Advanced Statistics: Ninja 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 | -0.089 | ||||
| SD | 0.068 | ||||
| Sharpe ratio (Glass type estimate) | -1.316 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.294 | ||||
| df | 47.000 | ||||
| t | -2.631 | ||||
| p | 0.994 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.324 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.294 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.309 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.280 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.447 | ||||
| Upside Potential Ratio | 0.366 | ||||
| Upside part of mean | 0.023 | ||||
| Downside part of mean | -0.112 | ||||
| Upside SD | 0.037 | ||||
| Downside SD | 0.062 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 46.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 48.000 | ||||
| Mean of predictor | 0.470 | ||||
| Mean of criterion | -0.089 | ||||
| SD of predictor | 0.309 | ||||
| SD of criterion | 0.068 | ||||
| Covariance | 0.001 | ||||
| r | 0.050 | ||||
| b (slope, estimate of beta) | 0.011 | ||||
| a (intercept, estimate of alpha) | -0.095 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 46.000 | ||||
| t(b) | 0.341 | ||||
| p(b) | 0.367 | ||||
| t(a) | -2.520 | ||||
| p(a) | 0.992 | ||||
| Lowerbound of 95% confidence interval for beta | -0.054 | ||||
| Upperbound of 95% confidence interval for beta | 0.076 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.170 | ||||
| Upperbound of 95% confidence interval for alpha | -0.019 | ||||
| Treynor index (mean / b) | -8.080 | ||||
| Jensen alpha (a) | -0.095 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.092 | ||||
| SD | 0.068 | ||||
| Sharpe ratio (Glass type estimate) | -1.342 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.320 | ||||
| df | 47.000 | ||||
| t | -2.683 | ||||
| p | 0.995 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.352 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.318 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.336 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.304 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.449 | ||||
| Upside Potential Ratio | 0.345 | ||||
| Upside part of mean | 0.022 | ||||
| Downside part of mean | -0.114 | ||||
| Upside SD | 0.036 | ||||
| Downside SD | 0.063 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 46.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 48.000 | ||||
| Mean of predictor | 0.418 | ||||
| Mean of criterion | -0.092 | ||||
| SD of predictor | 0.290 | ||||
| SD of criterion | 0.068 | ||||
| Covariance | 0.001 | ||||
| r | 0.052 | ||||
| b (slope, estimate of beta) | 0.012 | ||||
| a (intercept, estimate of alpha) | -0.097 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 46.000 | ||||
| t(b) | 0.353 | ||||
| p(b) | 0.363 | ||||
| t(a) | -2.587 | ||||
| p(a) | 0.994 | ||||
| Lowerbound of 95% confidence interval for beta | -0.058 | ||||
| Upperbound of 95% confidence interval for beta | 0.082 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.172 | ||||
| Upperbound of 95% confidence interval for alpha | -0.022 | ||||
| Treynor index (mean / b) | -7.478 | ||||
| Jensen alpha (a) | -0.097 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.039 | ||||
| Expected Shortfall on VaR | 0.047 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.031 | ||||
| Expected Shortfall on VaR | 0.055 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 48.000 | ||||
| Minimum | 0.937 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.075 | ||||
| Mean of quarter 1 | 0.977 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.008 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 9.000 | ||||
| Percentage of outliers low | 0.188 | ||||
| Mean of outliers low | 0.969 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.062 | ||||
| Mean of outliers high | 1.033 | ||||
| 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) | -1.256 | ||||
| VaR(95%) (regression method) | 0.029 | ||||
| Expected Shortfall (regression method) | 0.033 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.174 | ||||
| Quartile 1 | 0.174 | ||||
| Median | 0.174 | ||||
| Quartile 3 | 0.174 | ||||
| Maximum | 0.174 | ||||
| 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) | -0.043 | ||||
| Compounded annual return (geometric extrapolation) | -0.047 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.268 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.988 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.085 | ||||
| SD | 0.113 | ||||
| Sharpe ratio (Glass type estimate) | -0.747 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.747 | ||||
| df | 1063.000 | ||||
| t | -1.506 | ||||
| p | 0.529 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.720 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.226 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.720 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.226 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.056 | ||||
| Upside Potential Ratio | 2.862 | ||||
| Upside part of mean | 0.229 | ||||
| Downside part of mean | -0.314 | ||||
| Upside SD | 0.080 | ||||
| Downside SD | 0.080 | ||||
| N nonnegative terms | 94.000 | ||||
| N negative terms | 970.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1064.000 | ||||
| Mean of predictor | 0.499 | ||||
| Mean of criterion | -0.085 | ||||
| SD of predictor | 0.338 | ||||
| SD of criterion | 0.113 | ||||
| Covariance | -0.001 | ||||
| r | -0.037 | ||||
| b (slope, estimate of beta) | -0.013 | ||||
| a (intercept, estimate of alpha) | -0.078 | ||||
| Mean Square Error | 0.013 | ||||
| DF error | 1062.000 | ||||
| t(b) | -1.220 | ||||
| p(b) | 0.519 | ||||
| t(a) | -1.389 | ||||
| p(a) | 0.521 | ||||
| Lowerbound of 95% confidence interval for beta | -0.033 | ||||
| Upperbound of 95% confidence interval for beta | 0.008 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.189 | ||||
| Upperbound of 95% confidence interval for alpha | 0.032 | ||||
| Treynor index (mean / b) | 6.746 | ||||
| Jensen alpha (a) | -0.078 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.091 | ||||
| SD | 0.113 | ||||
| Sharpe ratio (Glass type estimate) | -0.805 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.805 | ||||
| df | 1063.000 | ||||
| t | -1.623 | ||||
| p | 0.532 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.778 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.168 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.778 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.168 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.116 | ||||
| Upside Potential Ratio | 2.773 | ||||
| Upside part of mean | 0.226 | ||||
| Downside part of mean | -0.317 | ||||
| Upside SD | 0.078 | ||||
| Downside SD | 0.082 | ||||
| N nonnegative terms | 94.000 | ||||
| N negative terms | 970.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1064.000 | ||||
| Mean of predictor | 0.442 | ||||
| Mean of criterion | -0.091 | ||||
| SD of predictor | 0.336 | ||||
| SD of criterion | 0.113 | ||||
| Covariance | -0.001 | ||||
| r | -0.036 | ||||
| b (slope, estimate of beta) | -0.012 | ||||
| a (intercept, estimate of alpha) | -0.086 | ||||
| Mean Square Error | 0.013 | ||||
| DF error | 1062.000 | ||||
| t(b) | -1.181 | ||||
| p(b) | 0.518 | ||||
| t(a) | -1.522 | ||||
| p(a) | 0.523 | ||||
| Lowerbound of 95% confidence interval for beta | -0.032 | ||||
| Upperbound of 95% confidence interval for beta | 0.008 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.196 | ||||
| Upperbound of 95% confidence interval for alpha | 0.025 | ||||
| Treynor index (mean / b) | 7.475 | ||||
| Jensen alpha (a) | -0.086 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.015 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1064.000 | ||||
| Minimum | 0.935 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.071 | ||||
| Mean of quarter 1 | 0.996 | ||||
| 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 | 113.000 | ||||
| Percentage of outliers low | 0.106 | ||||
| Mean of outliers low | 0.990 | ||||
| Number of outliers high | 103.000 | ||||
| Percentage of outliers high | 0.097 | ||||
| Mean of outliers high | 1.009 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.393 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.006 | ||||
| Extreme Value Index (regression method) | 0.139 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | 0.010 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.051 | ||||
| Quartile 1 | 0.064 | ||||
| Median | 0.077 | ||||
| Quartile 3 | 0.130 | ||||
| Maximum | 0.183 | ||||
| Mean of quarter 1 | 0.051 | ||||
| Mean of quarter 2 | 0.077 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.183 | ||||
| Inter Quartile Range | 0.066 | ||||
| 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) | -0.043 | ||||
| Compounded annual return (geometric extrapolation) | -0.046 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.251 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.251 | ||||
| Compounded annual return / Expected Shortfall lognormal | -3.138 | ||||
| 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 | 1.056 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.492 | ||||
| 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 | 0.933 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.495 | ||||
| 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) | -8740289270827845.000 | ||||
| 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) | -98798091896658438124256530268160.000 | ||||
| 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 | ||||