Advanced Statistics: Gap 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 | -0.129 | ||||
| SD | 0.156 | ||||
| Sharpe ratio (Glass type estimate) | -0.827 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.817 | ||||
| df | 63.000 | ||||
| t | -1.909 | ||||
| p | 0.970 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.684 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.037 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.677 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.044 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.818 | ||||
| Upside Potential Ratio | 0.061 | ||||
| Upside part of mean | 0.010 | ||||
| Downside part of mean | -0.138 | ||||
| Upside SD | 0.022 | ||||
| Downside SD | 0.157 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 63.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 64.000 | ||||
| Mean of predictor | 0.361 | ||||
| Mean of criterion | -0.129 | ||||
| SD of predictor | 0.272 | ||||
| SD of criterion | 0.156 | ||||
| Covariance | 0.008 | ||||
| r | 0.198 | ||||
| b (slope, estimate of beta) | 0.113 | ||||
| a (intercept, estimate of alpha) | -0.170 | ||||
| Mean Square Error | 0.024 | ||||
| DF error | 62.000 | ||||
| t(b) | 1.589 | ||||
| p(b) | 0.059 | ||||
| t(a) | -2.374 | ||||
| p(a) | 0.990 | ||||
| Lowerbound of 95% confidence interval for beta | -0.029 | ||||
| Upperbound of 95% confidence interval for beta | 0.256 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.312 | ||||
| Upperbound of 95% confidence interval for alpha | -0.027 | ||||
| Treynor index (mean / b) | -1.136 | ||||
| Jensen alpha (a) | -0.170 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.144 | ||||
| SD | 0.189 | ||||
| Sharpe ratio (Glass type estimate) | -0.766 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.757 | ||||
| df | 63.000 | ||||
| t | -1.769 | ||||
| p | 0.959 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.622 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.096 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.616 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.102 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.758 | ||||
| Upside Potential Ratio | 0.049 | ||||
| Upside part of mean | 0.009 | ||||
| Downside part of mean | -0.154 | ||||
| Upside SD | 0.022 | ||||
| Downside SD | 0.190 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 63.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 64.000 | ||||
| Mean of predictor | 0.319 | ||||
| Mean of criterion | -0.144 | ||||
| SD of predictor | 0.269 | ||||
| SD of criterion | 0.189 | ||||
| Covariance | 0.011 | ||||
| r | 0.211 | ||||
| b (slope, estimate of beta) | 0.148 | ||||
| a (intercept, estimate of alpha) | -0.192 | ||||
| Mean Square Error | 0.035 | ||||
| DF error | 62.000 | ||||
| t(b) | 1.701 | ||||
| p(b) | 0.047 | ||||
| t(a) | -2.252 | ||||
| p(a) | 0.986 | ||||
| Lowerbound of 95% confidence interval for beta | -0.026 | ||||
| Upperbound of 95% confidence interval for beta | 0.322 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.362 | ||||
| Upperbound of 95% confidence interval for alpha | -0.021 | ||||
| Treynor index (mean / b) | -0.975 | ||||
| Jensen alpha (a) | -0.192 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.097 | ||||
| Expected Shortfall on VaR | 0.117 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.040 | ||||
| Expected Shortfall on VaR | 0.086 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 64.000 | ||||
| Minimum | 0.654 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.055 | ||||
| Mean of quarter 1 | 0.968 | ||||
| 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 | 6.000 | ||||
| Percentage of outliers low | 0.094 | ||||
| Mean of outliers low | 0.915 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.031 | ||||
| Mean of outliers high | 1.028 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -3.392 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.005 | ||||
| Extreme Value Index (regression method) | 1.091 | ||||
| VaR(95%) (regression method) | 0.016 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.038 | ||||
| Quartile 1 | 0.135 | ||||
| Median | 0.231 | ||||
| Quartile 3 | 0.327 | ||||
| Maximum | 0.423 | ||||
| Mean of quarter 1 | 0.038 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.423 | ||||
| Inter Quartile Range | 0.192 | ||||
| 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) | -0.078 | ||||
| Compounded annual return (geometric extrapolation) | -0.096 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.226 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.226 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.818 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.081 | ||||
| SD | 0.354 | ||||
| Sharpe ratio (Glass type estimate) | -0.229 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.229 | ||||
| df | 1401.000 | ||||
| t | -0.530 | ||||
| p | 0.509 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.077 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.618 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.076 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.618 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.334 | ||||
| Upside Potential Ratio | 1.902 | ||||
| Upside part of mean | 0.463 | ||||
| Downside part of mean | -0.544 | ||||
| Upside SD | 0.258 | ||||
| Downside SD | 0.243 | ||||
| N nonnegative terms | 50.000 | ||||
| N negative terms | 1352.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1402.000 | ||||
| Mean of predictor | 0.512 | ||||
| Mean of criterion | -0.081 | ||||
| SD of predictor | 0.576 | ||||
| SD of criterion | 0.354 | ||||
| Covariance | 0.025 | ||||
| r | 0.123 | ||||
| b (slope, estimate of beta) | 0.076 | ||||
| a (intercept, estimate of alpha) | -0.120 | ||||
| Mean Square Error | 0.124 | ||||
| DF error | 1400.000 | ||||
| t(b) | 4.643 | ||||
| p(b) | 0.438 | ||||
| t(a) | -0.788 | ||||
| p(a) | 0.511 | ||||
| Lowerbound of 95% confidence interval for beta | 0.044 | ||||
| Upperbound of 95% confidence interval for beta | 0.108 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.419 | ||||
| Upperbound of 95% confidence interval for alpha | 0.179 | ||||
| Treynor index (mean / b) | -1.071 | ||||
| Jensen alpha (a) | -0.120 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.144 | ||||
| SD | 0.356 | ||||
| Sharpe ratio (Glass type estimate) | -0.405 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.405 | ||||
| df | 1401.000 | ||||
| t | -0.937 | ||||
| p | 0.516 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.252 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.442 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.252 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.443 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.545 | ||||
| Upside Potential Ratio | 1.638 | ||||
| Upside part of mean | 0.433 | ||||
| Downside part of mean | -0.577 | ||||
| Upside SD | 0.238 | ||||
| Downside SD | 0.264 | ||||
| N nonnegative terms | 50.000 | ||||
| N negative terms | 1352.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1402.000 | ||||
| Mean of predictor | 0.351 | ||||
| Mean of criterion | -0.144 | ||||
| SD of predictor | 0.564 | ||||
| SD of criterion | 0.356 | ||||
| Covariance | 0.022 | ||||
| r | 0.109 | ||||
| b (slope, estimate of beta) | 0.069 | ||||
| a (intercept, estimate of alpha) | -0.168 | ||||
| Mean Square Error | 0.125 | ||||
| DF error | 1400.000 | ||||
| t(b) | 4.094 | ||||
| p(b) | 0.446 | ||||
| t(a) | -1.099 | ||||
| p(a) | 0.515 | ||||
| Lowerbound of 95% confidence interval for beta | 0.036 | ||||
| Upperbound of 95% confidence interval for beta | 0.102 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.468 | ||||
| Upperbound of 95% confidence interval for alpha | 0.132 | ||||
| Treynor index (mean / b) | -2.099 | ||||
| Jensen alpha (a) | -0.168 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.036 | ||||
| Expected Shortfall on VaR | 0.045 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.016 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1402.000 | ||||
| Minimum | 0.762 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.206 | ||||
| Mean of quarter 1 | 0.992 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.007 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 66.000 | ||||
| Percentage of outliers low | 0.047 | ||||
| Mean of outliers low | 0.959 | ||||
| Number of outliers high | 50.000 | ||||
| Percentage of outliers high | 0.036 | ||||
| Mean of outliers high | 1.050 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.255 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| 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 | 0.503 | ||||
| Quartile 1 | 0.503 | ||||
| Median | 0.503 | ||||
| Quartile 3 | 0.503 | ||||
| Maximum | 0.503 | ||||
| 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) | -0.077 | ||||
| Compounded annual return (geometric extrapolation) | -0.095 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.189 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.125 | ||||
| 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 | 1.057 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.513 | ||||
| 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 | 0.925 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.514 | ||||
| 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) | -8745546843282343.000 | ||||
| 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) | 479348017404424979553047801757696.000 | ||||
| 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 | ||||