Advanced Statistics: Test Forex
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 | -0.213 | ||||
| SD | 0.713 | ||||
| Sharpe ratio (Glass type estimate) | -0.299 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.294 | ||||
| df | 49.000 | ||||
| t | -0.610 | ||||
| p | 0.728 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.259 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.665 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.256 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.668 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.427 | ||||
| Upside Potential Ratio | 0.858 | ||||
| Upside part of mean | 0.428 | ||||
| Downside part of mean | -0.641 | ||||
| Upside SD | 0.503 | ||||
| Downside SD | 0.499 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 43.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 50.000 | ||||
| Mean of predictor | 0.440 | ||||
| Mean of criterion | -0.213 | ||||
| SD of predictor | 0.281 | ||||
| SD of criterion | 0.713 | ||||
| Covariance | -0.007 | ||||
| r | -0.037 | ||||
| b (slope, estimate of beta) | -0.093 | ||||
| a (intercept, estimate of alpha) | -0.172 | ||||
| Mean Square Error | 0.518 | ||||
| DF error | 48.000 | ||||
| t(b) | -0.255 | ||||
| p(b) | 0.600 | ||||
| t(a) | -0.444 | ||||
| p(a) | 0.671 | ||||
| Lowerbound of 95% confidence interval for beta | -0.828 | ||||
| Upperbound of 95% confidence interval for beta | 0.642 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.952 | ||||
| Upperbound of 95% confidence interval for alpha | 0.607 | ||||
| Treynor index (mean / b) | 2.285 | ||||
| Jensen alpha (a) | -0.172 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.478 | ||||
| SD | 0.756 | ||||
| Sharpe ratio (Glass type estimate) | -0.632 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.623 | ||||
| df | 49.000 | ||||
| t | -1.291 | ||||
| p | 0.899 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.598 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.339 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.591 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.345 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.721 | ||||
| Upside Potential Ratio | 0.516 | ||||
| Upside part of mean | 0.342 | ||||
| Downside part of mean | -0.820 | ||||
| Upside SD | 0.373 | ||||
| Downside SD | 0.663 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 43.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 50.000 | ||||
| Mean of predictor | 0.395 | ||||
| Mean of criterion | -0.478 | ||||
| SD of predictor | 0.266 | ||||
| SD of criterion | 0.756 | ||||
| Covariance | 0.009 | ||||
| r | 0.045 | ||||
| b (slope, estimate of beta) | 0.127 | ||||
| a (intercept, estimate of alpha) | -0.528 | ||||
| Mean Square Error | 0.582 | ||||
| DF error | 48.000 | ||||
| t(b) | 0.309 | ||||
| p(b) | 0.379 | ||||
| t(a) | -1.296 | ||||
| p(a) | 0.899 | ||||
| Lowerbound of 95% confidence interval for beta | -0.697 | ||||
| Upperbound of 95% confidence interval for beta | 0.950 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.347 | ||||
| Upperbound of 95% confidence interval for alpha | 0.291 | ||||
| Treynor index (mean / b) | -3.774 | ||||
| Jensen alpha (a) | -0.528 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.329 | ||||
| Expected Shortfall on VaR | 0.385 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.170 | ||||
| Expected Shortfall on VaR | 0.347 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 50.000 | ||||
| Minimum | 0.498 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.925 | ||||
| Mean of quarter 1 | 0.807 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.139 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 9.000 | ||||
| Percentage of outliers low | 0.180 | ||||
| Mean of outliers low | 0.721 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.140 | ||||
| Mean of outliers high | 1.259 | ||||
| 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) | -1.285 | ||||
| VaR(95%) (regression method) | 0.246 | ||||
| Expected Shortfall (regression method) | 0.275 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.253 | ||||
| Quartile 1 | 0.378 | ||||
| Median | 0.502 | ||||
| Quartile 3 | 0.678 | ||||
| Maximum | 0.855 | ||||
| Mean of quarter 1 | 0.253 | ||||
| Mean of quarter 2 | 0.502 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.855 | ||||
| Inter Quartile Range | 0.301 | ||||
| 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) | -0.201 | ||||
| Compounded annual return (geometric extrapolation) | -0.352 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.412 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.412 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.914 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.085 | ||||
| SD | 0.889 | ||||
| Sharpe ratio (Glass type estimate) | -0.096 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.096 | ||||
| df | 1102.000 | ||||
| t | -0.196 | ||||
| p | 0.503 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.051 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.860 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.051 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.860 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.146 | ||||
| Upside Potential Ratio | 4.041 | ||||
| Upside part of mean | 2.356 | ||||
| Downside part of mean | -2.441 | ||||
| Upside SD | 0.671 | ||||
| Downside SD | 0.583 | ||||
| N nonnegative terms | 153.000 | ||||
| N negative terms | 950.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1103.000 | ||||
| Mean of predictor | 0.474 | ||||
| Mean of criterion | -0.085 | ||||
| SD of predictor | 0.341 | ||||
| SD of criterion | 0.889 | ||||
| Covariance | -0.032 | ||||
| r | -0.105 | ||||
| b (slope, estimate of beta) | -0.273 | ||||
| a (intercept, estimate of alpha) | 0.044 | ||||
| Mean Square Error | 0.783 | ||||
| DF error | 1101.000 | ||||
| t(b) | -3.489 | ||||
| p(b) | 0.566 | ||||
| t(a) | 0.102 | ||||
| p(a) | 0.498 | ||||
| Lowerbound of 95% confidence interval for beta | -0.426 | ||||
| Upperbound of 95% confidence interval for beta | -0.119 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.805 | ||||
| Upperbound of 95% confidence interval for alpha | 0.894 | ||||
| Treynor index (mean / b) | 0.312 | ||||
| Jensen alpha (a) | 0.044 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.473 | ||||
| SD | 0.891 | ||||
| Sharpe ratio (Glass type estimate) | -0.531 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.531 | ||||
| df | 1102.000 | ||||
| t | -1.090 | ||||
| p | 0.516 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.486 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.425 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.486 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.425 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.681 | ||||
| Upside Potential Ratio | 3.138 | ||||
| Upside part of mean | 2.180 | ||||
| Downside part of mean | -2.654 | ||||
| Upside SD | 0.559 | ||||
| Downside SD | 0.695 | ||||
| N nonnegative terms | 153.000 | ||||
| N negative terms | 950.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1103.000 | ||||
| Mean of predictor | 0.415 | ||||
| Mean of criterion | -0.473 | ||||
| SD of predictor | 0.342 | ||||
| SD of criterion | 0.891 | ||||
| Covariance | -0.032 | ||||
| r | -0.104 | ||||
| b (slope, estimate of beta) | -0.271 | ||||
| a (intercept, estimate of alpha) | -0.361 | ||||
| Mean Square Error | 0.787 | ||||
| DF error | 1101.000 | ||||
| t(b) | -3.475 | ||||
| p(b) | 0.566 | ||||
| t(a) | -0.833 | ||||
| p(a) | 0.516 | ||||
| Lowerbound of 95% confidence interval for beta | -0.424 | ||||
| Upperbound of 95% confidence interval for beta | -0.118 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.212 | ||||
| Upperbound of 95% confidence interval for alpha | 0.490 | ||||
| Treynor index (mean / b) | 1.746 | ||||
| Jensen alpha (a) | -0.361 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.088 | ||||
| Expected Shortfall on VaR | 0.109 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.030 | ||||
| Expected Shortfall on VaR | 0.064 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1103.000 | ||||
| Minimum | 0.473 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.920 | ||||
| Mean of quarter 1 | 0.963 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.036 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 179.000 | ||||
| Percentage of outliers low | 0.162 | ||||
| Mean of outliers low | 0.943 | ||||
| Number of outliers high | 154.000 | ||||
| Percentage of outliers high | 0.140 | ||||
| Mean of outliers high | 1.065 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.189 | ||||
| VaR(95%) (moments method) | 0.005 | ||||
| Expected Shortfall (moments method) | 0.008 | ||||
| Extreme Value Index (regression method) | 0.229 | ||||
| VaR(95%) (regression method) | 0.034 | ||||
| Expected Shortfall (regression method) | 0.077 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.012 | ||||
| Quartile 1 | 0.086 | ||||
| Median | 0.224 | ||||
| Quartile 3 | 0.413 | ||||
| Maximum | 0.882 | ||||
| Mean of quarter 1 | 0.041 | ||||
| Mean of quarter 2 | 0.140 | ||||
| Mean of quarter 3 | 0.326 | ||||
| Mean of quarter 4 | 0.648 | ||||
| Inter Quartile Range | 0.327 | ||||
| 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) | -5.350 | ||||
| VaR(95%) (moments method) | 0.711 | ||||
| Expected Shortfall (moments method) | 0.711 | ||||
| Extreme Value Index (regression method) | -0.843 | ||||
| VaR(95%) (regression method) | 0.974 | ||||
| Expected Shortfall (regression method) | 1.053 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.199 | ||||
| Compounded annual return (geometric extrapolation) | -0.349 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.396 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.539 | ||||
| Compounded annual return / Expected Shortfall lognormal | -3.208 | ||||
| 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 | 1.176 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.504 | ||||
| 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 | 1.046 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.508 | ||||
| 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) | -8729024806860767.000 | ||||
| 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) | 468798565237187146283464110637056.000 | ||||
| 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 | ||||