Advanced Statistics: System 14747274
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 | 24.813 | ||||
| SD | 68.295 | ||||
| Sharpe ratio (Glass type estimate) | 0.363 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.361 | ||||
| df | 98.000 | ||||
| t | 1.044 | ||||
| p | 0.150 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.322 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.047 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.324 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.045 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 39.025 | ||||
| Upside Potential Ratio | 40.109 | ||||
| Upside part of mean | 25.502 | ||||
| Downside part of mean | -0.689 | ||||
| Upside SD | 68.323 | ||||
| Downside SD | 0.636 | ||||
| N nonnegative terms | 11.000 | ||||
| N negative terms | 88.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 99.000 | ||||
| Mean of predictor | 0.184 | ||||
| Mean of criterion | 24.813 | ||||
| SD of predictor | 0.266 | ||||
| SD of criterion | 68.295 | ||||
| Covariance | 1.655 | ||||
| r | 0.091 | ||||
| b (slope, estimate of beta) | 23.443 | ||||
| a (intercept, estimate of alpha) | 20.496 | ||||
| Mean Square Error | 4673.103 | ||||
| DF error | 97.000 | ||||
| t(b) | 0.902 | ||||
| p(b) | 0.185 | ||||
| t(a) | 0.844 | ||||
| p(a) | 0.200 | ||||
| Lowerbound of 95% confidence interval for beta | -28.141 | ||||
| Upperbound of 95% confidence interval for beta | 75.026 | ||||
| Lowerbound of 95% confidence interval for alpha | -27.685 | ||||
| Upperbound of 95% confidence interval for alpha | 68.678 | ||||
| Treynor index (mean / b) | 1.058 | ||||
| Jensen alpha (a) | 20.496 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -1.365 | ||||
| SD | 4.865 | ||||
| Sharpe ratio (Glass type estimate) | -0.281 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.278 | ||||
| df | 98.000 | ||||
| t | -0.806 | ||||
| p | 0.789 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.963 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.404 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.962 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.405 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.311 | ||||
| Upside Potential Ratio | 0.305 | ||||
| Upside part of mean | 1.337 | ||||
| Downside part of mean | -2.702 | ||||
| Upside SD | 2.076 | ||||
| Downside SD | 4.390 | ||||
| N nonnegative terms | 11.000 | ||||
| N negative terms | 88.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 99.000 | ||||
| Mean of predictor | 0.148 | ||||
| Mean of criterion | -1.365 | ||||
| SD of predictor | 0.263 | ||||
| SD of criterion | 4.865 | ||||
| Covariance | 0.017 | ||||
| r | 0.013 | ||||
| b (slope, estimate of beta) | 0.243 | ||||
| a (intercept, estimate of alpha) | -1.401 | ||||
| Mean Square Error | 23.905 | ||||
| DF error | 97.000 | ||||
| t(b) | 0.130 | ||||
| p(b) | 0.449 | ||||
| t(a) | -0.812 | ||||
| p(a) | 0.791 | ||||
| Lowerbound of 95% confidence interval for beta | -3.484 | ||||
| Upperbound of 95% confidence interval for beta | 3.971 | ||||
| Lowerbound of 95% confidence interval for alpha | -4.824 | ||||
| Upperbound of 95% confidence interval for alpha | 2.022 | ||||
| Treynor index (mean / b) | -5.606 | ||||
| Jensen alpha (a) | -1.401 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.911 | ||||
| Expected Shortfall on VaR | 0.945 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.186 | ||||
| Expected Shortfall on VaR | 0.393 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 99.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 197.000 | ||||
| Mean of quarter 1 | 0.786 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 9.417 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 15.000 | ||||
| Percentage of outliers low | 0.152 | ||||
| Mean of outliers low | 0.643 | ||||
| Number of outliers high | 11.000 | ||||
| Percentage of outliers high | 0.111 | ||||
| Mean of outliers high | 20.130 | ||||
| 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) | -1.218 | ||||
| VaR(95%) (regression method) | 0.314 | ||||
| Expected Shortfall (regression method) | 0.369 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.087 | ||||
| Quartile 1 | 0.149 | ||||
| Median | 0.211 | ||||
| Quartile 3 | 0.605 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.087 | ||||
| Mean of quarter 2 | 0.211 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.456 | ||||
| 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) | -0.121 | ||||
| Compounded annual return (geometric extrapolation) | -0.733 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.733 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.733 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.776 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 30544.852 | ||||
| SD | 33635.513 | ||||
| Sharpe ratio (Glass type estimate) | 0.908 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.908 | ||||
| df | 2165.000 | ||||
| t | 2.611 | ||||
| p | 0.005 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.226 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.590 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.226 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.590 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 17445.462 | ||||
| Upside Potential Ratio | 17448.569 | ||||
| Upside part of mean | 30550.291 | ||||
| Downside part of mean | -5.439 | ||||
| Upside SD | 33680.654 | ||||
| Downside SD | 1.751 | ||||
| N nonnegative terms | 226.000 | ||||
| N negative terms | 1940.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2166.000 | ||||
| Mean of predictor | 0.287 | ||||
| Mean of criterion | 30544.852 | ||||
| SD of predictor | 0.538 | ||||
| SD of criterion | 33635.513 | ||||
| Covariance | 1010.025 | ||||
| r | 0.056 | ||||
| b (slope, estimate of beta) | 3485.215 | ||||
| a (intercept, estimate of alpha) | 29544.971 | ||||
| Mean Square Error | 1128348782.031 | ||||
| DF error | 2164.000 | ||||
| t(b) | 2.599 | ||||
| p(b) | 0.005 | ||||
| t(a) | 2.528 | ||||
| p(a) | 0.006 | ||||
| Lowerbound of 95% confidence interval for beta | 855.356 | ||||
| Upperbound of 95% confidence interval for beta | 6115.074 | ||||
| Lowerbound of 95% confidence interval for alpha | 6622.076 | ||||
| Upperbound of 95% confidence interval for alpha | 52467.866 | ||||
| Treynor index (mean / b) | 8.764 | ||||
| Jensen alpha (a) | 29544.971 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -1.362 | ||||
| SD | 17.025 | ||||
| Sharpe ratio (Glass type estimate) | -0.080 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.080 | ||||
| df | 2165.000 | ||||
| t | -0.230 | ||||
| p | 0.591 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.762 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.602 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.762 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.602 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.110 | ||||
| Upside Potential Ratio | 1.572 | ||||
| Upside part of mean | 19.399 | ||||
| Downside part of mean | -20.761 | ||||
| Upside SD | 11.725 | ||||
| Downside SD | 12.339 | ||||
| N nonnegative terms | 226.000 | ||||
| N negative terms | 1940.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2166.000 | ||||
| Mean of predictor | 0.141 | ||||
| Mean of criterion | -1.362 | ||||
| SD of predictor | 0.542 | ||||
| SD of criterion | 17.025 | ||||
| Covariance | 0.486 | ||||
| r | 0.053 | ||||
| b (slope, estimate of beta) | 1.653 | ||||
| a (intercept, estimate of alpha) | -1.595 | ||||
| Mean Square Error | 289.192 | ||||
| DF error | 2164.000 | ||||
| t(b) | 2.452 | ||||
| p(b) | 0.007 | ||||
| t(a) | -0.270 | ||||
| p(a) | 0.606 | ||||
| Lowerbound of 95% confidence interval for beta | 0.331 | ||||
| Upperbound of 95% confidence interval for beta | 2.975 | ||||
| Lowerbound of 95% confidence interval for alpha | -13.195 | ||||
| Upperbound of 95% confidence interval for alpha | 10.005 | ||||
| Treynor index (mean / b) | -0.824 | ||||
| Jensen alpha (a) | -1.595 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.824 | ||||
| Expected Shortfall on VaR | 0.879 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.067 | ||||
| Expected Shortfall on VaR | 0.150 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2166.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 77529.300 | ||||
| Mean of quarter 1 | 0.918 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 466.986 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 253.000 | ||||
| Percentage of outliers low | 0.117 | ||||
| Mean of outliers low | 0.824 | ||||
| Number of outliers high | 226.000 | ||||
| Percentage of outliers high | 0.104 | ||||
| Mean of outliers high | 1118.543 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.702 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.024 | ||||
| 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 | 9.000 | ||||
| Minimum | 0.151 | ||||
| Quartile 1 | 0.253 | ||||
| Median | 0.771 | ||||
| Quartile 3 | 0.860 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.218 | ||||
| Mean of quarter 2 | 0.751 | ||||
| Mean of quarter 3 | 0.823 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.607 | ||||
| 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) | -38627997729.086 | ||||
| VaR(95%) (moments method) | 0.990 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -17.977 | ||||
| VaR(95%) (regression method) | 23.609 | ||||
| Expected Shortfall (regression method) | 23.609 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.121 | ||||
| Compounded annual return (geometric extrapolation) | -0.732 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.732 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.732 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.833 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.043 | ||||
| SD | 1.414 | ||||
| Sharpe ratio (Glass type estimate) | -1.445 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.437 | ||||
| df | 130.000 | ||||
| t | -1.022 | ||||
| p | 0.545 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.220 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.335 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.214 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.340 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.445 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -2.043 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 1.414 | ||||
| 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 | 0.988 | ||||
| Mean of criterion | -2.043 | ||||
| SD of predictor | 0.466 | ||||
| SD of criterion | 1.414 | ||||
| Covariance | 0.085 | ||||
| r | 0.130 | ||||
| b (slope, estimate of beta) | 0.393 | ||||
| a (intercept, estimate of alpha) | -2.431 | ||||
| Mean Square Error | 1.980 | ||||
| DF error | 129.000 | ||||
| t(b) | 1.484 | ||||
| p(b) | 0.418 | ||||
| t(a) | -1.211 | ||||
| p(a) | 0.567 | ||||
| Lowerbound of 95% confidence interval for beta | -0.131 | ||||
| Upperbound of 95% confidence interval for beta | 0.917 | ||||
| Lowerbound of 95% confidence interval for alpha | -6.402 | ||||
| Upperbound of 95% confidence interval for alpha | 1.540 | ||||
| Treynor index (mean / b) | -5.201 | ||||
| Jensen alpha (a) | -2.431 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -15.325 | ||||
| SD | 10.805 | ||||
| Sharpe ratio (Glass type estimate) | -1.418 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.410 | ||||
| df | 130.000 | ||||
| t | -1.003 | ||||
| p | 0.544 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.193 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.362 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.187 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.367 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.418 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -15.325 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 10.806 | ||||
| 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 | 0.879 | ||||
| Mean of criterion | -15.325 | ||||
| SD of predictor | 0.466 | ||||
| SD of criterion | 10.805 | ||||
| Covariance | 0.658 | ||||
| r | 0.131 | ||||
| b (slope, estimate of beta) | 3.031 | ||||
| a (intercept, estimate of alpha) | -17.989 | ||||
| Mean Square Error | 115.654 | ||||
| DF error | 129.000 | ||||
| t(b) | 1.497 | ||||
| p(b) | 0.417 | ||||
| t(a) | -1.175 | ||||
| p(a) | 0.565 | ||||
| Lowerbound of 95% confidence interval for beta | -0.975 | ||||
| Upperbound of 95% confidence interval for beta | 7.038 | ||||
| Lowerbound of 95% confidence interval for alpha | -48.285 | ||||
| Upperbound of 95% confidence interval for alpha | 12.308 | ||||
| Treynor index (mean / b) | -5.056 | ||||
| Jensen alpha (a) | -17.989 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.685 | ||||
| Expected Shortfall on VaR | 0.755 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.027 | ||||
| Expected Shortfall on VaR | 0.062 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.970 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers low | 0.008 | ||||
| Mean of outliers low | 0.000 | ||||
| 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 | 1.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| 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) | -1.999 | ||||
| Compounded annual return (geometric extrapolation) | -1.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | -1.000 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.324 | ||||