Advanced Statistics: AventaFX
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 | 0.791 | ||||
| SD | 1.285 | ||||
| Sharpe ratio (Glass type estimate) | 0.616 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.603 | ||||
| df | 36.000 | ||||
| t | 1.081 | ||||
| p | 0.143 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.514 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.737 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.522 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.728 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.372 | ||||
| Upside Potential Ratio | 2.227 | ||||
| Upside part of mean | 1.285 | ||||
| Downside part of mean | -0.494 | ||||
| Upside SD | 1.152 | ||||
| Downside SD | 0.577 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 37.000 | ||||
| Mean of predictor | 0.515 | ||||
| Mean of criterion | 0.791 | ||||
| SD of predictor | 0.271 | ||||
| SD of criterion | 1.285 | ||||
| Covariance | 0.021 | ||||
| r | 0.061 | ||||
| b (slope, estimate of beta) | 0.287 | ||||
| a (intercept, estimate of alpha) | 0.643 | ||||
| Mean Square Error | 1.692 | ||||
| DF error | 35.000 | ||||
| t(b) | 0.359 | ||||
| p(b) | 0.361 | ||||
| t(a) | 0.759 | ||||
| p(a) | 0.226 | ||||
| Lowerbound of 95% confidence interval for beta | -1.336 | ||||
| Upperbound of 95% confidence interval for beta | 1.910 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.077 | ||||
| Upperbound of 95% confidence interval for alpha | 2.364 | ||||
| Treynor index (mean / b) | 2.756 | ||||
| Jensen alpha (a) | 0.643 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.011 | ||||
| SD | 1.361 | ||||
| Sharpe ratio (Glass type estimate) | 0.008 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.008 | ||||
| df | 36.000 | ||||
| t | 0.014 | ||||
| p | 0.494 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.108 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.124 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.108 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.124 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.010 | ||||
| Upside Potential Ratio | 0.812 | ||||
| Upside part of mean | 0.887 | ||||
| Downside part of mean | -0.876 | ||||
| Upside SD | 0.781 | ||||
| Downside SD | 1.092 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 37.000 | ||||
| Mean of predictor | 0.469 | ||||
| Mean of criterion | 0.011 | ||||
| SD of predictor | 0.261 | ||||
| SD of criterion | 1.361 | ||||
| Covariance | 0.066 | ||||
| r | 0.187 | ||||
| b (slope, estimate of beta) | 0.974 | ||||
| a (intercept, estimate of alpha) | -0.446 | ||||
| Mean Square Error | 1.839 | ||||
| DF error | 35.000 | ||||
| t(b) | 1.126 | ||||
| p(b) | 0.134 | ||||
| t(a) | -0.511 | ||||
| p(a) | 0.694 | ||||
| Lowerbound of 95% confidence interval for beta | -0.783 | ||||
| Upperbound of 95% confidence interval for beta | 2.730 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.217 | ||||
| Upperbound of 95% confidence interval for alpha | 1.325 | ||||
| Treynor index (mean / b) | 0.011 | ||||
| Jensen alpha (a) | -0.446 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.476 | ||||
| Expected Shortfall on VaR | 0.551 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.131 | ||||
| Expected Shortfall on VaR | 0.287 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 37.000 | ||||
| Minimum | 0.184 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.346 | ||||
| Mean of quarter 1 | 0.859 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.442 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.054 | ||||
| Mean of outliers low | 0.297 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.162 | ||||
| Mean of outliers high | 1.664 | ||||
| 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) | -2.399 | ||||
| VaR(95%) (regression method) | 0.868 | ||||
| Expected Shortfall (regression method) | 1.176 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.823 | ||||
| Quartile 1 | 0.823 | ||||
| Median | 0.823 | ||||
| Quartile 3 | 0.823 | ||||
| Maximum | 0.823 | ||||
| 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) | 0.060 | ||||
| Compounded annual return (geometric extrapolation) | 0.056 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.069 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.102 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 111.407 | ||||
| SD | 153.805 | ||||
| Sharpe ratio (Glass type estimate) | 0.724 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.724 | ||||
| df | 825.000 | ||||
| t | 1.286 | ||||
| p | 0.099 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.380 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.829 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.381 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.828 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 92.724 | ||||
| Upside Potential Ratio | 95.568 | ||||
| Upside part of mean | 114.824 | ||||
| Downside part of mean | -3.417 | ||||
| Upside SD | 153.861 | ||||
| Downside SD | 1.201 | ||||
| N nonnegative terms | 66.000 | ||||
| N negative terms | 760.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 826.000 | ||||
| Mean of predictor | 0.577 | ||||
| Mean of criterion | 111.407 | ||||
| SD of predictor | 0.369 | ||||
| SD of criterion | 153.805 | ||||
| Covariance | 1.603 | ||||
| r | 0.028 | ||||
| b (slope, estimate of beta) | 11.793 | ||||
| a (intercept, estimate of alpha) | 104.606 | ||||
| Mean Square Error | 23665.716 | ||||
| DF error | 824.000 | ||||
| t(b) | 0.812 | ||||
| p(b) | 0.209 | ||||
| t(a) | 1.202 | ||||
| p(a) | 0.115 | ||||
| Lowerbound of 95% confidence interval for beta | -16.720 | ||||
| Upperbound of 95% confidence interval for beta | 40.307 | ||||
| Lowerbound of 95% confidence interval for alpha | -66.249 | ||||
| Upperbound of 95% confidence interval for alpha | 275.461 | ||||
| Treynor index (mean / b) | 9.447 | ||||
| Jensen alpha (a) | 104.606 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.010 | ||||
| SD | 6.079 | ||||
| Sharpe ratio (Glass type estimate) | 0.002 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.002 | ||||
| df | 825.000 | ||||
| t | 0.003 | ||||
| p | 0.499 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.102 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.105 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.102 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.105 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.002 | ||||
| Upside Potential Ratio | 1.568 | ||||
| Upside part of mean | 6.750 | ||||
| Downside part of mean | -6.740 | ||||
| Upside SD | 4.288 | ||||
| Downside SD | 4.304 | ||||
| N nonnegative terms | 66.000 | ||||
| N negative terms | 760.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 826.000 | ||||
| Mean of predictor | 0.504 | ||||
| Mean of criterion | 0.010 | ||||
| SD of predictor | 0.388 | ||||
| SD of criterion | 6.079 | ||||
| Covariance | 0.112 | ||||
| r | 0.047 | ||||
| b (slope, estimate of beta) | 0.744 | ||||
| a (intercept, estimate of alpha) | -0.365 | ||||
| Mean Square Error | 36.918 | ||||
| DF error | 824.000 | ||||
| t(b) | 1.363 | ||||
| p(b) | 0.087 | ||||
| t(a) | -0.106 | ||||
| p(a) | 0.542 | ||||
| Lowerbound of 95% confidence interval for beta | -0.328 | ||||
| Upperbound of 95% confidence interval for beta | 1.815 | ||||
| Lowerbound of 95% confidence interval for alpha | -7.103 | ||||
| Upperbound of 95% confidence interval for alpha | 6.374 | ||||
| Treynor index (mean / b) | 0.013 | ||||
| Jensen alpha (a) | -0.365 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.461 | ||||
| Expected Shortfall on VaR | 0.535 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.043 | ||||
| Expected Shortfall on VaR | 0.096 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 826.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 260.118 | ||||
| Mean of quarter 1 | 0.949 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 2.749 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 67.000 | ||||
| Percentage of outliers low | 0.081 | ||||
| Mean of outliers low | 0.841 | ||||
| Number of outliers high | 66.000 | ||||
| Percentage of outliers high | 0.080 | ||||
| Mean of outliers high | 6.485 | ||||
| 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) | 0.001 | ||||
| VaR(95%) (regression method) | 0.041 | ||||
| Expected Shortfall (regression method) | 0.124 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.006 | ||||
| Quartile 1 | 0.031 | ||||
| Median | 0.037 | ||||
| Quartile 3 | 0.048 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.016 | ||||
| Mean of quarter 2 | 0.034 | ||||
| Mean of quarter 3 | 0.043 | ||||
| Mean of quarter 4 | 0.526 | ||||
| Inter Quartile Range | 0.017 | ||||
| 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 | 0.125 | ||||
| Mean of outliers high | 1.000 | ||||
| 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) | 0.058 | ||||
| Compounded annual return (geometric extrapolation) | 0.055 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.055 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.105 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.103 | ||||
| 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 | 0.978 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.491 | ||||
| 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 | 0.857 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.489 | ||||
| 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) | -8748281867392297.000 | ||||
| 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) | 102217202594170400896358067208192.000 | ||||
| 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 | ||||