Advanced Statistics: Bond007
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 | 42749.425 | ||||
| SD | 61704.703 | ||||
| Sharpe ratio (Glass type estimate) | 0.693 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.671 | ||||
| df | 24.000 | ||||
| t | 1.000 | ||||
| p | 0.164 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.686 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.058 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.700 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.042 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 43469.161 | ||||
| Upside Potential Ratio | 43470.179 | ||||
| Upside part of mean | 42750.426 | ||||
| Downside part of mean | -1.001 | ||||
| Upside SD | 61704.654 | ||||
| Downside SD | 0.983 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 23.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 25.000 | ||||
| Mean of predictor | 0.887 | ||||
| Mean of criterion | 42749.425 | ||||
| SD of predictor | 0.426 | ||||
| SD of criterion | 61704.703 | ||||
| Covariance | 2055.402 | ||||
| r | 0.078 | ||||
| b (slope, estimate of beta) | 11348.040 | ||||
| a (intercept, estimate of alpha) | 32683.778 | ||||
| Mean Square Error | 3948673631.453 | ||||
| DF error | 23.000 | ||||
| t(b) | 0.377 | ||||
| p(b) | 0.355 | ||||
| t(a) | 0.640 | ||||
| p(a) | 0.264 | ||||
| Lowerbound of 95% confidence interval for beta | -50999.703 | ||||
| Upperbound of 95% confidence interval for beta | 73695.784 | ||||
| Lowerbound of 95% confidence interval for alpha | -73000.826 | ||||
| Upperbound of 95% confidence interval for alpha | 138368.383 | ||||
| Treynor index (mean / b) | 3.767 | ||||
| Jensen alpha (a) | 32683.778 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -4.798 | ||||
| SD | 13.430 | ||||
| Sharpe ratio (Glass type estimate) | -0.357 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.346 | ||||
| df | 24.000 | ||||
| t | -0.516 | ||||
| p | 0.695 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.715 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.008 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.707 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.016 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.452 | ||||
| Upside Potential Ratio | 0.530 | ||||
| Upside part of mean | 5.627 | ||||
| Downside part of mean | -10.424 | ||||
| Upside SD | 7.897 | ||||
| Downside SD | 10.617 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 23.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 25.000 | ||||
| Mean of predictor | 0.783 | ||||
| Mean of criterion | -4.798 | ||||
| SD of predictor | 0.373 | ||||
| SD of criterion | 13.430 | ||||
| Covariance | 1.430 | ||||
| r | 0.285 | ||||
| b (slope, estimate of beta) | 10.267 | ||||
| a (intercept, estimate of alpha) | -12.841 | ||||
| Mean Square Error | 172.897 | ||||
| DF error | 23.000 | ||||
| t(b) | 1.428 | ||||
| p(b) | 0.083 | ||||
| t(a) | -1.199 | ||||
| p(a) | 0.879 | ||||
| Lowerbound of 95% confidence interval for beta | -4.609 | ||||
| Upperbound of 95% confidence interval for beta | 25.142 | ||||
| Lowerbound of 95% confidence interval for alpha | -34.998 | ||||
| Upperbound of 95% confidence interval for alpha | 9.317 | ||||
| Treynor index (mean / b) | -0.467 | ||||
| Jensen alpha (a) | -12.841 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.999 | ||||
| Expected Shortfall on VaR | 1.000 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.276 | ||||
| Expected Shortfall on VaR | 0.588 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 25.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 89064.000 | ||||
| Mean of quarter 1 | 0.714 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 14844.899 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.080 | ||||
| Mean of outliers low | 0.000 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.080 | ||||
| Mean of outliers high | 44532.697 | ||||
| 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) | -16.310 | ||||
| VaR(95%) (regression method) | 91.320 | ||||
| Expected Shortfall (regression method) | 91.320 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| 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 | NA | ||||
| Mean of quarter 3 | NA | ||||
| 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 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) | -0.480 | ||||
| Compounded annual return (geometric extrapolation) | -0.991 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.991 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.991 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.992 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 58474.598 | ||||
| SD | 84492.492 | ||||
| Sharpe ratio (Glass type estimate) | 0.692 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.691 | ||||
| df | 546.000 | ||||
| t | 1.000 | ||||
| p | 0.159 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.665 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.049 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.666 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.048 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 47034.766 | ||||
| Upside Potential Ratio | 47037.388 | ||||
| Upside part of mean | 58477.857 | ||||
| Downside part of mean | -3.259 | ||||
| Upside SD | 84492.489 | ||||
| Downside SD | 1.243 | ||||
| N nonnegative terms | 32.000 | ||||
| N negative terms | 515.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 547.000 | ||||
| Mean of predictor | 0.888 | ||||
| Mean of criterion | 58474.598 | ||||
| SD of predictor | 0.420 | ||||
| SD of criterion | 84492.492 | ||||
| Covariance | 129.353 | ||||
| r | 0.004 | ||||
| b (slope, estimate of beta) | 734.382 | ||||
| a (intercept, estimate of alpha) | 57822.318 | ||||
| Mean Square Error | 7151985048.147 | ||||
| DF error | 545.000 | ||||
| t(b) | 0.085 | ||||
| p(b) | 0.466 | ||||
| t(a) | 0.980 | ||||
| p(a) | 0.164 | ||||
| Lowerbound of 95% confidence interval for beta | -16205.203 | ||||
| Upperbound of 95% confidence interval for beta | 17673.968 | ||||
| Lowerbound of 95% confidence interval for alpha | -58127.852 | ||||
| Upperbound of 95% confidence interval for alpha | 173772.487 | ||||
| Treynor index (mean / b) | 79.624 | ||||
| Jensen alpha (a) | 57822.318 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -4.788 | ||||
| SD | 12.810 | ||||
| Sharpe ratio (Glass type estimate) | -0.374 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.373 | ||||
| df | 546.000 | ||||
| t | -0.540 | ||||
| p | 0.705 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.730 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.983 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.730 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.983 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.484 | ||||
| Upside Potential Ratio | 0.762 | ||||
| Upside part of mean | 7.536 | ||||
| Downside part of mean | -12.324 | ||||
| Upside SD | 8.136 | ||||
| Downside SD | 9.884 | ||||
| N nonnegative terms | 32.000 | ||||
| N negative terms | 515.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 547.000 | ||||
| Mean of predictor | 0.797 | ||||
| Mean of criterion | -4.788 | ||||
| SD of predictor | 0.427 | ||||
| SD of criterion | 12.810 | ||||
| Covariance | 0.245 | ||||
| r | 0.045 | ||||
| b (slope, estimate of beta) | 1.343 | ||||
| a (intercept, estimate of alpha) | -5.858 | ||||
| Mean Square Error | 164.071 | ||||
| DF error | 545.000 | ||||
| t(b) | 1.046 | ||||
| p(b) | 0.148 | ||||
| t(a) | -0.656 | ||||
| p(a) | 0.744 | ||||
| Lowerbound of 95% confidence interval for beta | -1.180 | ||||
| Upperbound of 95% confidence interval for beta | 3.865 | ||||
| Lowerbound of 95% confidence interval for alpha | -23.387 | ||||
| Upperbound of 95% confidence interval for alpha | 11.672 | ||||
| Treynor index (mean / b) | -3.566 | ||||
| Jensen alpha (a) | -5.858 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.733 | ||||
| Expected Shortfall on VaR | 0.801 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.042 | ||||
| Expected Shortfall on VaR | 0.094 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 547.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 122085.667 | ||||
| Mean of quarter 1 | 0.951 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 892.163 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 39.000 | ||||
| Percentage of outliers low | 0.071 | ||||
| Mean of outliers low | 0.828 | ||||
| Number of outliers high | 32.000 | ||||
| Percentage of outliers high | 0.059 | ||||
| Mean of outliers high | 3816.290 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -3.196 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | -0.507 | ||||
| VaR(95%) (regression method) | 0.041 | ||||
| Expected Shortfall (regression method) | 0.116 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.009 | ||||
| Quartile 1 | 0.079 | ||||
| Median | 0.603 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.044 | ||||
| Mean of quarter 2 | 0.603 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.921 | ||||
| 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) | -0.479 | ||||
| Compounded annual return (geometric extrapolation) | -0.991 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.991 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.991 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.238 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 244165.746 | ||||
| SD | 172653.811 | ||||
| Sharpe ratio (Glass type estimate) | 1.414 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.406 | ||||
| df | 130.000 | ||||
| t | 1.000 | ||||
| p | 0.456 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.366 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.189 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.371 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.183 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 137454.786 | ||||
| Upside Potential Ratio | 137458.376 | ||||
| Upside part of mean | 244172.122 | ||||
| Downside part of mean | -6.376 | ||||
| Upside SD | 172653.791 | ||||
| Downside SD | 1.776 | ||||
| N nonnegative terms | 12.000 | ||||
| N negative terms | 119.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 2.246 | ||||
| Mean of criterion | 244165.746 | ||||
| SD of predictor | 0.743 | ||||
| SD of criterion | 172653.811 | ||||
| Covariance | -731.730 | ||||
| r | -0.006 | ||||
| b (slope, estimate of beta) | -1326.344 | ||||
| a (intercept, estimate of alpha) | 247144.629 | ||||
| Mean Square Error | 30039440439.970 | ||||
| DF error | 129.000 | ||||
| t(b) | -0.065 | ||||
| p(b) | 0.504 | ||||
| t(a) | 0.991 | ||||
| p(a) | 0.445 | ||||
| Lowerbound of 95% confidence interval for beta | -41818.269 | ||||
| Upperbound of 95% confidence interval for beta | 39165.582 | ||||
| Lowerbound of 95% confidence interval for alpha | -246264.814 | ||||
| Upperbound of 95% confidence interval for alpha | 740554.073 | ||||
| Treynor index (mean / b) | -184.089 | ||||
| Jensen alpha (a) | 247144.629 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 22.264 | ||||
| Sharpe ratio (Glass type estimate) | -0.002 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.002 | ||||
| df | 130.000 | ||||
| t | -0.001 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.774 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.770 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.774 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.770 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.003 | ||||
| Upside Potential Ratio | 1.756 | ||||
| Upside part of mean | 25.869 | ||||
| Downside part of mean | -25.913 | ||||
| Upside SD | 16.582 | ||||
| Downside SD | 14.728 | ||||
| N nonnegative terms | 12.000 | ||||
| N negative terms | 119.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.956 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.761 | ||||
| SD of criterion | 22.264 | ||||
| Covariance | 0.850 | ||||
| r | 0.050 | ||||
| b (slope, estimate of beta) | 1.467 | ||||
| a (intercept, estimate of alpha) | -2.913 | ||||
| Mean Square Error | 498.252 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.570 | ||||
| p(b) | 0.468 | ||||
| t(a) | -0.091 | ||||
| p(a) | 0.505 | ||||
| Lowerbound of 95% confidence interval for beta | -3.623 | ||||
| Upperbound of 95% confidence interval for beta | 6.557 | ||||
| Lowerbound of 95% confidence interval for alpha | -66.159 | ||||
| Upperbound of 95% confidence interval for alpha | 60.332 | ||||
| Treynor index (mean / b) | -0.030 | ||||
| Jensen alpha (a) | -2.913 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.896 | ||||
| Expected Shortfall on VaR | 0.935 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.080 | ||||
| Expected Shortfall on VaR | 0.176 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 122085.667 | ||||
| Mean of quarter 1 | 0.904 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 3700.578 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 19.000 | ||||
| Percentage of outliers low | 0.145 | ||||
| Mean of outliers low | 0.833 | ||||
| Number of outliers high | 12.000 | ||||
| Percentage of outliers high | 0.092 | ||||
| Mean of outliers high | 10174.839 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -11.798 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.000 | ||||
| Extreme Value Index (regression method) | 0.628 | ||||
| VaR(95%) (regression method) | 0.080 | ||||
| Expected Shortfall (regression method) | 0.356 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||