Advanced Statistics: FxTiming
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 | 0.027 | ||||
| SD | 0.239 | ||||
| Sharpe ratio (Glass type estimate) | 0.113 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.111 | ||||
| df | 55.000 | ||||
| t | 0.244 | ||||
| p | 0.404 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.795 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.020 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.796 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.019 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.231 | ||||
| Upside Potential Ratio | 1.621 | ||||
| Upside part of mean | 0.190 | ||||
| Downside part of mean | -0.163 | ||||
| Upside SD | 0.206 | ||||
| Downside SD | 0.117 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 49.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 56.000 | ||||
| Mean of predictor | 0.398 | ||||
| Mean of criterion | 0.027 | ||||
| SD of predictor | 0.296 | ||||
| SD of criterion | 0.239 | ||||
| Covariance | -0.004 | ||||
| r | -0.056 | ||||
| b (slope, estimate of beta) | -0.045 | ||||
| a (intercept, estimate of alpha) | 0.045 | ||||
| Mean Square Error | 0.058 | ||||
| DF error | 54.000 | ||||
| t(b) | -0.410 | ||||
| p(b) | 0.658 | ||||
| t(a) | 0.375 | ||||
| p(a) | 0.355 | ||||
| Lowerbound of 95% confidence interval for beta | -0.265 | ||||
| Upperbound of 95% confidence interval for beta | 0.175 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.195 | ||||
| Upperbound of 95% confidence interval for alpha | 0.285 | ||||
| Treynor index (mean / b) | -0.599 | ||||
| Jensen alpha (a) | 0.045 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.002 | ||||
| SD | 0.222 | ||||
| Sharpe ratio (Glass type estimate) | 0.007 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.007 | ||||
| df | 55.000 | ||||
| t | 0.015 | ||||
| p | 0.494 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.900 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.914 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.900 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.914 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.013 | ||||
| Upside Potential Ratio | 1.378 | ||||
| Upside part of mean | 0.171 | ||||
| Downside part of mean | -0.169 | ||||
| Upside SD | 0.182 | ||||
| Downside SD | 0.124 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 49.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 56.000 | ||||
| Mean of predictor | 0.353 | ||||
| Mean of criterion | 0.002 | ||||
| SD of predictor | 0.270 | ||||
| SD of criterion | 0.222 | ||||
| Covariance | -0.003 | ||||
| r | -0.052 | ||||
| b (slope, estimate of beta) | -0.043 | ||||
| a (intercept, estimate of alpha) | 0.017 | ||||
| Mean Square Error | 0.050 | ||||
| DF error | 54.000 | ||||
| t(b) | -0.382 | ||||
| p(b) | 0.648 | ||||
| t(a) | 0.151 | ||||
| p(a) | 0.440 | ||||
| Lowerbound of 95% confidence interval for beta | -0.267 | ||||
| Upperbound of 95% confidence interval for beta | 0.182 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.206 | ||||
| Upperbound of 95% confidence interval for alpha | 0.239 | ||||
| Treynor index (mean / b) | -0.037 | ||||
| Jensen alpha (a) | 0.017 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.100 | ||||
| Expected Shortfall on VaR | 0.124 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.044 | ||||
| Expected Shortfall on VaR | 0.087 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 56.000 | ||||
| Minimum | 0.851 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.356 | ||||
| Mean of quarter 1 | 0.959 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.065 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 9.000 | ||||
| Percentage of outliers low | 0.161 | ||||
| Mean of outliers low | 0.936 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.125 | ||||
| Mean of outliers high | 1.130 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -64.512 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.729 | ||||
| VaR(95%) (regression method) | 0.066 | ||||
| Expected Shortfall (regression method) | 0.091 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.066 | ||||
| Quartile 1 | 0.108 | ||||
| Median | 0.149 | ||||
| Quartile 3 | 0.179 | ||||
| Maximum | 0.209 | ||||
| Mean of quarter 1 | 0.066 | ||||
| Mean of quarter 2 | 0.149 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.209 | ||||
| Inter Quartile Range | 0.071 | ||||
| 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) | 0.051 | ||||
| Compounded annual return (geometric extrapolation) | 0.047 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.224 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.224 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.378 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.055 | ||||
| SD | 0.320 | ||||
| Sharpe ratio (Glass type estimate) | 0.171 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.171 | ||||
| df | 1236.000 | ||||
| t | 0.371 | ||||
| p | 0.495 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.731 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.073 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.731 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.073 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.230 | ||||
| Upside Potential Ratio | 3.459 | ||||
| Upside part of mean | 0.824 | ||||
| Downside part of mean | -0.769 | ||||
| Upside SD | 0.214 | ||||
| Downside SD | 0.238 | ||||
| N nonnegative terms | 151.000 | ||||
| N negative terms | 1086.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1237.000 | ||||
| Mean of predictor | 0.413 | ||||
| Mean of criterion | 0.055 | ||||
| SD of predictor | 0.307 | ||||
| SD of criterion | 0.320 | ||||
| Covariance | -0.001 | ||||
| r | -0.006 | ||||
| b (slope, estimate of beta) | -0.006 | ||||
| a (intercept, estimate of alpha) | 0.057 | ||||
| Mean Square Error | 0.103 | ||||
| DF error | 1235.000 | ||||
| t(b) | -0.212 | ||||
| p(b) | 0.504 | ||||
| t(a) | 0.388 | ||||
| p(a) | 0.493 | ||||
| Lowerbound of 95% confidence interval for beta | -0.065 | ||||
| Upperbound of 95% confidence interval for beta | 0.052 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.233 | ||||
| Upperbound of 95% confidence interval for alpha | 0.348 | ||||
| Treynor index (mean / b) | -8.717 | ||||
| Jensen alpha (a) | 0.057 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.001 | ||||
| SD | 0.333 | ||||
| Sharpe ratio (Glass type estimate) | 0.003 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.003 | ||||
| df | 1236.000 | ||||
| t | 0.007 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.899 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.905 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.899 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.905 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.004 | ||||
| Upside Potential Ratio | 3.069 | ||||
| Upside part of mean | 0.802 | ||||
| Downside part of mean | -0.801 | ||||
| Upside SD | 0.205 | ||||
| Downside SD | 0.261 | ||||
| N nonnegative terms | 151.000 | ||||
| N negative terms | 1086.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1237.000 | ||||
| Mean of predictor | 0.365 | ||||
| Mean of criterion | 0.001 | ||||
| SD of predictor | 0.309 | ||||
| SD of criterion | 0.333 | ||||
| Covariance | -0.000 | ||||
| r | -0.004 | ||||
| b (slope, estimate of beta) | -0.004 | ||||
| a (intercept, estimate of alpha) | 0.003 | ||||
| Mean Square Error | 0.111 | ||||
| DF error | 1235.000 | ||||
| t(b) | -0.145 | ||||
| p(b) | 0.503 | ||||
| t(a) | 0.017 | ||||
| p(a) | 0.500 | ||||
| Lowerbound of 95% confidence interval for beta | -0.065 | ||||
| Upperbound of 95% confidence interval for beta | 0.056 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.299 | ||||
| Upperbound of 95% confidence interval for alpha | 0.304 | ||||
| Treynor index (mean / b) | -0.235 | ||||
| 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%) | 0.033 | ||||
| Expected Shortfall on VaR | 0.041 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.021 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1237.000 | ||||
| Minimum | 0.692 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.166 | ||||
| Mean of quarter 1 | 0.989 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.013 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 115.000 | ||||
| Percentage of outliers low | 0.093 | ||||
| Mean of outliers low | 0.970 | ||||
| Number of outliers high | 152.000 | ||||
| Percentage of outliers high | 0.123 | ||||
| Mean of outliers high | 1.026 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.059 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.005 | ||||
| Extreme Value Index (regression method) | 0.250 | ||||
| VaR(95%) (regression method) | 0.009 | ||||
| Expected Shortfall (regression method) | 0.030 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.051 | ||||
| Median | 0.096 | ||||
| Quartile 3 | 0.264 | ||||
| Maximum | 0.308 | ||||
| Mean of quarter 1 | 0.021 | ||||
| Mean of quarter 2 | 0.080 | ||||
| Mean of quarter 3 | 0.256 | ||||
| Mean of quarter 4 | 0.290 | ||||
| Inter Quartile Range | 0.213 | ||||
| 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) | 0.050 | ||||
| Compounded annual return (geometric extrapolation) | 0.046 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.149 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.159 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.112 | ||||
| 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 | 1.042 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.370 | ||||
| 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 | 0.971 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.373 | ||||
| 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) | -8687033088746137.000 | ||||
| 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) | 77530752905919110840648699215872.000 | ||||
| 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 | ||||