Advanced Statistics: Smart 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 | -0.044 | ||||
| SD | 0.015 | ||||
| Sharpe ratio (Glass type estimate) | -2.829 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.794 | ||||
| df | 60.000 | ||||
| t | -6.379 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.826 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.815 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.797 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.791 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.245 | ||||
| Upside Potential Ratio | 0.211 | ||||
| Upside part of mean | 0.004 | ||||
| Downside part of mean | -0.048 | ||||
| Upside SD | 0.004 | ||||
| Downside SD | 0.019 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 52.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.360 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.253 | ||||
| SD of criterion | 0.015 | ||||
| Covariance | 0.001 | ||||
| r | 0.269 | ||||
| b (slope, estimate of beta) | 0.016 | ||||
| a (intercept, estimate of alpha) | -0.050 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 59.000 | ||||
| t(b) | 2.144 | ||||
| p(b) | 0.018 | ||||
| t(a) | -6.888 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | 0.001 | ||||
| Upperbound of 95% confidence interval for beta | 0.032 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.064 | ||||
| Upperbound of 95% confidence interval for alpha | -0.035 | ||||
| Treynor index (mean / b) | -2.667 | ||||
| Jensen alpha (a) | -0.050 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.015 | ||||
| Sharpe ratio (Glass type estimate) | -2.827 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.792 | ||||
| df | 60.000 | ||||
| t | -6.374 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.823 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.813 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.794 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.789 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.243 | ||||
| Upside Potential Ratio | 0.210 | ||||
| Upside part of mean | 0.004 | ||||
| Downside part of mean | -0.048 | ||||
| Upside SD | 0.004 | ||||
| Downside SD | 0.019 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 52.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.323 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.252 | ||||
| SD of criterion | 0.015 | ||||
| Covariance | 0.001 | ||||
| r | 0.283 | ||||
| b (slope, estimate of beta) | 0.017 | ||||
| a (intercept, estimate of alpha) | -0.049 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 59.000 | ||||
| t(b) | 2.265 | ||||
| p(b) | 0.014 | ||||
| t(a) | -6.966 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | 0.002 | ||||
| Upperbound of 95% confidence interval for beta | 0.033 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.063 | ||||
| Upperbound of 95% confidence interval for alpha | -0.035 | ||||
| Treynor index (mean / b) | -2.517 | ||||
| Jensen alpha (a) | -0.049 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.013 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.015 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 61.000 | ||||
| Minimum | 0.985 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.003 | ||||
| Maximum | 1.010 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.005 | ||||
| Inter Quartile Range | 0.005 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.033 | ||||
| Mean of outliers low | 0.987 | ||||
| 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) | -0.191 | ||||
| VaR(95%) (moments method) | 0.005 | ||||
| Expected Shortfall (moments method) | 0.007 | ||||
| Extreme Value Index (regression method) | 0.170 | ||||
| VaR(95%) (regression method) | 0.006 | ||||
| Expected Shortfall (regression method) | 0.009 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.011 | ||||
| Quartile 3 | 0.011 | ||||
| Maximum | 0.028 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.010 | ||||
| Mean of quarter 3 | 0.011 | ||||
| Mean of quarter 4 | 0.020 | ||||
| Inter Quartile Range | 0.005 | ||||
| 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 | 0.143 | ||||
| Mean of outliers high | 0.028 | ||||
| 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) | 0.013 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.018 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.028 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.043 | ||||
| SD | 0.024 | ||||
| Sharpe ratio (Glass type estimate) | -1.785 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.784 | ||||
| df | 1338.000 | ||||
| t | -4.036 | ||||
| p | 0.555 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.655 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.915 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.654 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.915 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.296 | ||||
| Upside Potential Ratio | 5.151 | ||||
| Upside part of mean | 0.097 | ||||
| Downside part of mean | -0.141 | ||||
| Upside SD | 0.015 | ||||
| Downside SD | 0.019 | ||||
| N nonnegative terms | 566.000 | ||||
| N negative terms | 773.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1339.000 | ||||
| Mean of predictor | 0.419 | ||||
| Mean of criterion | -0.043 | ||||
| SD of predictor | 0.386 | ||||
| SD of criterion | 0.024 | ||||
| Covariance | -0.001 | ||||
| r | -0.129 | ||||
| b (slope, estimate of beta) | -0.008 | ||||
| a (intercept, estimate of alpha) | -0.040 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 1337.000 | ||||
| t(b) | -4.748 | ||||
| p(b) | 0.582 | ||||
| t(a) | -3.741 | ||||
| p(a) | 0.565 | ||||
| Lowerbound of 95% confidence interval for beta | -0.011 | ||||
| Upperbound of 95% confidence interval for beta | -0.005 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.061 | ||||
| Upperbound of 95% confidence interval for alpha | -0.019 | ||||
| Treynor index (mean / b) | 5.352 | ||||
| Jensen alpha (a) | -0.040 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.024 | ||||
| Sharpe ratio (Glass type estimate) | -1.796 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.795 | ||||
| df | 1338.000 | ||||
| t | -4.060 | ||||
| p | 0.555 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.665 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.926 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.665 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.925 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.304 | ||||
| Upside Potential Ratio | 5.127 | ||||
| Upside part of mean | 0.097 | ||||
| Downside part of mean | -0.141 | ||||
| Upside SD | 0.015 | ||||
| Downside SD | 0.019 | ||||
| N nonnegative terms | 566.000 | ||||
| N negative terms | 773.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1339.000 | ||||
| Mean of predictor | 0.340 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.404 | ||||
| SD of criterion | 0.024 | ||||
| Covariance | -0.001 | ||||
| r | -0.125 | ||||
| b (slope, estimate of beta) | -0.007 | ||||
| a (intercept, estimate of alpha) | -0.041 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 1337.000 | ||||
| t(b) | -4.590 | ||||
| p(b) | 0.579 | ||||
| t(a) | -3.846 | ||||
| p(a) | 0.566 | ||||
| Lowerbound of 95% confidence interval for beta | -0.011 | ||||
| Upperbound of 95% confidence interval for beta | -0.004 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.062 | ||||
| Upperbound of 95% confidence interval for alpha | -0.020 | ||||
| Treynor index (mean / b) | 5.828 | ||||
| Jensen alpha (a) | -0.041 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.003 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.003 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1339.000 | ||||
| Minimum | 0.983 | ||||
| Quartile 1 | 0.999 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.001 | ||||
| Maximum | 1.013 | ||||
| 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 | 0.001 | ||||
| Number outliers low | 44.000 | ||||
| Percentage of outliers low | 0.033 | ||||
| Mean of outliers low | 0.996 | ||||
| Number of outliers high | 37.000 | ||||
| Percentage of outliers high | 0.028 | ||||
| Mean of outliers high | 1.004 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.266 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| Extreme Value Index (regression method) | 0.223 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | 0.002 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.005 | ||||
| Quartile 3 | 0.018 | ||||
| Maximum | 0.033 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.003 | ||||
| Mean of quarter 3 | 0.010 | ||||
| Mean of quarter 4 | 0.032 | ||||
| Inter Quartile Range | 0.016 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.011 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.011 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.110 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.050 | ||||
| SD | 0.013 | ||||
| Sharpe ratio (Glass type estimate) | -3.801 | ||||
| Sharpe ratio (Hedges UMVUE) | -3.779 | ||||
| df | 130.000 | ||||
| t | -2.688 | ||||
| p | 0.615 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -6.604 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.984 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -6.589 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.970 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -4.389 | ||||
| Upside Potential Ratio | 4.250 | ||||
| Upside part of mean | 0.049 | ||||
| Downside part of mean | -0.099 | ||||
| Upside SD | 0.007 | ||||
| Downside SD | 0.011 | ||||
| N nonnegative terms | 46.000 | ||||
| N negative terms | 85.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.159 | ||||
| Mean of criterion | -0.050 | ||||
| SD of predictor | 0.358 | ||||
| SD of criterion | 0.013 | ||||
| Covariance | 0.001 | ||||
| r | 0.309 | ||||
| b (slope, estimate of beta) | 0.011 | ||||
| a (intercept, estimate of alpha) | -0.063 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | 3.697 | ||||
| p(b) | 0.306 | ||||
| t(a) | -3.488 | ||||
| p(a) | 0.684 | ||||
| Lowerbound of 95% confidence interval for beta | 0.005 | ||||
| Upperbound of 95% confidence interval for beta | 0.018 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.100 | ||||
| Upperbound of 95% confidence interval for alpha | -0.027 | ||||
| Treynor index (mean / b) | -4.396 | ||||
| Jensen alpha (a) | -0.063 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.050 | ||||
| SD | 0.013 | ||||
| Sharpe ratio (Glass type estimate) | -3.807 | ||||
| Sharpe ratio (Hedges UMVUE) | -3.785 | ||||
| df | 130.000 | ||||
| t | -2.692 | ||||
| p | 0.615 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -6.610 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.990 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -6.595 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.975 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -4.393 | ||||
| Upside Potential Ratio | 4.244 | ||||
| Upside part of mean | 0.049 | ||||
| Downside part of mean | -0.099 | ||||
| Upside SD | 0.007 | ||||
| Downside SD | 0.011 | ||||
| N nonnegative terms | 46.000 | ||||
| N negative terms | 85.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.093 | ||||
| Mean of criterion | -0.050 | ||||
| SD of predictor | 0.358 | ||||
| SD of criterion | 0.013 | ||||
| Covariance | 0.001 | ||||
| r | 0.314 | ||||
| b (slope, estimate of beta) | 0.012 | ||||
| a (intercept, estimate of alpha) | -0.063 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | 3.761 | ||||
| p(b) | 0.303 | ||||
| t(a) | -3.475 | ||||
| p(a) | 0.684 | ||||
| Lowerbound of 95% confidence interval for beta | 0.006 | ||||
| Upperbound of 95% confidence interval for beta | 0.018 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.099 | ||||
| Upperbound of 95% confidence interval for alpha | -0.027 | ||||
| Treynor index (mean / b) | -4.331 | ||||
| Jensen alpha (a) | -0.063 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.002 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.002 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.997 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.003 | ||||
| Mean of quarter 1 | 0.999 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.001 | ||||
| Inter Quartile Range | 0.001 | ||||
| Number outliers low | 13.000 | ||||
| Percentage of outliers low | 0.099 | ||||
| Mean of outliers low | 0.998 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.023 | ||||
| Mean of outliers high | 1.002 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.928 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | -0.223 | ||||
| VaR(95%) (regression method) | 0.001 | ||||
| Expected Shortfall (regression method) | 0.001 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.001 | ||||
| Quartile 3 | 0.005 | ||||
| Maximum | 0.007 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.001 | ||||
| Mean of quarter 3 | 0.002 | ||||
| Mean of quarter 4 | 0.006 | ||||
| Inter Quartile Range | 0.005 | ||||
| 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) | -0.006 | ||||
| Compounded annual return (geometric extrapolation) | -0.006 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.955 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.977 | ||||
| Compounded annual return / Expected Shortfall lognormal | -3.357 | ||||