Advanced Statistics: CTS Treasury Trader
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 | 0.017 | ||||
| SD | 0.130 | ||||
| Sharpe ratio (Glass type estimate) | 0.129 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.128 | ||||
| df | 97.000 | ||||
| t | 0.370 | ||||
| p | 0.356 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.557 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.815 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.558 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.815 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.325 | ||||
| Upside Potential Ratio | 2.176 | ||||
| Upside part of mean | 0.113 | ||||
| Downside part of mean | -0.096 | ||||
| Upside SD | 0.119 | ||||
| Downside SD | 0.052 | ||||
| N nonnegative terms | 26.000 | ||||
| N negative terms | 72.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 98.000 | ||||
| Mean of predictor | 0.124 | ||||
| Mean of criterion | 0.017 | ||||
| SD of predictor | 0.298 | ||||
| SD of criterion | 0.130 | ||||
| Covariance | 0.002 | ||||
| r | 0.049 | ||||
| b (slope, estimate of beta) | 0.021 | ||||
| a (intercept, estimate of alpha) | 0.014 | ||||
| Mean Square Error | 0.017 | ||||
| DF error | 96.000 | ||||
| t(b) | 0.478 | ||||
| p(b) | 0.317 | ||||
| t(a) | 0.309 | ||||
| p(a) | 0.379 | ||||
| Lowerbound of 95% confidence interval for beta | -0.067 | ||||
| Upperbound of 95% confidence interval for beta | 0.110 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.077 | ||||
| Upperbound of 95% confidence interval for alpha | 0.106 | ||||
| Treynor index (mean / b) | 0.791 | ||||
| Jensen alpha (a) | 0.014 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.009 | ||||
| SD | 0.121 | ||||
| Sharpe ratio (Glass type estimate) | 0.076 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.076 | ||||
| df | 97.000 | ||||
| t | 0.219 | ||||
| p | 0.414 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.610 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.762 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.610 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.762 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.175 | ||||
| Upside Potential Ratio | 2.010 | ||||
| Upside part of mean | 0.106 | ||||
| Downside part of mean | -0.097 | ||||
| Upside SD | 0.108 | ||||
| Downside SD | 0.053 | ||||
| N nonnegative terms | 26.000 | ||||
| N negative terms | 72.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 98.000 | ||||
| Mean of predictor | 0.079 | ||||
| Mean of criterion | 0.009 | ||||
| SD of predictor | 0.299 | ||||
| SD of criterion | 0.121 | ||||
| Covariance | 0.001 | ||||
| r | 0.031 | ||||
| b (slope, estimate of beta) | 0.012 | ||||
| a (intercept, estimate of alpha) | 0.008 | ||||
| Mean Square Error | 0.015 | ||||
| DF error | 96.000 | ||||
| t(b) | 0.300 | ||||
| p(b) | 0.382 | ||||
| t(a) | 0.194 | ||||
| p(a) | 0.423 | ||||
| Lowerbound of 95% confidence interval for beta | -0.069 | ||||
| Upperbound of 95% confidence interval for beta | 0.094 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.076 | ||||
| Upperbound of 95% confidence interval for alpha | 0.093 | ||||
| Treynor index (mean / b) | 0.747 | ||||
| Jensen alpha (a) | 0.008 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.055 | ||||
| Expected Shortfall on VaR | 0.069 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.023 | ||||
| Expected Shortfall on VaR | 0.041 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 98.000 | ||||
| Minimum | 0.934 | ||||
| Quartile 1 | 0.997 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.005 | ||||
| Maximum | 1.273 | ||||
| Mean of quarter 1 | 0.979 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.041 | ||||
| Inter Quartile Range | 0.008 | ||||
| Number outliers low | 17.000 | ||||
| Percentage of outliers low | 0.173 | ||||
| Mean of outliers low | 0.973 | ||||
| Number of outliers high | 15.000 | ||||
| Percentage of outliers high | 0.153 | ||||
| Mean of outliers high | 1.060 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.312 | ||||
| VaR(95%) (moments method) | 0.013 | ||||
| Expected Shortfall (moments method) | 0.013 | ||||
| Extreme Value Index (regression method) | -0.008 | ||||
| VaR(95%) (regression method) | 0.018 | ||||
| Expected Shortfall (regression method) | 0.026 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.015 | ||||
| Quartile 1 | 0.037 | ||||
| Median | 0.062 | ||||
| Quartile 3 | 0.104 | ||||
| Maximum | 0.179 | ||||
| Mean of quarter 1 | 0.015 | ||||
| Mean of quarter 2 | 0.044 | ||||
| Mean of quarter 3 | 0.080 | ||||
| Mean of quarter 4 | 0.179 | ||||
| Inter Quartile Range | 0.068 | ||||
| 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) | 0.067 | ||||
| Compounded annual return (geometric extrapolation) | 0.055 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.306 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.306 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.797 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.033 | ||||
| SD | 0.217 | ||||
| Sharpe ratio (Glass type estimate) | 0.150 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.150 | ||||
| df | 2139.000 | ||||
| t | 0.430 | ||||
| p | 0.334 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.535 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.836 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.535 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.836 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.222 | ||||
| Upside Potential Ratio | 4.003 | ||||
| Upside part of mean | 0.587 | ||||
| Downside part of mean | -0.554 | ||||
| Upside SD | 0.159 | ||||
| Downside SD | 0.147 | ||||
| N nonnegative terms | 462.000 | ||||
| N negative terms | 1678.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2140.000 | ||||
| Mean of predictor | 0.239 | ||||
| Mean of criterion | 0.033 | ||||
| SD of predictor | 0.568 | ||||
| SD of criterion | 0.217 | ||||
| Covariance | -0.015 | ||||
| r | -0.125 | ||||
| b (slope, estimate of beta) | -0.048 | ||||
| a (intercept, estimate of alpha) | 0.044 | ||||
| Mean Square Error | 0.046 | ||||
| DF error | 2138.000 | ||||
| t(b) | -5.821 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.584 | ||||
| p(a) | 0.280 | ||||
| Lowerbound of 95% confidence interval for beta | -0.064 | ||||
| Upperbound of 95% confidence interval for beta | -0.032 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.104 | ||||
| Upperbound of 95% confidence interval for alpha | 0.192 | ||||
| Treynor index (mean / b) | -0.684 | ||||
| Jensen alpha (a) | 0.044 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.009 | ||||
| SD | 0.216 | ||||
| Sharpe ratio (Glass type estimate) | 0.043 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.043 | ||||
| df | 2139.000 | ||||
| t | 0.122 | ||||
| p | 0.451 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.643 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.728 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.643 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.728 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.060 | ||||
| Upside Potential Ratio | 3.755 | ||||
| Upside part of mean | 0.575 | ||||
| Downside part of mean | -0.566 | ||||
| Upside SD | 0.152 | ||||
| Downside SD | 0.153 | ||||
| N nonnegative terms | 462.000 | ||||
| N negative terms | 1678.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2140.000 | ||||
| Mean of predictor | 0.079 | ||||
| Mean of criterion | 0.009 | ||||
| SD of predictor | 0.565 | ||||
| SD of criterion | 0.216 | ||||
| Covariance | -0.015 | ||||
| r | -0.122 | ||||
| b (slope, estimate of beta) | -0.047 | ||||
| a (intercept, estimate of alpha) | 0.013 | ||||
| Mean Square Error | 0.046 | ||||
| DF error | 2138.000 | ||||
| t(b) | -5.673 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.172 | ||||
| p(a) | 0.432 | ||||
| Lowerbound of 95% confidence interval for beta | -0.063 | ||||
| Upperbound of 95% confidence interval for beta | -0.030 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.134 | ||||
| Upperbound of 95% confidence interval for alpha | 0.160 | ||||
| Treynor index (mean / b) | -0.198 | ||||
| Jensen alpha (a) | 0.013 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.022 | ||||
| Expected Shortfall on VaR | 0.027 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.014 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2140.000 | ||||
| Minimum | 0.838 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.214 | ||||
| Mean of quarter 1 | 0.992 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.009 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 453.000 | ||||
| Percentage of outliers low | 0.212 | ||||
| Mean of outliers low | 0.991 | ||||
| Number of outliers high | 499.000 | ||||
| Percentage of outliers high | 0.233 | ||||
| Mean of outliers high | 1.010 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.823 | ||||
| VaR(95%) (moments method) | 0.005 | ||||
| Expected Shortfall (moments method) | 0.032 | ||||
| Extreme Value Index (regression method) | 0.529 | ||||
| VaR(95%) (regression method) | 0.006 | ||||
| Expected Shortfall (regression method) | 0.019 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 23.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.013 | ||||
| Median | 0.018 | ||||
| Quartile 3 | 0.031 | ||||
| Maximum | 0.189 | ||||
| Mean of quarter 1 | 0.007 | ||||
| Mean of quarter 2 | 0.016 | ||||
| Mean of quarter 3 | 0.022 | ||||
| Mean of quarter 4 | 0.110 | ||||
| Inter Quartile Range | 0.018 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.174 | ||||
| Mean of outliers high | 0.147 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.412 | ||||
| VaR(95%) (moments method) | 0.093 | ||||
| Expected Shortfall (moments method) | 0.115 | ||||
| Extreme Value Index (regression method) | -0.604 | ||||
| VaR(95%) (regression method) | 0.133 | ||||
| Expected Shortfall (regression method) | 0.156 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.067 | ||||
| Compounded annual return (geometric extrapolation) | 0.055 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.290 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.498 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.016 | ||||
| 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 | 0.985 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.586 | ||||
| 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 | 0.803 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.614 | ||||
| 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) | -8770995526032304.000 | ||||
| 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) | 128331142725390125565603297099776.000 | ||||
| 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 | ||||