Advanced Statistics: forex trends
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 | 0.581 | ||||
| SD | 0.867 | ||||
| Sharpe ratio (Glass type estimate) | 0.671 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.665 | ||||
| df | 95.000 | ||||
| t | 1.897 | ||||
| p | 0.030 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.031 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.368 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.034 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.365 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.562 | ||||
| Upside Potential Ratio | 3.141 | ||||
| Upside part of mean | 1.169 | ||||
| Downside part of mean | -0.587 | ||||
| Upside SD | 0.796 | ||||
| Downside SD | 0.372 | ||||
| N nonnegative terms | 46.000 | ||||
| N negative terms | 50.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 96.000 | ||||
| Mean of predictor | 0.251 | ||||
| Mean of criterion | 0.581 | ||||
| SD of predictor | 0.236 | ||||
| SD of criterion | 0.867 | ||||
| Covariance | 0.030 | ||||
| r | 0.148 | ||||
| b (slope, estimate of beta) | 0.545 | ||||
| a (intercept, estimate of alpha) | 0.444 | ||||
| Mean Square Error | 0.743 | ||||
| DF error | 94.000 | ||||
| t(b) | 1.452 | ||||
| p(b) | 0.075 | ||||
| t(a) | 1.393 | ||||
| p(a) | 0.083 | ||||
| Lowerbound of 95% confidence interval for beta | -0.200 | ||||
| Upperbound of 95% confidence interval for beta | 1.290 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.189 | ||||
| Upperbound of 95% confidence interval for alpha | 1.078 | ||||
| Treynor index (mean / b) | 1.067 | ||||
| Jensen alpha (a) | 0.444 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.274 | ||||
| SD | 0.759 | ||||
| Sharpe ratio (Glass type estimate) | 0.361 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.358 | ||||
| df | 95.000 | ||||
| t | 1.022 | ||||
| p | 0.155 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.335 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.055 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.336 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.053 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.567 | ||||
| Upside Potential Ratio | 1.978 | ||||
| Upside part of mean | 0.956 | ||||
| Downside part of mean | -0.682 | ||||
| Upside SD | 0.586 | ||||
| Downside SD | 0.483 | ||||
| N nonnegative terms | 46.000 | ||||
| N negative terms | 50.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 96.000 | ||||
| Mean of predictor | 0.222 | ||||
| Mean of criterion | 0.274 | ||||
| SD of predictor | 0.227 | ||||
| SD of criterion | 0.759 | ||||
| Covariance | 0.029 | ||||
| r | 0.167 | ||||
| b (slope, estimate of beta) | 0.559 | ||||
| a (intercept, estimate of alpha) | 0.150 | ||||
| Mean Square Error | 0.566 | ||||
| DF error | 94.000 | ||||
| t(b) | 1.647 | ||||
| p(b) | 0.051 | ||||
| t(a) | 0.543 | ||||
| p(a) | 0.294 | ||||
| Lowerbound of 95% confidence interval for beta | -0.115 | ||||
| Upperbound of 95% confidence interval for beta | 1.233 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.399 | ||||
| Upperbound of 95% confidence interval for alpha | 0.699 | ||||
| Treynor index (mean / b) | 0.491 | ||||
| Jensen alpha (a) | 0.150 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.287 | ||||
| Expected Shortfall on VaR | 0.347 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.115 | ||||
| Expected Shortfall on VaR | 0.231 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 96.000 | ||||
| Minimum | 0.388 | ||||
| Quartile 1 | 0.939 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.100 | ||||
| Maximum | 2.451 | ||||
| Mean of quarter 1 | 0.831 | ||||
| Mean of quarter 2 | 0.981 | ||||
| Mean of quarter 3 | 1.051 | ||||
| Mean of quarter 4 | 1.346 | ||||
| Inter Quartile Range | 0.160 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.042 | ||||
| Mean of outliers low | 0.597 | ||||
| Number of outliers high | 8.000 | ||||
| Percentage of outliers high | 0.083 | ||||
| Mean of outliers high | 1.681 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.335 | ||||
| VaR(95%) (moments method) | 0.171 | ||||
| Expected Shortfall (moments method) | 0.302 | ||||
| Extreme Value Index (regression method) | 0.523 | ||||
| VaR(95%) (regression method) | 0.156 | ||||
| Expected Shortfall (regression method) | 0.333 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.024 | ||||
| Median | 0.262 | ||||
| Quartile 3 | 0.455 | ||||
| Maximum | 0.612 | ||||
| Mean of quarter 1 | 0.016 | ||||
| Mean of quarter 2 | 0.161 | ||||
| Mean of quarter 3 | 0.418 | ||||
| Mean of quarter 4 | 0.590 | ||||
| Inter Quartile Range | 0.431 | ||||
| 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) | -23.181 | ||||
| VaR(95%) (moments method) | 0.578 | ||||
| Expected Shortfall (moments method) | 0.578 | ||||
| Extreme Value Index (regression method) | -2.354 | ||||
| VaR(95%) (regression method) | 0.701 | ||||
| Expected Shortfall (regression method) | 0.703 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 1.470 | ||||
| Compounded annual return (geometric extrapolation) | 0.375 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.612 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.635 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.080 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.785 | ||||
| SD | 1.094 | ||||
| Sharpe ratio (Glass type estimate) | 0.717 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.717 | ||||
| df | 2095.000 | ||||
| t | 2.028 | ||||
| p | 0.021 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.024 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.410 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.023 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.410 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.361 | ||||
| Upside Potential Ratio | 7.390 | ||||
| Upside part of mean | 4.261 | ||||
| Downside part of mean | -3.476 | ||||
| Upside SD | 0.931 | ||||
| Downside SD | 0.577 | ||||
| N nonnegative terms | 889.000 | ||||
| N negative terms | 1207.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2096.000 | ||||
| Mean of predictor | 0.269 | ||||
| Mean of criterion | 0.785 | ||||
| SD of predictor | 0.306 | ||||
| SD of criterion | 1.094 | ||||
| Covariance | 0.129 | ||||
| r | 0.387 | ||||
| b (slope, estimate of beta) | 1.386 | ||||
| a (intercept, estimate of alpha) | 0.412 | ||||
| Mean Square Error | 1.019 | ||||
| DF error | 2094.000 | ||||
| t(b) | 19.208 | ||||
| p(b) | 0.000 | ||||
| t(a) | 1.153 | ||||
| p(a) | 0.125 | ||||
| Lowerbound of 95% confidence interval for beta | 1.244 | ||||
| Upperbound of 95% confidence interval for beta | 1.527 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.289 | ||||
| Upperbound of 95% confidence interval for alpha | 1.113 | ||||
| Treynor index (mean / b) | 0.566 | ||||
| Jensen alpha (a) | 0.412 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.274 | ||||
| SD | 0.988 | ||||
| Sharpe ratio (Glass type estimate) | 0.277 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.277 | ||||
| df | 2095.000 | ||||
| t | 0.785 | ||||
| p | 0.216 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.416 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.970 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.416 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.970 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.412 | ||||
| Upside Potential Ratio | 5.936 | ||||
| Upside part of mean | 3.950 | ||||
| Downside part of mean | -3.676 | ||||
| Upside SD | 0.731 | ||||
| Downside SD | 0.665 | ||||
| N nonnegative terms | 889.000 | ||||
| N negative terms | 1207.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2096.000 | ||||
| Mean of predictor | 0.222 | ||||
| Mean of criterion | 0.274 | ||||
| SD of predictor | 0.305 | ||||
| SD of criterion | 0.988 | ||||
| Covariance | 0.116 | ||||
| r | 0.385 | ||||
| b (slope, estimate of beta) | 1.247 | ||||
| a (intercept, estimate of alpha) | -0.003 | ||||
| Mean Square Error | 0.833 | ||||
| DF error | 2094.000 | ||||
| t(b) | 19.060 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.009 | ||||
| p(a) | 0.503 | ||||
| Lowerbound of 95% confidence interval for beta | 1.119 | ||||
| Upperbound of 95% confidence interval for beta | 1.375 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.636 | ||||
| Upperbound of 95% confidence interval for alpha | 0.631 | ||||
| Treynor index (mean / b) | 0.220 | ||||
| Jensen alpha (a) | -0.003 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.095 | ||||
| Expected Shortfall on VaR | 0.117 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.033 | ||||
| Expected Shortfall on VaR | 0.070 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2096.000 | ||||
| Minimum | 0.449 | ||||
| Quartile 1 | 0.986 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.017 | ||||
| Maximum | 2.290 | ||||
| Mean of quarter 1 | 0.951 | ||||
| Mean of quarter 2 | 0.996 | ||||
| Mean of quarter 3 | 1.005 | ||||
| Mean of quarter 4 | 1.060 | ||||
| Inter Quartile Range | 0.030 | ||||
| Number outliers low | 115.000 | ||||
| Percentage of outliers low | 0.055 | ||||
| Mean of outliers low | 0.884 | ||||
| Number of outliers high | 134.000 | ||||
| Percentage of outliers high | 0.064 | ||||
| Mean of outliers high | 1.139 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.422 | ||||
| VaR(95%) (moments method) | 0.045 | ||||
| Expected Shortfall (moments method) | 0.091 | ||||
| Extreme Value Index (regression method) | 0.361 | ||||
| VaR(95%) (regression method) | 0.041 | ||||
| Expected Shortfall (regression method) | 0.075 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 57.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.008 | ||||
| Median | 0.041 | ||||
| Quartile 3 | 0.150 | ||||
| Maximum | 0.740 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.023 | ||||
| Mean of quarter 3 | 0.089 | ||||
| Mean of quarter 4 | 0.373 | ||||
| Inter Quartile Range | 0.141 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.105 | ||||
| Mean of outliers high | 0.571 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.140 | ||||
| VaR(95%) (moments method) | 0.358 | ||||
| Expected Shortfall (moments method) | 0.528 | ||||
| Extreme Value Index (regression method) | -0.037 | ||||
| VaR(95%) (regression method) | 0.402 | ||||
| Expected Shortfall (regression method) | 0.545 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 1.470 | ||||
| Compounded annual return (geometric extrapolation) | 0.375 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.506 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.006 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.197 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.747 | ||||
| SD | 0.672 | ||||
| Sharpe ratio (Glass type estimate) | -1.112 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.106 | ||||
| df | 130.000 | ||||
| t | -0.787 | ||||
| p | 0.534 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.885 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.665 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.881 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.669 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.559 | ||||
| Upside Potential Ratio | 7.291 | ||||
| Upside part of mean | 3.494 | ||||
| Downside part of mean | -4.241 | ||||
| Upside SD | 0.469 | ||||
| Downside SD | 0.479 | ||||
| N nonnegative terms | 49.000 | ||||
| N negative terms | 82.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.997 | ||||
| Mean of criterion | -0.747 | ||||
| SD of predictor | 0.423 | ||||
| SD of criterion | 0.672 | ||||
| Covariance | 0.118 | ||||
| r | 0.416 | ||||
| b (slope, estimate of beta) | 0.660 | ||||
| a (intercept, estimate of alpha) | -1.405 | ||||
| Mean Square Error | 0.376 | ||||
| DF error | 129.000 | ||||
| t(b) | 5.189 | ||||
| p(b) | 0.243 | ||||
| t(a) | -1.602 | ||||
| p(a) | 0.589 | ||||
| Lowerbound of 95% confidence interval for beta | 0.408 | ||||
| Upperbound of 95% confidence interval for beta | 0.911 | ||||
| Lowerbound of 95% confidence interval for alpha | -3.139 | ||||
| Upperbound of 95% confidence interval for alpha | 0.330 | ||||
| Treynor index (mean / b) | -1.133 | ||||
| Jensen alpha (a) | -1.405 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.972 | ||||
| SD | 0.671 | ||||
| Sharpe ratio (Glass type estimate) | -1.448 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.439 | ||||
| df | 130.000 | ||||
| t | -1.024 | ||||
| p | 0.545 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.222 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.332 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.217 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.338 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.953 | ||||
| Upside Potential Ratio | 6.808 | ||||
| Upside part of mean | 3.389 | ||||
| Downside part of mean | -4.361 | ||||
| Upside SD | 0.451 | ||||
| Downside SD | 0.498 | ||||
| N nonnegative terms | 49.000 | ||||
| N negative terms | 82.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.907 | ||||
| Mean of criterion | -0.972 | ||||
| SD of predictor | 0.421 | ||||
| SD of criterion | 0.671 | ||||
| Covariance | 0.120 | ||||
| r | 0.424 | ||||
| b (slope, estimate of beta) | 0.676 | ||||
| a (intercept, estimate of alpha) | -1.585 | ||||
| Mean Square Error | 0.373 | ||||
| DF error | 129.000 | ||||
| t(b) | 5.313 | ||||
| p(b) | 0.239 | ||||
| t(a) | -1.820 | ||||
| p(a) | 0.600 | ||||
| Lowerbound of 95% confidence interval for beta | 0.424 | ||||
| Upperbound of 95% confidence interval for beta | 0.928 | ||||
| Lowerbound of 95% confidence interval for alpha | -3.309 | ||||
| Upperbound of 95% confidence interval for alpha | 0.138 | ||||
| Treynor index (mean / b) | -1.438 | ||||
| Jensen alpha (a) | -1.585 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.069 | ||||
| Expected Shortfall on VaR | 0.085 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.043 | ||||
| Expected Shortfall on VaR | 0.076 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.865 | ||||
| Quartile 1 | 0.973 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.020 | ||||
| Maximum | 1.125 | ||||
| Mean of quarter 1 | 0.948 | ||||
| Mean of quarter 2 | 0.988 | ||||
| Mean of quarter 3 | 1.004 | ||||
| Mean of quarter 4 | 1.050 | ||||
| Inter Quartile Range | 0.047 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.008 | ||||
| Mean of outliers low | 0.865 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.031 | ||||
| Mean of outliers high | 1.114 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.059 | ||||
| VaR(95%) (moments method) | 0.054 | ||||
| Expected Shortfall (moments method) | 0.072 | ||||
| Extreme Value Index (regression method) | 0.031 | ||||
| VaR(95%) (regression method) | 0.059 | ||||
| Expected Shortfall (regression method) | 0.078 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.479 | ||||
| Quartile 1 | 0.479 | ||||
| Median | 0.479 | ||||
| Quartile 3 | 0.479 | ||||
| Maximum | 0.479 | ||||
| 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) | -0.743 | ||||
| Compounded annual return (geometric extrapolation) | -0.605 | ||||
| Calmar ratio (compounded annual return / max draw down) | -1.261 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -7.089 | ||||