Advanced Statistics: Forex-Money-Signal
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 | -0.009 | ||||
| SD | 0.148 | ||||
| Sharpe ratio (Glass type estimate) | -0.063 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.062 | ||||
| df | 63.000 | ||||
| t | -0.146 | ||||
| p | 0.558 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.912 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.786 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.911 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.786 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.116 | ||||
| Upside Potential Ratio | 0.848 | ||||
| Upside part of mean | 0.068 | ||||
| Downside part of mean | -0.078 | ||||
| Upside SD | 0.123 | ||||
| Downside SD | 0.081 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 62.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 64.000 | ||||
| Mean of predictor | 0.320 | ||||
| Mean of criterion | -0.009 | ||||
| SD of predictor | 0.362 | ||||
| SD of criterion | 0.148 | ||||
| Covariance | -0.001 | ||||
| r | -0.026 | ||||
| b (slope, estimate of beta) | -0.011 | ||||
| a (intercept, estimate of alpha) | -0.006 | ||||
| Mean Square Error | 0.022 | ||||
| DF error | 62.000 | ||||
| t(b) | -0.204 | ||||
| p(b) | 0.581 | ||||
| t(a) | -0.089 | ||||
| p(a) | 0.535 | ||||
| Lowerbound of 95% confidence interval for beta | -0.115 | ||||
| Upperbound of 95% confidence interval for beta | 0.093 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.140 | ||||
| Upperbound of 95% confidence interval for alpha | 0.128 | ||||
| Treynor index (mean / b) | 0.881 | ||||
| Jensen alpha (a) | -0.006 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.019 | ||||
| SD | 0.142 | ||||
| Sharpe ratio (Glass type estimate) | -0.137 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.136 | ||||
| df | 63.000 | ||||
| t | -0.317 | ||||
| p | 0.624 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.986 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.712 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.985 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.713 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.220 | ||||
| Upside Potential Ratio | 0.696 | ||||
| Upside part of mean | 0.062 | ||||
| Downside part of mean | -0.081 | ||||
| Upside SD | 0.110 | ||||
| Downside SD | 0.089 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 62.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 64.000 | ||||
| Mean of predictor | 0.258 | ||||
| Mean of criterion | -0.019 | ||||
| SD of predictor | 0.333 | ||||
| SD of criterion | 0.142 | ||||
| Covariance | -0.001 | ||||
| r | -0.023 | ||||
| b (slope, estimate of beta) | -0.010 | ||||
| a (intercept, estimate of alpha) | -0.017 | ||||
| Mean Square Error | 0.020 | ||||
| DF error | 62.000 | ||||
| t(b) | -0.182 | ||||
| p(b) | 0.572 | ||||
| t(a) | -0.267 | ||||
| p(a) | 0.605 | ||||
| Lowerbound of 95% confidence interval for beta | -0.118 | ||||
| Upperbound of 95% confidence interval for beta | 0.098 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.144 | ||||
| Upperbound of 95% confidence interval for alpha | 0.110 | ||||
| Treynor index (mean / b) | 1.974 | ||||
| Jensen alpha (a) | -0.017 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.067 | ||||
| Expected Shortfall on VaR | 0.082 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.022 | ||||
| Expected Shortfall on VaR | 0.047 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 64.000 | ||||
| Minimum | 0.820 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.271 | ||||
| Mean of quarter 1 | 0.988 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.023 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.078 | ||||
| Mean of outliers low | 0.963 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.094 | ||||
| Mean of outliers high | 1.062 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.488 | ||||
| VaR(95%) (moments method) | -0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 3.709 | ||||
| VaR(95%) (regression method) | -0.000 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.186 | ||||
| Quartile 1 | 0.186 | ||||
| Median | 0.186 | ||||
| Quartile 3 | 0.186 | ||||
| Maximum | 0.186 | ||||
| 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) | 0.026 | ||||
| Compounded annual return (geometric extrapolation) | 0.025 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.134 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.301 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.043 | ||||
| SD | 0.359 | ||||
| Sharpe ratio (Glass type estimate) | 0.120 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.120 | ||||
| df | 1398.000 | ||||
| t | 0.278 | ||||
| p | 0.496 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.728 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.969 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.728 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.969 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.194 | ||||
| Upside Potential Ratio | 1.979 | ||||
| Upside part of mean | 0.441 | ||||
| Downside part of mean | -0.398 | ||||
| Upside SD | 0.282 | ||||
| Downside SD | 0.223 | ||||
| N nonnegative terms | 30.000 | ||||
| N negative terms | 1369.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1399.000 | ||||
| Mean of predictor | 0.434 | ||||
| Mean of criterion | 0.043 | ||||
| SD of predictor | 0.580 | ||||
| SD of criterion | 0.359 | ||||
| Covariance | 0.014 | ||||
| r | 0.066 | ||||
| b (slope, estimate of beta) | 0.041 | ||||
| a (intercept, estimate of alpha) | 0.026 | ||||
| Mean Square Error | 0.129 | ||||
| DF error | 1397.000 | ||||
| t(b) | 2.455 | ||||
| p(b) | 0.458 | ||||
| t(a) | 0.165 | ||||
| p(a) | 0.497 | ||||
| Lowerbound of 95% confidence interval for beta | 0.008 | ||||
| Upperbound of 95% confidence interval for beta | 0.073 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.279 | ||||
| Upperbound of 95% confidence interval for alpha | 0.330 | ||||
| Treynor index (mean / b) | 1.066 | ||||
| Jensen alpha (a) | 0.026 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.020 | ||||
| SD | 0.353 | ||||
| Sharpe ratio (Glass type estimate) | -0.055 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.055 | ||||
| df | 1398.000 | ||||
| t | -0.128 | ||||
| p | 0.502 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.903 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.793 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.903 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.793 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.079 | ||||
| Upside Potential Ratio | 1.651 | ||||
| Upside part of mean | 0.407 | ||||
| Downside part of mean | -0.426 | ||||
| Upside SD | 0.253 | ||||
| Downside SD | 0.246 | ||||
| N nonnegative terms | 30.000 | ||||
| N negative terms | 1369.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1399.000 | ||||
| Mean of predictor | 0.266 | ||||
| Mean of criterion | -0.020 | ||||
| SD of predictor | 0.579 | ||||
| SD of criterion | 0.353 | ||||
| Covariance | 0.014 | ||||
| r | 0.068 | ||||
| b (slope, estimate of beta) | 0.041 | ||||
| a (intercept, estimate of alpha) | -0.030 | ||||
| Mean Square Error | 0.124 | ||||
| DF error | 1397.000 | ||||
| t(b) | 2.529 | ||||
| p(b) | 0.457 | ||||
| t(a) | -0.200 | ||||
| p(a) | 0.503 | ||||
| Lowerbound of 95% confidence interval for beta | 0.009 | ||||
| Upperbound of 95% confidence interval for beta | 0.073 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.330 | ||||
| Upperbound of 95% confidence interval for alpha | 0.269 | ||||
| Treynor index (mean / b) | -0.474 | ||||
| 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%) | 0.035 | ||||
| Expected Shortfall on VaR | 0.044 | ||||
| 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 | 1399.000 | ||||
| Minimum | 0.733 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.364 | ||||
| Mean of quarter 1 | 0.995 | ||||
| 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 | 64.000 | ||||
| Percentage of outliers low | 0.046 | ||||
| Mean of outliers low | 0.970 | ||||
| Number of outliers high | 61.000 | ||||
| Percentage of outliers high | 0.044 | ||||
| Mean of outliers high | 1.039 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.336 | ||||
| VaR(95%) (moments method) | -0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.152 | ||||
| VaR(95%) (regression method) | -0.013 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.020 | ||||
| Quartile 1 | 0.104 | ||||
| Median | 0.159 | ||||
| Quartile 3 | 0.198 | ||||
| Maximum | 0.267 | ||||
| Mean of quarter 1 | 0.055 | ||||
| Mean of quarter 2 | 0.146 | ||||
| Mean of quarter 3 | 0.173 | ||||
| Mean of quarter 4 | 0.236 | ||||
| Inter Quartile Range | 0.093 | ||||
| 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) | 0.026 | ||||
| Compounded annual return (geometric extrapolation) | 0.025 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.093 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.105 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.563 | ||||
| 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 | 2.005 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.696 | ||||
| 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 | 1.740 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.735 | ||||
| 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) | -8706370716544490.000 | ||||
| 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) | 200967354554518789990980817780736.000 | ||||
| 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 | ||||