Advanced Statistics: FONZ FX
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 | -0.848 | ||||
| SD | 0.819 | ||||
| Sharpe ratio (Glass type estimate) | -1.035 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.014 | ||||
| df | 38.000 | ||||
| t | -1.866 | ||||
| p | 0.965 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.140 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.083 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.125 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.097 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.003 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.848 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.845 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.471 | ||||
| Mean of criterion | -0.848 | ||||
| SD of predictor | 0.257 | ||||
| SD of criterion | 0.819 | ||||
| Covariance | 0.025 | ||||
| r | 0.119 | ||||
| b (slope, estimate of beta) | 0.380 | ||||
| a (intercept, estimate of alpha) | -1.027 | ||||
| Mean Square Error | 0.679 | ||||
| DF error | 37.000 | ||||
| t(b) | 0.732 | ||||
| p(b) | 0.234 | ||||
| t(a) | -1.980 | ||||
| p(a) | 0.972 | ||||
| Lowerbound of 95% confidence interval for beta | -0.673 | ||||
| Upperbound of 95% confidence interval for beta | 1.434 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.078 | ||||
| Upperbound of 95% confidence interval for alpha | 0.024 | ||||
| Treynor index (mean / b) | -2.228 | ||||
| Jensen alpha (a) | -1.027 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -3.586 | ||||
| SD | 4.689 | ||||
| Sharpe ratio (Glass type estimate) | -0.765 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.750 | ||||
| df | 38.000 | ||||
| t | -1.379 | ||||
| p | 0.912 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.861 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.341 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.850 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.350 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.756 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -3.586 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 4.743 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.431 | ||||
| Mean of criterion | -3.586 | ||||
| SD of predictor | 0.242 | ||||
| SD of criterion | 4.689 | ||||
| Covariance | 0.052 | ||||
| r | 0.046 | ||||
| b (slope, estimate of beta) | 0.889 | ||||
| a (intercept, estimate of alpha) | -3.970 | ||||
| Mean Square Error | 22.532 | ||||
| DF error | 37.000 | ||||
| t(b) | 0.280 | ||||
| p(b) | 0.391 | ||||
| t(a) | -1.337 | ||||
| p(a) | 0.905 | ||||
| Lowerbound of 95% confidence interval for beta | -5.550 | ||||
| Upperbound of 95% confidence interval for beta | 7.328 | ||||
| Lowerbound of 95% confidence interval for alpha | -9.984 | ||||
| Upperbound of 95% confidence interval for alpha | 2.045 | ||||
| Treynor index (mean / b) | -4.034 | ||||
| Jensen alpha (a) | -3.970 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.920 | ||||
| Expected Shortfall on VaR | 0.950 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.246 | ||||
| Expected Shortfall on VaR | 0.521 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 39.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.739 | ||||
| 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 | 3.000 | ||||
| Percentage of outliers low | 0.077 | ||||
| Mean of outliers low | 0.129 | ||||
| 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) | -2.020 | ||||
| VaR(95%) (regression method) | 0.603 | ||||
| Expected Shortfall (regression method) | 0.735 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| 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) | -0.308 | ||||
| Compounded annual return (geometric extrapolation) | -0.971 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.971 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.022 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.714 | ||||
| SD | 1.307 | ||||
| Sharpe ratio (Glass type estimate) | -0.546 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.546 | ||||
| df | 872.000 | ||||
| t | -0.998 | ||||
| p | 0.841 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.620 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.528 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.620 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.528 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.781 | ||||
| Upside Potential Ratio | 1.390 | ||||
| Upside part of mean | 1.271 | ||||
| Downside part of mean | -1.986 | ||||
| Upside SD | 0.934 | ||||
| Downside SD | 0.915 | ||||
| N nonnegative terms | 18.000 | ||||
| N negative terms | 855.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 873.000 | ||||
| Mean of predictor | 0.511 | ||||
| Mean of criterion | -0.714 | ||||
| SD of predictor | 0.307 | ||||
| SD of criterion | 1.307 | ||||
| Covariance | 0.030 | ||||
| r | 0.075 | ||||
| b (slope, estimate of beta) | 0.319 | ||||
| a (intercept, estimate of alpha) | -0.877 | ||||
| Mean Square Error | 1.701 | ||||
| DF error | 871.000 | ||||
| t(b) | 2.217 | ||||
| p(b) | 0.013 | ||||
| t(a) | -1.221 | ||||
| p(a) | 0.889 | ||||
| Lowerbound of 95% confidence interval for beta | 0.037 | ||||
| Upperbound of 95% confidence interval for beta | 0.601 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.287 | ||||
| Upperbound of 95% confidence interval for alpha | 0.533 | ||||
| Treynor index (mean / b) | -2.241 | ||||
| Jensen alpha (a) | -0.877 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -3.499 | ||||
| SD | 4.584 | ||||
| Sharpe ratio (Glass type estimate) | -0.763 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.763 | ||||
| df | 872.000 | ||||
| t | -1.393 | ||||
| p | 0.918 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.837 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.311 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.837 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.312 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.771 | ||||
| Upside Potential Ratio | 0.220 | ||||
| Upside part of mean | 1.000 | ||||
| Downside part of mean | -4.499 | ||||
| Upside SD | 0.658 | ||||
| Downside SD | 4.539 | ||||
| N nonnegative terms | 18.000 | ||||
| N negative terms | 855.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 873.000 | ||||
| Mean of predictor | 0.463 | ||||
| Mean of criterion | -3.499 | ||||
| SD of predictor | 0.308 | ||||
| SD of criterion | 4.584 | ||||
| Covariance | 0.045 | ||||
| r | 0.032 | ||||
| b (slope, estimate of beta) | 0.471 | ||||
| a (intercept, estimate of alpha) | -3.717 | ||||
| Mean Square Error | 21.018 | ||||
| DF error | 871.000 | ||||
| t(b) | 0.934 | ||||
| p(b) | 0.175 | ||||
| t(a) | -1.474 | ||||
| p(a) | 0.930 | ||||
| Lowerbound of 95% confidence interval for beta | -0.519 | ||||
| Upperbound of 95% confidence interval for beta | 1.460 | ||||
| Lowerbound of 95% confidence interval for alpha | -8.668 | ||||
| Upperbound of 95% confidence interval for alpha | 1.233 | ||||
| Treynor index (mean / b) | -7.430 | ||||
| Jensen alpha (a) | -3.717 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.381 | ||||
| Expected Shortfall on VaR | 0.447 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.026 | ||||
| Expected Shortfall on VaR | 0.059 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 873.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.335 | ||||
| Mean of quarter 1 | 0.970 | ||||
| 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 | 25.000 | ||||
| Percentage of outliers low | 0.029 | ||||
| Mean of outliers low | 0.741 | ||||
| Number of outliers high | 18.000 | ||||
| Percentage of outliers high | 0.021 | ||||
| Mean of outliers high | 1.236 | ||||
| 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) | 0.004 | ||||
| VaR(95%) (regression method) | -0.089 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| 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) | -0.300 | ||||
| Compounded annual return (geometric extrapolation) | -0.968 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.968 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.167 | ||||
| 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 | 1.002 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.515 | ||||
| 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 | 0.869 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.515 | ||||
| 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) | -8751909250090533.000 | ||||
| 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) | -341690157042239545130047781208064.000 | ||||
| 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 | ||||