Advanced Statistics: Dynamic System
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 | -0.064 | ||||
| SD | 0.098 | ||||
| Sharpe ratio (Glass type estimate) | -0.646 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.636 | ||||
| df | 51.000 | ||||
| t | -1.345 | ||||
| p | 0.908 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.593 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.307 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.586 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.313 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.797 | ||||
| Upside Potential Ratio | 0.832 | ||||
| Upside part of mean | 0.066 | ||||
| Downside part of mean | -0.130 | ||||
| Upside SD | 0.059 | ||||
| Downside SD | 0.080 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 45.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 52.000 | ||||
| Mean of predictor | 0.408 | ||||
| Mean of criterion | -0.064 | ||||
| SD of predictor | 0.238 | ||||
| SD of criterion | 0.098 | ||||
| Covariance | 0.008 | ||||
| r | 0.331 | ||||
| b (slope, estimate of beta) | 0.137 | ||||
| a (intercept, estimate of alpha) | -0.119 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 50.000 | ||||
| t(b) | 2.479 | ||||
| p(b) | 0.008 | ||||
| t(a) | -2.370 | ||||
| p(a) | 0.989 | ||||
| Lowerbound of 95% confidence interval for beta | 0.026 | ||||
| Upperbound of 95% confidence interval for beta | 0.248 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.221 | ||||
| Upperbound of 95% confidence interval for alpha | -0.018 | ||||
| Treynor index (mean / b) | -0.465 | ||||
| Jensen alpha (a) | -0.119 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.068 | ||||
| SD | 0.099 | ||||
| Sharpe ratio (Glass type estimate) | -0.688 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.678 | ||||
| df | 51.000 | ||||
| t | -1.432 | ||||
| p | 0.921 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.636 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.266 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.629 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.273 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.828 | ||||
| Upside Potential Ratio | 0.782 | ||||
| Upside part of mean | 0.065 | ||||
| Downside part of mean | -0.133 | ||||
| Upside SD | 0.057 | ||||
| Downside SD | 0.083 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 45.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 52.000 | ||||
| Mean of predictor | 0.375 | ||||
| Mean of criterion | -0.068 | ||||
| SD of predictor | 0.227 | ||||
| SD of criterion | 0.099 | ||||
| Covariance | 0.008 | ||||
| r | 0.358 | ||||
| b (slope, estimate of beta) | 0.157 | ||||
| a (intercept, estimate of alpha) | -0.127 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 50.000 | ||||
| t(b) | 2.710 | ||||
| p(b) | 0.005 | ||||
| t(a) | -2.543 | ||||
| p(a) | 0.993 | ||||
| Lowerbound of 95% confidence interval for beta | 0.041 | ||||
| Upperbound of 95% confidence interval for beta | 0.273 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.227 | ||||
| Upperbound of 95% confidence interval for alpha | -0.027 | ||||
| Treynor index (mean / b) | -0.437 | ||||
| Jensen alpha (a) | -0.127 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.052 | ||||
| Expected Shortfall on VaR | 0.063 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.035 | ||||
| Expected Shortfall on VaR | 0.065 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 52.000 | ||||
| Minimum | 0.911 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.073 | ||||
| Mean of quarter 1 | 0.969 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.024 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 10.000 | ||||
| Percentage of outliers low | 0.192 | ||||
| Mean of outliers low | 0.960 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.135 | ||||
| Mean of outliers high | 1.045 | ||||
| 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) | -0.556 | ||||
| VaR(95%) (regression method) | 0.049 | ||||
| Expected Shortfall (regression method) | 0.063 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.070 | ||||
| Median | 0.138 | ||||
| Quartile 3 | 0.207 | ||||
| Maximum | 0.275 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.275 | ||||
| Inter Quartile Range | 0.137 | ||||
| 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) | -0.023 | ||||
| Compounded annual return (geometric extrapolation) | -0.024 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.088 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.088 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.383 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.063 | ||||
| SD | 0.104 | ||||
| Sharpe ratio (Glass type estimate) | -0.602 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.602 | ||||
| df | 1151.000 | ||||
| t | -1.262 | ||||
| p | 0.524 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.537 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.333 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.537 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.333 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.817 | ||||
| Upside Potential Ratio | 3.869 | ||||
| Upside part of mean | 0.296 | ||||
| Downside part of mean | -0.359 | ||||
| Upside SD | 0.070 | ||||
| Downside SD | 0.077 | ||||
| N nonnegative terms | 148.000 | ||||
| N negative terms | 1004.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1152.000 | ||||
| Mean of predictor | 0.444 | ||||
| Mean of criterion | -0.063 | ||||
| SD of predictor | 0.347 | ||||
| SD of criterion | 0.104 | ||||
| Covariance | 0.005 | ||||
| r | 0.144 | ||||
| b (slope, estimate of beta) | 0.043 | ||||
| a (intercept, estimate of alpha) | -0.082 | ||||
| Mean Square Error | 0.011 | ||||
| DF error | 1150.000 | ||||
| t(b) | 4.926 | ||||
| p(b) | 0.428 | ||||
| t(a) | -1.659 | ||||
| p(a) | 0.524 | ||||
| Lowerbound of 95% confidence interval for beta | 0.026 | ||||
| Upperbound of 95% confidence interval for beta | 0.060 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.178 | ||||
| Upperbound of 95% confidence interval for alpha | 0.015 | ||||
| Treynor index (mean / b) | -1.453 | ||||
| Jensen alpha (a) | -0.082 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.068 | ||||
| SD | 0.104 | ||||
| Sharpe ratio (Glass type estimate) | -0.653 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.653 | ||||
| df | 1151.000 | ||||
| t | -1.369 | ||||
| p | 0.526 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.588 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.282 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.588 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.282 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.876 | ||||
| Upside Potential Ratio | 3.788 | ||||
| Upside part of mean | 0.294 | ||||
| Downside part of mean | -0.362 | ||||
| Upside SD | 0.070 | ||||
| Downside SD | 0.078 | ||||
| N nonnegative terms | 148.000 | ||||
| N negative terms | 1004.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1152.000 | ||||
| Mean of predictor | 0.380 | ||||
| Mean of criterion | -0.068 | ||||
| SD of predictor | 0.362 | ||||
| SD of criterion | 0.104 | ||||
| Covariance | 0.005 | ||||
| r | 0.138 | ||||
| b (slope, estimate of beta) | 0.040 | ||||
| a (intercept, estimate of alpha) | -0.083 | ||||
| Mean Square Error | 0.011 | ||||
| DF error | 1150.000 | ||||
| t(b) | 4.714 | ||||
| p(b) | 0.431 | ||||
| t(a) | -1.684 | ||||
| p(a) | 0.525 | ||||
| Lowerbound of 95% confidence interval for beta | 0.023 | ||||
| Upperbound of 95% confidence interval for beta | 0.056 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.180 | ||||
| Upperbound of 95% confidence interval for alpha | 0.014 | ||||
| Treynor index (mean / b) | -1.720 | ||||
| Jensen alpha (a) | -0.083 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.013 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1152.000 | ||||
| Minimum | 0.956 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.044 | ||||
| Mean of quarter 1 | 0.995 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.005 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 166.000 | ||||
| Percentage of outliers low | 0.144 | ||||
| Mean of outliers low | 0.992 | ||||
| Number of outliers high | 154.000 | ||||
| Percentage of outliers high | 0.134 | ||||
| Mean of outliers high | 1.009 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.139 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.004 | ||||
| Extreme Value Index (regression method) | -0.118 | ||||
| VaR(95%) (regression method) | 0.007 | ||||
| Expected Shortfall (regression method) | 0.012 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 22.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.004 | ||||
| Median | 0.011 | ||||
| Quartile 3 | 0.019 | ||||
| Maximum | 0.275 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.009 | ||||
| Mean of quarter 3 | 0.016 | ||||
| Mean of quarter 4 | 0.070 | ||||
| Inter Quartile Range | 0.015 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.045 | ||||
| Mean of outliers high | 0.275 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.896 | ||||
| VaR(95%) (moments method) | 0.076 | ||||
| Expected Shortfall (moments method) | 0.727 | ||||
| Extreme Value Index (regression method) | 1.540 | ||||
| VaR(95%) (regression method) | 0.070 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.023 | ||||
| Compounded annual return (geometric extrapolation) | -0.024 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.086 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.338 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.765 | ||||
| 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 | 1.173 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.419 | ||||
| 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 | 1.083 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.421 | ||||
| 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) | -8689786452260672.000 | ||||
| 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) | 131827361655213883093142887989248.000 | ||||
| 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 | ||||