Advanced Statistics: FX.WAVE
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 | 0.237 | ||||
| SD | 0.326 | ||||
| Sharpe ratio (Glass type estimate) | 0.728 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.720 | ||||
| df | 72.000 | ||||
| t | 1.795 | ||||
| p | 0.038 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.078 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.529 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.083 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.523 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.774 | ||||
| Upside Potential Ratio | 3.266 | ||||
| Upside part of mean | 0.437 | ||||
| Downside part of mean | -0.200 | ||||
| Upside SD | 0.303 | ||||
| Downside SD | 0.134 | ||||
| N nonnegative terms | 25.000 | ||||
| N negative terms | 48.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 73.000 | ||||
| Mean of predictor | 0.184 | ||||
| Mean of criterion | 0.237 | ||||
| SD of predictor | 0.310 | ||||
| SD of criterion | 0.326 | ||||
| Covariance | -0.010 | ||||
| r | -0.096 | ||||
| b (slope, estimate of beta) | -0.101 | ||||
| a (intercept, estimate of alpha) | 0.256 | ||||
| Mean Square Error | 0.107 | ||||
| DF error | 71.000 | ||||
| t(b) | -0.815 | ||||
| p(b) | 0.791 | ||||
| t(a) | 1.903 | ||||
| p(a) | 0.031 | ||||
| Lowerbound of 95% confidence interval for beta | -0.349 | ||||
| Upperbound of 95% confidence interval for beta | 0.147 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.012 | ||||
| Upperbound of 95% confidence interval for alpha | 0.524 | ||||
| Treynor index (mean / b) | -2.342 | ||||
| Jensen alpha (a) | 0.256 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.188 | ||||
| SD | 0.299 | ||||
| Sharpe ratio (Glass type estimate) | 0.630 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.623 | ||||
| df | 72.000 | ||||
| t | 1.553 | ||||
| p | 0.062 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.174 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.429 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.178 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.424 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.325 | ||||
| Upside Potential Ratio | 2.793 | ||||
| Upside part of mean | 0.397 | ||||
| Downside part of mean | -0.209 | ||||
| Upside SD | 0.266 | ||||
| Downside SD | 0.142 | ||||
| N nonnegative terms | 25.000 | ||||
| N negative terms | 48.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 73.000 | ||||
| Mean of predictor | 0.139 | ||||
| Mean of criterion | 0.188 | ||||
| SD of predictor | 0.293 | ||||
| SD of criterion | 0.299 | ||||
| Covariance | -0.006 | ||||
| r | -0.073 | ||||
| b (slope, estimate of beta) | -0.075 | ||||
| a (intercept, estimate of alpha) | 0.199 | ||||
| Mean Square Error | 0.090 | ||||
| DF error | 71.000 | ||||
| t(b) | -0.619 | ||||
| p(b) | 0.731 | ||||
| t(a) | 1.617 | ||||
| p(a) | 0.055 | ||||
| Lowerbound of 95% confidence interval for beta | -0.316 | ||||
| Upperbound of 95% confidence interval for beta | 0.166 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.046 | ||||
| Upperbound of 95% confidence interval for alpha | 0.444 | ||||
| Treynor index (mean / b) | -2.516 | ||||
| Jensen alpha (a) | 0.199 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.119 | ||||
| Expected Shortfall on VaR | 0.149 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.045 | ||||
| Expected Shortfall on VaR | 0.090 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 73.000 | ||||
| Minimum | 0.840 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.023 | ||||
| Maximum | 1.446 | ||||
| Mean of quarter 1 | 0.945 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.007 | ||||
| Mean of quarter 4 | 1.146 | ||||
| Inter Quartile Range | 0.023 | ||||
| Number outliers low | 11.000 | ||||
| Percentage of outliers low | 0.151 | ||||
| Mean of outliers low | 0.913 | ||||
| Number of outliers high | 15.000 | ||||
| Percentage of outliers high | 0.205 | ||||
| Mean of outliers high | 1.169 | ||||
| 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) | -0.468 | ||||
| VaR(95%) (regression method) | 0.062 | ||||
| Expected Shortfall (regression method) | 0.082 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.016 | ||||
| Quartile 1 | 0.021 | ||||
| Median | 0.077 | ||||
| Quartile 3 | 0.101 | ||||
| Maximum | 0.350 | ||||
| Mean of quarter 1 | 0.018 | ||||
| Mean of quarter 2 | 0.047 | ||||
| Mean of quarter 3 | 0.090 | ||||
| Mean of quarter 4 | 0.227 | ||||
| Inter Quartile Range | 0.080 | ||||
| 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 | 0.350 | ||||
| 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) | 0.511 | ||||
| Compounded annual return (geometric extrapolation) | 0.262 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.748 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.152 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.750 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.940 | ||||
| SD | 1.419 | ||||
| Sharpe ratio (Glass type estimate) | 0.663 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.662 | ||||
| df | 1598.000 | ||||
| t | 1.637 | ||||
| p | 0.480 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.131 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.456 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.131 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.456 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.461 | ||||
| Upside Potential Ratio | 5.175 | ||||
| Upside part of mean | 3.331 | ||||
| Downside part of mean | -2.391 | ||||
| Upside SD | 1.265 | ||||
| Downside SD | 0.644 | ||||
| N nonnegative terms | 423.000 | ||||
| N negative terms | 1176.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1599.000 | ||||
| Mean of predictor | 0.372 | ||||
| Mean of criterion | 0.940 | ||||
| SD of predictor | 0.635 | ||||
| SD of criterion | 1.419 | ||||
| Covariance | -0.177 | ||||
| r | -0.197 | ||||
| b (slope, estimate of beta) | -0.439 | ||||
| a (intercept, estimate of alpha) | 1.104 | ||||
| Mean Square Error | 1.937 | ||||
| DF error | 1597.000 | ||||
| t(b) | -8.013 | ||||
| p(b) | 0.624 | ||||
| t(a) | 1.958 | ||||
| p(a) | 0.469 | ||||
| Lowerbound of 95% confidence interval for beta | -0.547 | ||||
| Upperbound of 95% confidence interval for beta | -0.332 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.002 | ||||
| Upperbound of 95% confidence interval for alpha | 2.209 | ||||
| Treynor index (mean / b) | -2.142 | ||||
| Jensen alpha (a) | 1.104 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.188 | ||||
| SD | 1.200 | ||||
| Sharpe ratio (Glass type estimate) | 0.156 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.156 | ||||
| df | 1598.000 | ||||
| t | 0.386 | ||||
| p | 0.495 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.637 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.950 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.637 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.950 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.221 | ||||
| Upside Potential Ratio | 3.388 | ||||
| Upside part of mean | 2.872 | ||||
| Downside part of mean | -2.684 | ||||
| Upside SD | 0.849 | ||||
| Downside SD | 0.848 | ||||
| N nonnegative terms | 423.000 | ||||
| N negative terms | 1176.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1599.000 | ||||
| Mean of predictor | 0.177 | ||||
| Mean of criterion | 0.188 | ||||
| SD of predictor | 0.620 | ||||
| SD of criterion | 1.200 | ||||
| Covariance | -0.173 | ||||
| r | -0.232 | ||||
| b (slope, estimate of beta) | -0.450 | ||||
| a (intercept, estimate of alpha) | 0.267 | ||||
| Mean Square Error | 1.363 | ||||
| DF error | 1597.000 | ||||
| t(b) | -9.544 | ||||
| p(b) | 0.647 | ||||
| t(a) | 0.566 | ||||
| p(a) | 0.491 | ||||
| Lowerbound of 95% confidence interval for beta | -0.542 | ||||
| Upperbound of 95% confidence interval for beta | -0.357 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.660 | ||||
| Upperbound of 95% confidence interval for alpha | 1.194 | ||||
| Treynor index (mean / b) | -0.417 | ||||
| Jensen alpha (a) | 0.267 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.114 | ||||
| Expected Shortfall on VaR | 0.141 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.026 | ||||
| Expected Shortfall on VaR | 0.059 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1599.000 | ||||
| Minimum | 0.290 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.002 | ||||
| Maximum | 3.314 | ||||
| Mean of quarter 1 | 0.964 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.051 | ||||
| Inter Quartile Range | 0.002 | ||||
| Number outliers low | 367.000 | ||||
| Percentage of outliers low | 0.230 | ||||
| Mean of outliers low | 0.961 | ||||
| Number of outliers high | 375.000 | ||||
| Percentage of outliers high | 0.235 | ||||
| Mean of outliers high | 1.054 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.394 | ||||
| VaR(95%) (moments method) | 0.007 | ||||
| Expected Shortfall (moments method) | 0.016 | ||||
| Extreme Value Index (regression method) | 0.472 | ||||
| VaR(95%) (regression method) | 0.023 | ||||
| Expected Shortfall (regression method) | 0.061 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.048 | ||||
| Quartile 1 | 0.057 | ||||
| Median | 0.083 | ||||
| Quartile 3 | 0.328 | ||||
| Maximum | 0.774 | ||||
| Mean of quarter 1 | 0.050 | ||||
| Mean of quarter 2 | 0.070 | ||||
| Mean of quarter 3 | 0.123 | ||||
| Mean of quarter 4 | 0.560 | ||||
| Inter Quartile Range | 0.271 | ||||
| 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 | 0.100 | ||||
| Mean of outliers high | 0.774 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.200 | ||||
| VaR(95%) (moments method) | 0.652 | ||||
| Expected Shortfall (moments method) | 0.662 | ||||
| Extreme Value Index (regression method) | -0.106 | ||||
| VaR(95%) (regression method) | 0.827 | ||||
| Expected Shortfall (regression method) | 1.041 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.510 | ||||
| Compounded annual return (geometric extrapolation) | 0.261 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.337 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.465 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.851 | ||||
| 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 | 1.822 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.723 | ||||
| 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 | 1.564 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.710 | ||||
| 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) | -8718809963003148.000 | ||||
| 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) | 228722460684208561109321820143616.000 | ||||
| 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 | ||||