Advanced Statistics: Will Oli Forex
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 | -0.071 | ||||
| SD | 0.118 | ||||
| Sharpe ratio (Glass type estimate) | -0.601 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.588 | ||||
| df | 33.000 | ||||
| t | -1.012 | ||||
| p | 0.841 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.770 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.576 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.761 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.585 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.692 | ||||
| Upside Potential Ratio | 0.480 | ||||
| Upside part of mean | 0.049 | ||||
| Downside part of mean | -0.120 | ||||
| Upside SD | 0.059 | ||||
| Downside SD | 0.103 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.561 | ||||
| Mean of criterion | -0.071 | ||||
| SD of predictor | 0.311 | ||||
| SD of criterion | 0.118 | ||||
| Covariance | -0.002 | ||||
| r | -0.056 | ||||
| b (slope, estimate of beta) | -0.021 | ||||
| a (intercept, estimate of alpha) | -0.059 | ||||
| Mean Square Error | 0.014 | ||||
| DF error | 32.000 | ||||
| t(b) | -0.315 | ||||
| p(b) | 0.623 | ||||
| t(a) | -0.736 | ||||
| p(a) | 0.767 | ||||
| Lowerbound of 95% confidence interval for beta | -0.157 | ||||
| Upperbound of 95% confidence interval for beta | 0.115 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.223 | ||||
| Upperbound of 95% confidence interval for alpha | 0.105 | ||||
| Treynor index (mean / b) | 3.370 | ||||
| Jensen alpha (a) | -0.059 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.078 | ||||
| SD | 0.123 | ||||
| Sharpe ratio (Glass type estimate) | -0.633 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.618 | ||||
| df | 33.000 | ||||
| t | -1.065 | ||||
| p | 0.853 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.802 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.546 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.792 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.556 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.709 | ||||
| Upside Potential Ratio | 0.430 | ||||
| Upside part of mean | 0.047 | ||||
| Downside part of mean | -0.125 | ||||
| Upside SD | 0.056 | ||||
| Downside SD | 0.110 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.504 | ||||
| Mean of criterion | -0.078 | ||||
| SD of predictor | 0.291 | ||||
| SD of criterion | 0.123 | ||||
| Covariance | -0.002 | ||||
| r | -0.052 | ||||
| b (slope, estimate of beta) | -0.022 | ||||
| a (intercept, estimate of alpha) | -0.067 | ||||
| Mean Square Error | 0.016 | ||||
| DF error | 32.000 | ||||
| t(b) | -0.295 | ||||
| p(b) | 0.615 | ||||
| t(a) | -0.802 | ||||
| p(a) | 0.786 | ||||
| Lowerbound of 95% confidence interval for beta | -0.175 | ||||
| Upperbound of 95% confidence interval for beta | 0.131 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.237 | ||||
| Upperbound of 95% confidence interval for alpha | 0.103 | ||||
| Treynor index (mean / b) | 3.533 | ||||
| Jensen alpha (a) | -0.067 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.063 | ||||
| Expected Shortfall on VaR | 0.077 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.034 | ||||
| Expected Shortfall on VaR | 0.070 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 34.000 | ||||
| Minimum | 0.847 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.076 | ||||
| Mean of quarter 1 | 0.975 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.016 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.118 | ||||
| Mean of outliers low | 0.944 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.059 | ||||
| Mean of outliers high | 1.073 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.736 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.010 | ||||
| Extreme Value Index (regression method) | 1.641 | ||||
| VaR(95%) (regression method) | 0.024 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.066 | ||||
| Quartile 1 | 0.088 | ||||
| Median | 0.111 | ||||
| Quartile 3 | 0.134 | ||||
| Maximum | 0.157 | ||||
| Mean of quarter 1 | 0.066 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.157 | ||||
| Inter Quartile Range | 0.046 | ||||
| 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) | -0.032 | ||||
| Compounded annual return (geometric extrapolation) | -0.034 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.214 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.214 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.436 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.035 | ||||
| SD | 0.292 | ||||
| Sharpe ratio (Glass type estimate) | -0.121 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.120 | ||||
| df | 758.000 | ||||
| t | -0.205 | ||||
| p | 0.581 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.272 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.031 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.272 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.031 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.179 | ||||
| Upside Potential Ratio | 2.860 | ||||
| Upside part of mean | 0.562 | ||||
| Downside part of mean | -0.597 | ||||
| Upside SD | 0.215 | ||||
| Downside SD | 0.197 | ||||
| N nonnegative terms | 34.000 | ||||
| N negative terms | 725.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 759.000 | ||||
| Mean of predictor | 0.610 | ||||
| Mean of criterion | -0.035 | ||||
| SD of predictor | 0.359 | ||||
| SD of criterion | 0.292 | ||||
| Covariance | -0.002 | ||||
| r | -0.024 | ||||
| b (slope, estimate of beta) | -0.019 | ||||
| a (intercept, estimate of alpha) | -0.023 | ||||
| Mean Square Error | 0.085 | ||||
| DF error | 757.000 | ||||
| t(b) | -0.653 | ||||
| p(b) | 0.743 | ||||
| t(a) | -0.136 | ||||
| p(a) | 0.554 | ||||
| Lowerbound of 95% confidence interval for beta | -0.077 | ||||
| Upperbound of 95% confidence interval for beta | 0.039 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.362 | ||||
| Upperbound of 95% confidence interval for alpha | 0.315 | ||||
| Treynor index (mean / b) | 1.824 | ||||
| Jensen alpha (a) | -0.023 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.077 | ||||
| SD | 0.290 | ||||
| Sharpe ratio (Glass type estimate) | -0.266 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.266 | ||||
| df | 758.000 | ||||
| t | -0.453 | ||||
| p | 0.675 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.418 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.885 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.418 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.886 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.375 | ||||
| Upside Potential Ratio | 2.619 | ||||
| Upside part of mean | 0.541 | ||||
| Downside part of mean | -0.618 | ||||
| Upside SD | 0.204 | ||||
| Downside SD | 0.206 | ||||
| N nonnegative terms | 34.000 | ||||
| N negative terms | 725.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 759.000 | ||||
| Mean of predictor | 0.547 | ||||
| Mean of criterion | -0.077 | ||||
| SD of predictor | 0.351 | ||||
| SD of criterion | 0.290 | ||||
| Covariance | -0.002 | ||||
| r | -0.023 | ||||
| b (slope, estimate of beta) | -0.019 | ||||
| a (intercept, estimate of alpha) | -0.067 | ||||
| Mean Square Error | 0.084 | ||||
| DF error | 757.000 | ||||
| t(b) | -0.641 | ||||
| p(b) | 0.739 | ||||
| t(a) | -0.390 | ||||
| p(a) | 0.651 | ||||
| Lowerbound of 95% confidence interval for beta | -0.078 | ||||
| Upperbound of 95% confidence interval for beta | 0.040 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.404 | ||||
| Upperbound of 95% confidence interval for alpha | 0.270 | ||||
| Treynor index (mean / b) | 4.013 | ||||
| Jensen alpha (a) | -0.067 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.029 | ||||
| Expected Shortfall on VaR | 0.037 | ||||
| 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 | 759.000 | ||||
| Minimum | 0.858 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.170 | ||||
| Mean of quarter 1 | 0.992 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.009 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 43.000 | ||||
| Percentage of outliers low | 0.057 | ||||
| Mean of outliers low | 0.963 | ||||
| Number of outliers high | 34.000 | ||||
| Percentage of outliers high | 0.045 | ||||
| Mean of outliers high | 1.048 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -5.228 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | -0.121 | ||||
| VaR(95%) (regression method) | 0.003 | ||||
| Expected Shortfall (regression method) | 0.025 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.031 | ||||
| Quartile 1 | 0.051 | ||||
| Median | 0.141 | ||||
| Quartile 3 | 0.293 | ||||
| Maximum | 0.358 | ||||
| Mean of quarter 1 | 0.041 | ||||
| Mean of quarter 2 | 0.141 | ||||
| Mean of quarter 3 | 0.293 | ||||
| Mean of quarter 4 | 0.358 | ||||
| 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) | -0.032 | ||||
| Compounded annual return (geometric extrapolation) | -0.033 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.092 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.092 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.896 | ||||
| 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 | 0.960 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.430 | ||||
| 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 | 0.866 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.431 | ||||
| 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) | -8732286205432308.000 | ||||
| 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) | 270050817932995852662515385237504.000 | ||||
| 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 | ||||