Advanced Statistics: Rumor
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 | -0.039 | ||||
| SD | 0.103 | ||||
| Sharpe ratio (Glass type estimate) | -0.375 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.370 | ||||
| df | 60.000 | ||||
| t | -0.845 | ||||
| p | 0.799 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.245 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.499 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.242 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.502 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.704 | ||||
| Upside Potential Ratio | 0.703 | ||||
| Upside part of mean | 0.039 | ||||
| Downside part of mean | -0.077 | ||||
| Upside SD | 0.087 | ||||
| Downside SD | 0.055 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 60.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.372 | ||||
| Mean of criterion | -0.039 | ||||
| SD of predictor | 0.303 | ||||
| SD of criterion | 0.103 | ||||
| Covariance | -0.019 | ||||
| r | -0.604 | ||||
| b (slope, estimate of beta) | -0.205 | ||||
| a (intercept, estimate of alpha) | 0.038 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 59.000 | ||||
| t(b) | -5.822 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.965 | ||||
| p(a) | 0.169 | ||||
| Lowerbound of 95% confidence interval for beta | -0.276 | ||||
| Upperbound of 95% confidence interval for beta | -0.135 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.040 | ||||
| Upperbound of 95% confidence interval for alpha | 0.116 | ||||
| Treynor index (mean / b) | 0.188 | ||||
| Jensen alpha (a) | 0.038 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.043 | ||||
| SD | 0.098 | ||||
| Sharpe ratio (Glass type estimate) | -0.445 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.439 | ||||
| df | 60.000 | ||||
| t | -1.002 | ||||
| p | 0.840 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.316 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.430 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.312 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.434 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.759 | ||||
| Upside Potential Ratio | 0.614 | ||||
| Upside part of mean | 0.035 | ||||
| Downside part of mean | -0.079 | ||||
| Upside SD | 0.079 | ||||
| Downside SD | 0.057 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 60.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.317 | ||||
| Mean of criterion | -0.043 | ||||
| SD of predictor | 0.320 | ||||
| SD of criterion | 0.098 | ||||
| Covariance | -0.021 | ||||
| r | -0.659 | ||||
| b (slope, estimate of beta) | -0.201 | ||||
| a (intercept, estimate of alpha) | 0.020 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 59.000 | ||||
| t(b) | -6.723 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.598 | ||||
| p(a) | 0.276 | ||||
| Lowerbound of 95% confidence interval for beta | -0.261 | ||||
| Upperbound of 95% confidence interval for beta | -0.141 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.048 | ||||
| Upperbound of 95% confidence interval for alpha | 0.089 | ||||
| Treynor index (mean / b) | 0.216 | ||||
| Jensen alpha (a) | 0.020 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.049 | ||||
| Expected Shortfall on VaR | 0.060 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.022 | ||||
| Expected Shortfall on VaR | 0.043 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 61.000 | ||||
| Minimum | 0.901 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.200 | ||||
| Mean of quarter 1 | 0.989 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.014 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.115 | ||||
| Mean of outliers low | 0.974 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.082 | ||||
| Mean of outliers high | 1.041 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.426 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.293 | ||||
| VaR(95%) (regression method) | 0.006 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.166 | ||||
| Quartile 1 | 0.166 | ||||
| Median | 0.166 | ||||
| Quartile 3 | 0.166 | ||||
| Maximum | 0.166 | ||||
| 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) | 0.001 | ||||
| Compounded annual return (geometric extrapolation) | 0.001 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.004 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.010 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.030 | ||||
| SD | 0.163 | ||||
| Sharpe ratio (Glass type estimate) | -0.185 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.185 | ||||
| df | 1344.000 | ||||
| t | -0.419 | ||||
| p | 0.506 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.050 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.680 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.050 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.680 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.270 | ||||
| Upside Potential Ratio | 2.703 | ||||
| Upside part of mean | 0.302 | ||||
| Downside part of mean | -0.332 | ||||
| Upside SD | 0.119 | ||||
| Downside SD | 0.112 | ||||
| N nonnegative terms | 96.000 | ||||
| N negative terms | 1249.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1345.000 | ||||
| Mean of predictor | 0.405 | ||||
| Mean of criterion | -0.030 | ||||
| SD of predictor | 0.378 | ||||
| SD of criterion | 0.163 | ||||
| Covariance | -0.013 | ||||
| r | -0.212 | ||||
| b (slope, estimate of beta) | -0.091 | ||||
| a (intercept, estimate of alpha) | 0.007 | ||||
| Mean Square Error | 0.025 | ||||
| DF error | 1343.000 | ||||
| t(b) | -7.949 | ||||
| p(b) | 0.634 | ||||
| t(a) | 0.097 | ||||
| p(a) | 0.498 | ||||
| Lowerbound of 95% confidence interval for beta | -0.114 | ||||
| Upperbound of 95% confidence interval for beta | -0.069 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.131 | ||||
| Upperbound of 95% confidence interval for alpha | 0.145 | ||||
| Treynor index (mean / b) | 0.330 | ||||
| Jensen alpha (a) | 0.007 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.043 | ||||
| SD | 0.163 | ||||
| Sharpe ratio (Glass type estimate) | -0.267 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.267 | ||||
| df | 1344.000 | ||||
| t | -0.605 | ||||
| p | 0.508 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.132 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.598 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.132 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.598 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.378 | ||||
| Upside Potential Ratio | 2.568 | ||||
| Upside part of mean | 0.295 | ||||
| Downside part of mean | -0.338 | ||||
| Upside SD | 0.115 | ||||
| Downside SD | 0.115 | ||||
| N nonnegative terms | 96.000 | ||||
| N negative terms | 1249.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1345.000 | ||||
| Mean of predictor | 0.332 | ||||
| Mean of criterion | -0.043 | ||||
| SD of predictor | 0.383 | ||||
| SD of criterion | 0.163 | ||||
| Covariance | -0.014 | ||||
| r | -0.219 | ||||
| b (slope, estimate of beta) | -0.093 | ||||
| a (intercept, estimate of alpha) | -0.013 | ||||
| Mean Square Error | 0.025 | ||||
| DF error | 1343.000 | ||||
| t(b) | -8.218 | ||||
| p(b) | 0.638 | ||||
| t(a) | -0.179 | ||||
| p(a) | 0.503 | ||||
| Lowerbound of 95% confidence interval for beta | -0.115 | ||||
| Upperbound of 95% confidence interval for beta | -0.071 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.150 | ||||
| Upperbound of 95% confidence interval for alpha | 0.125 | ||||
| Treynor index (mean / b) | 0.468 | ||||
| Jensen alpha (a) | -0.013 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.021 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1345.000 | ||||
| Minimum | 0.923 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.106 | ||||
| Mean of quarter 1 | 0.996 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.005 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 90.000 | ||||
| Percentage of outliers low | 0.067 | ||||
| Mean of outliers low | 0.983 | ||||
| Number of outliers high | 98.000 | ||||
| Percentage of outliers high | 0.073 | ||||
| Mean of outliers high | 1.016 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.179 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| 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 | 8.000 | ||||
| Minimum | 0.048 | ||||
| Quartile 1 | 0.057 | ||||
| Median | 0.058 | ||||
| Quartile 3 | 0.072 | ||||
| Maximum | 0.209 | ||||
| Mean of quarter 1 | 0.052 | ||||
| Mean of quarter 2 | 0.057 | ||||
| Mean of quarter 3 | 0.062 | ||||
| Mean of quarter 4 | 0.151 | ||||
| Inter Quartile Range | 0.015 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.250 | ||||
| Mean of outliers high | 0.151 | ||||
| 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) | 0.001 | ||||
| Compounded annual return (geometric extrapolation) | 0.001 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.003 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.004 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.030 | ||||
| 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 | 1.451 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.378 | ||||
| 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 | 1.377 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.378 | ||||
| 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) | -8583984464085025.000 | ||||
| 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) | 79910882724007135177248084066304.000 | ||||
| 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 | ||||