Advanced Statistics: eminialerts
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 | 0.029 | ||||
| SD | 0.413 | ||||
| Sharpe ratio (Glass type estimate) | 0.071 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.070 | ||||
| df | 70.000 | ||||
| t | 0.173 | ||||
| p | 0.432 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.735 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.877 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.736 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.876 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.141 | ||||
| Upside Potential Ratio | 1.630 | ||||
| Upside part of mean | 0.338 | ||||
| Downside part of mean | -0.309 | ||||
| Upside SD | 0.354 | ||||
| Downside SD | 0.207 | ||||
| N nonnegative terms | 20.000 | ||||
| N negative terms | 51.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 71.000 | ||||
| Mean of predictor | 0.292 | ||||
| Mean of criterion | 0.029 | ||||
| SD of predictor | 0.243 | ||||
| SD of criterion | 0.413 | ||||
| Covariance | -0.007 | ||||
| r | -0.070 | ||||
| b (slope, estimate of beta) | -0.118 | ||||
| a (intercept, estimate of alpha) | 0.064 | ||||
| Mean Square Error | 0.172 | ||||
| DF error | 69.000 | ||||
| t(b) | -0.580 | ||||
| p(b) | 0.718 | ||||
| t(a) | 0.354 | ||||
| p(a) | 0.362 | ||||
| Lowerbound of 95% confidence interval for beta | -0.526 | ||||
| Upperbound of 95% confidence interval for beta | 0.289 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.297 | ||||
| Upperbound of 95% confidence interval for alpha | 0.425 | ||||
| Treynor index (mean / b) | -0.248 | ||||
| Jensen alpha (a) | 0.064 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.043 | ||||
| SD | 0.371 | ||||
| Sharpe ratio (Glass type estimate) | -0.115 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.114 | ||||
| df | 70.000 | ||||
| t | -0.280 | ||||
| p | 0.610 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.921 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.691 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.920 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.692 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.182 | ||||
| Upside Potential Ratio | 1.236 | ||||
| Upside part of mean | 0.290 | ||||
| Downside part of mean | -0.333 | ||||
| Upside SD | 0.285 | ||||
| Downside SD | 0.234 | ||||
| N nonnegative terms | 20.000 | ||||
| N negative terms | 51.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 71.000 | ||||
| Mean of predictor | 0.262 | ||||
| Mean of criterion | -0.043 | ||||
| SD of predictor | 0.224 | ||||
| SD of criterion | 0.371 | ||||
| Covariance | -0.004 | ||||
| r | -0.053 | ||||
| b (slope, estimate of beta) | -0.088 | ||||
| a (intercept, estimate of alpha) | -0.020 | ||||
| Mean Square Error | 0.140 | ||||
| DF error | 69.000 | ||||
| t(b) | -0.440 | ||||
| p(b) | 0.669 | ||||
| t(a) | -0.122 | ||||
| p(a) | 0.548 | ||||
| Lowerbound of 95% confidence interval for beta | -0.484 | ||||
| Upperbound of 95% confidence interval for beta | 0.309 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.343 | ||||
| Upperbound of 95% confidence interval for alpha | 0.304 | ||||
| Treynor index (mean / b) | 0.487 | ||||
| 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%) | 0.165 | ||||
| Expected Shortfall on VaR | 0.201 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.074 | ||||
| Expected Shortfall on VaR | 0.146 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 71.000 | ||||
| Minimum | 0.671 | ||||
| Quartile 1 | 0.983 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.012 | ||||
| Maximum | 1.693 | ||||
| Mean of quarter 1 | 0.912 | ||||
| Mean of quarter 2 | 0.997 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.114 | ||||
| Inter Quartile Range | 0.028 | ||||
| Number outliers low | 11.000 | ||||
| Percentage of outliers low | 0.155 | ||||
| Mean of outliers low | 0.873 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.085 | ||||
| Mean of outliers high | 1.285 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.386 | ||||
| VaR(95%) (moments method) | 0.068 | ||||
| Expected Shortfall (moments method) | 0.139 | ||||
| Extreme Value Index (regression method) | 0.570 | ||||
| VaR(95%) (regression method) | 0.077 | ||||
| Expected Shortfall (regression method) | 0.211 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.017 | ||||
| Quartile 1 | 0.173 | ||||
| Median | 0.329 | ||||
| Quartile 3 | 0.424 | ||||
| Maximum | 0.519 | ||||
| Mean of quarter 1 | 0.017 | ||||
| Mean of quarter 2 | 0.329 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.519 | ||||
| Inter Quartile Range | 0.251 | ||||
| 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) | 0.003 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.003 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.007 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.008 | ||||
| SD | 0.305 | ||||
| Sharpe ratio (Glass type estimate) | 0.027 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.027 | ||||
| df | 1563.000 | ||||
| t | 0.065 | ||||
| p | 0.499 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.776 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.829 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.776 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.829 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.034 | ||||
| Upside Potential Ratio | 3.869 | ||||
| Upside part of mean | 0.912 | ||||
| Downside part of mean | -0.904 | ||||
| Upside SD | 0.194 | ||||
| Downside SD | 0.236 | ||||
| N nonnegative terms | 408.000 | ||||
| N negative terms | 1156.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1564.000 | ||||
| Mean of predictor | 0.315 | ||||
| Mean of criterion | 0.008 | ||||
| SD of predictor | 0.268 | ||||
| SD of criterion | 0.305 | ||||
| Covariance | -0.009 | ||||
| r | -0.113 | ||||
| b (slope, estimate of beta) | -0.128 | ||||
| a (intercept, estimate of alpha) | 0.049 | ||||
| Mean Square Error | 0.092 | ||||
| DF error | 1562.000 | ||||
| t(b) | -4.484 | ||||
| p(b) | 0.556 | ||||
| t(a) | 0.390 | ||||
| p(a) | 0.495 | ||||
| Lowerbound of 95% confidence interval for beta | -0.185 | ||||
| Upperbound of 95% confidence interval for beta | -0.072 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.196 | ||||
| Upperbound of 95% confidence interval for alpha | 0.293 | ||||
| Treynor index (mean / b) | -0.063 | ||||
| Jensen alpha (a) | 0.049 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.043 | ||||
| SD | 0.327 | ||||
| Sharpe ratio (Glass type estimate) | -0.130 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.130 | ||||
| df | 1563.000 | ||||
| t | -0.319 | ||||
| p | 0.505 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.933 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.672 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.933 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.672 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.158 | ||||
| Upside Potential Ratio | 3.310 | ||||
| Upside part of mean | 0.894 | ||||
| Downside part of mean | -0.937 | ||||
| Upside SD | 0.185 | ||||
| Downside SD | 0.270 | ||||
| N nonnegative terms | 408.000 | ||||
| N negative terms | 1156.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1564.000 | ||||
| Mean of predictor | 0.279 | ||||
| Mean of criterion | -0.043 | ||||
| SD of predictor | 0.270 | ||||
| SD of criterion | 0.327 | ||||
| Covariance | -0.010 | ||||
| r | -0.116 | ||||
| b (slope, estimate of beta) | -0.141 | ||||
| a (intercept, estimate of alpha) | -0.003 | ||||
| Mean Square Error | 0.106 | ||||
| DF error | 1562.000 | ||||
| t(b) | -4.624 | ||||
| p(b) | 0.558 | ||||
| t(a) | -0.025 | ||||
| p(a) | 0.500 | ||||
| Lowerbound of 95% confidence interval for beta | -0.201 | ||||
| Upperbound of 95% confidence interval for beta | -0.081 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.265 | ||||
| Upperbound of 95% confidence interval for alpha | 0.258 | ||||
| Treynor index (mean / b) | 0.303 | ||||
| Jensen alpha (a) | -0.003 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.033 | ||||
| Expected Shortfall on VaR | 0.041 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.022 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1564.000 | ||||
| Minimum | 0.616 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.250 | ||||
| Mean of quarter 1 | 0.987 | ||||
| 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 | 342.000 | ||||
| Percentage of outliers low | 0.219 | ||||
| Mean of outliers low | 0.985 | ||||
| Number of outliers high | 337.000 | ||||
| Percentage of outliers high | 0.215 | ||||
| Mean of outliers high | 1.016 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.158 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.008 | ||||
| Extreme Value Index (regression method) | 0.391 | ||||
| VaR(95%) (regression method) | 0.011 | ||||
| Expected Shortfall (regression method) | 0.025 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.004 | ||||
| Median | 0.042 | ||||
| Quartile 3 | 0.136 | ||||
| Maximum | 0.544 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.022 | ||||
| Mean of quarter 3 | 0.048 | ||||
| Mean of quarter 4 | 0.468 | ||||
| Inter Quartile Range | 0.131 | ||||
| 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 | 0.468 | ||||
| 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) | 0.002 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.003 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.032 | ||||
| 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 | 1.080 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.482 | ||||
| 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 | 0.962 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.484 | ||||
| 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) | -8733725414787565.000 | ||||
| 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) | 103162586395563396627771229732864.000 | ||||
| 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 | ||||