Advanced Statistics: Simple 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 | 0.068 | ||||
| SD | 0.196 | ||||
| Sharpe ratio (Glass type estimate) | 0.349 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.342 | ||||
| df | 42.000 | ||||
| t | 0.660 | ||||
| p | 0.256 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.691 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.385 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.696 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.380 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.933 | ||||
| Upside Potential Ratio | 3.801 | ||||
| Upside part of mean | 0.135 | ||||
| Downside part of mean | -0.066 | ||||
| Upside SD | 0.192 | ||||
| Downside SD | 0.035 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 41.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 43.000 | ||||
| Mean of predictor | 0.468 | ||||
| Mean of criterion | 0.068 | ||||
| SD of predictor | 0.308 | ||||
| SD of criterion | 0.196 | ||||
| Covariance | -0.008 | ||||
| r | -0.134 | ||||
| b (slope, estimate of beta) | -0.085 | ||||
| a (intercept, estimate of alpha) | 0.108 | ||||
| Mean Square Error | 0.039 | ||||
| DF error | 41.000 | ||||
| t(b) | -0.864 | ||||
| p(b) | 0.804 | ||||
| t(a) | 0.952 | ||||
| p(a) | 0.173 | ||||
| Lowerbound of 95% confidence interval for beta | -0.285 | ||||
| Upperbound of 95% confidence interval for beta | 0.114 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.121 | ||||
| Upperbound of 95% confidence interval for alpha | 0.338 | ||||
| Treynor index (mean / b) | -0.802 | ||||
| Jensen alpha (a) | 0.108 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.052 | ||||
| SD | 0.173 | ||||
| Sharpe ratio (Glass type estimate) | 0.302 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.297 | ||||
| df | 42.000 | ||||
| t | 0.573 | ||||
| p | 0.285 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.737 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.338 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.740 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.334 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.452 | ||||
| Upside Potential Ratio | 3.300 | ||||
| Upside part of mean | 0.119 | ||||
| Downside part of mean | -0.067 | ||||
| Upside SD | 0.168 | ||||
| Downside SD | 0.036 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 41.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 43.000 | ||||
| Mean of predictor | 0.415 | ||||
| Mean of criterion | 0.052 | ||||
| SD of predictor | 0.292 | ||||
| SD of criterion | 0.173 | ||||
| Covariance | -0.006 | ||||
| r | -0.128 | ||||
| b (slope, estimate of beta) | -0.076 | ||||
| a (intercept, estimate of alpha) | 0.084 | ||||
| Mean Square Error | 0.030 | ||||
| DF error | 41.000 | ||||
| t(b) | -0.828 | ||||
| p(b) | 0.794 | ||||
| t(a) | 0.844 | ||||
| p(a) | 0.202 | ||||
| Lowerbound of 95% confidence interval for beta | -0.261 | ||||
| Upperbound of 95% confidence interval for beta | 0.109 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.117 | ||||
| Upperbound of 95% confidence interval for alpha | 0.284 | ||||
| Treynor index (mean / b) | -0.689 | ||||
| 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%) | 0.075 | ||||
| Expected Shortfall on VaR | 0.094 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.018 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 43.000 | ||||
| Minimum | 0.955 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.333 | ||||
| Mean of quarter 1 | 0.992 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.044 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.070 | ||||
| Mean of outliers low | 0.971 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.047 | ||||
| Mean of outliers high | 1.245 | ||||
| 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) | -0.826 | ||||
| VaR(95%) (regression method) | 0.019 | ||||
| Expected Shortfall (regression method) | 0.033 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.036 | ||||
| Quartile 1 | 0.039 | ||||
| Median | 0.043 | ||||
| Quartile 3 | 0.047 | ||||
| Maximum | 0.050 | ||||
| Mean of quarter 1 | 0.036 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.050 | ||||
| Inter Quartile Range | 0.007 | ||||
| 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) | 0.115 | ||||
| Compounded annual return (geometric extrapolation) | 0.101 | ||||
| Calmar ratio (compounded annual return / max draw down) | 2.007 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.007 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.079 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.313 | ||||
| SD | 0.772 | ||||
| Sharpe ratio (Glass type estimate) | 0.405 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.405 | ||||
| df | 943.000 | ||||
| t | 0.768 | ||||
| p | 0.221 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.628 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.437 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.628 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.437 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.777 | ||||
| Upside Potential Ratio | 3.136 | ||||
| Upside part of mean | 1.262 | ||||
| Downside part of mean | -0.949 | ||||
| Upside SD | 0.659 | ||||
| Downside SD | 0.402 | ||||
| N nonnegative terms | 42.000 | ||||
| N negative terms | 902.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 944.000 | ||||
| Mean of predictor | 0.453 | ||||
| Mean of criterion | 0.313 | ||||
| SD of predictor | 0.328 | ||||
| SD of criterion | 0.772 | ||||
| Covariance | -0.004 | ||||
| r | -0.016 | ||||
| b (slope, estimate of beta) | -0.038 | ||||
| a (intercept, estimate of alpha) | 0.330 | ||||
| Mean Square Error | 0.597 | ||||
| DF error | 942.000 | ||||
| t(b) | -0.498 | ||||
| p(b) | 0.691 | ||||
| t(a) | 0.808 | ||||
| p(a) | 0.210 | ||||
| Lowerbound of 95% confidence interval for beta | -0.188 | ||||
| Upperbound of 95% confidence interval for beta | 0.112 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.472 | ||||
| Upperbound of 95% confidence interval for alpha | 1.131 | ||||
| Treynor index (mean / b) | -8.198 | ||||
| Jensen alpha (a) | 0.330 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.052 | ||||
| SD | 0.711 | ||||
| Sharpe ratio (Glass type estimate) | 0.073 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.073 | ||||
| df | 943.000 | ||||
| t | 0.138 | ||||
| p | 0.445 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.960 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.105 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.960 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.105 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.107 | ||||
| Upside Potential Ratio | 2.289 | ||||
| Upside part of mean | 1.103 | ||||
| Downside part of mean | -1.051 | ||||
| Upside SD | 0.522 | ||||
| Downside SD | 0.482 | ||||
| N nonnegative terms | 42.000 | ||||
| N negative terms | 902.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 944.000 | ||||
| Mean of predictor | 0.397 | ||||
| Mean of criterion | 0.052 | ||||
| SD of predictor | 0.334 | ||||
| SD of criterion | 0.711 | ||||
| Covariance | -0.002 | ||||
| r | -0.010 | ||||
| b (slope, estimate of beta) | -0.022 | ||||
| a (intercept, estimate of alpha) | 0.060 | ||||
| Mean Square Error | 0.506 | ||||
| DF error | 942.000 | ||||
| t(b) | -0.318 | ||||
| p(b) | 0.625 | ||||
| t(a) | 0.161 | ||||
| p(a) | 0.436 | ||||
| Lowerbound of 95% confidence interval for beta | -0.158 | ||||
| Upperbound of 95% confidence interval for beta | 0.114 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.677 | ||||
| Upperbound of 95% confidence interval for alpha | 0.798 | ||||
| Treynor index (mean / b) | -2.342 | ||||
| Jensen alpha (a) | 0.060 | ||||
| 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 | 0.086 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.028 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 944.000 | ||||
| Minimum | 0.546 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.921 | ||||
| Mean of quarter 1 | 0.986 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.019 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 44.000 | ||||
| Percentage of outliers low | 0.047 | ||||
| Mean of outliers low | 0.926 | ||||
| Number of outliers high | 42.000 | ||||
| Percentage of outliers high | 0.044 | ||||
| Mean of outliers high | 1.108 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.519 | ||||
| VaR(95%) (moments method) | -0.002 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.321 | ||||
| VaR(95%) (regression method) | -0.005 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.047 | ||||
| Quartile 1 | 0.086 | ||||
| Median | 0.126 | ||||
| Quartile 3 | 0.145 | ||||
| Maximum | 0.496 | ||||
| Mean of quarter 1 | 0.067 | ||||
| Mean of quarter 2 | 0.115 | ||||
| Mean of quarter 3 | 0.144 | ||||
| Mean of quarter 4 | 0.382 | ||||
| Inter Quartile Range | 0.059 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.222 | ||||
| Mean of outliers high | 0.382 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -3.103 | ||||
| VaR(95%) (moments method) | 0.321 | ||||
| Expected Shortfall (moments method) | 0.322 | ||||
| Extreme Value Index (regression method) | -0.120 | ||||
| VaR(95%) (regression method) | 0.563 | ||||
| Expected Shortfall (regression method) | 0.750 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.114 | ||||
| Compounded annual return (geometric extrapolation) | 0.100 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.203 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.263 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.164 | ||||
| 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 | 0.946 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.417 | ||||
| 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 | 0.857 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.421 | ||||
| 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) | -8730509785649120.000 | ||||
| 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) | -111871805825937986401291139547136.000 | ||||
| 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 | ||||