Advanced Statistics: A.I. 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 | -0.109 | ||||
| SD | 0.091 | ||||
| Sharpe ratio (Glass type estimate) | -1.191 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.162 | ||||
| df | 31.000 | ||||
| t | -1.945 | ||||
| p | 0.970 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.418 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.054 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.397 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.073 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.142 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.109 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.095 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.594 | ||||
| Mean of criterion | -0.109 | ||||
| SD of predictor | 0.275 | ||||
| SD of criterion | 0.091 | ||||
| Covariance | 0.007 | ||||
| r | 0.265 | ||||
| b (slope, estimate of beta) | 0.088 | ||||
| a (intercept, estimate of alpha) | -0.161 | ||||
| Mean Square Error | 0.008 | ||||
| DF error | 30.000 | ||||
| t(b) | 1.507 | ||||
| p(b) | 0.071 | ||||
| t(a) | -2.483 | ||||
| p(a) | 0.991 | ||||
| Lowerbound of 95% confidence interval for beta | -0.031 | ||||
| Upperbound of 95% confidence interval for beta | 0.207 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.294 | ||||
| Upperbound of 95% confidence interval for alpha | -0.029 | ||||
| Treynor index (mean / b) | -1.235 | ||||
| Jensen alpha (a) | -0.161 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.113 | ||||
| SD | 0.099 | ||||
| Sharpe ratio (Glass type estimate) | -1.147 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.119 | ||||
| df | 31.000 | ||||
| t | -1.873 | ||||
| p | 0.965 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.372 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.095 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.351 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.113 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.105 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.113 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.103 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.545 | ||||
| Mean of criterion | -0.113 | ||||
| SD of predictor | 0.260 | ||||
| SD of criterion | 0.099 | ||||
| Covariance | 0.007 | ||||
| r | 0.275 | ||||
| b (slope, estimate of beta) | 0.104 | ||||
| a (intercept, estimate of alpha) | -0.170 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 30.000 | ||||
| t(b) | 1.564 | ||||
| p(b) | 0.064 | ||||
| t(a) | -2.451 | ||||
| p(a) | 0.990 | ||||
| Lowerbound of 95% confidence interval for beta | -0.032 | ||||
| Upperbound of 95% confidence interval for beta | 0.241 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.312 | ||||
| Upperbound of 95% confidence interval for alpha | -0.028 | ||||
| Treynor index (mean / b) | -1.086 | ||||
| Jensen alpha (a) | -0.170 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.055 | ||||
| Expected Shortfall on VaR | 0.066 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.032 | ||||
| Expected Shortfall on VaR | 0.065 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 32.000 | ||||
| Minimum | 0.851 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.978 | ||||
| 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 | 3.000 | ||||
| Percentage of outliers low | 0.094 | ||||
| Mean of outliers low | 0.943 | ||||
| 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) | 1.684 | ||||
| VaR(95%) (regression method) | 0.018 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.169 | ||||
| Quartile 1 | 0.169 | ||||
| Median | 0.169 | ||||
| Quartile 3 | 0.169 | ||||
| Maximum | 0.169 | ||||
| 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) | -0.063 | ||||
| Compounded annual return (geometric extrapolation) | -0.067 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.397 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.016 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.109 | ||||
| SD | 0.079 | ||||
| Sharpe ratio (Glass type estimate) | -1.377 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.376 | ||||
| df | 714.000 | ||||
| t | -2.275 | ||||
| p | 0.988 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.565 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.188 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.564 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.187 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.482 | ||||
| Upside Potential Ratio | 0.583 | ||||
| Upside part of mean | 0.043 | ||||
| Downside part of mean | -0.151 | ||||
| Upside SD | 0.030 | ||||
| Downside SD | 0.073 | ||||
| N nonnegative terms | 25.000 | ||||
| N negative terms | 690.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 715.000 | ||||
| Mean of predictor | 0.652 | ||||
| Mean of criterion | -0.109 | ||||
| SD of predictor | 0.362 | ||||
| SD of criterion | 0.079 | ||||
| Covariance | 0.001 | ||||
| r | 0.021 | ||||
| b (slope, estimate of beta) | 0.004 | ||||
| a (intercept, estimate of alpha) | -0.111 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 713.000 | ||||
| t(b) | 0.549 | ||||
| p(b) | 0.292 | ||||
| t(a) | -2.320 | ||||
| p(a) | 0.990 | ||||
| Lowerbound of 95% confidence interval for beta | -0.012 | ||||
| Upperbound of 95% confidence interval for beta | 0.020 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.206 | ||||
| Upperbound of 95% confidence interval for alpha | -0.017 | ||||
| Treynor index (mean / b) | -24.265 | ||||
| Jensen alpha (a) | -0.111 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.112 | ||||
| SD | 0.082 | ||||
| Sharpe ratio (Glass type estimate) | -1.371 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.369 | ||||
| df | 714.000 | ||||
| t | -2.265 | ||||
| p | 0.988 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.559 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.182 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.558 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.181 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.464 | ||||
| Upside Potential Ratio | 0.553 | ||||
| Upside part of mean | 0.042 | ||||
| Downside part of mean | -0.154 | ||||
| Upside SD | 0.029 | ||||
| Downside SD | 0.076 | ||||
| N nonnegative terms | 25.000 | ||||
| N negative terms | 690.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 715.000 | ||||
| Mean of predictor | 0.583 | ||||
| Mean of criterion | -0.112 | ||||
| SD of predictor | 0.373 | ||||
| SD of criterion | 0.082 | ||||
| Covariance | 0.001 | ||||
| r | 0.020 | ||||
| b (slope, estimate of beta) | 0.004 | ||||
| a (intercept, estimate of alpha) | -0.114 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 713.000 | ||||
| t(b) | 0.544 | ||||
| p(b) | 0.293 | ||||
| t(a) | -2.305 | ||||
| p(a) | 0.989 | ||||
| Lowerbound of 95% confidence interval for beta | -0.012 | ||||
| Upperbound of 95% confidence interval for beta | 0.021 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.212 | ||||
| Upperbound of 95% confidence interval for alpha | -0.017 | ||||
| Treynor index (mean / b) | -25.099 | ||||
| Jensen alpha (a) | -0.114 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.011 | ||||
| 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 | 715.000 | ||||
| Minimum | 0.899 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.043 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.001 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 34.000 | ||||
| Percentage of outliers low | 0.048 | ||||
| Mean of outliers low | 0.991 | ||||
| Number of outliers high | 25.000 | ||||
| Percentage of outliers high | 0.035 | ||||
| Mean of outliers high | 1.005 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.259 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.986 | ||||
| VaR(95%) (regression method) | 0.001 | ||||
| Expected Shortfall (regression method) | 0.078 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.017 | ||||
| Quartile 1 | 0.057 | ||||
| Median | 0.098 | ||||
| Quartile 3 | 0.138 | ||||
| Maximum | 0.179 | ||||
| Mean of quarter 1 | 0.017 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.179 | ||||
| Inter Quartile Range | 0.081 | ||||
| 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) | -0.062 | ||||
| Compounded annual return (geometric extrapolation) | -0.066 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.367 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.367 | ||||
| Compounded annual return / Expected Shortfall lognormal | -6.091 | ||||
| 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 | 1.079 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.462 | ||||
| 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 | 0.971 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.464 | ||||
| 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) | -8726652605332657.000 | ||||
| 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) | -173598742179256238264900355358720.000 | ||||
| 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 | ||||