Advanced Statistics: System 1200737
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 | 2422.966 | ||||
| SD | 7267.318 | ||||
| Sharpe ratio (Glass type estimate) | 0.333 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.331 | ||||
| df | 107.000 | ||||
| t | 1.000 | ||||
| p | 0.439 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.322 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.987 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.324 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.986 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 5047.269 | ||||
| Upside Potential Ratio | 5048.228 | ||||
| Upside part of mean | 2423.427 | ||||
| Downside part of mean | -0.461 | ||||
| Upside SD | 7267.332 | ||||
| Downside SD | 0.480 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 91.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 108.000 | ||||
| Mean of predictor | 0.159 | ||||
| Mean of criterion | 2422.966 | ||||
| SD of predictor | 0.261 | ||||
| SD of criterion | 7267.318 | ||||
| Covariance | -94.703 | ||||
| r | -0.050 | ||||
| b (slope, estimate of beta) | -1393.055 | ||||
| a (intercept, estimate of alpha) | 2644.550 | ||||
| Mean Square Error | 53178979.346 | ||||
| DF error | 106.000 | ||||
| t(b) | -0.515 | ||||
| p(b) | 0.525 | ||||
| t(a) | 1.071 | ||||
| p(a) | 0.448 | ||||
| Lowerbound of 95% confidence interval for beta | -6753.678 | ||||
| Upperbound of 95% confidence interval for beta | 3967.567 | ||||
| Lowerbound of 95% confidence interval for alpha | -2249.593 | ||||
| Upperbound of 95% confidence interval for alpha | 7538.694 | ||||
| Treynor index (mean / b) | -1.739 | ||||
| Jensen alpha (a) | 2644.550 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.056 | ||||
| SD | 5.207 | ||||
| Sharpe ratio (Glass type estimate) | -0.011 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.011 | ||||
| df | 107.000 | ||||
| t | -0.032 | ||||
| p | 0.502 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.664 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.643 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.664 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.643 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.014 | ||||
| Upside Potential Ratio | 0.430 | ||||
| Upside part of mean | 1.683 | ||||
| Downside part of mean | -1.739 | ||||
| Upside SD | 3.402 | ||||
| Downside SD | 3.910 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 91.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 108.000 | ||||
| Mean of predictor | 0.124 | ||||
| Mean of criterion | -0.056 | ||||
| SD of predictor | 0.264 | ||||
| SD of criterion | 5.207 | ||||
| Covariance | 0.007 | ||||
| r | 0.005 | ||||
| b (slope, estimate of beta) | 0.100 | ||||
| a (intercept, estimate of alpha) | -0.069 | ||||
| Mean Square Error | 27.371 | ||||
| DF error | 106.000 | ||||
| t(b) | 0.052 | ||||
| p(b) | 0.497 | ||||
| t(a) | -0.039 | ||||
| p(a) | 0.502 | ||||
| Lowerbound of 95% confidence interval for beta | -3.697 | ||||
| Upperbound of 95% confidence interval for beta | 3.896 | ||||
| Lowerbound of 95% confidence interval for alpha | -3.558 | ||||
| Upperbound of 95% confidence interval for alpha | 3.421 | ||||
| Treynor index (mean / b) | -0.566 | ||||
| Jensen alpha (a) | -0.069 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.916 | ||||
| Expected Shortfall on VaR | 0.949 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.120 | ||||
| Expected Shortfall on VaR | 0.260 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 108.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 21803.000 | ||||
| Mean of quarter 1 | 0.859 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 808.812 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 21.000 | ||||
| Percentage of outliers low | 0.194 | ||||
| Mean of outliers low | 0.818 | ||||
| Number of outliers high | 23.000 | ||||
| Percentage of outliers high | 0.213 | ||||
| Mean of outliers high | 949.300 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.801 | ||||
| VaR(95%) (moments method) | 0.042 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.165 | ||||
| VaR(95%) (regression method) | 0.087 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.106 | ||||
| Quartile 1 | 0.329 | ||||
| Median | 0.553 | ||||
| Quartile 3 | 0.776 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.106 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.447 | ||||
| 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) | -0.012 | ||||
| Compounded annual return (geometric extrapolation) | -0.012 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.012 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.012 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.013 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 62285.184 | ||||
| SD | 111181.035 | ||||
| Sharpe ratio (Glass type estimate) | 0.560 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.560 | ||||
| df | 2373.000 | ||||
| t | 1.686 | ||||
| p | 0.046 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.091 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.211 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.091 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.211 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 53062.966 | ||||
| Upside Potential Ratio | 53065.883 | ||||
| Upside part of mean | 62288.608 | ||||
| Downside part of mean | -3.424 | ||||
| Upside SD | 111224.200 | ||||
| Downside SD | 1.174 | ||||
| N nonnegative terms | 386.000 | ||||
| N negative terms | 1988.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2374.000 | ||||
| Mean of predictor | 0.288 | ||||
| Mean of criterion | 62285.184 | ||||
| SD of predictor | 0.571 | ||||
| SD of criterion | 111181.035 | ||||
| Covariance | 4278.269 | ||||
| r | 0.067 | ||||
| b (slope, estimate of beta) | 13116.890 | ||||
| a (intercept, estimate of alpha) | 58502.845 | ||||
| Mean Square Error | 12310292552.615 | ||||
| DF error | 2372.000 | ||||
| t(b) | 3.289 | ||||
| p(b) | 0.001 | ||||
| t(a) | 1.586 | ||||
| p(a) | 0.056 | ||||
| Lowerbound of 95% confidence interval for beta | 5296.356 | ||||
| Upperbound of 95% confidence interval for beta | 20937.425 | ||||
| Lowerbound of 95% confidence interval for alpha | -13811.666 | ||||
| Upperbound of 95% confidence interval for alpha | 130817.355 | ||||
| Treynor index (mean / b) | 4.748 | ||||
| Jensen alpha (a) | 58502.845 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.056 | ||||
| SD | 11.044 | ||||
| Sharpe ratio (Glass type estimate) | -0.005 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.005 | ||||
| df | 2373.000 | ||||
| t | -0.015 | ||||
| p | 0.506 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.656 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.646 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.656 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.646 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.007 | ||||
| Upside Potential Ratio | 1.136 | ||||
| Upside part of mean | 8.974 | ||||
| Downside part of mean | -9.030 | ||||
| Upside SD | 7.711 | ||||
| Downside SD | 7.903 | ||||
| N nonnegative terms | 386.000 | ||||
| N negative terms | 1988.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2374.000 | ||||
| Mean of predictor | 0.127 | ||||
| Mean of criterion | -0.056 | ||||
| SD of predictor | 0.567 | ||||
| SD of criterion | 11.044 | ||||
| Covariance | 0.679 | ||||
| r | 0.108 | ||||
| b (slope, estimate of beta) | 2.111 | ||||
| a (intercept, estimate of alpha) | -0.325 | ||||
| Mean Square Error | 120.585 | ||||
| DF error | 2372.000 | ||||
| t(b) | 5.309 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.089 | ||||
| p(a) | 0.535 | ||||
| Lowerbound of 95% confidence interval for beta | 1.331 | ||||
| Upperbound of 95% confidence interval for beta | 2.890 | ||||
| Lowerbound of 95% confidence interval for alpha | -7.479 | ||||
| Upperbound of 95% confidence interval for alpha | 6.829 | ||||
| Treynor index (mean / b) | -0.027 | ||||
| Jensen alpha (a) | -0.325 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.675 | ||||
| Expected Shortfall on VaR | 0.748 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.041 | ||||
| Expected Shortfall on VaR | 0.092 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2374.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 248083.429 | ||||
| Mean of quarter 1 | 0.948 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 951.171 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 531.000 | ||||
| Percentage of outliers low | 0.224 | ||||
| Mean of outliers low | 0.942 | ||||
| Number of outliers high | 500.000 | ||||
| Percentage of outliers high | 0.211 | ||||
| Mean of outliers high | 1129.803 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.204 | ||||
| VaR(95%) (moments method) | 0.011 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.421 | ||||
| VaR(95%) (regression method) | 0.027 | ||||
| Expected Shortfall (regression method) | 0.088 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.011 | ||||
| Quartile 1 | 0.173 | ||||
| Median | 0.546 | ||||
| Quartile 3 | 0.870 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.082 | ||||
| Mean of quarter 2 | 0.400 | ||||
| Mean of quarter 3 | 0.851 | ||||
| Mean of quarter 4 | 0.970 | ||||
| Inter Quartile Range | 0.696 | ||||
| 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) | -5.448 | ||||
| VaR(95%) (moments method) | 0.981 | ||||
| Expected Shortfall (moments method) | 0.981 | ||||
| Extreme Value Index (regression method) | -1.210 | ||||
| VaR(95%) (regression method) | 1.037 | ||||
| Expected Shortfall (regression method) | 1.049 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.012 | ||||
| Compounded annual return (geometric extrapolation) | -0.012 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.012 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.013 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.016 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.134 | ||||
| SD | 0.063 | ||||
| Sharpe ratio (Glass type estimate) | -2.109 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.097 | ||||
| df | 130.000 | ||||
| t | -1.492 | ||||
| p | 0.565 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.889 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.678 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.881 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.686 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.100 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.134 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.064 | ||||
| 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 | 0.842 | ||||
| Mean of criterion | -0.134 | ||||
| SD of predictor | 0.463 | ||||
| SD of criterion | 0.063 | ||||
| Covariance | 0.004 | ||||
| r | 0.122 | ||||
| b (slope, estimate of beta) | 0.017 | ||||
| a (intercept, estimate of alpha) | -0.148 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 129.000 | ||||
| t(b) | 1.396 | ||||
| p(b) | 0.423 | ||||
| t(a) | -1.644 | ||||
| p(a) | 0.591 | ||||
| Lowerbound of 95% confidence interval for beta | -0.007 | ||||
| Upperbound of 95% confidence interval for beta | 0.040 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.325 | ||||
| Upperbound of 95% confidence interval for alpha | 0.030 | ||||
| Treynor index (mean / b) | -7.998 | ||||
| Jensen alpha (a) | -0.148 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.136 | ||||
| SD | 0.065 | ||||
| Sharpe ratio (Glass type estimate) | -2.094 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.082 | ||||
| df | 130.000 | ||||
| t | -1.480 | ||||
| p | 0.564 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.873 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.694 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.865 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.702 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.084 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.136 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.065 | ||||
| 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 | 0.734 | ||||
| Mean of criterion | -0.136 | ||||
| SD of predictor | 0.466 | ||||
| SD of criterion | 0.065 | ||||
| Covariance | 0.004 | ||||
| r | 0.122 | ||||
| b (slope, estimate of beta) | 0.017 | ||||
| a (intercept, estimate of alpha) | -0.148 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 129.000 | ||||
| t(b) | 1.397 | ||||
| p(b) | 0.422 | ||||
| t(a) | -1.615 | ||||
| p(a) | 0.589 | ||||
| Lowerbound of 95% confidence interval for beta | -0.007 | ||||
| Upperbound of 95% confidence interval for beta | 0.041 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.330 | ||||
| Upperbound of 95% confidence interval for alpha | 0.033 | ||||
| Treynor index (mean / b) | -7.986 | ||||
| Jensen alpha (a) | -0.148 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.955 | ||||
| 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 | 0.955 | ||||
| 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 | 0.045 | ||||
| Quartile 1 | 0.045 | ||||
| Median | 0.045 | ||||
| Quartile 3 | 0.045 | ||||
| Maximum | 0.045 | ||||
| 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) | -0.090 | ||||
| Compounded annual return (geometric extrapolation) | -0.088 | ||||
| Calmar ratio (compounded annual return / max draw down) | -1.955 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -10.024 | ||||