| 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 | ||||