Advanced Statistics: Smart 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 | -0.052 | ||||
| SD | 0.044 | ||||
| Sharpe ratio (Glass type estimate) | -1.183 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.169 | ||||
| df | 62.000 | ||||
| t | -2.710 | ||||
| p | 0.996 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.059 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.298 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.048 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.289 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.162 | ||||
| Upside Potential Ratio | 0.162 | ||||
| Upside part of mean | 0.007 | ||||
| Downside part of mean | -0.059 | ||||
| Upside SD | 0.011 | ||||
| Downside SD | 0.045 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 59.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 63.000 | ||||
| Mean of predictor | 0.324 | ||||
| Mean of criterion | -0.052 | ||||
| SD of predictor | 0.280 | ||||
| SD of criterion | 0.044 | ||||
| Covariance | -0.000 | ||||
| r | -0.038 | ||||
| b (slope, estimate of beta) | -0.006 | ||||
| a (intercept, estimate of alpha) | -0.050 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 61.000 | ||||
| t(b) | -0.295 | ||||
| p(b) | 0.615 | ||||
| t(a) | -2.456 | ||||
| p(a) | 0.992 | ||||
| Lowerbound of 95% confidence interval for beta | -0.046 | ||||
| Upperbound of 95% confidence interval for beta | 0.034 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.091 | ||||
| Upperbound of 95% confidence interval for alpha | -0.009 | ||||
| Treynor index (mean / b) | 8.793 | ||||
| Jensen alpha (a) | -0.050 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.053 | ||||
| SD | 0.046 | ||||
| Sharpe ratio (Glass type estimate) | -1.153 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.139 | ||||
| df | 62.000 | ||||
| t | -2.642 | ||||
| p | 0.995 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.028 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.270 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.018 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.261 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.132 | ||||
| Upside Potential Ratio | 0.153 | ||||
| Upside part of mean | 0.007 | ||||
| Downside part of mean | -0.060 | ||||
| Upside SD | 0.011 | ||||
| Downside SD | 0.047 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 59.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 63.000 | ||||
| Mean of predictor | 0.281 | ||||
| Mean of criterion | -0.053 | ||||
| SD of predictor | 0.279 | ||||
| SD of criterion | 0.046 | ||||
| Covariance | -0.001 | ||||
| r | -0.049 | ||||
| b (slope, estimate of beta) | -0.008 | ||||
| a (intercept, estimate of alpha) | -0.051 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 61.000 | ||||
| t(b) | -0.385 | ||||
| p(b) | 0.649 | ||||
| t(a) | -2.409 | ||||
| p(a) | 0.990 | ||||
| Lowerbound of 95% confidence interval for beta | -0.050 | ||||
| Upperbound of 95% confidence interval for beta | 0.034 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.093 | ||||
| Upperbound of 95% confidence interval for alpha | -0.009 | ||||
| Treynor index (mean / b) | 6.522 | ||||
| Jensen alpha (a) | -0.051 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.026 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.033 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 63.000 | ||||
| Minimum | 0.905 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.027 | ||||
| Mean of quarter 1 | 0.993 | ||||
| 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 | 11.000 | ||||
| Percentage of outliers low | 0.175 | ||||
| Mean of outliers low | 0.990 | ||||
| Number of outliers high | 13.000 | ||||
| Percentage of outliers high | 0.206 | ||||
| Mean of outliers high | 1.005 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.571 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 3.041 | ||||
| VaR(95%) (regression method) | 0.001 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.100 | ||||
| Quartile 1 | 0.100 | ||||
| Median | 0.100 | ||||
| Quartile 3 | 0.100 | ||||
| Maximum | 0.100 | ||||
| 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) | -0.009 | ||||
| Compounded annual return (geometric extrapolation) | -0.009 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.091 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.289 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.046 | ||||
| SD | 0.122 | ||||
| Sharpe ratio (Glass type estimate) | -0.372 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.372 | ||||
| df | 1394.000 | ||||
| t | -0.858 | ||||
| p | 0.511 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.221 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.478 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.221 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.478 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.528 | ||||
| Upside Potential Ratio | 1.481 | ||||
| Upside part of mean | 0.128 | ||||
| Downside part of mean | -0.173 | ||||
| Upside SD | 0.087 | ||||
| Downside SD | 0.086 | ||||
| N nonnegative terms | 132.000 | ||||
| N negative terms | 1263.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1395.000 | ||||
| Mean of predictor | 0.477 | ||||
| Mean of criterion | -0.046 | ||||
| SD of predictor | 0.564 | ||||
| SD of criterion | 0.122 | ||||
| Covariance | -0.014 | ||||
| r | -0.197 | ||||
| b (slope, estimate of beta) | -0.043 | ||||
| a (intercept, estimate of alpha) | -0.025 | ||||
| Mean Square Error | 0.014 | ||||
| DF error | 1393.000 | ||||
| t(b) | -7.496 | ||||
| p(b) | 0.625 | ||||
| t(a) | -0.483 | ||||
| p(a) | 0.508 | ||||
| Lowerbound of 95% confidence interval for beta | -0.054 | ||||
| Upperbound of 95% confidence interval for beta | -0.032 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.127 | ||||
| Upperbound of 95% confidence interval for alpha | 0.077 | ||||
| Treynor index (mean / b) | 1.066 | ||||
| Jensen alpha (a) | -0.025 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.053 | ||||
| SD | 0.122 | ||||
| Sharpe ratio (Glass type estimate) | -0.433 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.433 | ||||
| df | 1394.000 | ||||
| t | -0.999 | ||||
| p | 0.513 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.283 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.417 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.282 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.417 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.590 | ||||
| Upside Potential Ratio | 1.383 | ||||
| Upside part of mean | 0.124 | ||||
| Downside part of mean | -0.177 | ||||
| Upside SD | 0.083 | ||||
| Downside SD | 0.090 | ||||
| N nonnegative terms | 132.000 | ||||
| N negative terms | 1263.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1395.000 | ||||
| Mean of predictor | 0.317 | ||||
| Mean of criterion | -0.053 | ||||
| SD of predictor | 0.567 | ||||
| SD of criterion | 0.122 | ||||
| Covariance | -0.014 | ||||
| r | -0.197 | ||||
| b (slope, estimate of beta) | -0.043 | ||||
| a (intercept, estimate of alpha) | -0.039 | ||||
| Mean Square Error | 0.014 | ||||
| DF error | 1393.000 | ||||
| t(b) | -7.504 | ||||
| p(b) | 0.625 | ||||
| t(a) | -0.759 | ||||
| p(a) | 0.513 | ||||
| Lowerbound of 95% confidence interval for beta | -0.054 | ||||
| Upperbound of 95% confidence interval for beta | -0.031 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.142 | ||||
| Upperbound of 95% confidence interval for alpha | 0.063 | ||||
| Treynor index (mean / b) | 1.245 | ||||
| Jensen alpha (a) | -0.039 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.013 | ||||
| Expected Shortfall on VaR | 0.016 | ||||
| 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 | 1395.000 | ||||
| Minimum | 0.903 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.107 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.002 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 157.000 | ||||
| Percentage of outliers low | 0.113 | ||||
| Mean of outliers low | 0.995 | ||||
| Number of outliers high | 190.000 | ||||
| Percentage of outliers high | 0.136 | ||||
| Mean of outliers high | 1.004 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.618 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| 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 | 2.000 | ||||
| Minimum | 0.021 | ||||
| Quartile 1 | 0.045 | ||||
| Median | 0.068 | ||||
| Quartile 3 | 0.091 | ||||
| Maximum | 0.114 | ||||
| Mean of quarter 1 | 0.021 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.114 | ||||
| Inter Quartile Range | 0.047 | ||||
| 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) | -0.009 | ||||
| Compounded annual return (geometric extrapolation) | -0.009 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.078 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.078 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.570 | ||||
| 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 | 1.005 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.430 | ||||
| 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 | 0.911 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.432 | ||||
| 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) | -8725610772201837.000 | ||||
| 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) | 146694848845475803965847827906560.000 | ||||
| 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 | ||||