Advanced Statistics: Not available
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 | 0.179 | ||||
| SD | 0.530 | ||||
| Sharpe ratio (Glass type estimate) | 0.337 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.334 | ||||
| df | 72.000 | ||||
| t | 0.832 | ||||
| p | 0.204 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.460 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.133 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.463 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.130 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.627 | ||||
| Upside Potential Ratio | 2.443 | ||||
| Upside part of mean | 0.696 | ||||
| Downside part of mean | -0.517 | ||||
| Upside SD | 0.445 | ||||
| Downside SD | 0.285 | ||||
| N nonnegative terms | 38.000 | ||||
| N negative terms | 35.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 73.000 | ||||
| Mean of predictor | 0.313 | ||||
| Mean of criterion | 0.179 | ||||
| SD of predictor | 0.356 | ||||
| SD of criterion | 0.530 | ||||
| Covariance | 0.138 | ||||
| r | 0.730 | ||||
| b (slope, estimate of beta) | 1.085 | ||||
| a (intercept, estimate of alpha) | -0.161 | ||||
| Mean Square Error | 0.133 | ||||
| DF error | 71.000 | ||||
| t(b) | 9.002 | ||||
| p(b) | -0.000 | ||||
| t(a) | -1.057 | ||||
| p(a) | 0.853 | ||||
| Lowerbound of 95% confidence interval for beta | 0.845 | ||||
| Upperbound of 95% confidence interval for beta | 1.325 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.465 | ||||
| Upperbound of 95% confidence interval for alpha | 0.143 | ||||
| Treynor index (mean / b) | 0.165 | ||||
| Jensen alpha (a) | -0.161 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.058 | ||||
| SD | 0.482 | ||||
| Sharpe ratio (Glass type estimate) | 0.119 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.118 | ||||
| df | 72.000 | ||||
| t | 0.294 | ||||
| p | 0.385 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.676 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.914 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.677 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.913 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.182 | ||||
| Upside Potential Ratio | 1.960 | ||||
| Upside part of mean | 0.619 | ||||
| Downside part of mean | -0.562 | ||||
| Upside SD | 0.360 | ||||
| Downside SD | 0.316 | ||||
| N nonnegative terms | 38.000 | ||||
| N negative terms | 35.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 73.000 | ||||
| Mean of predictor | 0.251 | ||||
| Mean of criterion | 0.058 | ||||
| SD of predictor | 0.337 | ||||
| SD of criterion | 0.482 | ||||
| Covariance | 0.118 | ||||
| r | 0.726 | ||||
| b (slope, estimate of beta) | 1.037 | ||||
| a (intercept, estimate of alpha) | -0.203 | ||||
| Mean Square Error | 0.112 | ||||
| DF error | 71.000 | ||||
| t(b) | 8.886 | ||||
| p(b) | -0.000 | ||||
| t(a) | -1.466 | ||||
| p(a) | 0.926 | ||||
| Lowerbound of 95% confidence interval for beta | 0.805 | ||||
| Upperbound of 95% confidence interval for beta | 1.270 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.479 | ||||
| Upperbound of 95% confidence interval for alpha | 0.073 | ||||
| Treynor index (mean / b) | 0.055 | ||||
| Jensen alpha (a) | -0.203 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.201 | ||||
| Expected Shortfall on VaR | 0.245 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.097 | ||||
| Expected Shortfall on VaR | 0.184 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 73.000 | ||||
| Minimum | 0.736 | ||||
| Quartile 1 | 0.940 | ||||
| Median | 1.009 | ||||
| Quartile 3 | 1.078 | ||||
| Maximum | 1.841 | ||||
| Mean of quarter 1 | 0.860 | ||||
| Mean of quarter 2 | 0.981 | ||||
| Mean of quarter 3 | 1.046 | ||||
| Mean of quarter 4 | 1.196 | ||||
| Inter Quartile Range | 0.138 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.041 | ||||
| Mean of outliers high | 1.477 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.017 | ||||
| VaR(95%) (moments method) | 0.134 | ||||
| Expected Shortfall (moments method) | 0.179 | ||||
| Extreme Value Index (regression method) | -0.375 | ||||
| VaR(95%) (regression method) | 0.140 | ||||
| Expected Shortfall (regression method) | 0.166 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.665 | ||||
| Quartile 1 | 0.665 | ||||
| Median | 0.665 | ||||
| Quartile 3 | 0.665 | ||||
| Maximum | 0.665 | ||||
| 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) | 0.140 | ||||
| Compounded annual return (geometric extrapolation) | 0.107 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.161 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.436 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.509 | ||||
| SD | 1.019 | ||||
| Sharpe ratio (Glass type estimate) | 0.499 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.499 | ||||
| df | 1602.000 | ||||
| t | 1.235 | ||||
| p | 0.485 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.293 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.292 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.293 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.292 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.819 | ||||
| Upside Potential Ratio | 6.622 | ||||
| Upside part of mean | 4.113 | ||||
| Downside part of mean | -3.604 | ||||
| Upside SD | 0.808 | ||||
| Downside SD | 0.621 | ||||
| N nonnegative terms | 852.000 | ||||
| N negative terms | 751.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1603.000 | ||||
| Mean of predictor | 0.463 | ||||
| Mean of criterion | 0.509 | ||||
| SD of predictor | 0.636 | ||||
| SD of criterion | 1.019 | ||||
| Covariance | 0.365 | ||||
| r | 0.564 | ||||
| b (slope, estimate of beta) | 0.903 | ||||
| a (intercept, estimate of alpha) | 0.090 | ||||
| Mean Square Error | 0.709 | ||||
| DF error | 1601.000 | ||||
| t(b) | 27.295 | ||||
| p(b) | 0.161 | ||||
| t(a) | 0.265 | ||||
| p(a) | 0.496 | ||||
| Lowerbound of 95% confidence interval for beta | 0.838 | ||||
| Upperbound of 95% confidence interval for beta | 0.968 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.578 | ||||
| Upperbound of 95% confidence interval for alpha | 0.759 | ||||
| Treynor index (mean / b) | 0.563 | ||||
| Jensen alpha (a) | 0.090 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.026 | ||||
| SD | 0.974 | ||||
| Sharpe ratio (Glass type estimate) | 0.026 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.026 | ||||
| df | 1602.000 | ||||
| t | 0.065 | ||||
| p | 0.499 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.766 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.819 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.766 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.819 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.037 | ||||
| Upside Potential Ratio | 5.585 | ||||
| Upside part of mean | 3.851 | ||||
| Downside part of mean | -3.825 | ||||
| Upside SD | 0.688 | ||||
| Downside SD | 0.689 | ||||
| N nonnegative terms | 852.000 | ||||
| N negative terms | 751.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1603.000 | ||||
| Mean of predictor | 0.266 | ||||
| Mean of criterion | 0.026 | ||||
| SD of predictor | 0.627 | ||||
| SD of criterion | 0.974 | ||||
| Covariance | 0.340 | ||||
| r | 0.557 | ||||
| b (slope, estimate of beta) | 0.865 | ||||
| a (intercept, estimate of alpha) | -0.204 | ||||
| Mean Square Error | 0.656 | ||||
| DF error | 1601.000 | ||||
| t(b) | 26.817 | ||||
| p(b) | 0.165 | ||||
| t(a) | -0.624 | ||||
| p(a) | 0.510 | ||||
| Lowerbound of 95% confidence interval for beta | 0.802 | ||||
| Upperbound of 95% confidence interval for beta | 0.928 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.846 | ||||
| Upperbound of 95% confidence interval for alpha | 0.438 | ||||
| Treynor index (mean / b) | 0.030 | ||||
| Jensen alpha (a) | -0.204 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.094 | ||||
| Expected Shortfall on VaR | 0.116 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.030 | ||||
| Expected Shortfall on VaR | 0.065 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1603.000 | ||||
| Minimum | 0.669 | ||||
| Quartile 1 | 0.989 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.013 | ||||
| Maximum | 2.030 | ||||
| Mean of quarter 1 | 0.949 | ||||
| Mean of quarter 2 | 0.996 | ||||
| Mean of quarter 3 | 1.006 | ||||
| Mean of quarter 4 | 1.057 | ||||
| Inter Quartile Range | 0.024 | ||||
| Number outliers low | 123.000 | ||||
| Percentage of outliers low | 0.077 | ||||
| Mean of outliers low | 0.885 | ||||
| Number of outliers high | 111.000 | ||||
| Percentage of outliers high | 0.069 | ||||
| Mean of outliers high | 1.140 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.736 | ||||
| VaR(95%) (moments method) | 0.048 | ||||
| Expected Shortfall (moments method) | 0.200 | ||||
| Extreme Value Index (regression method) | 0.416 | ||||
| VaR(95%) (regression method) | 0.041 | ||||
| Expected Shortfall (regression method) | 0.085 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.312 | ||||
| Quartile 1 | 0.404 | ||||
| Median | 0.495 | ||||
| Quartile 3 | 0.587 | ||||
| Maximum | 0.679 | ||||
| Mean of quarter 1 | 0.312 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.679 | ||||
| Inter Quartile Range | 0.184 | ||||
| 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) | 0.087 | ||||
| Compounded annual return (geometric extrapolation) | 0.072 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.106 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.106 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.619 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.904 | ||||
| SD | 0.810 | ||||
| Sharpe ratio (Glass type estimate) | 1.117 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.110 | ||||
| df | 130.000 | ||||
| t | 0.790 | ||||
| p | 0.465 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.661 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.890 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.665 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.885 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.666 | ||||
| Upside Potential Ratio | 8.915 | ||||
| Upside part of mean | 4.839 | ||||
| Downside part of mean | -3.935 | ||||
| Upside SD | 0.600 | ||||
| Downside SD | 0.543 | ||||
| N nonnegative terms | 69.000 | ||||
| N negative terms | 62.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.795 | ||||
| Mean of criterion | 0.904 | ||||
| SD of predictor | 0.550 | ||||
| SD of criterion | 0.810 | ||||
| Covariance | 0.251 | ||||
| r | 0.563 | ||||
| b (slope, estimate of beta) | 0.829 | ||||
| a (intercept, estimate of alpha) | -0.584 | ||||
| Mean Square Error | 0.452 | ||||
| DF error | 129.000 | ||||
| t(b) | 7.735 | ||||
| p(b) | 0.162 | ||||
| t(a) | -0.602 | ||||
| p(a) | 0.534 | ||||
| Lowerbound of 95% confidence interval for beta | 0.617 | ||||
| Upperbound of 95% confidence interval for beta | 1.041 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.502 | ||||
| Upperbound of 95% confidence interval for alpha | 1.335 | ||||
| Treynor index (mean / b) | 1.091 | ||||
| Jensen alpha (a) | -0.584 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.578 | ||||
| SD | 0.811 | ||||
| Sharpe ratio (Glass type estimate) | 0.713 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.709 | ||||
| df | 130.000 | ||||
| t | 0.504 | ||||
| p | 0.478 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.061 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.485 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.064 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.482 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.003 | ||||
| Upside Potential Ratio | 8.104 | ||||
| Upside part of mean | 4.672 | ||||
| Downside part of mean | -4.094 | ||||
| Upside SD | 0.566 | ||||
| Downside SD | 0.576 | ||||
| N nonnegative terms | 69.000 | ||||
| N negative terms | 62.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.637 | ||||
| Mean of criterion | 0.578 | ||||
| SD of predictor | 0.556 | ||||
| SD of criterion | 0.811 | ||||
| Covariance | 0.257 | ||||
| r | 0.570 | ||||
| b (slope, estimate of beta) | 0.831 | ||||
| a (intercept, estimate of alpha) | -0.782 | ||||
| Mean Square Error | 0.447 | ||||
| DF error | 129.000 | ||||
| t(b) | 7.873 | ||||
| p(b) | 0.158 | ||||
| t(a) | -0.813 | ||||
| p(a) | 0.545 | ||||
| Lowerbound of 95% confidence interval for beta | 0.622 | ||||
| Upperbound of 95% confidence interval for beta | 1.039 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.684 | ||||
| Upperbound of 95% confidence interval for alpha | 1.120 | ||||
| Treynor index (mean / b) | 0.696 | ||||
| Jensen alpha (a) | -0.782 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.077 | ||||
| Expected Shortfall on VaR | 0.096 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.033 | ||||
| Expected Shortfall on VaR | 0.068 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.806 | ||||
| Quartile 1 | 0.987 | ||||
| Median | 1.002 | ||||
| Quartile 3 | 1.027 | ||||
| Maximum | 1.224 | ||||
| Mean of quarter 1 | 0.946 | ||||
| Mean of quarter 2 | 0.995 | ||||
| Mean of quarter 3 | 1.015 | ||||
| Mean of quarter 4 | 1.059 | ||||
| Inter Quartile Range | 0.040 | ||||
| Number outliers low | 9.000 | ||||
| Percentage of outliers low | 0.069 | ||||
| Mean of outliers low | 0.894 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.046 | ||||
| Mean of outliers high | 1.133 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.131 | ||||
| VaR(95%) (moments method) | 0.040 | ||||
| Expected Shortfall (moments method) | 0.053 | ||||
| Extreme Value Index (regression method) | -0.021 | ||||
| VaR(95%) (regression method) | 0.045 | ||||
| Expected Shortfall (regression method) | 0.064 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.011 | ||||
| Quartile 1 | 0.032 | ||||
| Median | 0.041 | ||||
| Quartile 3 | 0.175 | ||||
| Maximum | 0.370 | ||||
| Mean of quarter 1 | 0.021 | ||||
| Mean of quarter 2 | 0.034 | ||||
| Mean of quarter 3 | 0.047 | ||||
| Mean of quarter 4 | 0.294 | ||||
| Inter Quartile Range | 0.143 | ||||
| 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) | 0.730 | ||||
| Compounded annual return (geometric extrapolation) | 0.863 | ||||
| Calmar ratio (compounded annual return / max draw down) | 2.331 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.935 | ||||
| Compounded annual return / Expected Shortfall lognormal | 8.991 | ||||