Advanced Statistics: ES-ES
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 | 222.092 | ||||
| SD | 363.296 | ||||
| Sharpe ratio (Glass type estimate) | 0.611 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.604 | ||||
| df | 59.000 | ||||
| t | 1.367 | ||||
| p | 0.088 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.275 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.492 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.280 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.487 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 242.414 | ||||
| Upside Potential Ratio | 243.695 | ||||
| Upside part of mean | 223.266 | ||||
| Downside part of mean | -1.174 | ||||
| Upside SD | 365.915 | ||||
| Downside SD | 0.916 | ||||
| N nonnegative terms | 12.000 | ||||
| N negative terms | 48.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 60.000 | ||||
| Mean of predictor | 0.373 | ||||
| Mean of criterion | 222.092 | ||||
| SD of predictor | 0.245 | ||||
| SD of criterion | 363.296 | ||||
| Covariance | -20.438 | ||||
| r | -0.230 | ||||
| b (slope, estimate of beta) | -341.052 | ||||
| a (intercept, estimate of alpha) | 349.219 | ||||
| Mean Square Error | 127168.584 | ||||
| DF error | 58.000 | ||||
| t(b) | -1.798 | ||||
| p(b) | 0.961 | ||||
| t(a) | 2.002 | ||||
| p(a) | 0.025 | ||||
| Lowerbound of 95% confidence interval for beta | -720.677 | ||||
| Upperbound of 95% confidence interval for beta | 38.573 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.029 | ||||
| Upperbound of 95% confidence interval for alpha | 698.408 | ||||
| Treynor index (mean / b) | -0.651 | ||||
| Jensen alpha (a) | 349.219 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -1.636 | ||||
| SD | 6.690 | ||||
| Sharpe ratio (Glass type estimate) | -0.244 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.241 | ||||
| df | 59.000 | ||||
| t | -0.547 | ||||
| p | 0.707 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.121 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.634 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.119 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.636 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.309 | ||||
| Upside Potential Ratio | 0.595 | ||||
| Upside part of mean | 3.152 | ||||
| Downside part of mean | -4.787 | ||||
| Upside SD | 4.017 | ||||
| Downside SD | 5.301 | ||||
| N nonnegative terms | 12.000 | ||||
| N negative terms | 48.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 60.000 | ||||
| Mean of predictor | 0.338 | ||||
| Mean of criterion | -1.636 | ||||
| SD of predictor | 0.235 | ||||
| SD of criterion | 6.690 | ||||
| Covariance | -0.446 | ||||
| r | -0.283 | ||||
| b (slope, estimate of beta) | -8.069 | ||||
| a (intercept, estimate of alpha) | 1.095 | ||||
| Mean Square Error | 41.869 | ||||
| DF error | 58.000 | ||||
| t(b) | -2.251 | ||||
| p(b) | 0.986 | ||||
| t(a) | 0.349 | ||||
| p(a) | 0.364 | ||||
| Lowerbound of 95% confidence interval for beta | -15.243 | ||||
| Upperbound of 95% confidence interval for beta | -0.895 | ||||
| Lowerbound of 95% confidence interval for alpha | -5.185 | ||||
| Upperbound of 95% confidence interval for alpha | 7.376 | ||||
| Treynor index (mean / b) | 0.203 | ||||
| Jensen alpha (a) | 1.095 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.964 | ||||
| Expected Shortfall on VaR | 0.980 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.298 | ||||
| Expected Shortfall on VaR | 0.612 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 60.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 717.000 | ||||
| Mean of quarter 1 | 0.620 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 75.425 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 11.000 | ||||
| Percentage of outliers low | 0.183 | ||||
| Mean of outliers low | 0.482 | ||||
| Number of outliers high | 12.000 | ||||
| Percentage of outliers high | 0.200 | ||||
| Mean of outliers high | 94.031 | ||||
| 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) | -2.531 | ||||
| VaR(95%) (regression method) | 0.532 | ||||
| Expected Shortfall (regression method) | 0.544 | ||||
| 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) | -0.200 | ||||
| Compounded annual return (geometric extrapolation) | -0.796 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.796 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.812 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 249.597 | ||||
| SD | 523.933 | ||||
| Sharpe ratio (Glass type estimate) | 0.476 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.476 | ||||
| df | 1312.000 | ||||
| t | 1.066 | ||||
| p | 0.485 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.399 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.352 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.400 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.352 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 138.477 | ||||
| Upside Potential Ratio | 142.296 | ||||
| Upside part of mean | 256.480 | ||||
| Downside part of mean | -6.883 | ||||
| Upside SD | 523.957 | ||||
| Downside SD | 1.802 | ||||
| N nonnegative terms | 237.000 | ||||
| N negative terms | 1076.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1313.000 | ||||
| Mean of predictor | 0.389 | ||||
| Mean of criterion | 249.597 | ||||
| SD of predictor | 0.318 | ||||
| SD of criterion | 523.933 | ||||
| Covariance | -6.607 | ||||
| r | -0.040 | ||||
| b (slope, estimate of beta) | -65.365 | ||||
| a (intercept, estimate of alpha) | 275.001 | ||||
| Mean Square Error | 274283.031 | ||||
| DF error | 1311.000 | ||||
| t(b) | -1.437 | ||||
| p(b) | 0.525 | ||||
| t(a) | 1.172 | ||||
| p(a) | 0.479 | ||||
| Lowerbound of 95% confidence interval for beta | -154.580 | ||||
| Upperbound of 95% confidence interval for beta | 23.850 | ||||
| Lowerbound of 95% confidence interval for alpha | -185.258 | ||||
| Upperbound of 95% confidence interval for alpha | 735.261 | ||||
| Treynor index (mean / b) | -3.819 | ||||
| Jensen alpha (a) | 275.001 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -1.632 | ||||
| SD | 7.260 | ||||
| Sharpe ratio (Glass type estimate) | -0.225 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.225 | ||||
| df | 1312.000 | ||||
| t | -0.503 | ||||
| p | 0.507 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.100 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.651 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.100 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.651 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.290 | ||||
| Upside Potential Ratio | 1.990 | ||||
| Upside part of mean | 11.191 | ||||
| Downside part of mean | -12.823 | ||||
| Upside SD | 4.590 | ||||
| Downside SD | 5.623 | ||||
| N nonnegative terms | 237.000 | ||||
| N negative terms | 1076.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1313.000 | ||||
| Mean of predictor | 0.337 | ||||
| Mean of criterion | -1.632 | ||||
| SD of predictor | 0.323 | ||||
| SD of criterion | 7.260 | ||||
| Covariance | -0.154 | ||||
| r | -0.066 | ||||
| b (slope, estimate of beta) | -1.483 | ||||
| a (intercept, estimate of alpha) | -1.132 | ||||
| Mean Square Error | 52.524 | ||||
| DF error | 1311.000 | ||||
| t(b) | -2.392 | ||||
| p(b) | 0.542 | ||||
| t(a) | -0.349 | ||||
| p(a) | 0.506 | ||||
| Lowerbound of 95% confidence interval for beta | -2.700 | ||||
| Upperbound of 95% confidence interval for beta | -0.267 | ||||
| Lowerbound of 95% confidence interval for alpha | -7.497 | ||||
| Upperbound of 95% confidence interval for alpha | 5.232 | ||||
| Treynor index (mean / b) | 1.100 | ||||
| Jensen alpha (a) | -1.132 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.525 | ||||
| Expected Shortfall on VaR | 0.601 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.081 | ||||
| Expected Shortfall on VaR | 0.179 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1313.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1173.571 | ||||
| Mean of quarter 1 | 0.896 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 4.919 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 208.000 | ||||
| Percentage of outliers low | 0.158 | ||||
| Mean of outliers low | 0.835 | ||||
| Number of outliers high | 238.000 | ||||
| Percentage of outliers high | 0.181 | ||||
| Mean of outliers high | 6.401 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.208 | ||||
| VaR(95%) (moments method) | 0.005 | ||||
| Expected Shortfall (moments method) | 0.011 | ||||
| Extreme Value Index (regression method) | 0.278 | ||||
| VaR(95%) (regression method) | 0.091 | ||||
| Expected Shortfall (regression method) | 0.220 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 18.000 | ||||
| Minimum | 0.014 | ||||
| Quartile 1 | 0.097 | ||||
| Median | 0.117 | ||||
| Quartile 3 | 0.155 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.043 | ||||
| Mean of quarter 2 | 0.112 | ||||
| Mean of quarter 3 | 0.123 | ||||
| Mean of quarter 4 | 0.372 | ||||
| Inter Quartile Range | 0.058 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.111 | ||||
| Mean of outliers high | 0.664 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.683 | ||||
| VaR(95%) (moments method) | 0.455 | ||||
| Expected Shortfall (moments method) | 1.443 | ||||
| Extreme Value Index (regression method) | 1.996 | ||||
| VaR(95%) (regression method) | 0.529 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.199 | ||||
| Compounded annual return (geometric extrapolation) | -0.796 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.796 | ||||
| Compounded annual return / average of 25% largest draw downs | -2.140 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.324 | ||||
| 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 | 1.027 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.366 | ||||
| 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 | 0.958 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.369 | ||||
| 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) | -8688153781558917.000 | ||||
| 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) | 53530295288961540928462473134080.000 | ||||
| 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 | ||||