Advanced Statistics: Fast 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 | 0.087 | ||||
| SD | 0.217 | ||||
| Sharpe ratio (Glass type estimate) | 0.400 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.390 | ||||
| df | 32.000 | ||||
| t | 0.663 | ||||
| p | 0.256 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.789 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.583 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.795 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.576 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 6.924 | ||||
| Upside Potential Ratio | 10.335 | ||||
| Upside part of mean | 0.130 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 0.215 | ||||
| Downside SD | 0.013 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 33.000 | ||||
| Mean of predictor | 0.567 | ||||
| Mean of criterion | 0.087 | ||||
| SD of predictor | 0.311 | ||||
| SD of criterion | 0.217 | ||||
| Covariance | -0.004 | ||||
| r | -0.053 | ||||
| b (slope, estimate of beta) | -0.037 | ||||
| a (intercept, estimate of alpha) | 0.108 | ||||
| Mean Square Error | 0.049 | ||||
| DF error | 31.000 | ||||
| t(b) | -0.297 | ||||
| p(b) | 0.616 | ||||
| t(a) | 0.716 | ||||
| p(a) | 0.240 | ||||
| Lowerbound of 95% confidence interval for beta | -0.293 | ||||
| Upperbound of 95% confidence interval for beta | 0.219 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.200 | ||||
| Upperbound of 95% confidence interval for alpha | 0.416 | ||||
| Treynor index (mean / b) | -2.331 | ||||
| Jensen alpha (a) | 0.108 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.068 | ||||
| SD | 0.186 | ||||
| Sharpe ratio (Glass type estimate) | 0.366 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.357 | ||||
| df | 32.000 | ||||
| t | 0.606 | ||||
| p | 0.274 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.823 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.548 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.828 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.542 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 5.416 | ||||
| Upside Potential Ratio | 8.827 | ||||
| Upside part of mean | 0.111 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 0.183 | ||||
| Downside SD | 0.013 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 33.000 | ||||
| Mean of predictor | 0.512 | ||||
| Mean of criterion | 0.068 | ||||
| SD of predictor | 0.285 | ||||
| SD of criterion | 0.186 | ||||
| Covariance | -0.003 | ||||
| r | -0.049 | ||||
| b (slope, estimate of beta) | -0.032 | ||||
| a (intercept, estimate of alpha) | 0.084 | ||||
| Mean Square Error | 0.035 | ||||
| DF error | 31.000 | ||||
| t(b) | -0.271 | ||||
| p(b) | 0.606 | ||||
| t(a) | 0.655 | ||||
| p(a) | 0.259 | ||||
| Lowerbound of 95% confidence interval for beta | -0.270 | ||||
| Upperbound of 95% confidence interval for beta | 0.206 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.178 | ||||
| Upperbound of 95% confidence interval for alpha | 0.346 | ||||
| Treynor index (mean / b) | -2.146 | ||||
| Jensen alpha (a) | 0.084 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.079 | ||||
| Expected Shortfall on VaR | 0.099 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 33.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.360 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.045 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.030 | ||||
| Mean of outliers low | 1.000 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.030 | ||||
| Mean of outliers high | 1.360 | ||||
| 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 | 1.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.000 | ||||
| Quartile 3 | 0.000 | ||||
| Maximum | 0.000 | ||||
| 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) | 0.131 | ||||
| Compounded annual return (geometric extrapolation) | 0.118 | ||||
| Calmar ratio (compounded annual return / max draw down) | 805.106 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.191 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.089 | ||||
| SD | 0.230 | ||||
| Sharpe ratio (Glass type estimate) | 0.388 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.388 | ||||
| df | 740.000 | ||||
| t | 0.653 | ||||
| p | 0.257 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.777 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.554 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.778 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.554 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.833 | ||||
| Upside Potential Ratio | 2.295 | ||||
| Upside part of mean | 0.246 | ||||
| Downside part of mean | -0.157 | ||||
| Upside SD | 0.203 | ||||
| Downside SD | 0.107 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 735.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 741.000 | ||||
| Mean of predictor | 0.616 | ||||
| Mean of criterion | 0.089 | ||||
| SD of predictor | 0.324 | ||||
| SD of criterion | 0.230 | ||||
| Covariance | -0.001 | ||||
| r | -0.019 | ||||
| b (slope, estimate of beta) | -0.014 | ||||
| a (intercept, estimate of alpha) | 0.098 | ||||
| Mean Square Error | 0.053 | ||||
| DF error | 739.000 | ||||
| t(b) | -0.520 | ||||
| p(b) | 0.699 | ||||
| t(a) | 0.709 | ||||
| p(a) | 0.239 | ||||
| Lowerbound of 95% confidence interval for beta | -0.065 | ||||
| Upperbound of 95% confidence interval for beta | 0.038 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.173 | ||||
| Upperbound of 95% confidence interval for alpha | 0.368 | ||||
| Treynor index (mean / b) | -6.583 | ||||
| Jensen alpha (a) | 0.098 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.065 | ||||
| SD | 0.217 | ||||
| Sharpe ratio (Glass type estimate) | 0.298 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.298 | ||||
| df | 740.000 | ||||
| t | 0.501 | ||||
| p | 0.308 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.868 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.463 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.868 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.463 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.570 | ||||
| Upside Potential Ratio | 2.003 | ||||
| Upside part of mean | 0.227 | ||||
| Downside part of mean | -0.163 | ||||
| Upside SD | 0.185 | ||||
| Downside SD | 0.114 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 735.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 741.000 | ||||
| Mean of predictor | 0.562 | ||||
| Mean of criterion | 0.065 | ||||
| SD of predictor | 0.327 | ||||
| SD of criterion | 0.217 | ||||
| Covariance | -0.001 | ||||
| r | -0.019 | ||||
| b (slope, estimate of beta) | -0.012 | ||||
| a (intercept, estimate of alpha) | 0.072 | ||||
| Mean Square Error | 0.047 | ||||
| DF error | 739.000 | ||||
| t(b) | -0.504 | ||||
| p(b) | 0.693 | ||||
| t(a) | 0.551 | ||||
| p(a) | 0.291 | ||||
| Lowerbound of 95% confidence interval for beta | -0.060 | ||||
| Upperbound of 95% confidence interval for beta | 0.036 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.184 | ||||
| Upperbound of 95% confidence interval for alpha | 0.327 | ||||
| Treynor index (mean / b) | -5.243 | ||||
| Jensen alpha (a) | 0.072 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.022 | ||||
| Expected Shortfall on VaR | 0.027 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 741.000 | ||||
| Minimum | 0.875 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.262 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.004 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 10.000 | ||||
| Percentage of outliers low | 0.013 | ||||
| Mean of outliers low | 0.968 | ||||
| Number of outliers high | 11.000 | ||||
| Percentage of outliers high | 0.015 | ||||
| Mean of outliers high | 1.063 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -34.621 | ||||
| VaR(95%) (moments method) | -2720217973346357855378621857792.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -1.481 | ||||
| VaR(95%) (regression method) | -2.509 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.058 | ||||
| Quartile 1 | 0.085 | ||||
| Median | 0.113 | ||||
| Quartile 3 | 0.129 | ||||
| Maximum | 0.146 | ||||
| Mean of quarter 1 | 0.058 | ||||
| Mean of quarter 2 | 0.113 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.146 | ||||
| Inter Quartile Range | 0.044 | ||||
| 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) | 0.127 | ||||
| Compounded annual return (geometric extrapolation) | 0.115 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.789 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.789 | ||||
| Compounded annual return / Expected Shortfall lognormal | 4.244 | ||||
| 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 | 1.019 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.457 | ||||
| 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 | 0.912 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.459 | ||||
| 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) | -8733673758896871.000 | ||||
| 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) | -109206561667150602811317791227904.000 | ||||
| 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 | ||||