Advanced Statistics: Seleukos Currency Overnight Portfolio
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 | 0.048 | ||||
| SD | 0.261 | ||||
| Sharpe ratio (Glass type estimate) | 0.182 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.181 | ||||
| df | 82.000 | ||||
| t | 0.480 | ||||
| p | 0.316 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.564 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.928 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.565 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.927 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.294 | ||||
| Upside Potential Ratio | 1.803 | ||||
| Upside part of mean | 0.292 | ||||
| Downside part of mean | -0.245 | ||||
| Upside SD | 0.203 | ||||
| Downside SD | 0.162 | ||||
| N nonnegative terms | 24.000 | ||||
| N negative terms | 59.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 83.000 | ||||
| Mean of predictor | 0.143 | ||||
| Mean of criterion | 0.048 | ||||
| SD of predictor | 0.283 | ||||
| SD of criterion | 0.261 | ||||
| Covariance | 0.007 | ||||
| r | 0.099 | ||||
| b (slope, estimate of beta) | 0.091 | ||||
| a (intercept, estimate of alpha) | 0.035 | ||||
| Mean Square Error | 0.068 | ||||
| DF error | 81.000 | ||||
| t(b) | 0.895 | ||||
| p(b) | 0.187 | ||||
| t(a) | 0.345 | ||||
| p(a) | 0.366 | ||||
| Lowerbound of 95% confidence interval for beta | -0.112 | ||||
| Upperbound of 95% confidence interval for beta | 0.294 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.165 | ||||
| Upperbound of 95% confidence interval for alpha | 0.234 | ||||
| Treynor index (mean / b) | 0.522 | ||||
| Jensen alpha (a) | 0.035 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.015 | ||||
| SD | 0.257 | ||||
| Sharpe ratio (Glass type estimate) | 0.057 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.057 | ||||
| df | 82.000 | ||||
| t | 0.150 | ||||
| p | 0.440 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.688 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.802 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.689 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.802 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.084 | ||||
| Upside Potential Ratio | 1.555 | ||||
| Upside part of mean | 0.273 | ||||
| Downside part of mean | -0.258 | ||||
| Upside SD | 0.185 | ||||
| Downside SD | 0.176 | ||||
| N nonnegative terms | 24.000 | ||||
| N negative terms | 59.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 83.000 | ||||
| Mean of predictor | 0.101 | ||||
| Mean of criterion | 0.015 | ||||
| SD of predictor | 0.291 | ||||
| SD of criterion | 0.257 | ||||
| Covariance | 0.011 | ||||
| r | 0.142 | ||||
| b (slope, estimate of beta) | 0.126 | ||||
| a (intercept, estimate of alpha) | 0.002 | ||||
| Mean Square Error | 0.065 | ||||
| DF error | 81.000 | ||||
| t(b) | 1.294 | ||||
| p(b) | 0.100 | ||||
| t(a) | 0.021 | ||||
| p(a) | 0.492 | ||||
| Lowerbound of 95% confidence interval for beta | -0.068 | ||||
| Upperbound of 95% confidence interval for beta | 0.319 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.193 | ||||
| Upperbound of 95% confidence interval for alpha | 0.197 | ||||
| Treynor index (mean / b) | 0.117 | ||||
| Jensen alpha (a) | 0.002 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.114 | ||||
| Expected Shortfall on VaR | 0.140 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.058 | ||||
| Expected Shortfall on VaR | 0.114 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 83.000 | ||||
| Minimum | 0.770 | ||||
| Quartile 1 | 0.997 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.021 | ||||
| Maximum | 1.319 | ||||
| Mean of quarter 1 | 0.930 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.099 | ||||
| Inter Quartile Range | 0.024 | ||||
| Number outliers low | 13.000 | ||||
| Percentage of outliers low | 0.157 | ||||
| Mean of outliers low | 0.898 | ||||
| Number of outliers high | 15.000 | ||||
| Percentage of outliers high | 0.181 | ||||
| Mean of outliers high | 1.124 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.333 | ||||
| VaR(95%) (moments method) | 0.025 | ||||
| Expected Shortfall (moments method) | 0.032 | ||||
| Extreme Value Index (regression method) | -0.033 | ||||
| VaR(95%) (regression method) | 0.070 | ||||
| Expected Shortfall (regression method) | 0.109 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.025 | ||||
| Quartile 1 | 0.060 | ||||
| Median | 0.087 | ||||
| Quartile 3 | 0.175 | ||||
| Maximum | 0.230 | ||||
| Mean of quarter 1 | 0.038 | ||||
| Mean of quarter 2 | 0.076 | ||||
| Mean of quarter 3 | 0.165 | ||||
| Mean of quarter 4 | 0.222 | ||||
| Inter Quartile Range | 0.116 | ||||
| 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) | -19.671 | ||||
| VaR(95%) (moments method) | 0.219 | ||||
| Expected Shortfall (moments method) | 0.219 | ||||
| Extreme Value Index (regression method) | -2.235 | ||||
| VaR(95%) (regression method) | 0.259 | ||||
| Expected Shortfall (regression method) | 0.260 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.072 | ||||
| Compounded annual return (geometric extrapolation) | 0.060 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.263 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.272 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.430 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.139 | ||||
| SD | 0.502 | ||||
| Sharpe ratio (Glass type estimate) | 0.277 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.277 | ||||
| df | 1830.000 | ||||
| t | 0.733 | ||||
| p | 0.491 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.464 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.019 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.464 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.018 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.421 | ||||
| Upside Potential Ratio | 5.077 | ||||
| Upside part of mean | 1.676 | ||||
| Downside part of mean | -1.537 | ||||
| Upside SD | 0.377 | ||||
| Downside SD | 0.330 | ||||
| N nonnegative terms | 415.000 | ||||
| N negative terms | 1416.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1831.000 | ||||
| Mean of predictor | 0.248 | ||||
| Mean of criterion | 0.139 | ||||
| SD of predictor | 0.551 | ||||
| SD of criterion | 0.502 | ||||
| Covariance | 0.041 | ||||
| r | 0.147 | ||||
| b (slope, estimate of beta) | 0.134 | ||||
| a (intercept, estimate of alpha) | 0.106 | ||||
| Mean Square Error | 0.246 | ||||
| DF error | 1829.000 | ||||
| t(b) | 6.343 | ||||
| p(b) | 0.407 | ||||
| t(a) | 0.564 | ||||
| p(a) | 0.492 | ||||
| Lowerbound of 95% confidence interval for beta | 0.092 | ||||
| Upperbound of 95% confidence interval for beta | 0.175 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.262 | ||||
| Upperbound of 95% confidence interval for alpha | 0.474 | ||||
| Treynor index (mean / b) | 1.041 | ||||
| Jensen alpha (a) | 0.106 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.014 | ||||
| SD | 0.500 | ||||
| Sharpe ratio (Glass type estimate) | 0.028 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.028 | ||||
| df | 1830.000 | ||||
| t | 0.074 | ||||
| p | 0.499 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.713 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.770 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.713 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.770 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.040 | ||||
| Upside Potential Ratio | 4.564 | ||||
| Upside part of mean | 1.611 | ||||
| Downside part of mean | -1.597 | ||||
| Upside SD | 0.354 | ||||
| Downside SD | 0.353 | ||||
| N nonnegative terms | 415.000 | ||||
| N negative terms | 1416.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1831.000 | ||||
| Mean of predictor | 0.098 | ||||
| Mean of criterion | 0.014 | ||||
| SD of predictor | 0.547 | ||||
| SD of criterion | 0.500 | ||||
| Covariance | 0.040 | ||||
| r | 0.145 | ||||
| b (slope, estimate of beta) | 0.132 | ||||
| a (intercept, estimate of alpha) | 0.001 | ||||
| Mean Square Error | 0.245 | ||||
| DF error | 1829.000 | ||||
| t(b) | 6.250 | ||||
| p(b) | 0.408 | ||||
| t(a) | 0.006 | ||||
| p(a) | 0.500 | ||||
| Lowerbound of 95% confidence interval for beta | 0.091 | ||||
| Upperbound of 95% confidence interval for beta | 0.174 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.366 | ||||
| Upperbound of 95% confidence interval for alpha | 0.368 | ||||
| Treynor index (mean / b) | 0.107 | ||||
| Jensen alpha (a) | 0.001 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.049 | ||||
| Expected Shortfall on VaR | 0.062 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.038 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1831.000 | ||||
| Minimum | 0.773 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.277 | ||||
| Mean of quarter 1 | 0.977 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.026 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 446.000 | ||||
| Percentage of outliers low | 0.244 | ||||
| Mean of outliers low | 0.976 | ||||
| Number of outliers high | 414.000 | ||||
| Percentage of outliers high | 0.226 | ||||
| Mean of outliers high | 1.028 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.560 | ||||
| VaR(95%) (moments method) | 0.007 | ||||
| Expected Shortfall (moments method) | 0.020 | ||||
| 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 | 22.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.079 | ||||
| Median | 0.107 | ||||
| Quartile 3 | 0.174 | ||||
| Maximum | 0.312 | ||||
| Mean of quarter 1 | 0.042 | ||||
| Mean of quarter 2 | 0.099 | ||||
| Mean of quarter 3 | 0.128 | ||||
| Mean of quarter 4 | 0.244 | ||||
| Inter Quartile Range | 0.095 | ||||
| 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) | -1.039 | ||||
| VaR(95%) (moments method) | 0.275 | ||||
| Expected Shortfall (moments method) | 0.288 | ||||
| Extreme Value Index (regression method) | -0.148 | ||||
| VaR(95%) (regression method) | 0.234 | ||||
| Expected Shortfall (regression method) | 0.260 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.072 | ||||
| Compounded annual return (geometric extrapolation) | 0.060 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.192 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.246 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.971 | ||||
| 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 | 0.776 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.542 | ||||
| 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 | 0.622 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.561 | ||||
| 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) | -8779067139957584.000 | ||||
| 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) | 304937997687594719096650522951680.000 | ||||
| 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 | ||||