Advanced Statistics: System 32171590
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 | -0.061 | ||||
| SD | 0.393 | ||||
| Sharpe ratio (Glass type estimate) | -0.156 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.154 | ||||
| df | 66.000 | ||||
| t | -0.368 | ||||
| p | 0.643 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.985 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.675 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.984 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.676 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.175 | ||||
| Upside Potential Ratio | 0.457 | ||||
| Upside part of mean | 0.160 | ||||
| Downside part of mean | -0.221 | ||||
| Upside SD | 0.173 | ||||
| Downside SD | 0.350 | ||||
| N nonnegative terms | 11.000 | ||||
| N negative terms | 56.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 67.000 | ||||
| Mean of predictor | 0.283 | ||||
| Mean of criterion | -0.061 | ||||
| SD of predictor | 0.274 | ||||
| SD of criterion | 0.393 | ||||
| Covariance | 0.020 | ||||
| r | 0.186 | ||||
| b (slope, estimate of beta) | 0.266 | ||||
| a (intercept, estimate of alpha) | -0.137 | ||||
| Mean Square Error | 0.152 | ||||
| DF error | 65.000 | ||||
| t(b) | 1.523 | ||||
| p(b) | 0.066 | ||||
| t(a) | -0.793 | ||||
| p(a) | 0.785 | ||||
| Lowerbound of 95% confidence interval for beta | -0.083 | ||||
| Upperbound of 95% confidence interval for beta | 0.615 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.480 | ||||
| Upperbound of 95% confidence interval for alpha | 0.207 | ||||
| Treynor index (mean / b) | -0.230 | ||||
| Jensen alpha (a) | -0.137 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.227 | ||||
| SD | 0.720 | ||||
| Sharpe ratio (Glass type estimate) | -0.315 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.311 | ||||
| df | 66.000 | ||||
| t | -0.744 | ||||
| p | 0.770 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.145 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.517 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.143 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.520 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.324 | ||||
| Upside Potential Ratio | 0.209 | ||||
| Upside part of mean | 0.147 | ||||
| Downside part of mean | -0.374 | ||||
| Upside SD | 0.154 | ||||
| Downside SD | 0.701 | ||||
| N nonnegative terms | 11.000 | ||||
| N negative terms | 56.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 67.000 | ||||
| Mean of predictor | 0.242 | ||||
| Mean of criterion | -0.227 | ||||
| SD of predictor | 0.274 | ||||
| SD of criterion | 0.720 | ||||
| Covariance | 0.042 | ||||
| r | 0.214 | ||||
| b (slope, estimate of beta) | 0.561 | ||||
| a (intercept, estimate of alpha) | -0.363 | ||||
| Mean Square Error | 0.503 | ||||
| DF error | 65.000 | ||||
| t(b) | 1.762 | ||||
| p(b) | 0.041 | ||||
| t(a) | -1.171 | ||||
| p(a) | 0.877 | ||||
| Lowerbound of 95% confidence interval for beta | -0.075 | ||||
| Upperbound of 95% confidence interval for beta | 1.197 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.982 | ||||
| Upperbound of 95% confidence interval for alpha | 0.256 | ||||
| Treynor index (mean / b) | -0.404 | ||||
| Jensen alpha (a) | -0.363 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.303 | ||||
| Expected Shortfall on VaR | 0.359 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.057 | ||||
| Expected Shortfall on VaR | 0.129 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 67.000 | ||||
| Minimum | 0.193 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.328 | ||||
| Mean of quarter 1 | 0.939 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.055 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.104 | ||||
| Mean of outliers low | 0.852 | ||||
| Number of outliers high | 15.000 | ||||
| Percentage of outliers high | 0.224 | ||||
| Mean of outliers high | 1.063 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.891 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 3.017 | ||||
| VaR(95%) (regression method) | 0.005 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.836 | ||||
| Quartile 1 | 0.836 | ||||
| Median | 0.836 | ||||
| Quartile 3 | 0.836 | ||||
| Maximum | 0.836 | ||||
| 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) | -0.115 | ||||
| Compounded annual return (geometric extrapolation) | -0.167 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.200 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.465 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 2.877 | ||||
| SD | 4.225 | ||||
| Sharpe ratio (Glass type estimate) | 0.681 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.681 | ||||
| df | 1472.000 | ||||
| t | 1.614 | ||||
| p | 0.479 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.146 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.508 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.146 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.507 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 3.519 | ||||
| Upside Potential Ratio | 5.224 | ||||
| Upside part of mean | 4.271 | ||||
| Downside part of mean | -1.394 | ||||
| Upside SD | 4.148 | ||||
| Downside SD | 0.818 | ||||
| N nonnegative terms | 186.000 | ||||
| N negative terms | 1287.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1473.000 | ||||
| Mean of predictor | 0.437 | ||||
| Mean of criterion | 2.877 | ||||
| SD of predictor | 0.599 | ||||
| SD of criterion | 4.225 | ||||
| Covariance | 0.950 | ||||
| r | 0.375 | ||||
| b (slope, estimate of beta) | 2.648 | ||||
| a (intercept, estimate of alpha) | 1.720 | ||||
| Mean Square Error | 15.350 | ||||
| DF error | 1471.000 | ||||
| t(b) | 15.527 | ||||
| p(b) | 0.267 | ||||
| t(a) | 1.040 | ||||
| p(a) | 0.483 | ||||
| Lowerbound of 95% confidence interval for beta | 2.313 | ||||
| Upperbound of 95% confidence interval for beta | 2.982 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.524 | ||||
| Upperbound of 95% confidence interval for alpha | 4.965 | ||||
| Treynor index (mean / b) | 1.087 | ||||
| Jensen alpha (a) | 1.720 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.226 | ||||
| SD | 2.218 | ||||
| Sharpe ratio (Glass type estimate) | -0.102 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.102 | ||||
| df | 1472.000 | ||||
| t | -0.241 | ||||
| p | 0.503 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.928 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.725 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.928 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.725 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.143 | ||||
| Upside Potential Ratio | 1.241 | ||||
| Upside part of mean | 1.955 | ||||
| Downside part of mean | -2.180 | ||||
| Upside SD | 1.559 | ||||
| Downside SD | 1.576 | ||||
| N nonnegative terms | 186.000 | ||||
| N negative terms | 1287.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1473.000 | ||||
| Mean of predictor | 0.259 | ||||
| Mean of criterion | -0.226 | ||||
| SD of predictor | 0.598 | ||||
| SD of criterion | 2.218 | ||||
| Covariance | 0.415 | ||||
| r | 0.313 | ||||
| b (slope, estimate of beta) | 1.162 | ||||
| a (intercept, estimate of alpha) | -0.527 | ||||
| Mean Square Error | 4.438 | ||||
| DF error | 1471.000 | ||||
| t(b) | 12.650 | ||||
| p(b) | 0.304 | ||||
| t(a) | -0.593 | ||||
| p(a) | 0.510 | ||||
| Lowerbound of 95% confidence interval for beta | 0.982 | ||||
| Upperbound of 95% confidence interval for beta | 1.343 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.270 | ||||
| Upperbound of 95% confidence interval for alpha | 1.217 | ||||
| Treynor index (mean / b) | -0.194 | ||||
| Jensen alpha (a) | -0.527 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.202 | ||||
| Expected Shortfall on VaR | 0.246 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.039 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1473.000 | ||||
| Minimum | 0.164 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 7.253 | ||||
| Mean of quarter 1 | 0.979 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.065 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 164.000 | ||||
| Percentage of outliers low | 0.111 | ||||
| Mean of outliers low | 0.954 | ||||
| Number of outliers high | 192.000 | ||||
| Percentage of outliers high | 0.130 | ||||
| Mean of outliers high | 1.125 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.800 | ||||
| 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 | 2.000 | ||||
| Minimum | 0.843 | ||||
| Quartile 1 | 0.851 | ||||
| Median | 0.858 | ||||
| Quartile 3 | 0.866 | ||||
| Maximum | 0.873 | ||||
| Mean of quarter 1 | 0.843 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.873 | ||||
| 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 | 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) | -0.114 | ||||
| Compounded annual return (geometric extrapolation) | -0.166 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.190 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.190 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.675 | ||||
| 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 | 1.014 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.512 | ||||
| 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 | 0.885 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.505 | ||||
| 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) | -8748291491123828.000 | ||||
| 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) | 311542279037683933531095466770432.000 | ||||
| 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 | ||||