Advanced Statistics: DoctorJascha
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 290.275 | ||||
| SD | 446.940 | ||||
| Sharpe ratio (Glass type estimate) | 0.649 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.632 | ||||
| df | 28.000 | ||||
| t | 1.010 | ||||
| p | 0.161 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.628 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.916 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.640 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.903 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 291.663 | ||||
| Upside Potential Ratio | 293.385 | ||||
| Upside part of mean | 291.988 | ||||
| Downside part of mean | -1.714 | ||||
| Upside SD | 447.088 | ||||
| Downside SD | 0.995 | ||||
| N nonnegative terms | 16.000 | ||||
| N negative terms | 13.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 29.000 | ||||
| Mean of predictor | 0.690 | ||||
| Mean of criterion | 290.275 | ||||
| SD of predictor | 0.287 | ||||
| SD of criterion | 446.940 | ||||
| Covariance | -5.135 | ||||
| r | -0.040 | ||||
| b (slope, estimate of beta) | -62.339 | ||||
| a (intercept, estimate of alpha) | 333.283 | ||||
| Mean Square Error | 206821.317 | ||||
| DF error | 27.000 | ||||
| t(b) | -0.208 | ||||
| p(b) | 0.582 | ||||
| t(a) | 0.931 | ||||
| p(a) | 0.180 | ||||
| Lowerbound of 95% confidence interval for beta | -676.781 | ||||
| Upperbound of 95% confidence interval for beta | 552.103 | ||||
| Lowerbound of 95% confidence interval for alpha | -401.565 | ||||
| Upperbound of 95% confidence interval for alpha | 1068.132 | ||||
| Treynor index (mean / b) | -4.656 | ||||
| Jensen alpha (a) | 333.283 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.289 | ||||
| SD | 6.915 | ||||
| Sharpe ratio (Glass type estimate) | -0.042 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.041 | ||||
| df | 28.000 | ||||
| t | -0.065 | ||||
| p | 0.526 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.302 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.219 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.301 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.220 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.057 | ||||
| Upside Potential Ratio | 0.921 | ||||
| Upside part of mean | 4.690 | ||||
| Downside part of mean | -4.978 | ||||
| Upside SD | 4.503 | ||||
| Downside SD | 5.089 | ||||
| N nonnegative terms | 16.000 | ||||
| N negative terms | 13.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 29.000 | ||||
| Mean of predictor | 0.634 | ||||
| Mean of criterion | -0.289 | ||||
| SD of predictor | 0.266 | ||||
| SD of criterion | 6.915 | ||||
| Covariance | -0.768 | ||||
| r | -0.417 | ||||
| b (slope, estimate of beta) | -10.857 | ||||
| a (intercept, estimate of alpha) | 6.594 | ||||
| Mean Square Error | 40.945 | ||||
| DF error | 27.000 | ||||
| t(b) | -2.387 | ||||
| p(b) | 0.988 | ||||
| t(a) | 1.312 | ||||
| p(a) | 0.100 | ||||
| Lowerbound of 95% confidence interval for beta | -20.189 | ||||
| Upperbound of 95% confidence interval for beta | -1.525 | ||||
| Lowerbound of 95% confidence interval for alpha | -3.717 | ||||
| Upperbound of 95% confidence interval for alpha | 16.906 | ||||
| Treynor index (mean / b) | 0.027 | ||||
| Jensen alpha (a) | 6.594 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.963 | ||||
| Expected Shortfall on VaR | 0.981 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.308 | ||||
| Expected Shortfall on VaR | 0.606 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 29.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.797 | ||||
| Median | 1.007 | ||||
| Quartile 3 | 1.122 | ||||
| Maximum | 696.000 | ||||
| Mean of quarter 1 | 0.528 | ||||
| Mean of quarter 2 | 0.956 | ||||
| Mean of quarter 3 | 1.058 | ||||
| Mean of quarter 4 | 101.754 | ||||
| Inter Quartile Range | 0.325 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.069 | ||||
| Mean of outliers low | 0.152 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.138 | ||||
| Mean of outliers high | 177.189 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.072 | ||||
| VaR(95%) (moments method) | 0.472 | ||||
| Expected Shortfall (moments method) | 0.667 | ||||
| Extreme Value Index (regression method) | 0.281 | ||||
| VaR(95%) (regression method) | 0.551 | ||||
| Expected Shortfall (regression method) | 0.913 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.030 | ||||
| Quartile 1 | 0.056 | ||||
| Median | 0.083 | ||||
| Quartile 3 | 0.542 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.030 | ||||
| Mean of quarter 2 | 0.083 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.485 | ||||
| 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) | -0.185 | ||||
| Compounded annual return (geometric extrapolation) | -0.217 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.217 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.217 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.221 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 343.644 | ||||
| SD | 376.169 | ||||
| Sharpe ratio (Glass type estimate) | 0.914 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.912 | ||||
| df | 637.000 | ||||
| t | 1.426 | ||||
| p | 0.077 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.344 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.170 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.345 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.169 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 244.189 | ||||
| Upside Potential Ratio | 249.197 | ||||
| Upside part of mean | 350.691 | ||||
| Downside part of mean | -7.046 | ||||
| Upside SD | 376.470 | ||||
| Downside SD | 1.407 | ||||
| N nonnegative terms | 267.000 | ||||
| N negative terms | 371.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 638.000 | ||||
| Mean of predictor | 0.737 | ||||
| Mean of criterion | 343.644 | ||||
| SD of predictor | 0.366 | ||||
| SD of criterion | 376.169 | ||||
| Covariance | 1.865 | ||||
| r | 0.014 | ||||
| b (slope, estimate of beta) | 13.899 | ||||
| a (intercept, estimate of alpha) | 333.407 | ||||
| Mean Square Error | 141699.289 | ||||
| DF error | 636.000 | ||||
| t(b) | 0.341 | ||||
| p(b) | 0.366 | ||||
| t(a) | 1.372 | ||||
| p(a) | 0.085 | ||||
| Lowerbound of 95% confidence interval for beta | -66.049 | ||||
| Upperbound of 95% confidence interval for beta | 93.847 | ||||
| Lowerbound of 95% confidence interval for alpha | -143.934 | ||||
| Upperbound of 95% confidence interval for alpha | 810.749 | ||||
| Treynor index (mean / b) | 24.725 | ||||
| Jensen alpha (a) | 333.407 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.179 | ||||
| SD | 8.505 | ||||
| Sharpe ratio (Glass type estimate) | -0.021 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.021 | ||||
| df | 637.000 | ||||
| t | -0.033 | ||||
| p | 0.513 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.277 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.235 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.277 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.235 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.029 | ||||
| Upside Potential Ratio | 1.992 | ||||
| Upside part of mean | 12.263 | ||||
| Downside part of mean | -12.442 | ||||
| Upside SD | 5.857 | ||||
| Downside SD | 6.157 | ||||
| N nonnegative terms | 267.000 | ||||
| N negative terms | 371.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 638.000 | ||||
| Mean of predictor | 0.668 | ||||
| Mean of criterion | -0.179 | ||||
| SD of predictor | 0.370 | ||||
| SD of criterion | 8.505 | ||||
| Covariance | -0.256 | ||||
| r | -0.081 | ||||
| b (slope, estimate of beta) | -1.872 | ||||
| a (intercept, estimate of alpha) | 1.072 | ||||
| Mean Square Error | 71.961 | ||||
| DF error | 636.000 | ||||
| t(b) | -2.059 | ||||
| p(b) | 0.980 | ||||
| t(a) | 0.196 | ||||
| p(a) | 0.422 | ||||
| Lowerbound of 95% confidence interval for beta | -3.658 | ||||
| Upperbound of 95% confidence interval for beta | -0.087 | ||||
| Lowerbound of 95% confidence interval for alpha | -9.670 | ||||
| Upperbound of 95% confidence interval for alpha | 11.813 | ||||
| Treynor index (mean / b) | 0.095 | ||||
| Jensen alpha (a) | 1.072 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.579 | ||||
| Expected Shortfall on VaR | 0.656 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.066 | ||||
| Expected Shortfall on VaR | 0.147 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 638.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.981 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.014 | ||||
| Maximum | 462.000 | ||||
| Mean of quarter 1 | 0.900 | ||||
| Mean of quarter 2 | 0.993 | ||||
| Mean of quarter 3 | 1.004 | ||||
| Mean of quarter 4 | 6.334 | ||||
| Inter Quartile Range | 0.033 | ||||
| Number outliers low | 57.000 | ||||
| Percentage of outliers low | 0.089 | ||||
| Mean of outliers low | 0.788 | ||||
| Number of outliers high | 62.000 | ||||
| Percentage of outliers high | 0.097 | ||||
| Mean of outliers high | 14.718 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.733 | ||||
| VaR(95%) (moments method) | 0.089 | ||||
| Expected Shortfall (moments method) | 0.366 | ||||
| Extreme Value Index (regression method) | 0.385 | ||||
| VaR(95%) (regression method) | 0.081 | ||||
| Expected Shortfall (regression method) | 0.164 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 14.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.003 | ||||
| Median | 0.016 | ||||
| Quartile 3 | 0.058 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.009 | ||||
| Mean of quarter 3 | 0.030 | ||||
| Mean of quarter 4 | 0.315 | ||||
| Inter Quartile Range | 0.054 | ||||
| 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 | 0.071 | ||||
| Mean of outliers high | 1.000 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.177 | ||||
| VaR(95%) (moments method) | 0.343 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 4.157 | ||||
| VaR(95%) (regression method) | 0.991 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.115 | ||||
| Compounded annual return (geometric extrapolation) | -0.126 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.126 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.400 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.192 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1676.716 | ||||
| SD | 827.497 | ||||
| Sharpe ratio (Glass type estimate) | 2.026 | ||||
| Sharpe ratio (Hedges UMVUE) | 2.015 | ||||
| df | 130.000 | ||||
| t | 1.433 | ||||
| p | 0.438 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.760 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.805 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.768 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.797 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 803.895 | ||||
| Upside Potential Ratio | 810.122 | ||||
| Upside part of mean | 1689.705 | ||||
| Downside part of mean | -12.989 | ||||
| Upside SD | 830.813 | ||||
| Downside SD | 2.086 | ||||
| N nonnegative terms | 46.000 | ||||
| N negative terms | 85.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.486 | ||||
| Mean of criterion | 1676.716 | ||||
| SD of predictor | 0.527 | ||||
| SD of criterion | 827.497 | ||||
| Covariance | 4.767 | ||||
| r | 0.011 | ||||
| b (slope, estimate of beta) | 17.136 | ||||
| a (intercept, estimate of alpha) | 1651.252 | ||||
| Mean Square Error | 689977.289 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.124 | ||||
| p(b) | 0.493 | ||||
| t(a) | 1.385 | ||||
| p(a) | 0.423 | ||||
| Lowerbound of 95% confidence interval for beta | -256.159 | ||||
| Upperbound of 95% confidence interval for beta | 290.431 | ||||
| Lowerbound of 95% confidence interval for alpha | -708.164 | ||||
| Upperbound of 95% confidence interval for alpha | 4010.669 | ||||
| Treynor index (mean / b) | 97.849 | ||||
| Jensen alpha (a) | 1651.252 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 19.107 | ||||
| SD | 15.406 | ||||
| Sharpe ratio (Glass type estimate) | 1.240 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.233 | ||||
| df | 130.000 | ||||
| t | 0.877 | ||||
| p | 0.462 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.538 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.014 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.543 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.009 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.236 | ||||
| Upside Potential Ratio | 5.079 | ||||
| Upside part of mean | 43.405 | ||||
| Downside part of mean | -24.298 | ||||
| Upside SD | 12.802 | ||||
| Downside SD | 8.547 | ||||
| N nonnegative terms | 46.000 | ||||
| N negative terms | 85.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.343 | ||||
| Mean of criterion | 19.107 | ||||
| SD of predictor | 0.530 | ||||
| SD of criterion | 15.406 | ||||
| Covariance | -0.777 | ||||
| r | -0.095 | ||||
| b (slope, estimate of beta) | -2.768 | ||||
| a (intercept, estimate of alpha) | 22.826 | ||||
| Mean Square Error | 237.025 | ||||
| DF error | 129.000 | ||||
| t(b) | -1.086 | ||||
| p(b) | 0.561 | ||||
| t(a) | 1.036 | ||||
| p(a) | 0.442 | ||||
| Lowerbound of 95% confidence interval for beta | -7.810 | ||||
| Upperbound of 95% confidence interval for beta | 2.274 | ||||
| Lowerbound of 95% confidence interval for alpha | -20.781 | ||||
| Upperbound of 95% confidence interval for alpha | 66.432 | ||||
| Treynor index (mean / b) | -6.903 | ||||
| Jensen alpha (a) | 22.826 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.775 | ||||
| Expected Shortfall on VaR | 0.841 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.133 | ||||
| Expected Shortfall on VaR | 0.276 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.953 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.036 | ||||
| Maximum | 462.000 | ||||
| Mean of quarter 1 | 0.815 | ||||
| Mean of quarter 2 | 0.989 | ||||
| Mean of quarter 3 | 1.006 | ||||
| Mean of quarter 4 | 26.596 | ||||
| Inter Quartile Range | 0.083 | ||||
| Number outliers low | 13.000 | ||||
| Percentage of outliers low | 0.099 | ||||
| Mean of outliers low | 0.675 | ||||
| Number of outliers high | 18.000 | ||||
| Percentage of outliers high | 0.137 | ||||
| Mean of outliers high | 47.845 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.319 | ||||
| VaR(95%) (moments method) | 0.157 | ||||
| Expected Shortfall (moments method) | 0.285 | ||||
| Extreme Value Index (regression method) | 0.149 | ||||
| VaR(95%) (regression method) | 0.175 | ||||
| Expected Shortfall (regression method) | 0.280 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.172 | ||||
| Median | 0.272 | ||||
| Quartile 3 | 0.755 | ||||
| Maximum | 0.997 | ||||
| Mean of quarter 1 | 0.040 | ||||
| Mean of quarter 2 | 0.208 | ||||
| Mean of quarter 3 | 0.521 | ||||
| Mean of quarter 4 | 0.941 | ||||
| Inter Quartile Range | 0.584 | ||||
| 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) | 28820.000 | ||||
| Compounded annual return (geometric extrapolation) | 207676920.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 208247460.989 | ||||
| Compounded annual return / average of 25% largest draw downs | 220788994.560 | ||||
| Compounded annual return / Expected Shortfall lognormal | 247021519.496 | ||||