Advanced Statistics: Pannonia II
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 | 4.193 | ||||
| SD | 9.670 | ||||
| Sharpe ratio (Glass type estimate) | 0.434 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.430 | ||||
| df | 83.000 | ||||
| t | 1.147 | ||||
| p | 0.127 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.311 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.176 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.314 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.173 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 9.110 | ||||
| Upside Potential Ratio | 9.968 | ||||
| Upside part of mean | 4.589 | ||||
| Downside part of mean | -0.395 | ||||
| Upside SD | 9.678 | ||||
| Downside SD | 0.460 | ||||
| N nonnegative terms | 12.000 | ||||
| N negative terms | 72.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 84.000 | ||||
| Mean of predictor | 0.215 | ||||
| Mean of criterion | 4.193 | ||||
| SD of predictor | 0.272 | ||||
| SD of criterion | 9.670 | ||||
| Covariance | 0.012 | ||||
| r | 0.005 | ||||
| b (slope, estimate of beta) | 0.163 | ||||
| a (intercept, estimate of alpha) | 4.158 | ||||
| Mean Square Error | 94.654 | ||||
| DF error | 82.000 | ||||
| t(b) | 0.041 | ||||
| p(b) | 0.484 | ||||
| t(a) | 1.102 | ||||
| p(a) | 0.137 | ||||
| Lowerbound of 95% confidence interval for beta | -7.639 | ||||
| Upperbound of 95% confidence interval for beta | 7.964 | ||||
| Lowerbound of 95% confidence interval for alpha | -3.346 | ||||
| Upperbound of 95% confidence interval for alpha | 11.663 | ||||
| Treynor index (mean / b) | 25.779 | ||||
| Jensen alpha (a) | 4.158 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.464 | ||||
| SD | 1.645 | ||||
| Sharpe ratio (Glass type estimate) | 0.282 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.280 | ||||
| df | 83.000 | ||||
| t | 0.746 | ||||
| p | 0.229 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.461 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.023 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.462 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.022 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.556 | ||||
| Upside Potential Ratio | 1.304 | ||||
| Upside part of mean | 1.088 | ||||
| Downside part of mean | -0.624 | ||||
| Upside SD | 1.412 | ||||
| Downside SD | 0.835 | ||||
| N nonnegative terms | 12.000 | ||||
| N negative terms | 72.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 84.000 | ||||
| Mean of predictor | 0.177 | ||||
| Mean of criterion | 0.464 | ||||
| SD of predictor | 0.268 | ||||
| SD of criterion | 1.645 | ||||
| Covariance | 0.059 | ||||
| r | 0.134 | ||||
| b (slope, estimate of beta) | 0.821 | ||||
| a (intercept, estimate of alpha) | 0.319 | ||||
| Mean Square Error | 2.689 | ||||
| DF error | 82.000 | ||||
| t(b) | 1.220 | ||||
| p(b) | 0.113 | ||||
| t(a) | 0.505 | ||||
| p(a) | 0.307 | ||||
| Lowerbound of 95% confidence interval for beta | -0.517 | ||||
| Upperbound of 95% confidence interval for beta | 2.159 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.937 | ||||
| Upperbound of 95% confidence interval for alpha | 1.574 | ||||
| Treynor index (mean / b) | 0.565 | ||||
| Jensen alpha (a) | 0.319 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.524 | ||||
| Expected Shortfall on VaR | 0.604 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.104 | ||||
| Expected Shortfall on VaR | 0.228 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 84.000 | ||||
| Minimum | 0.190 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 26.409 | ||||
| Mean of quarter 1 | 0.881 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 2.532 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 9.000 | ||||
| Percentage of outliers low | 0.107 | ||||
| Mean of outliers low | 0.722 | ||||
| Number of outliers high | 12.000 | ||||
| Percentage of outliers high | 0.143 | ||||
| Mean of outliers high | 3.680 | ||||
| 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 | 2.000 | ||||
| Minimum | 0.175 | ||||
| Quartile 1 | 0.356 | ||||
| Median | 0.537 | ||||
| Quartile 3 | 0.718 | ||||
| Maximum | 0.899 | ||||
| Mean of quarter 1 | 0.175 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.899 | ||||
| Inter Quartile Range | 0.362 | ||||
| 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) | 4.858 | ||||
| Compounded annual return (geometric extrapolation) | 0.662 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.737 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.737 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.096 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 7.217 | ||||
| SD | 6.995 | ||||
| Sharpe ratio (Glass type estimate) | 1.032 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.031 | ||||
| df | 1841.000 | ||||
| t | 2.736 | ||||
| p | 0.460 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.292 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.772 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.291 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.771 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 6.161 | ||||
| Upside Potential Ratio | 8.540 | ||||
| Upside part of mean | 10.004 | ||||
| Downside part of mean | -2.787 | ||||
| Upside SD | 6.908 | ||||
| Downside SD | 1.171 | ||||
| N nonnegative terms | 163.000 | ||||
| N negative terms | 1679.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1842.000 | ||||
| Mean of predictor | 0.357 | ||||
| Mean of criterion | 7.217 | ||||
| SD of predictor | 0.581 | ||||
| SD of criterion | 6.995 | ||||
| Covariance | 0.557 | ||||
| r | 0.137 | ||||
| b (slope, estimate of beta) | 1.647 | ||||
| a (intercept, estimate of alpha) | 6.629 | ||||
| Mean Square Error | 48.034 | ||||
| DF error | 1840.000 | ||||
| t(b) | 5.928 | ||||
| p(b) | 0.432 | ||||
| t(a) | 2.534 | ||||
| p(a) | 0.471 | ||||
| Lowerbound of 95% confidence interval for beta | 1.102 | ||||
| Upperbound of 95% confidence interval for beta | 2.192 | ||||
| Lowerbound of 95% confidence interval for alpha | 1.499 | ||||
| Upperbound of 95% confidence interval for alpha | 11.759 | ||||
| Treynor index (mean / b) | 4.381 | ||||
| Jensen alpha (a) | 6.629 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.462 | ||||
| SD | 3.133 | ||||
| Sharpe ratio (Glass type estimate) | 0.147 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.147 | ||||
| df | 1841.000 | ||||
| t | 0.391 | ||||
| p | 0.494 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.592 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.887 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.592 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.887 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.220 | ||||
| Upside Potential Ratio | 2.241 | ||||
| Upside part of mean | 4.712 | ||||
| Downside part of mean | -4.251 | ||||
| Upside SD | 2.322 | ||||
| Downside SD | 2.103 | ||||
| N nonnegative terms | 163.000 | ||||
| N negative terms | 1679.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1842.000 | ||||
| Mean of predictor | 0.189 | ||||
| Mean of criterion | 0.462 | ||||
| SD of predictor | 0.580 | ||||
| SD of criterion | 3.133 | ||||
| Covariance | 0.419 | ||||
| r | 0.230 | ||||
| b (slope, estimate of beta) | 1.244 | ||||
| a (intercept, estimate of alpha) | 0.226 | ||||
| Mean Square Error | 9.300 | ||||
| DF error | 1840.000 | ||||
| t(b) | 10.159 | ||||
| p(b) | 0.385 | ||||
| t(a) | 0.197 | ||||
| p(a) | 0.498 | ||||
| Lowerbound of 95% confidence interval for beta | 1.004 | ||||
| Upperbound of 95% confidence interval for beta | 1.484 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.030 | ||||
| Upperbound of 95% confidence interval for alpha | 2.482 | ||||
| Treynor index (mean / b) | 0.371 | ||||
| Jensen alpha (a) | 0.226 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.271 | ||||
| Expected Shortfall on VaR | 0.326 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.035 | ||||
| Expected Shortfall on VaR | 0.079 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1842.000 | ||||
| Minimum | 0.124 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 13.704 | ||||
| Mean of quarter 1 | 0.958 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.153 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 125.000 | ||||
| Percentage of outliers low | 0.068 | ||||
| Mean of outliers low | 0.845 | ||||
| Number of outliers high | 163.000 | ||||
| Percentage of outliers high | 0.088 | ||||
| Mean of outliers high | 1.432 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.714 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| 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 | 6.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.064 | ||||
| Median | 0.273 | ||||
| Quartile 3 | 0.612 | ||||
| Maximum | 0.949 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.231 | ||||
| Mean of quarter 3 | 0.314 | ||||
| Mean of quarter 4 | 0.830 | ||||
| Inter Quartile Range | 0.547 | ||||
| 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) | 4.837 | ||||
| Compounded annual return (geometric extrapolation) | 0.658 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.694 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.793 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.017 | ||||
| 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 | 1.174 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.500 | ||||
| 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 | 1.046 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.504 | ||||
| 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) | -8727791040807861.000 | ||||
| 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) | -210591148924450882127042327871488.000 | ||||
| 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 | ||||