Advanced Statistics: System 18570303
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 | 6261.172 | ||||
| SD | 17416.178 | ||||
| Sharpe ratio (Glass type estimate) | 0.360 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.357 | ||||
| df | 92.000 | ||||
| t | 1.001 | ||||
| p | 0.160 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.347 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.064 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.349 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.062 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 11224.400 | ||||
| Upside Potential Ratio | 11225.472 | ||||
| Upside part of mean | 6261.770 | ||||
| Downside part of mean | -0.598 | ||||
| Upside SD | 17416.330 | ||||
| Downside SD | 0.558 | ||||
| N nonnegative terms | 15.000 | ||||
| N negative terms | 78.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 93.000 | ||||
| Mean of predictor | 0.196 | ||||
| Mean of criterion | 6261.172 | ||||
| SD of predictor | 0.272 | ||||
| SD of criterion | 17416.178 | ||||
| Covariance | 170.101 | ||||
| r | 0.036 | ||||
| b (slope, estimate of beta) | 2292.387 | ||||
| a (intercept, estimate of alpha) | 5811.631 | ||||
| Mean Square Error | 306262241.768 | ||||
| DF error | 91.000 | ||||
| t(b) | 0.342 | ||||
| p(b) | 0.366 | ||||
| t(a) | 0.905 | ||||
| p(a) | 0.184 | ||||
| Lowerbound of 95% confidence interval for beta | -11012.329 | ||||
| Upperbound of 95% confidence interval for beta | 15597.103 | ||||
| Lowerbound of 95% confidence interval for alpha | -6945.018 | ||||
| Upperbound of 95% confidence interval for alpha | 18568.280 | ||||
| Treynor index (mean / b) | 2.731 | ||||
| Jensen alpha (a) | 5811.631 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.147 | ||||
| SD | 6.310 | ||||
| Sharpe ratio (Glass type estimate) | 0.023 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.023 | ||||
| df | 92.000 | ||||
| t | 0.065 | ||||
| p | 0.474 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.681 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.727 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.681 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.727 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.031 | ||||
| Upside Potential Ratio | 0.516 | ||||
| Upside part of mean | 2.439 | ||||
| Downside part of mean | -2.292 | ||||
| Upside SD | 4.124 | ||||
| Downside SD | 4.731 | ||||
| N nonnegative terms | 15.000 | ||||
| N negative terms | 78.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 93.000 | ||||
| Mean of predictor | 0.158 | ||||
| Mean of criterion | 0.147 | ||||
| SD of predictor | 0.269 | ||||
| SD of criterion | 6.310 | ||||
| Covariance | 0.102 | ||||
| r | 0.060 | ||||
| b (slope, estimate of beta) | 1.405 | ||||
| a (intercept, estimate of alpha) | -0.075 | ||||
| Mean Square Error | 40.114 | ||||
| DF error | 91.000 | ||||
| t(b) | 0.573 | ||||
| p(b) | 0.284 | ||||
| t(a) | -0.033 | ||||
| p(a) | 0.513 | ||||
| Lowerbound of 95% confidence interval for beta | -3.466 | ||||
| Upperbound of 95% confidence interval for beta | 6.276 | ||||
| Lowerbound of 95% confidence interval for alpha | -4.660 | ||||
| Upperbound of 95% confidence interval for alpha | 4.509 | ||||
| Treynor index (mean / b) | 0.104 | ||||
| Jensen alpha (a) | -0.075 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.949 | ||||
| Expected Shortfall on VaR | 0.972 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.156 | ||||
| Expected Shortfall on VaR | 0.332 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 93.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 48486.000 | ||||
| Mean of quarter 1 | 0.819 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 2110.947 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 15.000 | ||||
| Percentage of outliers low | 0.161 | ||||
| Mean of outliers low | 0.710 | ||||
| Number of outliers high | 17.000 | ||||
| Percentage of outliers high | 0.183 | ||||
| Mean of outliers high | 2855.634 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.874 | ||||
| VaR(95%) (moments method) | 0.036 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.019 | ||||
| VaR(95%) (regression method) | 0.118 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.034 | ||||
| Quartile 1 | 0.343 | ||||
| Median | 0.652 | ||||
| Quartile 3 | 0.826 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.034 | ||||
| Mean of quarter 2 | 0.652 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.483 | ||||
| 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) | 0.437 | ||||
| Compounded annual return (geometric extrapolation) | 0.210 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.210 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.210 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.216 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 97354.438 | ||||
| SD | 115727.645 | ||||
| Sharpe ratio (Glass type estimate) | 0.841 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.841 | ||||
| df | 2040.000 | ||||
| t | 2.348 | ||||
| p | 0.009 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.138 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.544 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.138 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.544 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 54547.961 | ||||
| Upside Potential Ratio | 54551.180 | ||||
| Upside part of mean | 97360.185 | ||||
| Downside part of mean | -5.746 | ||||
| Upside SD | 115855.517 | ||||
| Downside SD | 1.785 | ||||
| N nonnegative terms | 319.000 | ||||
| N negative terms | 1722.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2041.000 | ||||
| Mean of predictor | 0.312 | ||||
| Mean of criterion | 97354.438 | ||||
| SD of predictor | 0.535 | ||||
| SD of criterion | 115727.645 | ||||
| Covariance | 5747.071 | ||||
| r | 0.093 | ||||
| b (slope, estimate of beta) | 20076.322 | ||||
| a (intercept, estimate of alpha) | 91098.481 | ||||
| Mean Square Error | 13284019445.404 | ||||
| DF error | 2039.000 | ||||
| t(b) | 4.209 | ||||
| p(b) | 0.000 | ||||
| t(a) | 2.205 | ||||
| p(a) | 0.014 | ||||
| Lowerbound of 95% confidence interval for beta | 10722.818 | ||||
| Upperbound of 95% confidence interval for beta | 29429.826 | ||||
| Lowerbound of 95% confidence interval for alpha | 10061.946 | ||||
| Upperbound of 95% confidence interval for alpha | 172135.015 | ||||
| Treynor index (mean / b) | 4.849 | ||||
| Jensen alpha (a) | 91098.481 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.146 | ||||
| SD | 16.664 | ||||
| Sharpe ratio (Glass type estimate) | 0.009 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.009 | ||||
| df | 2040.000 | ||||
| t | 0.024 | ||||
| p | 0.490 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.693 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.711 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.693 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.711 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.012 | ||||
| Upside Potential Ratio | 1.602 | ||||
| Upside part of mean | 18.801 | ||||
| Downside part of mean | -18.655 | ||||
| Upside SD | 11.825 | ||||
| Downside SD | 11.735 | ||||
| N nonnegative terms | 319.000 | ||||
| N negative terms | 1722.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2041.000 | ||||
| Mean of predictor | 0.170 | ||||
| Mean of criterion | 0.146 | ||||
| SD of predictor | 0.531 | ||||
| SD of criterion | 16.664 | ||||
| Covariance | 1.611 | ||||
| r | 0.182 | ||||
| b (slope, estimate of beta) | 5.715 | ||||
| a (intercept, estimate of alpha) | -0.828 | ||||
| Mean Square Error | 268.602 | ||||
| DF error | 2039.000 | ||||
| t(b) | 8.362 | ||||
| p(b) | -0.000 | ||||
| t(a) | -0.141 | ||||
| p(a) | 0.556 | ||||
| Lowerbound of 95% confidence interval for beta | 4.374 | ||||
| Upperbound of 95% confidence interval for beta | 7.055 | ||||
| Lowerbound of 95% confidence interval for alpha | -12.346 | ||||
| Upperbound of 95% confidence interval for alpha | 10.690 | ||||
| Treynor index (mean / b) | 0.026 | ||||
| Jensen alpha (a) | -0.828 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.816 | ||||
| Expected Shortfall on VaR | 0.873 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.068 | ||||
| Expected Shortfall on VaR | 0.153 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2041.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 231609.917 | ||||
| Mean of quarter 1 | 0.913 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1488.144 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 448.000 | ||||
| Percentage of outliers low | 0.220 | ||||
| Mean of outliers low | 0.901 | ||||
| Number of outliers high | 416.000 | ||||
| Percentage of outliers high | 0.204 | ||||
| Mean of outliers high | 1824.181 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.449 | ||||
| VaR(95%) (moments method) | 0.009 | ||||
| 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 | 20.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.000 | ||||
| Quartile 3 | 0.733 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.000 | ||||
| Mean of quarter 3 | 0.152 | ||||
| Mean of quarter 4 | 0.873 | ||||
| Inter Quartile Range | 0.733 | ||||
| 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) | -0.536 | ||||
| VaR(95%) (moments method) | 0.950 | ||||
| Expected Shortfall (moments method) | 1.012 | ||||
| Extreme Value Index (regression method) | -8.857 | ||||
| VaR(95%) (regression method) | 1.877 | ||||
| Expected Shortfall (regression method) | 1.877 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.435 | ||||
| Compounded annual return (geometric extrapolation) | 0.209 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.209 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.240 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.240 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.095 | ||||
| SD | 0.036 | ||||
| Sharpe ratio (Glass type estimate) | -2.646 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.631 | ||||
| df | 130.000 | ||||
| t | -1.871 | ||||
| p | 0.581 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -5.432 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.149 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -5.421 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.159 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.621 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.095 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.036 | ||||
| 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 | 0.969 | ||||
| Mean of criterion | -0.095 | ||||
| SD of predictor | 0.437 | ||||
| SD of criterion | 0.036 | ||||
| Covariance | 0.002 | ||||
| r | 0.100 | ||||
| b (slope, estimate of beta) | 0.008 | ||||
| a (intercept, estimate of alpha) | -0.102 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 129.000 | ||||
| t(b) | 1.139 | ||||
| p(b) | 0.437 | ||||
| t(a) | -2.011 | ||||
| p(a) | 0.610 | ||||
| Lowerbound of 95% confidence interval for beta | -0.006 | ||||
| Upperbound of 95% confidence interval for beta | 0.022 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.203 | ||||
| Upperbound of 95% confidence interval for alpha | -0.002 | ||||
| Treynor index (mean / b) | -11.596 | ||||
| Jensen alpha (a) | -0.102 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.095 | ||||
| SD | 0.036 | ||||
| Sharpe ratio (Glass type estimate) | -2.631 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.615 | ||||
| df | 130.000 | ||||
| t | -1.860 | ||||
| p | 0.581 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -5.416 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.165 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -5.405 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.175 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.606 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.095 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.037 | ||||
| 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 | 0.872 | ||||
| Mean of criterion | -0.095 | ||||
| SD of predictor | 0.438 | ||||
| SD of criterion | 0.036 | ||||
| Covariance | 0.002 | ||||
| r | 0.099 | ||||
| b (slope, estimate of beta) | 0.008 | ||||
| a (intercept, estimate of alpha) | -0.102 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 129.000 | ||||
| t(b) | 1.136 | ||||
| p(b) | 0.437 | ||||
| t(a) | -1.987 | ||||
| p(a) | 0.609 | ||||
| Lowerbound of 95% confidence interval for beta | -0.006 | ||||
| Upperbound of 95% confidence interval for beta | 0.023 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.204 | ||||
| Upperbound of 95% confidence interval for alpha | -0.000 | ||||
| Treynor index (mean / b) | -11.587 | ||||
| Jensen alpha (a) | -0.102 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.003 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.975 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.999 | ||||
| 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 | 0.975 | ||||
| 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 | 0.025 | ||||
| Quartile 1 | 0.025 | ||||
| Median | 0.025 | ||||
| Quartile 3 | 0.025 | ||||
| Maximum | 0.025 | ||||
| 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) | -0.051 | ||||
| Compounded annual return (geometric extrapolation) | -0.050 | ||||
| Calmar ratio (compounded annual return / max draw down) | -1.975 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -10.054 | ||||