Advanced Statistics: Spear Group 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 | -0.152 | ||||
| SD | 0.938 | ||||
| Sharpe ratio (Glass type estimate) | -0.162 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.158 | ||||
| df | 37.000 | ||||
| t | -0.288 | ||||
| p | 0.612 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.263 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.941 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.260 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.944 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.198 | ||||
| Upside Potential Ratio | 0.678 | ||||
| Upside part of mean | 0.519 | ||||
| Downside part of mean | -0.670 | ||||
| Upside SD | 0.523 | ||||
| Downside SD | 0.765 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 38.000 | ||||
| Mean of predictor | 0.485 | ||||
| Mean of criterion | -0.152 | ||||
| SD of predictor | 0.240 | ||||
| SD of criterion | 0.938 | ||||
| Covariance | -0.030 | ||||
| r | -0.133 | ||||
| b (slope, estimate of beta) | -0.520 | ||||
| a (intercept, estimate of alpha) | 0.100 | ||||
| Mean Square Error | 0.888 | ||||
| DF error | 36.000 | ||||
| t(b) | -0.806 | ||||
| p(b) | 0.787 | ||||
| t(a) | 0.163 | ||||
| p(a) | 0.436 | ||||
| Lowerbound of 95% confidence interval for beta | -1.829 | ||||
| Upperbound of 95% confidence interval for beta | 0.789 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.147 | ||||
| Upperbound of 95% confidence interval for alpha | 1.348 | ||||
| Treynor index (mean / b) | 0.292 | ||||
| Jensen alpha (a) | 0.100 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.953 | ||||
| SD | 4.723 | ||||
| Sharpe ratio (Glass type estimate) | -0.625 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.613 | ||||
| df | 37.000 | ||||
| t | -1.113 | ||||
| p | 0.864 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.732 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.489 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.723 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.498 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.626 | ||||
| Upside Potential Ratio | 0.089 | ||||
| Upside part of mean | 0.422 | ||||
| Downside part of mean | -3.375 | ||||
| Upside SD | 0.400 | ||||
| Downside SD | 4.721 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 38.000 | ||||
| Mean of predictor | 0.448 | ||||
| Mean of criterion | -2.953 | ||||
| SD of predictor | 0.226 | ||||
| SD of criterion | 4.723 | ||||
| Covariance | -0.069 | ||||
| r | -0.064 | ||||
| b (slope, estimate of beta) | -1.348 | ||||
| a (intercept, estimate of alpha) | -2.349 | ||||
| Mean Square Error | 22.832 | ||||
| DF error | 36.000 | ||||
| t(b) | -0.388 | ||||
| p(b) | 0.650 | ||||
| t(a) | -0.757 | ||||
| p(a) | 0.773 | ||||
| Lowerbound of 95% confidence interval for beta | -8.400 | ||||
| Upperbound of 95% confidence interval for beta | 5.703 | ||||
| Lowerbound of 95% confidence interval for alpha | -8.646 | ||||
| Upperbound of 95% confidence interval for alpha | 3.948 | ||||
| Treynor index (mean / b) | 2.190 | ||||
| Jensen alpha (a) | -2.349 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.917 | ||||
| Expected Shortfall on VaR | 0.948 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.175 | ||||
| Expected Shortfall on VaR | 0.383 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 38.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.822 | ||||
| Mean of quarter 1 | 0.800 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.166 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.105 | ||||
| Mean of outliers low | 0.499 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.158 | ||||
| Mean of outliers high | 1.277 | ||||
| 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) | 0.132 | ||||
| VaR(95%) (regression method) | 0.165 | ||||
| Expected Shortfall (regression method) | 0.379 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.037 | ||||
| Quartile 1 | 0.278 | ||||
| Median | 0.519 | ||||
| Quartile 3 | 0.759 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.037 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.481 | ||||
| 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) | -0.316 | ||||
| Compounded annual return (geometric extrapolation) | -0.945 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.946 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.946 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.997 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 662.974 | ||||
| SD | 1194.029 | ||||
| Sharpe ratio (Glass type estimate) | 0.555 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.555 | ||||
| df | 849.000 | ||||
| t | 1.000 | ||||
| p | 0.159 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.533 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.644 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.534 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.643 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 529.284 | ||||
| Upside Potential Ratio | 532.289 | ||||
| Upside part of mean | 666.739 | ||||
| Downside part of mean | -3.764 | ||||
| Upside SD | 1194.028 | ||||
| Downside SD | 1.253 | ||||
| N nonnegative terms | 97.000 | ||||
| N negative terms | 753.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 850.000 | ||||
| Mean of predictor | 0.564 | ||||
| Mean of criterion | 662.974 | ||||
| SD of predictor | 0.357 | ||||
| SD of criterion | 1194.029 | ||||
| Covariance | 28.751 | ||||
| r | 0.067 | ||||
| b (slope, estimate of beta) | 225.525 | ||||
| a (intercept, estimate of alpha) | 535.887 | ||||
| Mean Square Error | 1420894.728 | ||||
| DF error | 848.000 | ||||
| t(b) | 1.968 | ||||
| p(b) | 0.025 | ||||
| t(a) | 0.806 | ||||
| p(a) | 0.210 | ||||
| Lowerbound of 95% confidence interval for beta | 0.638 | ||||
| Upperbound of 95% confidence interval for beta | 450.411 | ||||
| Lowerbound of 95% confidence interval for alpha | -769.225 | ||||
| Upperbound of 95% confidence interval for alpha | 1840.999 | ||||
| Treynor index (mean / b) | 2.940 | ||||
| Jensen alpha (a) | 535.887 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.884 | ||||
| SD | 7.219 | ||||
| Sharpe ratio (Glass type estimate) | -0.399 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.399 | ||||
| df | 849.000 | ||||
| t | -0.720 | ||||
| p | 0.764 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.488 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.689 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.487 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.689 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.505 | ||||
| Upside Potential Ratio | 0.937 | ||||
| Upside part of mean | 5.349 | ||||
| Downside part of mean | -8.233 | ||||
| Upside SD | 4.414 | ||||
| Downside SD | 5.710 | ||||
| N nonnegative terms | 97.000 | ||||
| N negative terms | 753.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 850.000 | ||||
| Mean of predictor | 0.496 | ||||
| Mean of criterion | -2.884 | ||||
| SD of predictor | 0.372 | ||||
| SD of criterion | 7.219 | ||||
| Covariance | 0.110 | ||||
| r | 0.041 | ||||
| b (slope, estimate of beta) | 0.798 | ||||
| a (intercept, estimate of alpha) | -3.280 | ||||
| Mean Square Error | 52.088 | ||||
| DF error | 848.000 | ||||
| t(b) | 1.198 | ||||
| p(b) | 0.116 | ||||
| t(a) | -0.816 | ||||
| p(a) | 0.793 | ||||
| Lowerbound of 95% confidence interval for beta | -0.510 | ||||
| Upperbound of 95% confidence interval for beta | 2.106 | ||||
| Lowerbound of 95% confidence interval for alpha | -11.171 | ||||
| Upperbound of 95% confidence interval for alpha | 4.612 | ||||
| Treynor index (mean / b) | -3.612 | ||||
| Jensen alpha (a) | -3.280 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.525 | ||||
| Expected Shortfall on VaR | 0.601 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.046 | ||||
| Expected Shortfall on VaR | 0.104 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 850.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2151.667 | ||||
| Mean of quarter 1 | 0.943 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 11.155 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 78.000 | ||||
| Percentage of outliers low | 0.092 | ||||
| Mean of outliers low | 0.845 | ||||
| Number of outliers high | 97.000 | ||||
| Percentage of outliers high | 0.114 | ||||
| Mean of outliers high | 23.300 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.218 | ||||
| VaR(95%) (moments method) | 0.005 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.186 | ||||
| VaR(95%) (regression method) | 0.040 | ||||
| Expected Shortfall (regression method) | 0.125 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 11.000 | ||||
| Minimum | 0.007 | ||||
| Quartile 1 | 0.020 | ||||
| Median | 0.055 | ||||
| Quartile 3 | 0.089 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.010 | ||||
| Mean of quarter 2 | 0.037 | ||||
| Mean of quarter 3 | 0.060 | ||||
| Mean of quarter 4 | 0.427 | ||||
| Inter Quartile Range | 0.070 | ||||
| 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 | 0.091 | ||||
| Mean of outliers high | 1.000 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.765 | ||||
| VaR(95%) (moments method) | 0.436 | ||||
| Expected Shortfall (moments method) | 2.096 | ||||
| Extreme Value Index (regression method) | 3.001 | ||||
| VaR(95%) (regression method) | 1.391 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.308 | ||||
| Compounded annual return (geometric extrapolation) | -0.942 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.942 | ||||
| Compounded annual return / average of 25% largest draw downs | -2.204 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.567 | ||||
| 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 | 1.068 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.512 | ||||
| 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 | 0.935 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.517 | ||||
| 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) | -8744953286033832.000 | ||||
| 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) | 168531396080312072030733985644544.000 | ||||
| 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 | ||||