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 | -0.014 | ||||
| SD | 0.159 | ||||
| Sharpe ratio (Glass type estimate) | -0.086 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.085 | ||||
| df | 58.000 | ||||
| t | -0.190 | ||||
| p | 0.575 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.969 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.799 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.969 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.799 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.167 | ||||
| Upside Potential Ratio | 0.995 | ||||
| Upside part of mean | 0.082 | ||||
| Downside part of mean | -0.095 | ||||
| Upside SD | 0.135 | ||||
| Downside SD | 0.082 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 55.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 59.000 | ||||
| Mean of predictor | 0.002 | ||||
| Mean of criterion | -0.014 | ||||
| SD of predictor | 0.219 | ||||
| SD of criterion | 0.159 | ||||
| Covariance | 0.002 | ||||
| r | 0.070 | ||||
| b (slope, estimate of beta) | 0.051 | ||||
| a (intercept, estimate of alpha) | -0.014 | ||||
| Mean Square Error | 0.026 | ||||
| DF error | 57.000 | ||||
| t(b) | 0.532 | ||||
| p(b) | 0.299 | ||||
| t(a) | -0.190 | ||||
| p(a) | 0.575 | ||||
| Lowerbound of 95% confidence interval for beta | -0.141 | ||||
| Upperbound of 95% confidence interval for beta | 0.244 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.159 | ||||
| Upperbound of 95% confidence interval for alpha | 0.131 | ||||
| Treynor index (mean / b) | -0.268 | ||||
| Jensen alpha (a) | -0.014 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.025 | ||||
| SD | 0.149 | ||||
| Sharpe ratio (Glass type estimate) | -0.167 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.165 | ||||
| df | 58.000 | ||||
| t | -0.371 | ||||
| p | 0.644 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.051 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.718 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.050 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.719 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.283 | ||||
| Upside Potential Ratio | 0.834 | ||||
| Upside part of mean | 0.074 | ||||
| Downside part of mean | -0.099 | ||||
| Upside SD | 0.119 | ||||
| Downside SD | 0.088 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 55.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 59.000 | ||||
| Mean of predictor | -0.023 | ||||
| Mean of criterion | -0.025 | ||||
| SD of predictor | 0.230 | ||||
| SD of criterion | 0.149 | ||||
| Covariance | 0.002 | ||||
| r | 0.069 | ||||
| b (slope, estimate of beta) | 0.045 | ||||
| a (intercept, estimate of alpha) | -0.024 | ||||
| Mean Square Error | 0.023 | ||||
| DF error | 57.000 | ||||
| t(b) | 0.525 | ||||
| p(b) | 0.301 | ||||
| t(a) | -0.354 | ||||
| p(a) | 0.638 | ||||
| Lowerbound of 95% confidence interval for beta | -0.127 | ||||
| Upperbound of 95% confidence interval for beta | 0.217 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.160 | ||||
| Upperbound of 95% confidence interval for alpha | 0.112 | ||||
| Treynor index (mean / b) | -0.556 | ||||
| Jensen alpha (a) | -0.024 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.070 | ||||
| Expected Shortfall on VaR | 0.087 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.026 | ||||
| Expected Shortfall on VaR | 0.055 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 59.000 | ||||
| Minimum | 0.838 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.293 | ||||
| Mean of quarter 1 | 0.982 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.028 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 11.000 | ||||
| Percentage of outliers low | 0.186 | ||||
| Mean of outliers low | 0.975 | ||||
| Number of outliers high | 14.000 | ||||
| Percentage of outliers high | 0.237 | ||||
| Mean of outliers high | 1.030 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.788 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.071 | ||||
| VaR(95%) (regression method) | 0.007 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.027 | ||||
| Quartile 1 | 0.068 | ||||
| Median | 0.110 | ||||
| Quartile 3 | 0.151 | ||||
| Maximum | 0.192 | ||||
| Mean of quarter 1 | 0.027 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.192 | ||||
| Inter Quartile Range | 0.083 | ||||
| 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) | 0.020 | ||||
| Compounded annual return (geometric extrapolation) | 0.019 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.100 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.100 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.221 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.061 | ||||
| SD | 0.432 | ||||
| Sharpe ratio (Glass type estimate) | 0.140 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.140 | ||||
| df | 1692.000 | ||||
| t | 0.312 | ||||
| p | 0.496 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.743 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.024 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.743 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.024 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.247 | ||||
| Upside Potential Ratio | 2.352 | ||||
| Upside part of mean | 0.577 | ||||
| Downside part of mean | -0.517 | ||||
| Upside SD | 0.356 | ||||
| Downside SD | 0.245 | ||||
| N nonnegative terms | 159.000 | ||||
| N negative terms | 1534.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1693.000 | ||||
| Mean of predictor | 0.022 | ||||
| Mean of criterion | 0.061 | ||||
| SD of predictor | 0.273 | ||||
| SD of criterion | 0.432 | ||||
| Covariance | 0.000 | ||||
| r | 0.004 | ||||
| b (slope, estimate of beta) | 0.006 | ||||
| a (intercept, estimate of alpha) | 0.061 | ||||
| Mean Square Error | 0.187 | ||||
| DF error | 1691.000 | ||||
| t(b) | 0.167 | ||||
| p(b) | 0.497 | ||||
| t(a) | 0.311 | ||||
| p(a) | 0.495 | ||||
| Lowerbound of 95% confidence interval for beta | -0.069 | ||||
| Upperbound of 95% confidence interval for beta | 0.082 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.322 | ||||
| Upperbound of 95% confidence interval for alpha | 0.443 | ||||
| Treynor index (mean / b) | 9.408 | ||||
| Jensen alpha (a) | 0.061 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.025 | ||||
| SD | 0.411 | ||||
| Sharpe ratio (Glass type estimate) | -0.061 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.061 | ||||
| df | 1692.000 | ||||
| t | -0.135 | ||||
| p | 0.502 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.944 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.823 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.944 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.823 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.086 | ||||
| Upside Potential Ratio | 1.821 | ||||
| Upside part of mean | 0.529 | ||||
| Downside part of mean | -0.554 | ||||
| Upside SD | 0.291 | ||||
| Downside SD | 0.291 | ||||
| N nonnegative terms | 159.000 | ||||
| N negative terms | 1534.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1693.000 | ||||
| Mean of predictor | -0.015 | ||||
| Mean of criterion | -0.025 | ||||
| SD of predictor | 0.273 | ||||
| SD of criterion | 0.411 | ||||
| Covariance | 0.000 | ||||
| r | 0.003 | ||||
| b (slope, estimate of beta) | 0.004 | ||||
| a (intercept, estimate of alpha) | -0.025 | ||||
| Mean Square Error | 0.169 | ||||
| DF error | 1691.000 | ||||
| t(b) | 0.114 | ||||
| p(b) | 0.498 | ||||
| t(a) | -0.135 | ||||
| p(a) | 0.502 | ||||
| Lowerbound of 95% confidence interval for beta | -0.068 | ||||
| Upperbound of 95% confidence interval for beta | 0.076 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.389 | ||||
| Upperbound of 95% confidence interval for alpha | 0.339 | ||||
| Treynor index (mean / b) | -5.995 | ||||
| Jensen alpha (a) | -0.025 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.036 | ||||
| Expected Shortfall on VaR | 0.045 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.011 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1693.000 | ||||
| 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 | 248.000 | ||||
| Percentage of outliers low | 0.146 | ||||
| Mean of outliers low | 0.991 | ||||
| Number of outliers high | 289.000 | ||||
| Percentage of outliers high | 0.171 | ||||
| Mean of outliers high | 1.010 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.268 | ||||
| VaR(95%) (moments method) | -0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.200 | ||||
| VaR(95%) (regression method) | -0.006 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.013 | ||||
| Median | 0.030 | ||||
| Quartile 3 | 0.231 | ||||
| Maximum | 0.549 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.021 | ||||
| Mean of quarter 3 | 0.119 | ||||
| Mean of quarter 4 | 0.431 | ||||
| Inter Quartile Range | 0.218 | ||||
| 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) | 0.020 | ||||
| Compounded annual return (geometric extrapolation) | 0.019 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.035 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.044 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.428 | ||||
| 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 | -18.547 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.002 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 172.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 172.000 | ||||
| Mean of predictor | 0.628 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.264 | ||||
| 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) | -7936535306446244.000 | ||||
| Sharpe ratio (Hedges UMVUE) | -7901674975671223.000 | ||||
| df | 171.000 | ||||
| t | -5611977934314593.000 | ||||
| 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) | -8739115425704417.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -7064234525638030.000 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -18.547 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.002 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 172.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 172.000 | ||||
| Mean of predictor | 0.593 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.263 | ||||
| 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 | 170.000 | ||||
| t(b) | 0.000 | ||||
| p(b) | 0.500 | ||||
| t(a) | -5554533974305903.000 | ||||
| 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) | -38747465829090244404896306561024.000 | ||||
| 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 | 172.000 | ||||
| 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 | ||||
