Advanced Statistics: Zen-Kerma 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 | -0.016 | ||||
| SD | 0.248 | ||||
| Sharpe ratio (Glass type estimate) | -0.066 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.065 | ||||
| df | 79.000 | ||||
| t | -0.171 | ||||
| p | 0.568 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.825 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.693 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.825 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.694 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.120 | ||||
| Upside Potential Ratio | 0.581 | ||||
| Upside part of mean | 0.079 | ||||
| Downside part of mean | -0.096 | ||||
| Upside SD | 0.205 | ||||
| Downside SD | 0.137 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 79.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 80.000 | ||||
| Mean of predictor | 0.227 | ||||
| Mean of criterion | -0.016 | ||||
| SD of predictor | 0.289 | ||||
| SD of criterion | 0.248 | ||||
| Covariance | -0.011 | ||||
| r | -0.148 | ||||
| b (slope, estimate of beta) | -0.127 | ||||
| a (intercept, estimate of alpha) | 0.012 | ||||
| Mean Square Error | 0.061 | ||||
| DF error | 78.000 | ||||
| t(b) | -1.323 | ||||
| p(b) | 0.905 | ||||
| t(a) | 0.128 | ||||
| p(a) | 0.449 | ||||
| Lowerbound of 95% confidence interval for beta | -0.318 | ||||
| Upperbound of 95% confidence interval for beta | 0.064 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.182 | ||||
| Upperbound of 95% confidence interval for alpha | 0.207 | ||||
| Treynor index (mean / b) | 0.129 | ||||
| Jensen alpha (a) | 0.012 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.235 | ||||
| Sharpe ratio (Glass type estimate) | -0.187 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.185 | ||||
| df | 79.000 | ||||
| t | -0.483 | ||||
| p | 0.685 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.946 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.573 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.945 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.574 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.263 | ||||
| Upside Potential Ratio | 0.380 | ||||
| Upside part of mean | 0.063 | ||||
| Downside part of mean | -0.107 | ||||
| Upside SD | 0.164 | ||||
| Downside SD | 0.167 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 79.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 80.000 | ||||
| Mean of predictor | 0.185 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.281 | ||||
| SD of criterion | 0.235 | ||||
| Covariance | -0.010 | ||||
| r | -0.147 | ||||
| b (slope, estimate of beta) | -0.123 | ||||
| a (intercept, estimate of alpha) | -0.021 | ||||
| Mean Square Error | 0.055 | ||||
| DF error | 78.000 | ||||
| t(b) | -1.315 | ||||
| p(b) | 0.904 | ||||
| t(a) | -0.230 | ||||
| p(a) | 0.590 | ||||
| Lowerbound of 95% confidence interval for beta | -0.310 | ||||
| Upperbound of 95% confidence interval for beta | 0.063 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.205 | ||||
| Upperbound of 95% confidence interval for alpha | 0.163 | ||||
| Treynor index (mean / b) | 0.357 | ||||
| Jensen alpha (a) | -0.021 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.109 | ||||
| Expected Shortfall on VaR | 0.134 | ||||
| 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 | 80.000 | ||||
| Minimum | 0.653 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.532 | ||||
| Mean of quarter 1 | 0.983 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.027 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.037 | ||||
| Mean of outliers low | 0.884 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.037 | ||||
| Mean of outliers high | 1.178 | ||||
| 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 | 0.348 | ||||
| Quartile 1 | 0.348 | ||||
| Median | 0.348 | ||||
| Quartile 3 | 0.348 | ||||
| Maximum | 0.348 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.033 | ||||
| SD | 0.148 | ||||
| Sharpe ratio (Glass type estimate) | -0.220 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.220 | ||||
| df | 1756.000 | ||||
| t | -0.570 | ||||
| p | 0.507 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.977 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.537 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.977 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.537 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.298 | ||||
| Upside Potential Ratio | 0.639 | ||||
| Upside part of mean | 0.070 | ||||
| Downside part of mean | -0.103 | ||||
| Upside SD | 0.100 | ||||
| Downside SD | 0.109 | ||||
| N nonnegative terms | 24.000 | ||||
| N negative terms | 1733.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1757.000 | ||||
| Mean of predictor | 0.331 | ||||
| Mean of criterion | -0.033 | ||||
| SD of predictor | 0.544 | ||||
| SD of criterion | 0.148 | ||||
| Covariance | -0.002 | ||||
| r | -0.027 | ||||
| b (slope, estimate of beta) | -0.007 | ||||
| a (intercept, estimate of alpha) | -0.030 | ||||
| Mean Square Error | 0.022 | ||||
| DF error | 1755.000 | ||||
| t(b) | -1.116 | ||||
| p(b) | 0.517 | ||||
| t(a) | -0.528 | ||||
| p(a) | 0.508 | ||||
| Lowerbound of 95% confidence interval for beta | -0.020 | ||||
| Upperbound of 95% confidence interval for beta | 0.005 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.143 | ||||
| Upperbound of 95% confidence interval for alpha | 0.082 | ||||
| Treynor index (mean / b) | 4.499 | ||||
| Jensen alpha (a) | -0.030 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.153 | ||||
| Sharpe ratio (Glass type estimate) | -0.288 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.288 | ||||
| df | 1756.000 | ||||
| t | -0.746 | ||||
| p | 0.509 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.045 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.469 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.045 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.469 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.357 | ||||
| Upside Potential Ratio | 0.532 | ||||
| Upside part of mean | 0.066 | ||||
| Downside part of mean | -0.110 | ||||
| Upside SD | 0.090 | ||||
| Downside SD | 0.123 | ||||
| N nonnegative terms | 24.000 | ||||
| N negative terms | 1733.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1757.000 | ||||
| Mean of predictor | 0.184 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.544 | ||||
| SD of criterion | 0.153 | ||||
| Covariance | -0.002 | ||||
| r | -0.025 | ||||
| b (slope, estimate of beta) | -0.007 | ||||
| a (intercept, estimate of alpha) | -0.043 | ||||
| Mean Square Error | 0.023 | ||||
| DF error | 1755.000 | ||||
| t(b) | -1.052 | ||||
| p(b) | 0.516 | ||||
| t(a) | -0.724 | ||||
| p(a) | 0.511 | ||||
| Lowerbound of 95% confidence interval for beta | -0.020 | ||||
| Upperbound of 95% confidence interval for beta | 0.006 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.158 | ||||
| Upperbound of 95% confidence interval for alpha | 0.073 | ||||
| Treynor index (mean / b) | 6.245 | ||||
| Jensen alpha (a) | -0.043 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.019 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.003 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1757.000 | ||||
| Minimum | 0.760 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.247 | ||||
| Mean of quarter 1 | 0.999 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.001 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 14.000 | ||||
| Percentage of outliers low | 0.008 | ||||
| Mean of outliers low | 0.972 | ||||
| Number of outliers high | 29.000 | ||||
| Percentage of outliers high | 0.017 | ||||
| Mean of outliers high | 1.016 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.176 | ||||
| VaR(95%) (moments method) | -0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.378 | ||||
| VaR(95%) (regression method) | -0.017 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.005 | ||||
| Quartile 1 | 0.092 | ||||
| Median | 0.179 | ||||
| Quartile 3 | 0.267 | ||||
| Maximum | 0.354 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.354 | ||||
| Inter Quartile Range | 0.175 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.000 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| 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 | 1.051 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.463 | ||||
| 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 | 0.944 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.460 | ||||
| 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) | -8729299016957607.000 | ||||
| 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) | -278948038932145086754410219962368.000 | ||||
| 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 | ||||