Advanced Statistics: Forex Swing 2012
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 | -0.109 | ||||
| SD | 0.458 | ||||
| Sharpe ratio (Glass type estimate) | -0.238 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.233 | ||||
| df | 33.000 | ||||
| t | -0.401 | ||||
| p | 0.655 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.402 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.929 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.399 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.933 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.342 | ||||
| Upside Potential Ratio | 0.595 | ||||
| Upside part of mean | 0.190 | ||||
| Downside part of mean | -0.299 | ||||
| Upside SD | 0.320 | ||||
| Downside SD | 0.320 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.587 | ||||
| Mean of criterion | -0.109 | ||||
| SD of predictor | 0.315 | ||||
| SD of criterion | 0.458 | ||||
| Covariance | -0.003 | ||||
| r | -0.022 | ||||
| b (slope, estimate of beta) | -0.032 | ||||
| a (intercept, estimate of alpha) | -0.090 | ||||
| Mean Square Error | 0.216 | ||||
| DF error | 32.000 | ||||
| t(b) | -0.126 | ||||
| p(b) | 0.550 | ||||
| t(a) | -0.287 | ||||
| p(a) | 0.612 | ||||
| Lowerbound of 95% confidence interval for beta | -0.555 | ||||
| Upperbound of 95% confidence interval for beta | 0.491 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.731 | ||||
| Upperbound of 95% confidence interval for alpha | 0.551 | ||||
| Treynor index (mean / b) | 3.387 | ||||
| Jensen alpha (a) | -0.090 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.223 | ||||
| SD | 0.507 | ||||
| Sharpe ratio (Glass type estimate) | -0.440 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.430 | ||||
| df | 33.000 | ||||
| t | -0.741 | ||||
| p | 0.768 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.606 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.732 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.599 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.739 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.514 | ||||
| Upside Potential Ratio | 0.350 | ||||
| Upside part of mean | 0.152 | ||||
| Downside part of mean | -0.375 | ||||
| Upside SD | 0.255 | ||||
| Downside SD | 0.434 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.528 | ||||
| Mean of criterion | -0.223 | ||||
| SD of predictor | 0.300 | ||||
| SD of criterion | 0.507 | ||||
| Covariance | -0.001 | ||||
| r | -0.010 | ||||
| b (slope, estimate of beta) | -0.016 | ||||
| a (intercept, estimate of alpha) | -0.214 | ||||
| Mean Square Error | 0.265 | ||||
| DF error | 32.000 | ||||
| t(b) | -0.054 | ||||
| p(b) | 0.521 | ||||
| t(a) | -0.624 | ||||
| p(a) | 0.731 | ||||
| Lowerbound of 95% confidence interval for beta | -0.625 | ||||
| Upperbound of 95% confidence interval for beta | 0.592 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.915 | ||||
| Upperbound of 95% confidence interval for alpha | 0.486 | ||||
| Treynor index (mean / b) | 13.822 | ||||
| Jensen alpha (a) | -0.214 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.228 | ||||
| Expected Shortfall on VaR | 0.273 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.085 | ||||
| Expected Shortfall on VaR | 0.183 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 34.000 | ||||
| Minimum | 0.496 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.542 | ||||
| Mean of quarter 1 | 0.919 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.060 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.118 | ||||
| Mean of outliers low | 0.818 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.059 | ||||
| Mean of outliers high | 1.272 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -20.304 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| Extreme Value Index (regression method) | 0.573 | ||||
| VaR(95%) (regression method) | 0.157 | ||||
| Expected Shortfall (regression method) | 0.715 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.610 | ||||
| Quartile 1 | 0.610 | ||||
| Median | 0.610 | ||||
| Quartile 3 | 0.610 | ||||
| Maximum | 0.610 | ||||
| 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) | -0.140 | ||||
| Compounded annual return (geometric extrapolation) | -0.164 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.269 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.600 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.194 | ||||
| SD | 0.229 | ||||
| Sharpe ratio (Glass type estimate) | -0.846 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.845 | ||||
| df | 747.000 | ||||
| t | -1.430 | ||||
| p | 0.923 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.007 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.315 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.006 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.315 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.002 | ||||
| Upside Potential Ratio | 1.953 | ||||
| Upside part of mean | 0.379 | ||||
| Downside part of mean | -0.573 | ||||
| Upside SD | 0.123 | ||||
| Downside SD | 0.194 | ||||
| N nonnegative terms | 44.000 | ||||
| N negative terms | 704.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 748.000 | ||||
| Mean of predictor | 0.607 | ||||
| Mean of criterion | -0.194 | ||||
| SD of predictor | 0.317 | ||||
| SD of criterion | 0.229 | ||||
| Covariance | 0.001 | ||||
| r | 0.011 | ||||
| b (slope, estimate of beta) | 0.008 | ||||
| a (intercept, estimate of alpha) | -0.199 | ||||
| Mean Square Error | 0.053 | ||||
| DF error | 746.000 | ||||
| t(b) | 0.302 | ||||
| p(b) | 0.381 | ||||
| t(a) | -1.454 | ||||
| p(a) | 0.927 | ||||
| Lowerbound of 95% confidence interval for beta | -0.044 | ||||
| Upperbound of 95% confidence interval for beta | 0.060 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.468 | ||||
| Upperbound of 95% confidence interval for alpha | 0.070 | ||||
| Treynor index (mean / b) | -24.231 | ||||
| Jensen alpha (a) | -0.199 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.222 | ||||
| SD | 0.237 | ||||
| Sharpe ratio (Glass type estimate) | -0.935 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.934 | ||||
| df | 747.000 | ||||
| t | -1.580 | ||||
| p | 0.943 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.096 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.226 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.095 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.227 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.083 | ||||
| Upside Potential Ratio | 1.814 | ||||
| Upside part of mean | 0.371 | ||||
| Downside part of mean | -0.593 | ||||
| Upside SD | 0.120 | ||||
| Downside SD | 0.205 | ||||
| N nonnegative terms | 44.000 | ||||
| N negative terms | 704.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 748.000 | ||||
| Mean of predictor | 0.556 | ||||
| Mean of criterion | -0.222 | ||||
| SD of predictor | 0.318 | ||||
| SD of criterion | 0.237 | ||||
| Covariance | 0.001 | ||||
| r | 0.010 | ||||
| b (slope, estimate of beta) | 0.008 | ||||
| a (intercept, estimate of alpha) | -0.226 | ||||
| Mean Square Error | 0.056 | ||||
| DF error | 746.000 | ||||
| t(b) | 0.278 | ||||
| p(b) | 0.391 | ||||
| t(a) | -1.600 | ||||
| p(a) | 0.945 | ||||
| Lowerbound of 95% confidence interval for beta | -0.046 | ||||
| Upperbound of 95% confidence interval for beta | 0.061 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.503 | ||||
| Upperbound of 95% confidence interval for alpha | 0.051 | ||||
| Treynor index (mean / b) | -29.217 | ||||
| Jensen alpha (a) | -0.226 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.025 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.016 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 748.000 | ||||
| Minimum | 0.852 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.076 | ||||
| Mean of quarter 1 | 0.992 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.006 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 47.000 | ||||
| Percentage of outliers low | 0.063 | ||||
| Mean of outliers low | 0.968 | ||||
| Number of outliers high | 44.000 | ||||
| Percentage of outliers high | 0.059 | ||||
| Mean of outliers high | 1.025 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -3.595 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | 0.104 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | 0.024 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.010 | ||||
| Median | 0.032 | ||||
| Quartile 3 | 0.083 | ||||
| Maximum | 0.613 | ||||
| Mean of quarter 1 | 0.007 | ||||
| Mean of quarter 2 | 0.032 | ||||
| Mean of quarter 3 | 0.083 | ||||
| Mean of quarter 4 | 0.613 | ||||
| Inter Quartile Range | 0.073 | ||||
| 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 | 0.200 | ||||
| Mean of outliers high | 0.613 | ||||
| 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) | -0.139 | ||||
| Compounded annual return (geometric extrapolation) | -0.163 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.265 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.265 | ||||
| Compounded annual return / Expected Shortfall lognormal | -5.327 | ||||
| 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 | 1.037 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.461 | ||||
| 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 | 0.929 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.462 | ||||
| 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) | -8732251502339241.000 | ||||
| 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) | 775458370645459652946936320753664.000 | ||||
| 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 | ||||