Advanced Statistics: S E L E K T I V E -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 | -0.186 | ||||
| SD | 0.505 | ||||
| Sharpe ratio (Glass type estimate) | -0.369 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.366 | ||||
| df | 110.000 | ||||
| t | -1.121 | ||||
| p | 0.553 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.014 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.279 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.012 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.280 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.425 | ||||
| Upside Potential Ratio | 0.480 | ||||
| Upside part of mean | 0.211 | ||||
| Downside part of mean | -0.397 | ||||
| Upside SD | 0.252 | ||||
| Downside SD | 0.438 | ||||
| N nonnegative terms | 15.000 | ||||
| N negative terms | 96.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 111.000 | ||||
| Mean of predictor | 0.146 | ||||
| Mean of criterion | -0.186 | ||||
| SD of predictor | 0.286 | ||||
| SD of criterion | 0.505 | ||||
| Covariance | -0.005 | ||||
| r | -0.033 | ||||
| b (slope, estimate of beta) | -0.059 | ||||
| a (intercept, estimate of alpha) | -0.177 | ||||
| Mean Square Error | 0.257 | ||||
| DF error | 109.000 | ||||
| t(b) | -0.350 | ||||
| p(b) | 0.521 | ||||
| t(a) | -1.053 | ||||
| p(a) | 0.564 | ||||
| Lowerbound of 95% confidence interval for beta | -0.394 | ||||
| Upperbound of 95% confidence interval for beta | 0.276 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.512 | ||||
| Upperbound of 95% confidence interval for alpha | 0.157 | ||||
| Treynor index (mean / b) | 3.145 | ||||
| Jensen alpha (a) | -0.177 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -1.279 | ||||
| SD | 3.412 | ||||
| Sharpe ratio (Glass type estimate) | -0.375 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.372 | ||||
| df | 110.000 | ||||
| t | -1.140 | ||||
| p | 0.554 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.020 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.272 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.019 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.274 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.375 | ||||
| Upside Potential Ratio | 0.054 | ||||
| Upside part of mean | 0.185 | ||||
| Downside part of mean | -1.464 | ||||
| Upside SD | 0.212 | ||||
| Downside SD | 3.410 | ||||
| N nonnegative terms | 15.000 | ||||
| N negative terms | 96.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 111.000 | ||||
| Mean of predictor | 0.109 | ||||
| Mean of criterion | -1.279 | ||||
| SD of predictor | 0.267 | ||||
| SD of criterion | 3.412 | ||||
| Covariance | -0.031 | ||||
| r | -0.034 | ||||
| b (slope, estimate of beta) | -0.440 | ||||
| a (intercept, estimate of alpha) | -1.231 | ||||
| Mean Square Error | 11.734 | ||||
| DF error | 109.000 | ||||
| t(b) | -0.360 | ||||
| p(b) | 0.522 | ||||
| t(a) | -1.086 | ||||
| p(a) | 0.566 | ||||
| Lowerbound of 95% confidence interval for beta | -2.865 | ||||
| Upperbound of 95% confidence interval for beta | 1.985 | ||||
| Lowerbound of 95% confidence interval for alpha | -3.479 | ||||
| Upperbound of 95% confidence interval for alpha | 1.017 | ||||
| Treynor index (mean / b) | 2.907 | ||||
| Jensen alpha (a) | -1.231 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.822 | ||||
| Expected Shortfall on VaR | 0.875 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.105 | ||||
| Expected Shortfall on VaR | 0.229 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 111.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.538 | ||||
| Mean of quarter 1 | 0.882 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.072 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 22.000 | ||||
| Percentage of outliers low | 0.198 | ||||
| Mean of outliers low | 0.849 | ||||
| Number of outliers high | 17.000 | ||||
| Percentage of outliers high | 0.153 | ||||
| Mean of outliers high | 1.118 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.039 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | 0.827 | ||||
| VaR(95%) (regression method) | 0.111 | ||||
| Expected Shortfall (regression method) | 0.888 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.050 | ||||
| Quartile 1 | 0.130 | ||||
| Median | 0.211 | ||||
| Quartile 3 | 0.605 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.050 | ||||
| Mean of quarter 2 | 0.211 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.475 | ||||
| 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) | -0.108 | ||||
| Compounded annual return (geometric extrapolation) | -0.709 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.709 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.709 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.810 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1309.652 | ||||
| SD | 3314.900 | ||||
| Sharpe ratio (Glass type estimate) | 0.395 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.395 | ||||
| df | 2431.000 | ||||
| t | 1.204 | ||||
| p | 0.114 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.248 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.038 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.248 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.038 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1445.500 | ||||
| Upside Potential Ratio | 1448.419 | ||||
| Upside part of mean | 1312.297 | ||||
| Downside part of mean | -2.645 | ||||
| Upside SD | 3315.206 | ||||
| Downside SD | 0.906 | ||||
| N nonnegative terms | 302.000 | ||||
| N negative terms | 2130.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2432.000 | ||||
| Mean of predictor | 0.253 | ||||
| Mean of criterion | 1309.652 | ||||
| SD of predictor | 0.522 | ||||
| SD of criterion | 3314.900 | ||||
| Covariance | -15.398 | ||||
| r | -0.009 | ||||
| b (slope, estimate of beta) | -56.568 | ||||
| a (intercept, estimate of alpha) | 1323.965 | ||||
| Mean Square Error | 10992213.559 | ||||
| DF error | 2430.000 | ||||
| t(b) | -0.439 | ||||
| p(b) | 0.670 | ||||
| t(a) | 1.216 | ||||
| p(a) | 0.112 | ||||
| Lowerbound of 95% confidence interval for beta | -309.307 | ||||
| Upperbound of 95% confidence interval for beta | 196.171 | ||||
| Lowerbound of 95% confidence interval for alpha | -810.902 | ||||
| Upperbound of 95% confidence interval for alpha | 3458.832 | ||||
| Treynor index (mean / b) | -23.152 | ||||
| Jensen alpha (a) | 1323.965 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -1.275 | ||||
| SD | 6.479 | ||||
| Sharpe ratio (Glass type estimate) | -0.197 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.197 | ||||
| df | 2431.000 | ||||
| t | -0.599 | ||||
| p | 0.726 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.840 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.447 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.840 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.447 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.252 | ||||
| Upside Potential Ratio | 0.833 | ||||
| Upside part of mean | 4.215 | ||||
| Downside part of mean | -5.490 | ||||
| Upside SD | 4.040 | ||||
| Downside SD | 5.063 | ||||
| N nonnegative terms | 302.000 | ||||
| N negative terms | 2130.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2432.000 | ||||
| Mean of predictor | 0.121 | ||||
| Mean of criterion | -1.275 | ||||
| SD of predictor | 0.511 | ||||
| SD of criterion | 6.479 | ||||
| Covariance | -0.155 | ||||
| r | -0.047 | ||||
| b (slope, estimate of beta) | -0.594 | ||||
| a (intercept, estimate of alpha) | -1.203 | ||||
| Mean Square Error | 41.897 | ||||
| DF error | 2430.000 | ||||
| t(b) | -2.314 | ||||
| p(b) | 0.990 | ||||
| t(a) | -0.566 | ||||
| p(a) | 0.714 | ||||
| Lowerbound of 95% confidence interval for beta | -1.098 | ||||
| Upperbound of 95% confidence interval for beta | -0.091 | ||||
| Lowerbound of 95% confidence interval for alpha | -5.369 | ||||
| Upperbound of 95% confidence interval for alpha | 2.964 | ||||
| Treynor index (mean / b) | 2.145 | ||||
| Jensen alpha (a) | -1.203 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.485 | ||||
| Expected Shortfall on VaR | 0.560 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.032 | ||||
| Expected Shortfall on VaR | 0.073 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2432.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 9830.000 | ||||
| Mean of quarter 1 | 0.960 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 21.035 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 486.000 | ||||
| Percentage of outliers low | 0.200 | ||||
| Mean of outliers low | 0.950 | ||||
| Number of outliers high | 307.000 | ||||
| Percentage of outliers high | 0.126 | ||||
| Mean of outliers high | 40.679 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.741 | ||||
| VaR(95%) (moments method) | 0.009 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.505 | ||||
| VaR(95%) (regression method) | 0.023 | ||||
| Expected Shortfall (regression method) | 0.078 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 11.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.066 | ||||
| Median | 0.152 | ||||
| Quartile 3 | 0.272 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.026 | ||||
| Mean of quarter 2 | 0.125 | ||||
| Mean of quarter 3 | 0.254 | ||||
| Mean of quarter 4 | 0.520 | ||||
| Inter Quartile Range | 0.206 | ||||
| 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 | 0.091 | ||||
| Mean of outliers high | 1.000 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.620 | ||||
| VaR(95%) (moments method) | 0.634 | ||||
| Expected Shortfall (moments method) | 1.692 | ||||
| Extreme Value Index (regression method) | 6.026 | ||||
| VaR(95%) (regression method) | 2.863 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.108 | ||||
| Compounded annual return (geometric extrapolation) | -0.708 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.708 | ||||
| Compounded annual return / average of 25% largest draw downs | -1.362 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.265 | ||||
| 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 | 0.943 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.779 | ||||
| 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 | 0.700 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.661 | ||||
| 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) | -8780828976592827.000 | ||||
| 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) | 904815021367867733499939957768192.000 | ||||
| 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 | ||||