Advanced Statistics: TMD:Trader
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.282 | ||||
| SD | 0.820 | ||||
| Sharpe ratio (Glass type estimate) | 0.344 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.340 | ||||
| df | 68.000 | ||||
| t | 0.824 | ||||
| p | 0.206 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.477 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.162 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.480 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.159 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.825 | ||||
| Upside Potential Ratio | 2.301 | ||||
| Upside part of mean | 0.785 | ||||
| Downside part of mean | -0.504 | ||||
| Upside SD | 0.744 | ||||
| Downside SD | 0.341 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 52.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 69.000 | ||||
| Mean of predictor | 0.248 | ||||
| Mean of criterion | 0.282 | ||||
| SD of predictor | 0.304 | ||||
| SD of criterion | 0.820 | ||||
| Covariance | -0.069 | ||||
| r | -0.275 | ||||
| b (slope, estimate of beta) | -0.744 | ||||
| a (intercept, estimate of alpha) | 0.466 | ||||
| Mean Square Error | 0.631 | ||||
| DF error | 67.000 | ||||
| t(b) | -2.346 | ||||
| p(b) | 0.989 | ||||
| t(a) | 1.370 | ||||
| p(a) | 0.088 | ||||
| Lowerbound of 95% confidence interval for beta | -1.376 | ||||
| Upperbound of 95% confidence interval for beta | -0.111 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.213 | ||||
| Upperbound of 95% confidence interval for alpha | 1.146 | ||||
| Treynor index (mean / b) | -0.379 | ||||
| Jensen alpha (a) | 0.466 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.037 | ||||
| SD | 0.663 | ||||
| Sharpe ratio (Glass type estimate) | 0.056 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.056 | ||||
| df | 68.000 | ||||
| t | 0.135 | ||||
| p | 0.446 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.761 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.874 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.762 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.873 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.094 | ||||
| Upside Potential Ratio | 1.532 | ||||
| Upside part of mean | 0.611 | ||||
| Downside part of mean | -0.573 | ||||
| Upside SD | 0.524 | ||||
| Downside SD | 0.399 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 52.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 69.000 | ||||
| Mean of predictor | 0.201 | ||||
| Mean of criterion | 0.037 | ||||
| SD of predictor | 0.297 | ||||
| SD of criterion | 0.663 | ||||
| Covariance | -0.050 | ||||
| r | -0.252 | ||||
| b (slope, estimate of beta) | -0.562 | ||||
| a (intercept, estimate of alpha) | 0.151 | ||||
| Mean Square Error | 0.418 | ||||
| DF error | 67.000 | ||||
| t(b) | -2.132 | ||||
| p(b) | 0.982 | ||||
| t(a) | 0.548 | ||||
| p(a) | 0.293 | ||||
| Lowerbound of 95% confidence interval for beta | -1.088 | ||||
| Upperbound of 95% confidence interval for beta | -0.036 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.398 | ||||
| Upperbound of 95% confidence interval for alpha | 0.699 | ||||
| Treynor index (mean / b) | -0.066 | ||||
| Jensen alpha (a) | 0.151 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.268 | ||||
| Expected Shortfall on VaR | 0.322 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.123 | ||||
| Expected Shortfall on VaR | 0.244 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 69.000 | ||||
| Minimum | 0.653 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.313 | ||||
| Mean of quarter 1 | 0.850 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.269 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 16.000 | ||||
| Percentage of outliers low | 0.232 | ||||
| Mean of outliers low | 0.831 | ||||
| Number of outliers high | 17.000 | ||||
| Percentage of outliers high | 0.246 | ||||
| Mean of outliers high | 1.269 | ||||
| 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) | -0.541 | ||||
| VaR(95%) (regression method) | 0.139 | ||||
| Expected Shortfall (regression method) | 0.176 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.100 | ||||
| Quartile 1 | 0.198 | ||||
| Median | 0.272 | ||||
| Quartile 3 | 0.402 | ||||
| Maximum | 0.669 | ||||
| Mean of quarter 1 | 0.100 | ||||
| Mean of quarter 2 | 0.231 | ||||
| Mean of quarter 3 | 0.312 | ||||
| Mean of quarter 4 | 0.669 | ||||
| Inter Quartile Range | 0.203 | ||||
| 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) | 0.104 | ||||
| Compounded annual return (geometric extrapolation) | 0.085 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.127 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.127 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.263 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.888 | ||||
| SD | 2.221 | ||||
| Sharpe ratio (Glass type estimate) | 0.850 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.850 | ||||
| df | 1521.000 | ||||
| t | 2.049 | ||||
| p | 0.467 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.036 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.664 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.036 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.663 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.943 | ||||
| Upside Potential Ratio | 6.018 | ||||
| Upside part of mean | 5.850 | ||||
| Downside part of mean | -3.961 | ||||
| Upside SD | 2.000 | ||||
| Downside SD | 0.972 | ||||
| N nonnegative terms | 320.000 | ||||
| N negative terms | 1202.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1522.000 | ||||
| Mean of predictor | 0.407 | ||||
| Mean of criterion | 1.888 | ||||
| SD of predictor | 0.583 | ||||
| SD of criterion | 2.221 | ||||
| Covariance | -0.489 | ||||
| r | -0.378 | ||||
| b (slope, estimate of beta) | -1.439 | ||||
| a (intercept, estimate of alpha) | 2.474 | ||||
| Mean Square Error | 4.234 | ||||
| DF error | 1520.000 | ||||
| t(b) | -15.896 | ||||
| p(b) | 0.689 | ||||
| t(a) | 2.895 | ||||
| p(a) | 0.463 | ||||
| Lowerbound of 95% confidence interval for beta | -1.616 | ||||
| Upperbound of 95% confidence interval for beta | -1.261 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.797 | ||||
| Upperbound of 95% confidence interval for alpha | 4.150 | ||||
| Treynor index (mean / b) | -1.313 | ||||
| Jensen alpha (a) | 2.474 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.037 | ||||
| SD | 1.891 | ||||
| Sharpe ratio (Glass type estimate) | 0.019 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.019 | ||||
| df | 1521.000 | ||||
| t | 0.047 | ||||
| p | 0.499 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.794 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.833 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.794 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.832 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.027 | ||||
| Upside Potential Ratio | 3.487 | ||||
| Upside part of mean | 4.719 | ||||
| Downside part of mean | -4.682 | ||||
| Upside SD | 1.320 | ||||
| Downside SD | 1.353 | ||||
| N nonnegative terms | 320.000 | ||||
| N negative terms | 1202.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1522.000 | ||||
| Mean of predictor | 0.241 | ||||
| Mean of criterion | 0.037 | ||||
| SD of predictor | 0.574 | ||||
| SD of criterion | 1.891 | ||||
| Covariance | -0.449 | ||||
| r | -0.414 | ||||
| b (slope, estimate of beta) | -1.364 | ||||
| a (intercept, estimate of alpha) | 0.366 | ||||
| Mean Square Error | 2.965 | ||||
| DF error | 1520.000 | ||||
| t(b) | -17.723 | ||||
| p(b) | 0.707 | ||||
| t(a) | 0.512 | ||||
| p(a) | 0.493 | ||||
| Lowerbound of 95% confidence interval for beta | -1.515 | ||||
| Upperbound of 95% confidence interval for beta | -1.213 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.036 | ||||
| Upperbound of 95% confidence interval for alpha | 1.768 | ||||
| Treynor index (mean / b) | -0.027 | ||||
| Jensen alpha (a) | 0.366 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.175 | ||||
| Expected Shortfall on VaR | 0.213 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.045 | ||||
| Expected Shortfall on VaR | 0.100 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1522.000 | ||||
| Minimum | 0.256 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 3.372 | ||||
| Mean of quarter 1 | 0.940 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.089 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 326.000 | ||||
| Percentage of outliers low | 0.214 | ||||
| Mean of outliers low | 0.930 | ||||
| Number of outliers high | 320.000 | ||||
| Percentage of outliers high | 0.210 | ||||
| Mean of outliers high | 1.106 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.053 | ||||
| VaR(95%) (moments method) | 0.006 | ||||
| Expected Shortfall (moments method) | 0.009 | ||||
| Extreme Value Index (regression method) | 0.437 | ||||
| VaR(95%) (regression method) | 0.045 | ||||
| Expected Shortfall (regression method) | 0.119 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 20.000 | ||||
| Minimum | 0.011 | ||||
| Quartile 1 | 0.079 | ||||
| Median | 0.167 | ||||
| Quartile 3 | 0.472 | ||||
| Maximum | 0.806 | ||||
| Mean of quarter 1 | 0.040 | ||||
| Mean of quarter 2 | 0.108 | ||||
| Mean of quarter 3 | 0.362 | ||||
| Mean of quarter 4 | 0.679 | ||||
| Inter Quartile Range | 0.394 | ||||
| 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) | -0.796 | ||||
| VaR(95%) (moments method) | 0.753 | ||||
| Expected Shortfall (moments method) | 0.796 | ||||
| Extreme Value Index (regression method) | -0.340 | ||||
| VaR(95%) (regression method) | 0.699 | ||||
| Expected Shortfall (regression method) | 0.752 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.103 | ||||
| Compounded annual return (geometric extrapolation) | 0.084 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.104 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.124 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.393 | ||||
| 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 | 2.076 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.609 | ||||
| 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 | 1.886 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.605 | ||||
| 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) | -8640015955596112.000 | ||||
| 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) | -1120219766865925495373198822211584.000 | ||||
| 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 | ||||