Advanced Statistics: THRIVING FX
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 | 0.057 | ||||
| SD | 0.383 | ||||
| Sharpe ratio (Glass type estimate) | 0.150 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.147 | ||||
| df | 36.000 | ||||
| t | 0.263 | ||||
| p | 0.397 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.968 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.266 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.970 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.263 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.255 | ||||
| Upside Potential Ratio | 1.831 | ||||
| Upside part of mean | 0.413 | ||||
| Downside part of mean | -0.355 | ||||
| Upside SD | 0.304 | ||||
| Downside SD | 0.226 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 20.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 37.000 | ||||
| Mean of predictor | 0.560 | ||||
| Mean of criterion | 0.057 | ||||
| SD of predictor | 0.228 | ||||
| SD of criterion | 0.383 | ||||
| Covariance | 0.027 | ||||
| r | 0.312 | ||||
| b (slope, estimate of beta) | 0.524 | ||||
| a (intercept, estimate of alpha) | -0.236 | ||||
| Mean Square Error | 0.136 | ||||
| DF error | 35.000 | ||||
| t(b) | 1.944 | ||||
| p(b) | 0.030 | ||||
| t(a) | -0.913 | ||||
| p(a) | 0.816 | ||||
| Lowerbound of 95% confidence interval for beta | -0.023 | ||||
| Upperbound of 95% confidence interval for beta | 1.071 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.762 | ||||
| Upperbound of 95% confidence interval for alpha | 0.289 | ||||
| Treynor index (mean / b) | 0.110 | ||||
| Jensen alpha (a) | -0.236 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.009 | ||||
| SD | 0.366 | ||||
| Sharpe ratio (Glass type estimate) | -0.025 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.025 | ||||
| df | 36.000 | ||||
| t | -0.045 | ||||
| p | 0.518 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.141 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.091 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.141 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.091 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.037 | ||||
| Upside Potential Ratio | 1.476 | ||||
| Upside part of mean | 0.375 | ||||
| Downside part of mean | -0.384 | ||||
| Upside SD | 0.257 | ||||
| Downside SD | 0.254 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 20.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 37.000 | ||||
| Mean of predictor | 0.523 | ||||
| Mean of criterion | -0.009 | ||||
| SD of predictor | 0.215 | ||||
| SD of criterion | 0.366 | ||||
| Covariance | 0.024 | ||||
| r | 0.306 | ||||
| b (slope, estimate of beta) | 0.521 | ||||
| a (intercept, estimate of alpha) | -0.282 | ||||
| Mean Square Error | 0.125 | ||||
| DF error | 35.000 | ||||
| t(b) | 1.900 | ||||
| p(b) | 0.033 | ||||
| t(a) | -1.138 | ||||
| p(a) | 0.869 | ||||
| Lowerbound of 95% confidence interval for beta | -0.036 | ||||
| Upperbound of 95% confidence interval for beta | 1.077 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.783 | ||||
| Upperbound of 95% confidence interval for alpha | 0.220 | ||||
| Treynor index (mean / b) | -0.018 | ||||
| Jensen alpha (a) | -0.282 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.160 | ||||
| Expected Shortfall on VaR | 0.196 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.071 | ||||
| Expected Shortfall on VaR | 0.143 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 37.000 | ||||
| Minimum | 0.734 | ||||
| Quartile 1 | 0.970 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.041 | ||||
| Maximum | 1.476 | ||||
| Mean of quarter 1 | 0.909 | ||||
| Mean of quarter 2 | 0.987 | ||||
| Mean of quarter 3 | 1.020 | ||||
| Mean of quarter 4 | 1.128 | ||||
| Inter Quartile Range | 0.071 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.054 | ||||
| Mean of outliers low | 0.755 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.027 | ||||
| Mean of outliers high | 1.476 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.593 | ||||
| VaR(95%) (moments method) | 0.101 | ||||
| Expected Shortfall (moments method) | 0.269 | ||||
| Extreme Value Index (regression method) | 0.695 | ||||
| VaR(95%) (regression method) | 0.075 | ||||
| Expected Shortfall (regression method) | 0.224 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.026 | ||||
| Quartile 1 | 0.147 | ||||
| Median | 0.268 | ||||
| Quartile 3 | 0.388 | ||||
| Maximum | 0.509 | ||||
| Mean of quarter 1 | 0.026 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.509 | ||||
| Inter Quartile Range | 0.241 | ||||
| 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) | 0.037 | ||||
| Compounded annual return (geometric extrapolation) | 0.035 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.069 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.069 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.180 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.027 | ||||
| SD | 0.269 | ||||
| Sharpe ratio (Glass type estimate) | 0.100 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.100 | ||||
| df | 813.000 | ||||
| t | 0.176 | ||||
| p | 0.430 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.012 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.212 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.012 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.212 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.135 | ||||
| Upside Potential Ratio | 6.386 | ||||
| Upside part of mean | 1.272 | ||||
| Downside part of mean | -1.245 | ||||
| Upside SD | 0.181 | ||||
| Downside SD | 0.199 | ||||
| N nonnegative terms | 389.000 | ||||
| N negative terms | 425.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 814.000 | ||||
| Mean of predictor | 0.582 | ||||
| Mean of criterion | 0.027 | ||||
| SD of predictor | 0.316 | ||||
| SD of criterion | 0.269 | ||||
| Covariance | 0.008 | ||||
| r | 0.097 | ||||
| b (slope, estimate of beta) | 0.083 | ||||
| a (intercept, estimate of alpha) | -0.021 | ||||
| Mean Square Error | 0.072 | ||||
| DF error | 812.000 | ||||
| t(b) | 2.786 | ||||
| p(b) | 0.003 | ||||
| t(a) | -0.139 | ||||
| p(a) | 0.555 | ||||
| Lowerbound of 95% confidence interval for beta | 0.024 | ||||
| Upperbound of 95% confidence interval for beta | 0.141 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.322 | ||||
| Upperbound of 95% confidence interval for alpha | 0.279 | ||||
| Treynor index (mean / b) | 0.325 | ||||
| Jensen alpha (a) | -0.021 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.010 | ||||
| SD | 0.271 | ||||
| Sharpe ratio (Glass type estimate) | -0.035 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.035 | ||||
| df | 813.000 | ||||
| t | -0.062 | ||||
| p | 0.525 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.147 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.077 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.147 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.077 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.046 | ||||
| Upside Potential Ratio | 6.103 | ||||
| Upside part of mean | 1.256 | ||||
| Downside part of mean | -1.265 | ||||
| Upside SD | 0.176 | ||||
| Downside SD | 0.206 | ||||
| N nonnegative terms | 389.000 | ||||
| N negative terms | 425.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 814.000 | ||||
| Mean of predictor | 0.531 | ||||
| Mean of criterion | -0.010 | ||||
| SD of predictor | 0.318 | ||||
| SD of criterion | 0.271 | ||||
| Covariance | 0.008 | ||||
| r | 0.097 | ||||
| b (slope, estimate of beta) | 0.082 | ||||
| a (intercept, estimate of alpha) | -0.053 | ||||
| Mean Square Error | 0.073 | ||||
| DF error | 812.000 | ||||
| t(b) | 2.772 | ||||
| p(b) | 0.003 | ||||
| t(a) | -0.346 | ||||
| p(a) | 0.635 | ||||
| Lowerbound of 95% confidence interval for beta | 0.024 | ||||
| Upperbound of 95% confidence interval for beta | 0.141 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.355 | ||||
| Upperbound of 95% confidence interval for alpha | 0.249 | ||||
| Treynor index (mean / b) | -0.116 | ||||
| Jensen alpha (a) | -0.053 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.027 | ||||
| Expected Shortfall on VaR | 0.034 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.024 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 814.000 | ||||
| Minimum | 0.868 | ||||
| Quartile 1 | 0.995 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.006 | ||||
| Maximum | 1.135 | ||||
| Mean of quarter 1 | 0.983 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.003 | ||||
| Mean of quarter 4 | 1.017 | ||||
| Inter Quartile Range | 0.011 | ||||
| Number outliers low | 48.000 | ||||
| Percentage of outliers low | 0.059 | ||||
| Mean of outliers low | 0.961 | ||||
| Number of outliers high | 33.000 | ||||
| Percentage of outliers high | 0.041 | ||||
| Mean of outliers high | 1.041 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.525 | ||||
| VaR(95%) (moments method) | 0.017 | ||||
| Expected Shortfall (moments method) | 0.040 | ||||
| Extreme Value Index (regression method) | 0.348 | ||||
| VaR(95%) (regression method) | 0.015 | ||||
| Expected Shortfall (regression method) | 0.028 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.011 | ||||
| Median | 0.074 | ||||
| Quartile 3 | 0.112 | ||||
| Maximum | 0.555 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | 0.074 | ||||
| Mean of quarter 3 | 0.112 | ||||
| Mean of quarter 4 | 0.555 | ||||
| Inter Quartile Range | 0.101 | ||||
| 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 | 0.555 | ||||
| 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) | 0.036 | ||||
| Compounded annual return (geometric extrapolation) | 0.035 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.063 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.063 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.032 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.392 | ||||
| SD | 0.197 | ||||
| Sharpe ratio (Glass type estimate) | 1.986 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.974 | ||||
| df | 130.000 | ||||
| t | 1.404 | ||||
| p | 0.439 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.800 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.764 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.808 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.756 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.734 | ||||
| Upside Potential Ratio | 9.520 | ||||
| Upside part of mean | 1.364 | ||||
| Downside part of mean | -0.973 | ||||
| Upside SD | 0.137 | ||||
| Downside SD | 0.143 | ||||
| N nonnegative terms | 72.000 | ||||
| N negative terms | 59.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.897 | ||||
| Mean of criterion | 0.392 | ||||
| SD of predictor | 0.459 | ||||
| SD of criterion | 0.197 | ||||
| Covariance | -0.010 | ||||
| r | -0.110 | ||||
| b (slope, estimate of beta) | -0.047 | ||||
| a (intercept, estimate of alpha) | 0.434 | ||||
| Mean Square Error | 0.039 | ||||
| DF error | 129.000 | ||||
| t(b) | -1.259 | ||||
| p(b) | 0.570 | ||||
| t(a) | 1.549 | ||||
| p(a) | 0.414 | ||||
| Lowerbound of 95% confidence interval for beta | -0.122 | ||||
| Upperbound of 95% confidence interval for beta | 0.027 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.121 | ||||
| Upperbound of 95% confidence interval for alpha | 0.989 | ||||
| Treynor index (mean / b) | -8.263 | ||||
| Jensen alpha (a) | 0.434 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.372 | ||||
| SD | 0.198 | ||||
| Sharpe ratio (Glass type estimate) | 1.879 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.868 | ||||
| df | 130.000 | ||||
| t | 1.328 | ||||
| p | 0.442 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.906 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.656 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.913 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.649 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.563 | ||||
| Upside Potential Ratio | 9.334 | ||||
| Upside part of mean | 1.355 | ||||
| Downside part of mean | -0.983 | ||||
| Upside SD | 0.136 | ||||
| Downside SD | 0.145 | ||||
| N nonnegative terms | 72.000 | ||||
| N negative terms | 59.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.791 | ||||
| Mean of criterion | 0.372 | ||||
| SD of predictor | 0.461 | ||||
| SD of criterion | 0.198 | ||||
| Covariance | -0.010 | ||||
| r | -0.107 | ||||
| b (slope, estimate of beta) | -0.046 | ||||
| a (intercept, estimate of alpha) | 0.408 | ||||
| Mean Square Error | 0.039 | ||||
| DF error | 129.000 | ||||
| t(b) | -1.225 | ||||
| p(b) | 0.568 | ||||
| t(a) | 1.453 | ||||
| p(a) | 0.419 | ||||
| Lowerbound of 95% confidence interval for beta | -0.120 | ||||
| Upperbound of 95% confidence interval for beta | 0.028 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.148 | ||||
| Upperbound of 95% confidence interval for alpha | 0.965 | ||||
| Treynor index (mean / b) | -8.080 | ||||
| Jensen alpha (a) | 0.408 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.024 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.017 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.965 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.011 | ||||
| Maximum | 1.029 | ||||
| Mean of quarter 1 | 0.986 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.006 | ||||
| Mean of quarter 4 | 1.015 | ||||
| Inter Quartile Range | 0.013 | ||||
| Number outliers low | 10.000 | ||||
| Percentage of outliers low | 0.076 | ||||
| Mean of outliers low | 0.972 | ||||
| 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) | 0.485 | ||||
| VaR(95%) (moments method) | 0.011 | ||||
| Expected Shortfall (moments method) | 0.026 | ||||
| Extreme Value Index (regression method) | -0.272 | ||||
| VaR(95%) (regression method) | 0.016 | ||||
| Expected Shortfall (regression method) | 0.021 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.009 | ||||
| Median | 0.017 | ||||
| Quartile 3 | 0.042 | ||||
| Maximum | 0.112 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.014 | ||||
| Mean of quarter 3 | 0.024 | ||||
| Mean of quarter 4 | 0.093 | ||||
| Inter Quartile Range | 0.033 | ||||
| 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 | 0.125 | ||||
| Mean of outliers high | 0.112 | ||||
| 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) | 0.463 | ||||
| Compounded annual return (geometric extrapolation) | 0.516 | ||||
| Calmar ratio (compounded annual return / max draw down) | 4.588 | ||||
| Compounded annual return / average of 25% largest draw downs | 5.533 | ||||
| Compounded annual return / Expected Shortfall lognormal | 21.933 | ||||