Advanced Statistics: FX Sulaco
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 | 0.217 | ||||
| SD | 0.373 | ||||
| Sharpe ratio (Glass type estimate) | 0.581 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.568 | ||||
| df | 35.000 | ||||
| t | 1.006 | ||||
| p | 0.161 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.563 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.717 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.571 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.708 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.408 | ||||
| Upside Potential Ratio | 2.411 | ||||
| Upside part of mean | 0.371 | ||||
| Downside part of mean | -0.154 | ||||
| Upside SD | 0.340 | ||||
| Downside SD | 0.154 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.521 | ||||
| Mean of criterion | 0.217 | ||||
| SD of predictor | 0.260 | ||||
| SD of criterion | 0.373 | ||||
| Covariance | 0.007 | ||||
| r | 0.072 | ||||
| b (slope, estimate of beta) | 0.103 | ||||
| a (intercept, estimate of alpha) | 0.163 | ||||
| Mean Square Error | 0.143 | ||||
| DF error | 34.000 | ||||
| t(b) | 0.420 | ||||
| p(b) | 0.339 | ||||
| t(a) | 0.646 | ||||
| p(a) | 0.261 | ||||
| Lowerbound of 95% confidence interval for beta | -0.395 | ||||
| Upperbound of 95% confidence interval for beta | 0.601 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.350 | ||||
| Upperbound of 95% confidence interval for alpha | 0.677 | ||||
| Treynor index (mean / b) | 2.106 | ||||
| Jensen alpha (a) | 0.163 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.155 | ||||
| SD | 0.343 | ||||
| Sharpe ratio (Glass type estimate) | 0.452 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.442 | ||||
| df | 35.000 | ||||
| t | 0.782 | ||||
| p | 0.220 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.688 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.585 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.694 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.578 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.884 | ||||
| Upside Potential Ratio | 1.844 | ||||
| Upside part of mean | 0.323 | ||||
| Downside part of mean | -0.168 | ||||
| Upside SD | 0.293 | ||||
| Downside SD | 0.175 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.478 | ||||
| Mean of criterion | 0.155 | ||||
| SD of predictor | 0.246 | ||||
| SD of criterion | 0.343 | ||||
| Covariance | 0.010 | ||||
| r | 0.116 | ||||
| b (slope, estimate of beta) | 0.161 | ||||
| a (intercept, estimate of alpha) | 0.078 | ||||
| Mean Square Error | 0.119 | ||||
| DF error | 34.000 | ||||
| t(b) | 0.680 | ||||
| p(b) | 0.251 | ||||
| t(a) | 0.339 | ||||
| p(a) | 0.368 | ||||
| Lowerbound of 95% confidence interval for beta | -0.321 | ||||
| Upperbound of 95% confidence interval for beta | 0.643 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.389 | ||||
| Upperbound of 95% confidence interval for alpha | 0.544 | ||||
| Treynor index (mean / b) | 0.960 | ||||
| Jensen alpha (a) | 0.078 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.139 | ||||
| Expected Shortfall on VaR | 0.174 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.042 | ||||
| Expected Shortfall on VaR | 0.089 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 36.000 | ||||
| Minimum | 0.751 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.379 | ||||
| Mean of quarter 1 | 0.962 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.125 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.111 | ||||
| Mean of outliers low | 0.914 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.111 | ||||
| Mean of outliers high | 1.282 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -36.391 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.000 | ||||
| Extreme Value Index (regression method) | 0.864 | ||||
| VaR(95%) (regression method) | 0.059 | ||||
| Expected Shortfall (regression method) | 0.833 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.022 | ||||
| Quartile 1 | 0.093 | ||||
| Median | 0.164 | ||||
| Quartile 3 | 0.234 | ||||
| Maximum | 0.305 | ||||
| Mean of quarter 1 | 0.022 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.305 | ||||
| Inter Quartile Range | 0.141 | ||||
| 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) | 0.272 | ||||
| Compounded annual return (geometric extrapolation) | 0.220 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.721 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.721 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.268 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.202 | ||||
| SD | 0.330 | ||||
| Sharpe ratio (Glass type estimate) | 0.611 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.610 | ||||
| df | 803.000 | ||||
| t | 1.070 | ||||
| p | 0.142 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.509 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.730 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.509 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.729 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.131 | ||||
| Upside Potential Ratio | 4.196 | ||||
| Upside part of mean | 0.749 | ||||
| Downside part of mean | -0.547 | ||||
| Upside SD | 0.278 | ||||
| Downside SD | 0.179 | ||||
| N nonnegative terms | 64.000 | ||||
| N negative terms | 740.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 804.000 | ||||
| Mean of predictor | 0.573 | ||||
| Mean of criterion | 0.202 | ||||
| SD of predictor | 0.318 | ||||
| SD of criterion | 0.330 | ||||
| Covariance | 0.004 | ||||
| r | 0.038 | ||||
| b (slope, estimate of beta) | 0.039 | ||||
| a (intercept, estimate of alpha) | 0.179 | ||||
| Mean Square Error | 0.109 | ||||
| DF error | 802.000 | ||||
| t(b) | 1.076 | ||||
| p(b) | 0.141 | ||||
| t(a) | 0.944 | ||||
| p(a) | 0.173 | ||||
| Lowerbound of 95% confidence interval for beta | -0.032 | ||||
| Upperbound of 95% confidence interval for beta | 0.111 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.193 | ||||
| Upperbound of 95% confidence interval for alpha | 0.552 | ||||
| Treynor index (mean / b) | 5.121 | ||||
| Jensen alpha (a) | 0.179 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.150 | ||||
| SD | 0.317 | ||||
| Sharpe ratio (Glass type estimate) | 0.475 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.475 | ||||
| df | 803.000 | ||||
| t | 0.832 | ||||
| p | 0.203 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.644 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.594 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.645 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.594 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.803 | ||||
| Upside Potential Ratio | 3.818 | ||||
| Upside part of mean | 0.715 | ||||
| Downside part of mean | -0.564 | ||||
| Upside SD | 0.255 | ||||
| Downside SD | 0.187 | ||||
| N nonnegative terms | 64.000 | ||||
| N negative terms | 740.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 804.000 | ||||
| Mean of predictor | 0.521 | ||||
| Mean of criterion | 0.150 | ||||
| SD of predictor | 0.322 | ||||
| SD of criterion | 0.317 | ||||
| Covariance | 0.004 | ||||
| r | 0.038 | ||||
| b (slope, estimate of beta) | 0.038 | ||||
| a (intercept, estimate of alpha) | 0.131 | ||||
| Mean Square Error | 0.100 | ||||
| DF error | 802.000 | ||||
| t(b) | 1.090 | ||||
| p(b) | 0.138 | ||||
| t(a) | 0.720 | ||||
| p(a) | 0.236 | ||||
| Lowerbound of 95% confidence interval for beta | -0.030 | ||||
| Upperbound of 95% confidence interval for beta | 0.106 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.226 | ||||
| Upperbound of 95% confidence interval for alpha | 0.487 | ||||
| Treynor index (mean / b) | 3.983 | ||||
| Jensen alpha (a) | 0.131 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.031 | ||||
| Expected Shortfall on VaR | 0.039 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.015 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 804.000 | ||||
| Minimum | 0.850 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.323 | ||||
| Mean of quarter 1 | 0.992 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.011 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 59.000 | ||||
| Percentage of outliers low | 0.073 | ||||
| Mean of outliers low | 0.974 | ||||
| Number of outliers high | 64.000 | ||||
| Percentage of outliers high | 0.080 | ||||
| Mean of outliers high | 1.036 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.388 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.005 | ||||
| Extreme Value Index (regression method) | 0.357 | ||||
| VaR(95%) (regression method) | 0.005 | ||||
| Expected Shortfall (regression method) | 0.027 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.010 | ||||
| Quartile 1 | 0.023 | ||||
| Median | 0.042 | ||||
| Quartile 3 | 0.136 | ||||
| Maximum | 0.377 | ||||
| Mean of quarter 1 | 0.010 | ||||
| Mean of quarter 2 | 0.030 | ||||
| Mean of quarter 3 | 0.069 | ||||
| Mean of quarter 4 | 0.331 | ||||
| Inter Quartile Range | 0.113 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.125 | ||||
| Mean of outliers high | 0.377 | ||||
| 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) | 0.266 | ||||
| Compounded annual return (geometric extrapolation) | 0.215 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.568 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.649 | ||||
| Compounded annual return / Expected Shortfall lognormal | 5.507 | ||||
| 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 | 1.003 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.481 | ||||
| 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 | 0.885 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.485 | ||||
| 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) | -8743864592128845.000 | ||||
| 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) | -973558312276865529674265782124544.000 | ||||
| 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 | ||||