Advanced Statistics: System 65149161
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 | 0.038 | ||||
| SD | 1.011 | ||||
| Sharpe ratio (Glass type estimate) | 0.038 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.037 | ||||
| df | 39.000 | ||||
| t | 0.069 | ||||
| p | 0.473 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.036 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.111 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.036 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.111 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.058 | ||||
| Upside Potential Ratio | 0.938 | ||||
| Upside part of mean | 0.621 | ||||
| Downside part of mean | -0.583 | ||||
| Upside SD | 0.747 | ||||
| Downside SD | 0.662 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 35.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 40.000 | ||||
| Mean of predictor | 0.472 | ||||
| Mean of criterion | 0.038 | ||||
| SD of predictor | 0.237 | ||||
| SD of criterion | 1.011 | ||||
| Covariance | 0.022 | ||||
| r | 0.091 | ||||
| b (slope, estimate of beta) | 0.389 | ||||
| a (intercept, estimate of alpha) | -0.145 | ||||
| Mean Square Error | 1.040 | ||||
| DF error | 38.000 | ||||
| t(b) | 0.565 | ||||
| p(b) | 0.288 | ||||
| t(a) | -0.225 | ||||
| p(a) | 0.588 | ||||
| Lowerbound of 95% confidence interval for beta | -1.006 | ||||
| Upperbound of 95% confidence interval for beta | 1.785 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.454 | ||||
| Upperbound of 95% confidence interval for alpha | 1.163 | ||||
| Treynor index (mean / b) | 0.099 | ||||
| Jensen alpha (a) | -0.145 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -3.497 | ||||
| SD | 6.513 | ||||
| Sharpe ratio (Glass type estimate) | -0.537 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.527 | ||||
| df | 39.000 | ||||
| t | -0.980 | ||||
| p | 0.834 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.614 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.546 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.606 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.553 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.539 | ||||
| Upside Potential Ratio | 0.070 | ||||
| Upside part of mean | 0.452 | ||||
| Downside part of mean | -3.949 | ||||
| Upside SD | 0.510 | ||||
| Downside SD | 6.490 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 35.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 40.000 | ||||
| Mean of predictor | 0.437 | ||||
| Mean of criterion | -3.497 | ||||
| SD of predictor | 0.222 | ||||
| SD of criterion | 6.513 | ||||
| Covariance | 0.002 | ||||
| r | 0.001 | ||||
| b (slope, estimate of beta) | 0.035 | ||||
| a (intercept, estimate of alpha) | -3.512 | ||||
| Mean Square Error | 43.537 | ||||
| DF error | 38.000 | ||||
| t(b) | 0.007 | ||||
| p(b) | 0.497 | ||||
| t(a) | -0.842 | ||||
| p(a) | 0.797 | ||||
| Lowerbound of 95% confidence interval for beta | -9.620 | ||||
| Upperbound of 95% confidence interval for beta | 9.689 | ||||
| Lowerbound of 95% confidence interval for alpha | -11.956 | ||||
| Upperbound of 95% confidence interval for alpha | 4.932 | ||||
| Treynor index (mean / b) | -100.928 | ||||
| Jensen alpha (a) | -3.512 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.966 | ||||
| Expected Shortfall on VaR | 0.981 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.156 | ||||
| Expected Shortfall on VaR | 0.340 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 40.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.222 | ||||
| Mean of quarter 1 | 0.819 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.209 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.100 | ||||
| Mean of outliers low | 0.546 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.125 | ||||
| Mean of outliers high | 1.418 | ||||
| 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) | 0.845 | ||||
| VaR(95%) (regression method) | 0.167 | ||||
| Expected Shortfall (regression method) | 1.887 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.071 | ||||
| Quartile 1 | 0.303 | ||||
| Median | 0.536 | ||||
| Quartile 3 | 0.768 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.071 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.464 | ||||
| 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) | -0.300 | ||||
| Compounded annual return (geometric extrapolation) | -0.968 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.968 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.968 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.987 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.470 | ||||
| SD | 1.314 | ||||
| Sharpe ratio (Glass type estimate) | 0.358 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.358 | ||||
| df | 891.000 | ||||
| t | 0.661 | ||||
| p | 0.255 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.704 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.420 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.705 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.420 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.717 | ||||
| Upside Potential Ratio | 3.077 | ||||
| Upside part of mean | 2.020 | ||||
| Downside part of mean | -1.549 | ||||
| Upside SD | 1.138 | ||||
| Downside SD | 0.656 | ||||
| N nonnegative terms | 97.000 | ||||
| N negative terms | 795.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 892.000 | ||||
| Mean of predictor | 0.547 | ||||
| Mean of criterion | 0.470 | ||||
| SD of predictor | 0.322 | ||||
| SD of criterion | 1.314 | ||||
| Covariance | -0.012 | ||||
| r | -0.028 | ||||
| b (slope, estimate of beta) | -0.115 | ||||
| a (intercept, estimate of alpha) | 0.533 | ||||
| Mean Square Error | 1.727 | ||||
| DF error | 890.000 | ||||
| t(b) | -0.840 | ||||
| p(b) | 0.799 | ||||
| t(a) | 0.745 | ||||
| p(a) | 0.228 | ||||
| Lowerbound of 95% confidence interval for beta | -0.383 | ||||
| Upperbound of 95% confidence interval for beta | 0.153 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.872 | ||||
| Upperbound of 95% confidence interval for alpha | 1.939 | ||||
| Treynor index (mean / b) | -4.099 | ||||
| Jensen alpha (a) | 0.533 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -3.425 | ||||
| SD | 7.015 | ||||
| Sharpe ratio (Glass type estimate) | -0.488 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.488 | ||||
| df | 891.000 | ||||
| t | -0.901 | ||||
| p | 0.816 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.551 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.574 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.550 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.575 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.491 | ||||
| Upside Potential Ratio | 0.241 | ||||
| Upside part of mean | 1.684 | ||||
| Downside part of mean | -5.109 | ||||
| Upside SD | 0.704 | ||||
| Downside SD | 6.979 | ||||
| N nonnegative terms | 97.000 | ||||
| N negative terms | 795.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 892.000 | ||||
| Mean of predictor | 0.494 | ||||
| Mean of criterion | -3.425 | ||||
| SD of predictor | 0.324 | ||||
| SD of criterion | 7.015 | ||||
| Covariance | 0.058 | ||||
| r | 0.025 | ||||
| b (slope, estimate of beta) | 0.550 | ||||
| a (intercept, estimate of alpha) | -3.697 | ||||
| Mean Square Error | 49.238 | ||||
| DF error | 890.000 | ||||
| t(b) | 0.759 | ||||
| p(b) | 0.224 | ||||
| t(a) | -0.968 | ||||
| p(a) | 0.833 | ||||
| Lowerbound of 95% confidence interval for beta | -0.872 | ||||
| Upperbound of 95% confidence interval for beta | 1.972 | ||||
| Lowerbound of 95% confidence interval for alpha | -11.194 | ||||
| Upperbound of 95% confidence interval for alpha | 3.800 | ||||
| Treynor index (mean / b) | -6.229 | ||||
| Jensen alpha (a) | -3.697 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.516 | ||||
| Expected Shortfall on VaR | 0.591 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.043 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 892.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.942 | ||||
| Mean of quarter 1 | 0.977 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.031 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 88.000 | ||||
| Percentage of outliers low | 0.099 | ||||
| Mean of outliers low | 0.942 | ||||
| Number of outliers high | 97.000 | ||||
| Percentage of outliers high | 0.109 | ||||
| Mean of outliers high | 1.071 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.665 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.006 | ||||
| Extreme Value Index (regression method) | 0.420 | ||||
| VaR(95%) (regression method) | 0.015 | ||||
| Expected Shortfall (regression method) | 0.060 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.029 | ||||
| Median | 0.062 | ||||
| Quartile 3 | 0.144 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.014 | ||||
| Mean of quarter 2 | 0.044 | ||||
| Mean of quarter 3 | 0.083 | ||||
| Mean of quarter 4 | 0.456 | ||||
| Inter Quartile Range | 0.115 | ||||
| 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 | 0.100 | ||||
| Mean of outliers high | 1.000 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.655 | ||||
| VaR(95%) (moments method) | 0.537 | ||||
| Expected Shortfall (moments method) | 1.741 | ||||
| Extreme Value Index (regression method) | 3.024 | ||||
| VaR(95%) (regression method) | 1.747 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.294 | ||||
| Compounded annual return (geometric extrapolation) | -0.966 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.966 | ||||
| Compounded annual return / average of 25% largest draw downs | -2.120 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.633 | ||||
| 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 | 1.138 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.508 | ||||
| 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 | 1.007 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.509 | ||||
| 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) | -8734290888598481.000 | ||||
| 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) | -836379617452411662354977262665728.000 | ||||
| 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 | ||||