Advanced Statistics: quantum-fx version 2
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 | -0.022 | ||||
| SD | 0.211 | ||||
| Sharpe ratio (Glass type estimate) | -0.103 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.102 | ||||
| df | 62.000 | ||||
| t | -0.236 | ||||
| p | 0.593 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.958 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.753 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.957 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.754 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.135 | ||||
| Upside Potential Ratio | 0.957 | ||||
| Upside part of mean | 0.154 | ||||
| Downside part of mean | -0.175 | ||||
| Upside SD | 0.134 | ||||
| Downside SD | 0.160 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 53.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 63.000 | ||||
| Mean of predictor | 0.319 | ||||
| Mean of criterion | -0.022 | ||||
| SD of predictor | 0.349 | ||||
| SD of criterion | 0.211 | ||||
| Covariance | -0.019 | ||||
| r | -0.255 | ||||
| b (slope, estimate of beta) | -0.154 | ||||
| a (intercept, estimate of alpha) | 0.027 | ||||
| Mean Square Error | 0.042 | ||||
| DF error | 61.000 | ||||
| t(b) | -2.057 | ||||
| p(b) | 0.978 | ||||
| t(a) | 0.295 | ||||
| p(a) | 0.385 | ||||
| Lowerbound of 95% confidence interval for beta | -0.304 | ||||
| Upperbound of 95% confidence interval for beta | -0.004 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.158 | ||||
| Upperbound of 95% confidence interval for alpha | 0.213 | ||||
| Treynor index (mean / b) | 0.141 | ||||
| Jensen alpha (a) | 0.027 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.046 | ||||
| SD | 0.227 | ||||
| Sharpe ratio (Glass type estimate) | -0.201 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.199 | ||||
| df | 62.000 | ||||
| t | -0.461 | ||||
| p | 0.677 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.056 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.656 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.055 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.657 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.243 | ||||
| Upside Potential Ratio | 0.771 | ||||
| Upside part of mean | 0.145 | ||||
| Downside part of mean | -0.190 | ||||
| Upside SD | 0.125 | ||||
| Downside SD | 0.188 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 53.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 63.000 | ||||
| Mean of predictor | 0.260 | ||||
| Mean of criterion | -0.046 | ||||
| SD of predictor | 0.325 | ||||
| SD of criterion | 0.227 | ||||
| Covariance | -0.019 | ||||
| r | -0.261 | ||||
| b (slope, estimate of beta) | -0.182 | ||||
| a (intercept, estimate of alpha) | 0.002 | ||||
| Mean Square Error | 0.049 | ||||
| DF error | 61.000 | ||||
| t(b) | -2.112 | ||||
| p(b) | 0.981 | ||||
| t(a) | 0.018 | ||||
| p(a) | 0.493 | ||||
| Lowerbound of 95% confidence interval for beta | -0.355 | ||||
| Upperbound of 95% confidence interval for beta | -0.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.196 | ||||
| Upperbound of 95% confidence interval for alpha | 0.200 | ||||
| Treynor index (mean / b) | 0.251 | ||||
| Jensen alpha (a) | 0.002 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.106 | ||||
| Expected Shortfall on VaR | 0.130 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.046 | ||||
| Expected Shortfall on VaR | 0.097 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 63.000 | ||||
| Minimum | 0.677 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.216 | ||||
| Mean of quarter 1 | 0.954 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.053 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 14.000 | ||||
| Percentage of outliers low | 0.222 | ||||
| Mean of outliers low | 0.948 | ||||
| Number of outliers high | 14.000 | ||||
| Percentage of outliers high | 0.222 | ||||
| Mean of outliers high | 1.060 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.039 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | 0.592 | ||||
| VaR(95%) (regression method) | 0.037 | ||||
| Expected Shortfall (regression method) | 0.134 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.153 | ||||
| Quartile 1 | 0.210 | ||||
| Median | 0.267 | ||||
| Quartile 3 | 0.324 | ||||
| Maximum | 0.381 | ||||
| Mean of quarter 1 | 0.153 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.381 | ||||
| Inter Quartile Range | 0.114 | ||||
| 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) | -0.002 | ||||
| Compounded annual return (geometric extrapolation) | -0.002 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.004 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.004 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.013 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.061 | ||||
| SD | 0.460 | ||||
| Sharpe ratio (Glass type estimate) | 0.132 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.132 | ||||
| df | 1395.000 | ||||
| t | 0.306 | ||||
| p | 0.495 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.717 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.982 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.717 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.981 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.197 | ||||
| Upside Potential Ratio | 3.170 | ||||
| Upside part of mean | 0.980 | ||||
| Downside part of mean | -0.919 | ||||
| Upside SD | 0.340 | ||||
| Downside SD | 0.309 | ||||
| N nonnegative terms | 162.000 | ||||
| N negative terms | 1234.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1396.000 | ||||
| Mean of predictor | 0.477 | ||||
| Mean of criterion | 0.061 | ||||
| SD of predictor | 0.598 | ||||
| SD of criterion | 0.460 | ||||
| Covariance | -0.120 | ||||
| r | -0.435 | ||||
| b (slope, estimate of beta) | -0.334 | ||||
| a (intercept, estimate of alpha) | 0.220 | ||||
| Mean Square Error | 0.172 | ||||
| DF error | 1394.000 | ||||
| t(b) | -18.015 | ||||
| p(b) | 0.717 | ||||
| t(a) | 1.226 | ||||
| p(a) | 0.484 | ||||
| Lowerbound of 95% confidence interval for beta | -0.371 | ||||
| Upperbound of 95% confidence interval for beta | -0.298 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.132 | ||||
| Upperbound of 95% confidence interval for alpha | 0.573 | ||||
| Treynor index (mean / b) | -0.182 | ||||
| Jensen alpha (a) | 0.220 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.046 | ||||
| SD | 0.465 | ||||
| Sharpe ratio (Glass type estimate) | -0.098 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.098 | ||||
| df | 1395.000 | ||||
| t | -0.227 | ||||
| p | 0.504 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.947 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.751 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.947 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.751 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.132 | ||||
| Upside Potential Ratio | 2.680 | ||||
| Upside part of mean | 0.929 | ||||
| Downside part of mean | -0.975 | ||||
| Upside SD | 0.309 | ||||
| Downside SD | 0.347 | ||||
| N nonnegative terms | 162.000 | ||||
| N negative terms | 1234.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1396.000 | ||||
| Mean of predictor | 0.302 | ||||
| Mean of criterion | -0.046 | ||||
| SD of predictor | 0.591 | ||||
| SD of criterion | 0.465 | ||||
| Covariance | -0.120 | ||||
| r | -0.438 | ||||
| b (slope, estimate of beta) | -0.344 | ||||
| a (intercept, estimate of alpha) | 0.058 | ||||
| Mean Square Error | 0.175 | ||||
| DF error | 1394.000 | ||||
| t(b) | -18.176 | ||||
| p(b) | 0.719 | ||||
| t(a) | 0.322 | ||||
| p(a) | 0.496 | ||||
| Lowerbound of 95% confidence interval for beta | -0.381 | ||||
| Upperbound of 95% confidence interval for beta | -0.307 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.297 | ||||
| Upperbound of 95% confidence interval for alpha | 0.414 | ||||
| Treynor index (mean / b) | 0.133 | ||||
| Jensen alpha (a) | 0.058 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.046 | ||||
| Expected Shortfall on VaR | 0.058 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.025 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1396.000 | ||||
| Minimum | 0.653 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.388 | ||||
| Mean of quarter 1 | 0.987 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.015 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 189.000 | ||||
| Percentage of outliers low | 0.135 | ||||
| Mean of outliers low | 0.975 | ||||
| Number of outliers high | 192.000 | ||||
| Percentage of outliers high | 0.138 | ||||
| Mean of outliers high | 1.027 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.687 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.017 | ||||
| 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 | 8.000 | ||||
| Minimum | 0.018 | ||||
| Quartile 1 | 0.031 | ||||
| Median | 0.115 | ||||
| Quartile 3 | 0.199 | ||||
| Maximum | 0.405 | ||||
| Mean of quarter 1 | 0.018 | ||||
| Mean of quarter 2 | 0.072 | ||||
| Mean of quarter 3 | 0.143 | ||||
| Mean of quarter 4 | 0.356 | ||||
| Inter Quartile Range | 0.168 | ||||
| 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) | -0.002 | ||||
| Compounded annual return (geometric extrapolation) | -0.002 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.004 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.005 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.028 | ||||
| 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 | 2.018 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.723 | ||||
| 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 | 1.759 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.709 | ||||
| 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) | -8697583782006501.000 | ||||
| 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) | -58427782049331241097927467615649792.000 | ||||
| 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 | ||||