Advanced Statistics: Precise
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 | -0.038 | ||||
| SD | 0.009 | ||||
| Sharpe ratio (Glass type estimate) | -4.050 | ||||
| Sharpe ratio (Hedges UMVUE) | -3.944 | ||||
| df | 29.000 | ||||
| t | -6.403 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -5.645 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -2.413 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -5.546 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.342 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.047 | ||||
| Upside Potential Ratio | 0.358 | ||||
| Upside part of mean | 0.004 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 0.007 | ||||
| Downside SD | 0.013 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 29.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 30.000 | ||||
| Mean of predictor | 0.622 | ||||
| Mean of criterion | -0.038 | ||||
| SD of predictor | 0.303 | ||||
| SD of criterion | 0.009 | ||||
| Covariance | -0.000 | ||||
| r | -0.019 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | -0.038 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 28.000 | ||||
| t(b) | -0.098 | ||||
| p(b) | 0.539 | ||||
| t(a) | -5.338 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.013 | ||||
| Upperbound of 95% confidence interval for beta | 0.011 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.052 | ||||
| Upperbound of 95% confidence interval for alpha | -0.023 | ||||
| Treynor index (mean / b) | 66.107 | ||||
| Jensen alpha (a) | -0.038 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.038 | ||||
| SD | 0.009 | ||||
| Sharpe ratio (Glass type estimate) | -4.076 | ||||
| Sharpe ratio (Hedges UMVUE) | -3.970 | ||||
| df | 29.000 | ||||
| t | -6.445 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -5.676 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -2.434 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -5.576 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.363 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.050 | ||||
| Upside Potential Ratio | 0.356 | ||||
| Upside part of mean | 0.004 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 0.007 | ||||
| Downside SD | 0.012 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 29.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 30.000 | ||||
| Mean of predictor | 0.564 | ||||
| Mean of criterion | -0.038 | ||||
| SD of predictor | 0.291 | ||||
| SD of criterion | 0.009 | ||||
| Covariance | -0.000 | ||||
| r | -0.011 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.038 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 28.000 | ||||
| t(b) | -0.057 | ||||
| p(b) | 0.523 | ||||
| t(a) | -5.477 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.013 | ||||
| Upperbound of 95% confidence interval for beta | 0.012 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.052 | ||||
| Upperbound of 95% confidence interval for alpha | -0.024 | ||||
| Treynor index (mean / b) | 109.982 | ||||
| Jensen alpha (a) | -0.038 | ||||
| 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 | 0.009 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 30.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.015 | ||||
| Mean of quarter 1 | 1.000 | ||||
| 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 | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.033 | ||||
| Mean of outliers high | 1.015 | ||||
| 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) | 0.006 | ||||
| Compounded annual return (geometric extrapolation) | 0.006 | ||||
| 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 | 0.681 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.038 | ||||
| SD | 0.009 | ||||
| Sharpe ratio (Glass type estimate) | -4.126 | ||||
| Sharpe ratio (Hedges UMVUE) | -4.121 | ||||
| df | 675.000 | ||||
| t | -6.627 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -5.364 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -2.885 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -5.361 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.881 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -14.075 | ||||
| Upside Potential Ratio | 2.100 | ||||
| Upside part of mean | 0.006 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.009 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 675.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 676.000 | ||||
| Mean of predictor | 0.682 | ||||
| Mean of criterion | -0.038 | ||||
| SD of predictor | 0.357 | ||||
| SD of criterion | 0.009 | ||||
| Covariance | -0.000 | ||||
| r | -0.002 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.038 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 674.000 | ||||
| t(b) | -0.060 | ||||
| p(b) | 0.524 | ||||
| t(a) | -6.570 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.002 | ||||
| Upperbound of 95% confidence interval for beta | 0.002 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.050 | ||||
| Upperbound of 95% confidence interval for alpha | -0.027 | ||||
| Treynor index (mean / b) | 634.877 | ||||
| Jensen alpha (a) | -0.038 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.038 | ||||
| SD | 0.009 | ||||
| Sharpe ratio (Glass type estimate) | -4.161 | ||||
| Sharpe ratio (Hedges UMVUE) | -4.156 | ||||
| df | 675.000 | ||||
| t | -6.683 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -5.400 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -2.919 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -5.396 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.916 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -14.090 | ||||
| Upside Potential Ratio | 2.084 | ||||
| Upside part of mean | 0.006 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.009 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 675.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 676.000 | ||||
| Mean of predictor | 0.617 | ||||
| Mean of criterion | -0.038 | ||||
| SD of predictor | 0.362 | ||||
| SD of criterion | 0.009 | ||||
| Covariance | -0.000 | ||||
| r | -0.002 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.038 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 674.000 | ||||
| t(b) | -0.048 | ||||
| p(b) | 0.519 | ||||
| t(a) | -6.637 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.002 | ||||
| Upperbound of 95% confidence interval for beta | 0.002 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.050 | ||||
| Upperbound of 95% confidence interval for alpha | -0.027 | ||||
| Treynor index (mean / b) | 812.927 | ||||
| Jensen alpha (a) | -0.038 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.001 | ||||
| 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 | 676.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.015 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers high | 0.001 | ||||
| Mean of outliers high | 1.015 | ||||
| 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) | 0.006 | ||||
| Compounded annual return (geometric extrapolation) | 0.006 | ||||
| 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 | 4.359 | ||||
| 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 | 1.041 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.497 | ||||
| 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 | 0.917 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.494 | ||||
| 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) | -8742133863219368.000 | ||||
| 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) | 112617976446207798565145497567232.000 | ||||
| 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 | ||||