Advanced Statistics: Forex Volatility Breakout
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 | -0.055 | ||||
| SD | 0.017 | ||||
| Sharpe ratio (Glass type estimate) | -3.175 | ||||
| Sharpe ratio (Hedges UMVUE) | -3.097 | ||||
| df | 31.000 | ||||
| t | -5.184 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.592 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.722 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.524 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.671 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.361 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.055 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.023 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.616 | ||||
| Mean of criterion | -0.055 | ||||
| SD of predictor | 0.312 | ||||
| SD of criterion | 0.017 | ||||
| Covariance | 0.001 | ||||
| r | 0.098 | ||||
| b (slope, estimate of beta) | 0.005 | ||||
| a (intercept, estimate of alpha) | -0.058 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 30.000 | ||||
| t(b) | 0.539 | ||||
| p(b) | 0.297 | ||||
| t(a) | -4.706 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.015 | ||||
| Upperbound of 95% confidence interval for beta | 0.026 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.083 | ||||
| Upperbound of 95% confidence interval for alpha | -0.033 | ||||
| Treynor index (mean / b) | -10.134 | ||||
| Jensen alpha (a) | -0.058 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.055 | ||||
| SD | 0.017 | ||||
| Sharpe ratio (Glass type estimate) | -3.134 | ||||
| Sharpe ratio (Hedges UMVUE) | -3.057 | ||||
| df | 31.000 | ||||
| t | -5.118 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.546 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.686 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.479 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.636 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.344 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.055 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.023 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.556 | ||||
| Mean of criterion | -0.055 | ||||
| SD of predictor | 0.297 | ||||
| SD of criterion | 0.017 | ||||
| Covariance | 0.000 | ||||
| r | 0.092 | ||||
| b (slope, estimate of beta) | 0.005 | ||||
| a (intercept, estimate of alpha) | -0.058 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 30.000 | ||||
| t(b) | 0.508 | ||||
| p(b) | 0.307 | ||||
| t(a) | -4.677 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.016 | ||||
| Upperbound of 95% confidence interval for beta | 0.027 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.083 | ||||
| Upperbound of 95% confidence interval for alpha | -0.033 | ||||
| Treynor index (mean / b) | -10.063 | ||||
| Jensen alpha (a) | -0.058 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.013 | ||||
| Expected Shortfall on VaR | 0.015 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.020 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 32.000 | ||||
| Minimum | 0.972 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.996 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers low | 0.031 | ||||
| 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) | 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 | 1.000 | ||||
| Minimum | 0.028 | ||||
| Quartile 1 | 0.028 | ||||
| Median | 0.028 | ||||
| Quartile 3 | 0.028 | ||||
| Maximum | 0.028 | ||||
| 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) | -0.011 | ||||
| Compounded annual return (geometric extrapolation) | -0.011 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.378 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.716 | ||||
| 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 | 0.013 | ||||
| Sharpe ratio (Glass type estimate) | -4.302 | ||||
| Sharpe ratio (Hedges UMVUE) | -4.298 | ||||
| df | 704.000 | ||||
| t | -7.057 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -5.517 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -3.085 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -5.513 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.082 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -4.161 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.055 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.013 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 705.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 705.000 | ||||
| Mean of predictor | 0.605 | ||||
| Mean of criterion | -0.055 | ||||
| SD of predictor | 0.377 | ||||
| SD of criterion | 0.013 | ||||
| Covariance | 0.000 | ||||
| r | 0.002 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.055 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 703.000 | ||||
| t(b) | 0.042 | ||||
| p(b) | 0.483 | ||||
| t(a) | -7.022 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.002 | ||||
| Upperbound of 95% confidence interval for beta | 0.003 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.070 | ||||
| Upperbound of 95% confidence interval for alpha | -0.039 | ||||
| Treynor index (mean / b) | -1021.012 | ||||
| Jensen alpha (a) | -0.055 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.055 | ||||
| SD | 0.013 | ||||
| Sharpe ratio (Glass type estimate) | -4.270 | ||||
| Sharpe ratio (Hedges UMVUE) | -4.265 | ||||
| df | 704.000 | ||||
| t | -7.004 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -5.484 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -3.053 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -5.481 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.050 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -4.131 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.055 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.013 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 705.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 705.000 | ||||
| Mean of predictor | 0.530 | ||||
| Mean of criterion | -0.055 | ||||
| SD of predictor | 0.392 | ||||
| SD of criterion | 0.013 | ||||
| Covariance | 0.000 | ||||
| r | 0.001 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.055 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 703.000 | ||||
| t(b) | 0.025 | ||||
| p(b) | 0.490 | ||||
| t(a) | -6.977 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.002 | ||||
| Upperbound of 95% confidence interval for beta | 0.002 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.070 | ||||
| Upperbound of 95% confidence interval for alpha | -0.039 | ||||
| Treynor index (mean / b) | -1800.018 | ||||
| Jensen alpha (a) | -0.055 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.002 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.002 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 705.000 | ||||
| Minimum | 0.981 | ||||
| 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 | 3.000 | ||||
| Percentage of outliers low | 0.004 | ||||
| Mean of outliers low | 0.991 | ||||
| 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) | 0.766 | ||||
| VaR(95%) (regression method) | -0.005 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.028 | ||||
| Quartile 1 | 0.028 | ||||
| Median | 0.028 | ||||
| Quartile 3 | 0.028 | ||||
| Maximum | 0.028 | ||||
| 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) | -0.010 | ||||
| Compounded annual return (geometric extrapolation) | -0.011 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.375 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -5.738 | ||||
| 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 | 1.013 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.464 | ||||
| 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 | 0.904 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.464 | ||||
| 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) | -8736179678283452.000 | ||||
| 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) | -1136234840772741745836570565410816.000 | ||||
| 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 | ||||