Advanced Statistics: EX (no more trades, open for study )
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 | -0.018 | ||||
| SD | 0.080 | ||||
| Sharpe ratio (Glass type estimate) | -0.219 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.214 | ||||
| df | 35.000 | ||||
| t | -0.379 | ||||
| p | 0.646 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.350 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.916 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.347 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.919 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.493 | ||||
| Upside Potential Ratio | 1.341 | ||||
| Upside part of mean | 0.048 | ||||
| Downside part of mean | -0.065 | ||||
| Upside SD | 0.071 | ||||
| Downside SD | 0.036 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.541 | ||||
| Mean of criterion | -0.018 | ||||
| SD of predictor | 0.296 | ||||
| SD of criterion | 0.080 | ||||
| Covariance | -0.004 | ||||
| r | -0.148 | ||||
| b (slope, estimate of beta) | -0.040 | ||||
| a (intercept, estimate of alpha) | 0.004 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 34.000 | ||||
| t(b) | -0.872 | ||||
| p(b) | 0.805 | ||||
| t(a) | 0.079 | ||||
| p(a) | 0.469 | ||||
| Lowerbound of 95% confidence interval for beta | -0.134 | ||||
| Upperbound of 95% confidence interval for beta | 0.053 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.103 | ||||
| Upperbound of 95% confidence interval for alpha | 0.111 | ||||
| Treynor index (mean / b) | 0.438 | ||||
| Jensen alpha (a) | 0.004 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.020 | ||||
| SD | 0.077 | ||||
| Sharpe ratio (Glass type estimate) | -0.266 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.261 | ||||
| df | 35.000 | ||||
| t | -0.461 | ||||
| p | 0.676 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.398 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.869 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.394 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.873 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.565 | ||||
| Upside Potential Ratio | 1.249 | ||||
| Upside part of mean | 0.045 | ||||
| Downside part of mean | -0.066 | ||||
| Upside SD | 0.067 | ||||
| Downside SD | 0.036 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.489 | ||||
| Mean of criterion | -0.020 | ||||
| SD of predictor | 0.282 | ||||
| SD of criterion | 0.077 | ||||
| Covariance | -0.003 | ||||
| r | -0.151 | ||||
| b (slope, estimate of beta) | -0.041 | ||||
| a (intercept, estimate of alpha) | -0.000 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 34.000 | ||||
| t(b) | -0.888 | ||||
| p(b) | 0.810 | ||||
| t(a) | -0.008 | ||||
| p(a) | 0.503 | ||||
| Lowerbound of 95% confidence interval for beta | -0.135 | ||||
| Upperbound of 95% confidence interval for beta | 0.053 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.102 | ||||
| Upperbound of 95% confidence interval for alpha | 0.101 | ||||
| Treynor index (mean / b) | 0.499 | ||||
| Jensen alpha (a) | -0.000 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.038 | ||||
| Expected Shortfall on VaR | 0.046 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.018 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 36.000 | ||||
| Minimum | 0.952 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.124 | ||||
| Mean of quarter 1 | 0.992 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.017 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.056 | ||||
| Mean of outliers low | 0.964 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.056 | ||||
| Mean of outliers high | 1.075 | ||||
| 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) | -0.970 | ||||
| VaR(95%) (regression method) | 0.027 | ||||
| Expected Shortfall (regression method) | 0.049 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.024 | ||||
| Quartile 1 | 0.030 | ||||
| Median | 0.036 | ||||
| Quartile 3 | 0.042 | ||||
| Maximum | 0.048 | ||||
| Mean of quarter 1 | 0.024 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.048 | ||||
| Inter Quartile Range | 0.012 | ||||
| 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) | 0.024 | ||||
| Compounded annual return (geometric extrapolation) | 0.024 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.499 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.499 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.514 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.018 | ||||
| SD | 0.076 | ||||
| Sharpe ratio (Glass type estimate) | -0.235 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.235 | ||||
| df | 789.000 | ||||
| t | -0.409 | ||||
| p | 0.659 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.364 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.893 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.364 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.894 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.397 | ||||
| Upside Potential Ratio | 2.648 | ||||
| Upside part of mean | 0.119 | ||||
| Downside part of mean | -0.136 | ||||
| Upside SD | 0.061 | ||||
| Downside SD | 0.045 | ||||
| N nonnegative terms | 35.000 | ||||
| N negative terms | 755.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 790.000 | ||||
| Mean of predictor | 0.535 | ||||
| Mean of criterion | -0.018 | ||||
| SD of predictor | 0.361 | ||||
| SD of criterion | 0.076 | ||||
| Covariance | 0.000 | ||||
| r | 0.018 | ||||
| b (slope, estimate of beta) | 0.004 | ||||
| a (intercept, estimate of alpha) | -0.020 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 788.000 | ||||
| t(b) | 0.505 | ||||
| p(b) | 0.307 | ||||
| t(a) | -0.453 | ||||
| p(a) | 0.675 | ||||
| Lowerbound of 95% confidence interval for beta | -0.011 | ||||
| Upperbound of 95% confidence interval for beta | 0.018 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.106 | ||||
| Upperbound of 95% confidence interval for alpha | 0.066 | ||||
| Treynor index (mean / b) | -4.720 | ||||
| Jensen alpha (a) | -0.020 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.021 | ||||
| SD | 0.075 | ||||
| Sharpe ratio (Glass type estimate) | -0.275 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.275 | ||||
| df | 789.000 | ||||
| t | -0.478 | ||||
| p | 0.684 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.404 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.853 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.404 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.854 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.453 | ||||
| Upside Potential Ratio | 2.569 | ||||
| Upside part of mean | 0.117 | ||||
| Downside part of mean | -0.137 | ||||
| Upside SD | 0.059 | ||||
| Downside SD | 0.045 | ||||
| N nonnegative terms | 35.000 | ||||
| N negative terms | 755.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 790.000 | ||||
| Mean of predictor | 0.466 | ||||
| Mean of criterion | -0.021 | ||||
| SD of predictor | 0.375 | ||||
| SD of criterion | 0.075 | ||||
| Covariance | 0.000 | ||||
| r | 0.017 | ||||
| b (slope, estimate of beta) | 0.003 | ||||
| a (intercept, estimate of alpha) | -0.022 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 788.000 | ||||
| t(b) | 0.473 | ||||
| p(b) | 0.318 | ||||
| t(a) | -0.513 | ||||
| p(a) | 0.696 | ||||
| Lowerbound of 95% confidence interval for beta | -0.011 | ||||
| Upperbound of 95% confidence interval for beta | 0.017 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.107 | ||||
| Upperbound of 95% confidence interval for alpha | 0.063 | ||||
| Treynor index (mean / b) | -6.131 | ||||
| Jensen alpha (a) | -0.022 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.010 | ||||
| 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 | 790.000 | ||||
| Minimum | 0.958 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.074 | ||||
| Mean of quarter 1 | 0.999 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.002 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 25.000 | ||||
| Percentage of outliers low | 0.032 | ||||
| Mean of outliers low | 0.989 | ||||
| Number of outliers high | 36.000 | ||||
| Percentage of outliers high | 0.046 | ||||
| Mean of outliers high | 1.010 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.446 | ||||
| VaR(95%) (moments method) | -0.002 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.016 | ||||
| VaR(95%) (regression method) | -0.002 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.003 | ||||
| Quartile 3 | 0.054 | ||||
| Maximum | 0.123 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.003 | ||||
| Mean of quarter 3 | 0.046 | ||||
| Mean of quarter 4 | 0.093 | ||||
| Inter Quartile Range | 0.052 | ||||
| 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) | 0.024 | ||||
| Compounded annual return (geometric extrapolation) | 0.024 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.193 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.255 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.478 | ||||
| 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 | 0.966 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.473 | ||||
| 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 | 0.854 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.472 | ||||
| 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) | -8745033265007231.000 | ||||
| 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) | -275604381373722977676968220164096.000 | ||||
| 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 | ||||