Advanced Statistics: Forex Wealth Builder
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 | -0.019 | ||||
| SD | 0.129 | ||||
| Sharpe ratio (Glass type estimate) | -0.150 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.149 | ||||
| df | 77.000 | ||||
| t | -0.383 | ||||
| p | 0.649 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.919 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.619 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.918 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.620 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.266 | ||||
| Upside Potential Ratio | 0.855 | ||||
| Upside part of mean | 0.062 | ||||
| Downside part of mean | -0.082 | ||||
| Upside SD | 0.106 | ||||
| Downside SD | 0.073 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 74.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 78.000 | ||||
| Mean of predictor | 0.175 | ||||
| Mean of criterion | -0.019 | ||||
| SD of predictor | 0.266 | ||||
| SD of criterion | 0.129 | ||||
| Covariance | 0.001 | ||||
| r | 0.043 | ||||
| b (slope, estimate of beta) | 0.021 | ||||
| a (intercept, estimate of alpha) | -0.023 | ||||
| Mean Square Error | 0.017 | ||||
| DF error | 76.000 | ||||
| t(b) | 0.373 | ||||
| p(b) | 0.355 | ||||
| t(a) | -0.444 | ||||
| p(a) | 0.671 | ||||
| Lowerbound of 95% confidence interval for beta | -0.090 | ||||
| Upperbound of 95% confidence interval for beta | 0.132 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.126 | ||||
| Upperbound of 95% confidence interval for alpha | 0.080 | ||||
| Treynor index (mean / b) | -0.934 | ||||
| Jensen alpha (a) | -0.023 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.027 | ||||
| SD | 0.124 | ||||
| Sharpe ratio (Glass type estimate) | -0.219 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.216 | ||||
| df | 77.000 | ||||
| t | -0.557 | ||||
| p | 0.711 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.987 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.552 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.986 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.553 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.345 | ||||
| Upside Potential Ratio | 0.731 | ||||
| Upside part of mean | 0.057 | ||||
| Downside part of mean | -0.084 | ||||
| Upside SD | 0.095 | ||||
| Downside SD | 0.078 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 74.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 78.000 | ||||
| Mean of predictor | 0.137 | ||||
| Mean of criterion | -0.027 | ||||
| SD of predictor | 0.273 | ||||
| SD of criterion | 0.124 | ||||
| Covariance | 0.002 | ||||
| r | 0.048 | ||||
| b (slope, estimate of beta) | 0.022 | ||||
| a (intercept, estimate of alpha) | -0.030 | ||||
| Mean Square Error | 0.016 | ||||
| DF error | 76.000 | ||||
| t(b) | 0.415 | ||||
| p(b) | 0.340 | ||||
| t(a) | -0.609 | ||||
| p(a) | 0.728 | ||||
| Lowerbound of 95% confidence interval for beta | -0.082 | ||||
| Upperbound of 95% confidence interval for beta | 0.125 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.128 | ||||
| Upperbound of 95% confidence interval for alpha | 0.068 | ||||
| Treynor index (mean / b) | -1.254 | ||||
| Jensen alpha (a) | -0.030 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.059 | ||||
| Expected Shortfall on VaR | 0.073 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.023 | ||||
| Expected Shortfall on VaR | 0.048 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 78.000 | ||||
| Minimum | 0.838 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.252 | ||||
| Mean of quarter 1 | 0.987 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.022 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 9.000 | ||||
| Percentage of outliers low | 0.115 | ||||
| Mean of outliers low | 0.970 | ||||
| Number of outliers high | 14.000 | ||||
| Percentage of outliers high | 0.179 | ||||
| Mean of outliers high | 1.031 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.141 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.798 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.212 | ||||
| Quartile 1 | 0.212 | ||||
| Median | 0.212 | ||||
| Quartile 3 | 0.212 | ||||
| Maximum | 0.212 | ||||
| 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) | 0.018 | ||||
| Compounded annual return (geometric extrapolation) | 0.017 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.081 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.234 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.045 | ||||
| SD | 0.394 | ||||
| Sharpe ratio (Glass type estimate) | 0.113 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.113 | ||||
| df | 1706.000 | ||||
| t | 0.289 | ||||
| p | 0.496 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.655 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.881 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.655 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.881 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.198 | ||||
| Upside Potential Ratio | 2.095 | ||||
| Upside part of mean | 0.472 | ||||
| Downside part of mean | -0.427 | ||||
| Upside SD | 0.323 | ||||
| Downside SD | 0.225 | ||||
| N nonnegative terms | 149.000 | ||||
| N negative terms | 1558.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1707.000 | ||||
| Mean of predictor | 0.280 | ||||
| Mean of criterion | 0.045 | ||||
| SD of predictor | 0.575 | ||||
| SD of criterion | 0.394 | ||||
| Covariance | 0.011 | ||||
| r | 0.047 | ||||
| b (slope, estimate of beta) | 0.032 | ||||
| a (intercept, estimate of alpha) | 0.036 | ||||
| Mean Square Error | 0.155 | ||||
| DF error | 1705.000 | ||||
| t(b) | 1.940 | ||||
| p(b) | 0.470 | ||||
| t(a) | 0.231 | ||||
| p(a) | 0.496 | ||||
| Lowerbound of 95% confidence interval for beta | -0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.065 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.267 | ||||
| Upperbound of 95% confidence interval for alpha | 0.339 | ||||
| Treynor index (mean / b) | 1.388 | ||||
| Jensen alpha (a) | 0.036 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.027 | ||||
| SD | 0.376 | ||||
| Sharpe ratio (Glass type estimate) | -0.072 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.072 | ||||
| df | 1706.000 | ||||
| t | -0.184 | ||||
| p | 0.502 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.840 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.696 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.840 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.696 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.103 | ||||
| Upside Potential Ratio | 1.631 | ||||
| Upside part of mean | 0.432 | ||||
| Downside part of mean | -0.459 | ||||
| Upside SD | 0.268 | ||||
| Downside SD | 0.265 | ||||
| N nonnegative terms | 149.000 | ||||
| N negative terms | 1558.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1707.000 | ||||
| Mean of predictor | 0.115 | ||||
| Mean of criterion | -0.027 | ||||
| SD of predictor | 0.577 | ||||
| SD of criterion | 0.376 | ||||
| Covariance | 0.011 | ||||
| r | 0.049 | ||||
| b (slope, estimate of beta) | 0.032 | ||||
| a (intercept, estimate of alpha) | -0.031 | ||||
| Mean Square Error | 0.141 | ||||
| DF error | 1705.000 | ||||
| t(b) | 2.013 | ||||
| p(b) | 0.469 | ||||
| t(a) | -0.209 | ||||
| p(a) | 0.503 | ||||
| Lowerbound of 95% confidence interval for beta | 0.001 | ||||
| Upperbound of 95% confidence interval for beta | 0.063 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.320 | ||||
| Upperbound of 95% confidence interval for alpha | 0.258 | ||||
| Treynor index (mean / b) | -0.854 | ||||
| Jensen alpha (a) | -0.031 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.038 | ||||
| Expected Shortfall on VaR | 0.047 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.012 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1707.000 | ||||
| Minimum | 0.596 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.658 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.007 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 200.000 | ||||
| Percentage of outliers low | 0.117 | ||||
| Mean of outliers low | 0.987 | ||||
| Number of outliers high | 226.000 | ||||
| Percentage of outliers high | 0.132 | ||||
| Mean of outliers high | 1.014 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.813 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.087 | ||||
| VaR(95%) (regression method) | 0.000 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.007 | ||||
| Quartile 1 | 0.067 | ||||
| Median | 0.144 | ||||
| Quartile 3 | 0.237 | ||||
| Maximum | 0.549 | ||||
| Mean of quarter 1 | 0.008 | ||||
| Mean of quarter 2 | 0.135 | ||||
| Mean of quarter 3 | 0.161 | ||||
| Mean of quarter 4 | 0.431 | ||||
| Inter Quartile Range | 0.170 | ||||
| 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 | 0.143 | ||||
| Mean of outliers high | 0.549 | ||||
| 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) | 0.018 | ||||
| Compounded annual return (geometric extrapolation) | 0.017 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.031 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.040 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.363 | ||||
| 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 | 0.804 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.486 | ||||
| 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 | 0.681 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.500 | ||||
| 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) | -8768598107083369.000 | ||||
| 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) | 726868671147226375845073035198464.000 | ||||
| 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 | ||||