Advanced Statistics: System 25286922
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 | 22.025 | ||||
| SD | 56.994 | ||||
| Sharpe ratio (Glass type estimate) | 0.386 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.383 | ||||
| df | 79.000 | ||||
| t | 0.998 | ||||
| p | 0.161 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.376 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.147 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.379 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.144 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 48.711 | ||||
| Upside Potential Ratio | 49.671 | ||||
| Upside part of mean | 22.459 | ||||
| Downside part of mean | -0.434 | ||||
| Upside SD | 56.991 | ||||
| Downside SD | 0.452 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 73.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 80.000 | ||||
| Mean of predictor | 0.221 | ||||
| Mean of criterion | 22.025 | ||||
| SD of predictor | 0.251 | ||||
| SD of criterion | 56.994 | ||||
| Covariance | 0.446 | ||||
| r | 0.031 | ||||
| b (slope, estimate of beta) | 7.102 | ||||
| a (intercept, estimate of alpha) | 20.457 | ||||
| Mean Square Error | 3286.759 | ||||
| DF error | 78.000 | ||||
| t(b) | 0.276 | ||||
| p(b) | 0.392 | ||||
| t(a) | 0.893 | ||||
| p(a) | 0.187 | ||||
| Lowerbound of 95% confidence interval for beta | -44.153 | ||||
| Upperbound of 95% confidence interval for beta | 58.358 | ||||
| Lowerbound of 95% confidence interval for alpha | -25.172 | ||||
| Upperbound of 95% confidence interval for alpha | 66.087 | ||||
| Treynor index (mean / b) | 3.101 | ||||
| Jensen alpha (a) | 20.457 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.408 | ||||
| SD | 2.126 | ||||
| Sharpe ratio (Glass type estimate) | 0.192 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.190 | ||||
| df | 79.000 | ||||
| t | 0.496 | ||||
| p | 0.311 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.568 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.951 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.569 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.950 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.536 | ||||
| Upside Potential Ratio | 1.367 | ||||
| Upside part of mean | 1.041 | ||||
| Downside part of mean | -0.633 | ||||
| Upside SD | 1.974 | ||||
| Downside SD | 0.762 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 73.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 80.000 | ||||
| Mean of predictor | 0.188 | ||||
| Mean of criterion | 0.408 | ||||
| SD of predictor | 0.244 | ||||
| SD of criterion | 2.126 | ||||
| Covariance | 0.021 | ||||
| r | 0.041 | ||||
| b (slope, estimate of beta) | 0.353 | ||||
| a (intercept, estimate of alpha) | 0.342 | ||||
| Mean Square Error | 4.569 | ||||
| DF error | 78.000 | ||||
| t(b) | 0.359 | ||||
| p(b) | 0.360 | ||||
| t(a) | 0.403 | ||||
| p(a) | 0.344 | ||||
| Lowerbound of 95% confidence interval for beta | -1.607 | ||||
| Upperbound of 95% confidence interval for beta | 2.313 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.347 | ||||
| Upperbound of 95% confidence interval for alpha | 2.031 | ||||
| Treynor index (mean / b) | 1.156 | ||||
| Jensen alpha (a) | 0.342 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.623 | ||||
| Expected Shortfall on VaR | 0.701 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.119 | ||||
| Expected Shortfall on VaR | 0.256 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 80.000 | ||||
| Minimum | 0.203 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 148.147 | ||||
| Mean of quarter 1 | 0.869 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 8.488 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 19.000 | ||||
| Percentage of outliers low | 0.237 | ||||
| Mean of outliers low | 0.862 | ||||
| Number of outliers high | 11.000 | ||||
| Percentage of outliers high | 0.138 | ||||
| Mean of outliers high | 14.614 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.947 | ||||
| VaR(95%) (moments method) | 0.016 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.095 | ||||
| VaR(95%) (regression method) | 0.090 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.005 | ||||
| Quartile 3 | 0.087 | ||||
| Maximum | 0.917 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.005 | ||||
| Mean of quarter 3 | 0.087 | ||||
| Mean of quarter 4 | 0.917 | ||||
| Inter Quartile Range | 0.087 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.200 | ||||
| Mean of outliers high | 0.917 | ||||
| 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) | 2.914 | ||||
| Compounded annual return (geometric extrapolation) | 0.572 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.624 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.624 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.816 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 120633.223 | ||||
| SD | 135572.989 | ||||
| Sharpe ratio (Glass type estimate) | 0.890 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.889 | ||||
| df | 1756.000 | ||||
| t | 2.304 | ||||
| p | 0.473 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.132 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.647 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.132 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.647 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 65941.969 | ||||
| Upside Potential Ratio | 65944.510 | ||||
| Upside part of mean | 120637.870 | ||||
| Downside part of mean | -4.648 | ||||
| Upside SD | 135739.153 | ||||
| Downside SD | 1.829 | ||||
| N nonnegative terms | 153.000 | ||||
| N negative terms | 1604.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1757.000 | ||||
| Mean of predictor | 0.350 | ||||
| Mean of criterion | 120633.223 | ||||
| SD of predictor | 0.550 | ||||
| SD of criterion | 135572.989 | ||||
| Covariance | 7114.028 | ||||
| r | 0.095 | ||||
| b (slope, estimate of beta) | 23509.083 | ||||
| a (intercept, estimate of alpha) | 112410.977 | ||||
| Mean Square Error | 18223168763.332 | ||||
| DF error | 1755.000 | ||||
| t(b) | 4.014 | ||||
| p(b) | 0.439 | ||||
| t(a) | 2.155 | ||||
| p(a) | 0.467 | ||||
| Lowerbound of 95% confidence interval for beta | 12023.383 | ||||
| Upperbound of 95% confidence interval for beta | 34994.784 | ||||
| Lowerbound of 95% confidence interval for alpha | 10091.238 | ||||
| Upperbound of 95% confidence interval for alpha | 214730.717 | ||||
| Treynor index (mean / b) | 5.131 | ||||
| Jensen alpha (a) | 112410.977 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.406 | ||||
| SD | 18.715 | ||||
| Sharpe ratio (Glass type estimate) | 0.022 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.022 | ||||
| df | 1756.000 | ||||
| t | 0.056 | ||||
| p | 0.499 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.735 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.779 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.735 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.779 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.031 | ||||
| Upside Potential Ratio | 1.617 | ||||
| Upside part of mean | 21.332 | ||||
| Downside part of mean | -20.926 | ||||
| Upside SD | 13.266 | ||||
| Downside SD | 13.194 | ||||
| N nonnegative terms | 153.000 | ||||
| N negative terms | 1604.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1757.000 | ||||
| Mean of predictor | 0.201 | ||||
| Mean of criterion | 0.406 | ||||
| SD of predictor | 0.544 | ||||
| SD of criterion | 18.715 | ||||
| Covariance | 1.484 | ||||
| r | 0.146 | ||||
| b (slope, estimate of beta) | 5.007 | ||||
| a (intercept, estimate of alpha) | -0.601 | ||||
| Mean Square Error | 343.010 | ||||
| DF error | 1755.000 | ||||
| t(b) | 6.168 | ||||
| p(b) | 0.408 | ||||
| t(a) | -0.084 | ||||
| p(a) | 0.501 | ||||
| Lowerbound of 95% confidence interval for beta | 3.415 | ||||
| Upperbound of 95% confidence interval for beta | 6.600 | ||||
| Lowerbound of 95% confidence interval for alpha | -14.632 | ||||
| Upperbound of 95% confidence interval for alpha | 13.430 | ||||
| Treynor index (mean / b) | 0.081 | ||||
| Jensen alpha (a) | -0.601 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.850 | ||||
| Expected Shortfall on VaR | 0.900 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.058 | ||||
| Expected Shortfall on VaR | 0.131 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1757.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 208788.462 | ||||
| Mean of quarter 1 | 0.930 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1843.848 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 303.000 | ||||
| Percentage of outliers low | 0.172 | ||||
| Mean of outliers low | 0.898 | ||||
| Number of outliers high | 278.000 | ||||
| Percentage of outliers high | 0.158 | ||||
| Mean of outliers high | 2911.110 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.338 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| 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 | 26.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.008 | ||||
| Quartile 3 | 0.755 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.001 | ||||
| Mean of quarter 3 | 0.455 | ||||
| Mean of quarter 4 | 0.904 | ||||
| Inter Quartile Range | 0.755 | ||||
| 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) | -2.177 | ||||
| VaR(95%) (moments method) | 0.971 | ||||
| Expected Shortfall (moments method) | 0.976 | ||||
| Extreme Value Index (regression method) | -6.009 | ||||
| VaR(95%) (regression method) | 1.158 | ||||
| Expected Shortfall (regression method) | 1.158 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 2.896 | ||||
| Compounded annual return (geometric extrapolation) | 0.568 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.568 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.629 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.631 | ||||
| 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 | 1.051 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.499 | ||||
| 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 | 0.924 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.503 | ||||
| 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) | -8743310875853627.000 | ||||
| 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) | -262477047866693599406969115901952.000 | ||||
| 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 | ||||