Advanced Statistics: Pussy Forex
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.059 | ||||
| SD | 0.505 | ||||
| Sharpe ratio (Glass type estimate) | 0.117 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.116 | ||||
| df | 96.000 | ||||
| t | 0.333 | ||||
| p | 0.370 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.573 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.807 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.573 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.806 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.209 | ||||
| Upside Potential Ratio | 1.814 | ||||
| Upside part of mean | 0.514 | ||||
| Downside part of mean | -0.454 | ||||
| Upside SD | 0.415 | ||||
| Downside SD | 0.283 | ||||
| N nonnegative terms | 47.000 | ||||
| N negative terms | 50.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 97.000 | ||||
| Mean of predictor | 0.115 | ||||
| Mean of criterion | 0.059 | ||||
| SD of predictor | 0.266 | ||||
| SD of criterion | 0.505 | ||||
| Covariance | 0.019 | ||||
| r | 0.141 | ||||
| b (slope, estimate of beta) | 0.266 | ||||
| a (intercept, estimate of alpha) | 0.028 | ||||
| Mean Square Error | 0.252 | ||||
| DF error | 95.000 | ||||
| t(b) | 1.383 | ||||
| p(b) | 0.085 | ||||
| t(a) | 0.160 | ||||
| p(a) | 0.437 | ||||
| Lowerbound of 95% confidence interval for beta | -0.116 | ||||
| Upperbound of 95% confidence interval for beta | 0.649 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.325 | ||||
| Upperbound of 95% confidence interval for alpha | 0.382 | ||||
| Treynor index (mean / b) | 0.222 | ||||
| Jensen alpha (a) | 0.028 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.051 | ||||
| SD | 0.465 | ||||
| Sharpe ratio (Glass type estimate) | -0.109 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.109 | ||||
| df | 96.000 | ||||
| t | -0.311 | ||||
| p | 0.622 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.799 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.580 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.798 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.581 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.151 | ||||
| Upside Potential Ratio | 1.342 | ||||
| Upside part of mean | 0.452 | ||||
| Downside part of mean | -0.503 | ||||
| Upside SD | 0.318 | ||||
| Downside SD | 0.337 | ||||
| N nonnegative terms | 47.000 | ||||
| N negative terms | 50.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 97.000 | ||||
| Mean of predictor | 0.078 | ||||
| Mean of criterion | -0.051 | ||||
| SD of predictor | 0.278 | ||||
| SD of criterion | 0.465 | ||||
| Covariance | 0.020 | ||||
| r | 0.156 | ||||
| b (slope, estimate of beta) | 0.261 | ||||
| a (intercept, estimate of alpha) | -0.071 | ||||
| Mean Square Error | 0.213 | ||||
| DF error | 95.000 | ||||
| t(b) | 1.537 | ||||
| p(b) | 0.064 | ||||
| t(a) | -0.437 | ||||
| p(a) | 0.668 | ||||
| Lowerbound of 95% confidence interval for beta | -0.076 | ||||
| Upperbound of 95% confidence interval for beta | 0.597 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.395 | ||||
| Upperbound of 95% confidence interval for alpha | 0.252 | ||||
| Treynor index (mean / b) | -0.195 | ||||
| Jensen alpha (a) | -0.071 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.202 | ||||
| Expected Shortfall on VaR | 0.244 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.089 | ||||
| Expected Shortfall on VaR | 0.177 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 97.000 | ||||
| Minimum | 0.563 | ||||
| Quartile 1 | 0.948 | ||||
| Median | 1.003 | ||||
| Quartile 3 | 1.054 | ||||
| Maximum | 2.000 | ||||
| Mean of quarter 1 | 0.879 | ||||
| Mean of quarter 2 | 0.980 | ||||
| Mean of quarter 3 | 1.024 | ||||
| Mean of quarter 4 | 1.156 | ||||
| Inter Quartile Range | 0.106 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.041 | ||||
| Mean of outliers low | 0.668 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.031 | ||||
| Mean of outliers high | 1.498 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.558 | ||||
| VaR(95%) (moments method) | 0.139 | ||||
| Expected Shortfall (moments method) | 0.325 | ||||
| Extreme Value Index (regression method) | 0.541 | ||||
| VaR(95%) (regression method) | 0.116 | ||||
| Expected Shortfall (regression method) | 0.244 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.019 | ||||
| Quartile 1 | 0.058 | ||||
| Median | 0.086 | ||||
| Quartile 3 | 0.087 | ||||
| Maximum | 0.734 | ||||
| Mean of quarter 1 | 0.038 | ||||
| Mean of quarter 2 | 0.086 | ||||
| Mean of quarter 3 | 0.087 | ||||
| Mean of quarter 4 | 0.734 | ||||
| Inter Quartile Range | 0.029 | ||||
| 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 | 0.200 | ||||
| Mean of outliers high | 0.734 | ||||
| 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) | -0.007 | ||||
| Compounded annual return (geometric extrapolation) | -0.007 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.009 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.009 | ||||
| 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 | 1.134 | ||||
| SD | 1.721 | ||||
| Sharpe ratio (Glass type estimate) | 0.659 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.659 | ||||
| df | 2133.000 | ||||
| t | 1.882 | ||||
| p | 0.030 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.028 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.346 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.028 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.346 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.438 | ||||
| Upside Potential Ratio | 5.751 | ||||
| Upside part of mean | 4.537 | ||||
| Downside part of mean | -3.403 | ||||
| Upside SD | 1.530 | ||||
| Downside SD | 0.789 | ||||
| N nonnegative terms | 1013.000 | ||||
| N negative terms | 1121.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2134.000 | ||||
| Mean of predictor | 0.328 | ||||
| Mean of criterion | 1.134 | ||||
| SD of predictor | 0.591 | ||||
| SD of criterion | 1.721 | ||||
| Covariance | 0.402 | ||||
| r | 0.395 | ||||
| b (slope, estimate of beta) | 1.151 | ||||
| a (intercept, estimate of alpha) | 0.757 | ||||
| Mean Square Error | 2.499 | ||||
| DF error | 2132.000 | ||||
| t(b) | 19.871 | ||||
| p(b) | 0.000 | ||||
| t(a) | 1.365 | ||||
| p(a) | 0.086 | ||||
| Lowerbound of 95% confidence interval for beta | 1.038 | ||||
| Upperbound of 95% confidence interval for beta | 1.265 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.330 | ||||
| Upperbound of 95% confidence interval for alpha | 1.843 | ||||
| Treynor index (mean / b) | 0.985 | ||||
| Jensen alpha (a) | 0.757 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.013 | ||||
| SD | 1.479 | ||||
| Sharpe ratio (Glass type estimate) | -0.009 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.009 | ||||
| df | 2133.000 | ||||
| t | -0.024 | ||||
| p | 0.510 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.695 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.678 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.695 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.678 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.012 | ||||
| Upside Potential Ratio | 3.689 | ||||
| Upside part of mean | 3.835 | ||||
| Downside part of mean | -3.848 | ||||
| Upside SD | 1.051 | ||||
| Downside SD | 1.040 | ||||
| N nonnegative terms | 1013.000 | ||||
| N negative terms | 1121.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2134.000 | ||||
| Mean of predictor | 0.156 | ||||
| Mean of criterion | -0.013 | ||||
| SD of predictor | 0.587 | ||||
| SD of criterion | 1.479 | ||||
| Covariance | 0.345 | ||||
| r | 0.397 | ||||
| b (slope, estimate of beta) | 0.999 | ||||
| a (intercept, estimate of alpha) | -0.168 | ||||
| Mean Square Error | 1.844 | ||||
| DF error | 2132.000 | ||||
| t(b) | 19.955 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.354 | ||||
| p(a) | 0.638 | ||||
| Lowerbound of 95% confidence interval for beta | 0.901 | ||||
| Upperbound of 95% confidence interval for beta | 1.097 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.102 | ||||
| Upperbound of 95% confidence interval for alpha | 0.765 | ||||
| Treynor index (mean / b) | -0.013 | ||||
| Jensen alpha (a) | -0.168 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.140 | ||||
| Expected Shortfall on VaR | 0.171 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.030 | ||||
| Expected Shortfall on VaR | 0.068 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2134.000 | ||||
| Minimum | 0.315 | ||||
| Quartile 1 | 0.990 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.010 | ||||
| Maximum | 3.335 | ||||
| Mean of quarter 1 | 0.953 | ||||
| Mean of quarter 2 | 0.996 | ||||
| Mean of quarter 3 | 1.004 | ||||
| Mean of quarter 4 | 1.065 | ||||
| Inter Quartile Range | 0.021 | ||||
| Number outliers low | 124.000 | ||||
| Percentage of outliers low | 0.058 | ||||
| Mean of outliers low | 0.864 | ||||
| Number of outliers high | 133.000 | ||||
| Percentage of outliers high | 0.062 | ||||
| Mean of outliers high | 1.199 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.828 | ||||
| VaR(95%) (moments method) | 0.044 | ||||
| Expected Shortfall (moments method) | 0.264 | ||||
| Extreme Value Index (regression method) | 0.621 | ||||
| VaR(95%) (regression method) | 0.031 | ||||
| Expected Shortfall (regression method) | 0.083 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 12.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.004 | ||||
| Median | 0.034 | ||||
| Quartile 3 | 0.312 | ||||
| Maximum | 0.782 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.013 | ||||
| Mean of quarter 3 | 0.125 | ||||
| Mean of quarter 4 | 0.675 | ||||
| Inter Quartile Range | 0.308 | ||||
| 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 | 0.083 | ||||
| Mean of outliers high | 0.782 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -13.514 | ||||
| VaR(95%) (moments method) | 0.724 | ||||
| Expected Shortfall (moments method) | 0.724 | ||||
| Extreme Value Index (regression method) | -1.864 | ||||
| VaR(95%) (regression method) | 0.875 | ||||
| Expected Shortfall (regression method) | 0.888 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.036 | ||||
| Compounded annual return (geometric extrapolation) | 0.032 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.041 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.047 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.186 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.614 | ||||
| SD | 0.624 | ||||
| Sharpe ratio (Glass type estimate) | 0.983 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.978 | ||||
| df | 130.000 | ||||
| t | 0.695 | ||||
| p | 0.470 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.793 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.756 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.797 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.752 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.621 | ||||
| Upside Potential Ratio | 9.513 | ||||
| Upside part of mean | 3.602 | ||||
| Downside part of mean | -2.988 | ||||
| Upside SD | 0.495 | ||||
| Downside SD | 0.379 | ||||
| N nonnegative terms | 60.000 | ||||
| N negative terms | 71.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 2.070 | ||||
| Mean of criterion | 0.614 | ||||
| SD of predictor | 0.561 | ||||
| SD of criterion | 0.624 | ||||
| Covariance | 0.038 | ||||
| r | 0.109 | ||||
| b (slope, estimate of beta) | 0.121 | ||||
| a (intercept, estimate of alpha) | 0.364 | ||||
| Mean Square Error | 0.388 | ||||
| DF error | 129.000 | ||||
| t(b) | 1.242 | ||||
| p(b) | 0.431 | ||||
| t(a) | 0.402 | ||||
| p(a) | 0.477 | ||||
| Lowerbound of 95% confidence interval for beta | -0.072 | ||||
| Upperbound of 95% confidence interval for beta | 0.314 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.424 | ||||
| Upperbound of 95% confidence interval for alpha | 2.151 | ||||
| Treynor index (mean / b) | 5.076 | ||||
| Jensen alpha (a) | 0.364 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.424 | ||||
| SD | 0.616 | ||||
| Sharpe ratio (Glass type estimate) | 0.688 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.684 | ||||
| df | 130.000 | ||||
| t | 0.486 | ||||
| p | 0.479 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.086 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.460 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.089 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.457 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.073 | ||||
| Upside Potential Ratio | 8.833 | ||||
| Upside part of mean | 3.487 | ||||
| Downside part of mean | -3.063 | ||||
| Upside SD | 0.470 | ||||
| Downside SD | 0.395 | ||||
| N nonnegative terms | 60.000 | ||||
| N negative terms | 71.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.904 | ||||
| Mean of criterion | 0.424 | ||||
| SD of predictor | 0.565 | ||||
| SD of criterion | 0.616 | ||||
| Covariance | 0.034 | ||||
| r | 0.099 | ||||
| b (slope, estimate of beta) | 0.108 | ||||
| a (intercept, estimate of alpha) | 0.219 | ||||
| Mean Square Error | 0.378 | ||||
| DF error | 129.000 | ||||
| t(b) | 1.128 | ||||
| p(b) | 0.437 | ||||
| t(a) | 0.246 | ||||
| p(a) | 0.486 | ||||
| Lowerbound of 95% confidence interval for beta | -0.081 | ||||
| Upperbound of 95% confidence interval for beta | 0.296 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.540 | ||||
| Upperbound of 95% confidence interval for alpha | 1.977 | ||||
| Treynor index (mean / b) | 3.935 | ||||
| Jensen alpha (a) | 0.219 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.059 | ||||
| Expected Shortfall on VaR | 0.074 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.054 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.855 | ||||
| Quartile 1 | 0.984 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.014 | ||||
| Maximum | 1.197 | ||||
| Mean of quarter 1 | 0.962 | ||||
| Mean of quarter 2 | 0.993 | ||||
| Mean of quarter 3 | 1.006 | ||||
| Mean of quarter 4 | 1.049 | ||||
| Inter Quartile Range | 0.030 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.031 | ||||
| Mean of outliers low | 0.905 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.069 | ||||
| Mean of outliers high | 1.094 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.229 | ||||
| VaR(95%) (moments method) | 0.038 | ||||
| Expected Shortfall (moments method) | 0.060 | ||||
| Extreme Value Index (regression method) | 0.181 | ||||
| VaR(95%) (regression method) | 0.037 | ||||
| Expected Shortfall (regression method) | 0.056 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.011 | ||||
| Quartile 1 | 0.018 | ||||
| Median | 0.025 | ||||
| Quartile 3 | 0.128 | ||||
| Maximum | 0.385 | ||||
| Mean of quarter 1 | 0.013 | ||||
| Mean of quarter 2 | 0.023 | ||||
| Mean of quarter 3 | 0.091 | ||||
| Mean of quarter 4 | 0.275 | ||||
| Inter Quartile Range | 0.110 | ||||
| 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 | 0.385 | ||||
| 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) | 0.527 | ||||
| Compounded annual return (geometric extrapolation) | 0.596 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.550 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.171 | ||||
| Compounded annual return / Expected Shortfall lognormal | 8.070 | ||||