Advanced Statistics: Sinersys
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 | -0.262 | ||||
| SD | 0.309 | ||||
| Sharpe ratio (Glass type estimate) | -0.847 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.826 | ||||
| df | 31.000 | ||||
| t | -1.383 | ||||
| p | 0.912 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.059 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.378 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.044 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.391 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.840 | ||||
| Upside Potential Ratio | 0.166 | ||||
| Upside part of mean | 0.052 | ||||
| Downside part of mean | -0.313 | ||||
| Upside SD | 0.034 | ||||
| Downside SD | 0.311 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 22.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.583 | ||||
| Mean of criterion | -0.262 | ||||
| SD of predictor | 0.313 | ||||
| SD of criterion | 0.309 | ||||
| Covariance | 0.013 | ||||
| r | 0.134 | ||||
| b (slope, estimate of beta) | 0.132 | ||||
| a (intercept, estimate of alpha) | -0.339 | ||||
| Mean Square Error | 0.097 | ||||
| DF error | 30.000 | ||||
| t(b) | 0.742 | ||||
| p(b) | 0.232 | ||||
| t(a) | -1.561 | ||||
| p(a) | 0.935 | ||||
| Lowerbound of 95% confidence interval for beta | -0.232 | ||||
| Upperbound of 95% confidence interval for beta | 0.497 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.782 | ||||
| Upperbound of 95% confidence interval for alpha | 0.105 | ||||
| Treynor index (mean / b) | -1.978 | ||||
| Jensen alpha (a) | -0.339 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.328 | ||||
| SD | 0.393 | ||||
| Sharpe ratio (Glass type estimate) | -0.835 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.815 | ||||
| df | 31.000 | ||||
| t | -1.364 | ||||
| p | 0.909 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.047 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.389 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.032 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.402 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.827 | ||||
| Upside Potential Ratio | 0.129 | ||||
| Upside part of mean | 0.051 | ||||
| Downside part of mean | -0.379 | ||||
| Upside SD | 0.033 | ||||
| Downside SD | 0.396 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 22.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.525 | ||||
| Mean of criterion | -0.328 | ||||
| SD of predictor | 0.295 | ||||
| SD of criterion | 0.393 | ||||
| Covariance | 0.015 | ||||
| r | 0.126 | ||||
| b (slope, estimate of beta) | 0.167 | ||||
| a (intercept, estimate of alpha) | -0.415 | ||||
| Mean Square Error | 0.157 | ||||
| DF error | 30.000 | ||||
| t(b) | 0.693 | ||||
| p(b) | 0.247 | ||||
| t(a) | -1.520 | ||||
| p(a) | 0.930 | ||||
| Lowerbound of 95% confidence interval for beta | -0.325 | ||||
| Upperbound of 95% confidence interval for beta | 0.658 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.974 | ||||
| Upperbound of 95% confidence interval for alpha | 0.143 | ||||
| Treynor index (mean / b) | -1.966 | ||||
| Jensen alpha (a) | -0.415 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.192 | ||||
| Expected Shortfall on VaR | 0.229 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.072 | ||||
| Expected Shortfall on VaR | 0.158 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 32.000 | ||||
| Minimum | 0.561 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.006 | ||||
| Maximum | 1.036 | ||||
| Mean of quarter 1 | 0.906 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.021 | ||||
| Inter Quartile Range | 0.006 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.156 | ||||
| Mean of outliers low | 0.849 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.156 | ||||
| Mean of outliers high | 1.027 | ||||
| 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) | 1.211 | ||||
| VaR(95%) (regression method) | 0.114 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.579 | ||||
| Quartile 1 | 0.579 | ||||
| Median | 0.579 | ||||
| Quartile 3 | 0.579 | ||||
| Maximum | 0.579 | ||||
| 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) | -0.199 | ||||
| Compounded annual return (geometric extrapolation) | -0.247 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.427 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.079 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.297 | ||||
| SD | 0.210 | ||||
| Sharpe ratio (Glass type estimate) | -1.416 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.414 | ||||
| df | 716.000 | ||||
| t | -2.342 | ||||
| p | 0.990 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.603 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.228 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.602 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.227 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.548 | ||||
| Upside Potential Ratio | 1.392 | ||||
| Upside part of mean | 0.267 | ||||
| Downside part of mean | -0.564 | ||||
| Upside SD | 0.086 | ||||
| Downside SD | 0.192 | ||||
| N nonnegative terms | 148.000 | ||||
| N negative terms | 569.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 717.000 | ||||
| Mean of predictor | 0.632 | ||||
| Mean of criterion | -0.297 | ||||
| SD of predictor | 0.333 | ||||
| SD of criterion | 0.210 | ||||
| Covariance | 0.002 | ||||
| r | 0.033 | ||||
| b (slope, estimate of beta) | 0.021 | ||||
| a (intercept, estimate of alpha) | -0.311 | ||||
| Mean Square Error | 0.044 | ||||
| DF error | 715.000 | ||||
| t(b) | 0.896 | ||||
| p(b) | 0.185 | ||||
| t(a) | -2.431 | ||||
| p(a) | 0.992 | ||||
| Lowerbound of 95% confidence interval for beta | -0.025 | ||||
| Upperbound of 95% confidence interval for beta | 0.067 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.561 | ||||
| Upperbound of 95% confidence interval for alpha | -0.060 | ||||
| Treynor index (mean / b) | -14.068 | ||||
| Jensen alpha (a) | -0.311 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.321 | ||||
| SD | 0.219 | ||||
| Sharpe ratio (Glass type estimate) | -1.461 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.460 | ||||
| df | 716.000 | ||||
| t | -2.417 | ||||
| p | 0.992 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.648 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.273 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.647 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.272 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.575 | ||||
| Upside Potential Ratio | 1.295 | ||||
| Upside part of mean | 0.264 | ||||
| Downside part of mean | -0.584 | ||||
| Upside SD | 0.084 | ||||
| Downside SD | 0.204 | ||||
| N nonnegative terms | 148.000 | ||||
| N negative terms | 569.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 717.000 | ||||
| Mean of predictor | 0.576 | ||||
| Mean of criterion | -0.321 | ||||
| SD of predictor | 0.333 | ||||
| SD of criterion | 0.219 | ||||
| Covariance | 0.002 | ||||
| r | 0.032 | ||||
| b (slope, estimate of beta) | 0.021 | ||||
| a (intercept, estimate of alpha) | -0.333 | ||||
| Mean Square Error | 0.048 | ||||
| DF error | 715.000 | ||||
| t(b) | 0.864 | ||||
| p(b) | 0.194 | ||||
| t(a) | -2.495 | ||||
| p(a) | 0.994 | ||||
| Lowerbound of 95% confidence interval for beta | -0.027 | ||||
| Upperbound of 95% confidence interval for beta | 0.070 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.595 | ||||
| Upperbound of 95% confidence interval for alpha | -0.071 | ||||
| Treynor index (mean / b) | -15.079 | ||||
| Jensen alpha (a) | -0.333 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.023 | ||||
| Expected Shortfall on VaR | 0.029 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.015 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 717.000 | ||||
| Minimum | 0.839 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.088 | ||||
| Mean of quarter 1 | 0.992 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.004 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 133.000 | ||||
| Percentage of outliers low | 0.185 | ||||
| Mean of outliers low | 0.989 | ||||
| Number of outliers high | 154.000 | ||||
| Percentage of outliers high | 0.215 | ||||
| Mean of outliers high | 1.005 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.185 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.033 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.580 | ||||
| Quartile 1 | 0.580 | ||||
| Median | 0.580 | ||||
| Quartile 3 | 0.580 | ||||
| Maximum | 0.580 | ||||
| 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) | -0.194 | ||||
| Compounded annual return (geometric extrapolation) | -0.242 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.416 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -8.404 | ||||
| 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 | 1.079 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.462 | ||||
| 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 | 0.971 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.464 | ||||
| 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) | -8726652605332657.000 | ||||
| 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) | -173598742179256238264900355358720.000 | ||||
| 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 | ||||