Advanced Statistics: Forex Automated Trading Systems(FATS)
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 | -0.071 | ||||
| SD | 0.071 | ||||
| Sharpe ratio (Glass type estimate) | -1.004 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.989 | ||||
| df | 51.000 | ||||
| t | -2.089 | ||||
| p | 0.979 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.960 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.038 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.950 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.028 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.019 | ||||
| Upside Potential Ratio | 0.258 | ||||
| Upside part of mean | 0.018 | ||||
| Downside part of mean | -0.089 | ||||
| Upside SD | 0.022 | ||||
| Downside SD | 0.070 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 48.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 52.000 | ||||
| Mean of predictor | 0.400 | ||||
| Mean of criterion | -0.071 | ||||
| SD of predictor | 0.283 | ||||
| SD of criterion | 0.071 | ||||
| Covariance | 0.001 | ||||
| r | 0.033 | ||||
| b (slope, estimate of beta) | 0.008 | ||||
| a (intercept, estimate of alpha) | -0.074 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 50.000 | ||||
| t(b) | 0.234 | ||||
| p(b) | 0.408 | ||||
| t(a) | -2.003 | ||||
| p(a) | 0.975 | ||||
| Lowerbound of 95% confidence interval for beta | -0.063 | ||||
| Upperbound of 95% confidence interval for beta | 0.079 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.149 | ||||
| Upperbound of 95% confidence interval for alpha | 0.000 | ||||
| Treynor index (mean / b) | -8.589 | ||||
| Jensen alpha (a) | -0.074 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.074 | ||||
| SD | 0.074 | ||||
| Sharpe ratio (Glass type estimate) | -0.997 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.982 | ||||
| df | 51.000 | ||||
| t | -2.076 | ||||
| p | 0.979 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.954 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.031 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.943 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.022 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.008 | ||||
| Upside Potential Ratio | 0.242 | ||||
| Upside part of mean | 0.018 | ||||
| Downside part of mean | -0.091 | ||||
| Upside SD | 0.021 | ||||
| Downside SD | 0.073 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 48.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 52.000 | ||||
| Mean of predictor | 0.357 | ||||
| Mean of criterion | -0.074 | ||||
| SD of predictor | 0.266 | ||||
| SD of criterion | 0.074 | ||||
| Covariance | 0.001 | ||||
| r | 0.038 | ||||
| b (slope, estimate of beta) | 0.011 | ||||
| a (intercept, estimate of alpha) | -0.077 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 50.000 | ||||
| t(b) | 0.268 | ||||
| p(b) | 0.395 | ||||
| t(a) | -2.013 | ||||
| p(a) | 0.975 | ||||
| Lowerbound of 95% confidence interval for beta | -0.068 | ||||
| Upperbound of 95% confidence interval for beta | 0.090 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.155 | ||||
| Upperbound of 95% confidence interval for alpha | -0.000 | ||||
| Treynor index (mean / b) | -6.996 | ||||
| Jensen alpha (a) | -0.077 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.040 | ||||
| Expected Shortfall on VaR | 0.049 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.025 | ||||
| Expected Shortfall on VaR | 0.050 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 52.000 | ||||
| Minimum | 0.896 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.036 | ||||
| Mean of quarter 1 | 0.983 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.008 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 10.000 | ||||
| Percentage of outliers low | 0.192 | ||||
| Mean of outliers low | 0.978 | ||||
| Number of outliers high | 12.000 | ||||
| Percentage of outliers high | 0.231 | ||||
| Mean of outliers high | 1.009 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.688 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.140 | ||||
| VaR(95%) (regression method) | 0.011 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.007 | ||||
| Quartile 3 | 0.054 | ||||
| Maximum | 0.193 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.006 | ||||
| Mean of quarter 3 | 0.007 | ||||
| Mean of quarter 4 | 0.193 | ||||
| Inter Quartile Range | 0.049 | ||||
| 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 | 0.250 | ||||
| Mean of outliers high | 0.193 | ||||
| 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) | -0.028 | ||||
| Compounded annual return (geometric extrapolation) | -0.029 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.152 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.152 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.598 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.071 | ||||
| SD | 0.066 | ||||
| Sharpe ratio (Glass type estimate) | -1.086 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.085 | ||||
| df | 1148.000 | ||||
| t | -2.274 | ||||
| p | 0.533 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.023 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.149 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.022 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.148 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.282 | ||||
| Upside Potential Ratio | 1.727 | ||||
| Upside part of mean | 0.096 | ||||
| Downside part of mean | -0.167 | ||||
| Upside SD | 0.035 | ||||
| Downside SD | 0.055 | ||||
| N nonnegative terms | 129.000 | ||||
| N negative terms | 1020.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1149.000 | ||||
| Mean of predictor | 0.437 | ||||
| Mean of criterion | -0.071 | ||||
| SD of predictor | 0.327 | ||||
| SD of criterion | 0.066 | ||||
| Covariance | 0.004 | ||||
| r | 0.181 | ||||
| b (slope, estimate of beta) | 0.036 | ||||
| a (intercept, estimate of alpha) | -0.087 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 1147.000 | ||||
| t(b) | 6.218 | ||||
| p(b) | 0.386 | ||||
| t(a) | -2.815 | ||||
| p(a) | 0.553 | ||||
| Lowerbound of 95% confidence interval for beta | 0.025 | ||||
| Upperbound of 95% confidence interval for beta | 0.048 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.148 | ||||
| Upperbound of 95% confidence interval for alpha | -0.026 | ||||
| Treynor index (mean / b) | -1.964 | ||||
| Jensen alpha (a) | -0.087 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.073 | ||||
| SD | 0.067 | ||||
| Sharpe ratio (Glass type estimate) | -1.101 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.101 | ||||
| df | 1148.000 | ||||
| t | -2.307 | ||||
| p | 0.534 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.038 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.164 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.038 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.164 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.286 | ||||
| Upside Potential Ratio | 1.670 | ||||
| Upside part of mean | 0.095 | ||||
| Downside part of mean | -0.169 | ||||
| Upside SD | 0.035 | ||||
| Downside SD | 0.057 | ||||
| N nonnegative terms | 129.000 | ||||
| N negative terms | 1020.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1149.000 | ||||
| Mean of predictor | 0.382 | ||||
| Mean of criterion | -0.073 | ||||
| SD of predictor | 0.329 | ||||
| SD of criterion | 0.067 | ||||
| Covariance | 0.004 | ||||
| r | 0.178 | ||||
| b (slope, estimate of beta) | 0.036 | ||||
| a (intercept, estimate of alpha) | -0.087 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 1147.000 | ||||
| t(b) | 6.111 | ||||
| p(b) | 0.388 | ||||
| t(a) | -2.775 | ||||
| p(a) | 0.552 | ||||
| Lowerbound of 95% confidence interval for beta | 0.024 | ||||
| Upperbound of 95% confidence interval for beta | 0.048 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.149 | ||||
| Upperbound of 95% confidence interval for alpha | -0.026 | ||||
| Treynor index (mean / b) | -2.038 | ||||
| Jensen alpha (a) | -0.087 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1149.000 | ||||
| Minimum | 0.918 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.046 | ||||
| Mean of quarter 1 | 0.998 | ||||
| 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 | 192.000 | ||||
| Percentage of outliers low | 0.167 | ||||
| Mean of outliers low | 0.997 | ||||
| Number of outliers high | 208.000 | ||||
| Percentage of outliers high | 0.181 | ||||
| Mean of outliers high | 1.002 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.787 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.010 | ||||
| Extreme Value Index (regression method) | 0.516 | ||||
| VaR(95%) (regression method) | 0.001 | ||||
| Expected Shortfall (regression method) | 0.006 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 20.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.000 | ||||
| Quartile 3 | 0.001 | ||||
| Maximum | 0.195 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.000 | ||||
| Mean of quarter 3 | 0.001 | ||||
| Mean of quarter 4 | 0.057 | ||||
| Inter Quartile Range | 0.001 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.200 | ||||
| Mean of outliers high | 0.070 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.675 | ||||
| VaR(95%) (moments method) | 0.019 | ||||
| Expected Shortfall (moments method) | 0.075 | ||||
| Extreme Value Index (regression method) | 1.219 | ||||
| VaR(95%) (regression method) | 0.087 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.028 | ||||
| Compounded annual return (geometric extrapolation) | -0.029 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.148 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.509 | ||||
| Compounded annual return / Expected Shortfall lognormal | -3.313 | ||||
| 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 | 1.185 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.493 | ||||
| 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 | 1.060 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.498 | ||||
| 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) | -8723970273597837.000 | ||||
| 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) | 171240218770615603133065736486912.000 | ||||
| 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 | ||||