Advanced Statistics: Stellar--not supp. since 08.22.08
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 | -0.062 | ||||
| SD | 0.156 | ||||
| Sharpe ratio (Glass type estimate) | -0.395 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.391 | ||||
| df | 69.000 | ||||
| t | -0.954 | ||||
| p | 0.828 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.208 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.421 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.205 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.424 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.679 | ||||
| Upside Potential Ratio | 0.769 | ||||
| Upside part of mean | 0.070 | ||||
| Downside part of mean | -0.131 | ||||
| Upside SD | 0.127 | ||||
| Downside SD | 0.091 | ||||
| N nonnegative terms | 14.000 | ||||
| N negative terms | 56.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 70.000 | ||||
| Mean of predictor | 0.300 | ||||
| Mean of criterion | -0.062 | ||||
| SD of predictor | 0.260 | ||||
| SD of criterion | 0.156 | ||||
| Covariance | -0.004 | ||||
| r | -0.099 | ||||
| b (slope, estimate of beta) | -0.059 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.024 | ||||
| DF error | 68.000 | ||||
| t(b) | -0.819 | ||||
| p(b) | 0.792 | ||||
| t(a) | -0.642 | ||||
| p(a) | 0.738 | ||||
| Lowerbound of 95% confidence interval for beta | -0.203 | ||||
| Upperbound of 95% confidence interval for beta | 0.085 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.180 | ||||
| Upperbound of 95% confidence interval for alpha | 0.092 | ||||
| Treynor index (mean / b) | 1.039 | ||||
| Jensen alpha (a) | -0.044 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.072 | ||||
| SD | 0.145 | ||||
| Sharpe ratio (Glass type estimate) | -0.498 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.492 | ||||
| df | 69.000 | ||||
| t | -1.203 | ||||
| p | 0.883 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.312 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.320 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.308 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.323 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.762 | ||||
| Upside Potential Ratio | 0.660 | ||||
| Upside part of mean | 0.063 | ||||
| Downside part of mean | -0.135 | ||||
| Upside SD | 0.111 | ||||
| Downside SD | 0.095 | ||||
| N nonnegative terms | 14.000 | ||||
| N negative terms | 56.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 70.000 | ||||
| Mean of predictor | 0.263 | ||||
| Mean of criterion | -0.072 | ||||
| SD of predictor | 0.253 | ||||
| SD of criterion | 0.145 | ||||
| Covariance | -0.004 | ||||
| r | -0.111 | ||||
| b (slope, estimate of beta) | -0.064 | ||||
| a (intercept, estimate of alpha) | -0.056 | ||||
| Mean Square Error | 0.021 | ||||
| DF error | 68.000 | ||||
| t(b) | -0.919 | ||||
| p(b) | 0.819 | ||||
| t(a) | -0.883 | ||||
| p(a) | 0.810 | ||||
| Lowerbound of 95% confidence interval for beta | -0.202 | ||||
| Upperbound of 95% confidence interval for beta | 0.074 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.181 | ||||
| Upperbound of 95% confidence interval for alpha | 0.070 | ||||
| Treynor index (mean / b) | 1.136 | ||||
| Jensen alpha (a) | -0.056 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.072 | ||||
| Expected Shortfall on VaR | 0.088 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.033 | ||||
| Expected Shortfall on VaR | 0.066 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 70.000 | ||||
| Minimum | 0.880 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.003 | ||||
| Maximum | 1.307 | ||||
| Mean of quarter 1 | 0.968 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.026 | ||||
| Inter Quartile Range | 0.005 | ||||
| Number outliers low | 11.000 | ||||
| Percentage of outliers low | 0.157 | ||||
| Mean of outliers low | 0.950 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.086 | ||||
| Mean of outliers high | 1.068 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.405 | ||||
| VaR(95%) (moments method) | 0.026 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.744 | ||||
| VaR(95%) (regression method) | 0.028 | ||||
| Expected Shortfall (regression method) | 0.134 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.120 | ||||
| Quartile 1 | 0.156 | ||||
| Median | 0.191 | ||||
| Quartile 3 | 0.227 | ||||
| Maximum | 0.263 | ||||
| Mean of quarter 1 | 0.120 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.263 | ||||
| Inter Quartile Range | 0.072 | ||||
| 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) | -0.026 | ||||
| Compounded annual return (geometric extrapolation) | -0.028 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.106 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.106 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.316 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.092 | ||||
| SD | 0.378 | ||||
| Sharpe ratio (Glass type estimate) | -0.244 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.244 | ||||
| df | 1539.000 | ||||
| t | -0.593 | ||||
| p | 0.510 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.053 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.564 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.053 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.564 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.371 | ||||
| Upside Potential Ratio | 2.609 | ||||
| Upside part of mean | 0.648 | ||||
| Downside part of mean | -0.740 | ||||
| Upside SD | 0.284 | ||||
| Downside SD | 0.248 | ||||
| N nonnegative terms | 542.000 | ||||
| N negative terms | 998.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1540.000 | ||||
| Mean of predictor | 0.440 | ||||
| Mean of criterion | -0.092 | ||||
| SD of predictor | 0.571 | ||||
| SD of criterion | 0.378 | ||||
| Covariance | 0.025 | ||||
| r | 0.118 | ||||
| b (slope, estimate of beta) | 0.078 | ||||
| a (intercept, estimate of alpha) | -0.127 | ||||
| Mean Square Error | 0.141 | ||||
| DF error | 1538.000 | ||||
| t(b) | 4.660 | ||||
| p(b) | 0.441 | ||||
| t(a) | -0.817 | ||||
| p(a) | 0.510 | ||||
| Lowerbound of 95% confidence interval for beta | 0.045 | ||||
| Upperbound of 95% confidence interval for beta | 0.111 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.430 | ||||
| Upperbound of 95% confidence interval for alpha | 0.177 | ||||
| Treynor index (mean / b) | -1.183 | ||||
| Jensen alpha (a) | -0.127 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.162 | ||||
| SD | 0.373 | ||||
| Sharpe ratio (Glass type estimate) | -0.435 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.434 | ||||
| df | 1539.000 | ||||
| t | -1.054 | ||||
| p | 0.517 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.243 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.374 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.243 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.374 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.606 | ||||
| Upside Potential Ratio | 2.287 | ||||
| Upside part of mean | 0.612 | ||||
| Downside part of mean | -0.774 | ||||
| Upside SD | 0.260 | ||||
| Downside SD | 0.268 | ||||
| N nonnegative terms | 542.000 | ||||
| N negative terms | 998.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1540.000 | ||||
| Mean of predictor | 0.278 | ||||
| Mean of criterion | -0.162 | ||||
| SD of predictor | 0.569 | ||||
| SD of criterion | 0.373 | ||||
| Covariance | 0.024 | ||||
| r | 0.112 | ||||
| b (slope, estimate of beta) | 0.073 | ||||
| a (intercept, estimate of alpha) | -0.183 | ||||
| Mean Square Error | 0.138 | ||||
| DF error | 1538.000 | ||||
| t(b) | 4.419 | ||||
| p(b) | 0.444 | ||||
| t(a) | -1.193 | ||||
| p(a) | 0.515 | ||||
| Lowerbound of 95% confidence interval for beta | 0.041 | ||||
| Upperbound of 95% confidence interval for beta | 0.106 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.483 | ||||
| Upperbound of 95% confidence interval for alpha | 0.118 | ||||
| Treynor index (mean / b) | -2.208 | ||||
| Jensen alpha (a) | -0.183 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.038 | ||||
| Expected Shortfall on VaR | 0.047 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.017 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1540.000 | ||||
| Minimum | 0.788 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.308 | ||||
| Mean of quarter 1 | 0.989 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.010 | ||||
| Inter Quartile Range | 0.001 | ||||
| Number outliers low | 196.000 | ||||
| Percentage of outliers low | 0.127 | ||||
| Mean of outliers low | 0.980 | ||||
| Number of outliers high | 167.000 | ||||
| Percentage of outliers high | 0.108 | ||||
| Mean of outliers high | 1.022 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.410 | ||||
| VaR(95%) (moments method) | 0.006 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.940 | ||||
| VaR(95%) (regression method) | 0.005 | ||||
| Expected Shortfall (regression method) | 0.095 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 11.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.121 | ||||
| Median | 0.160 | ||||
| Quartile 3 | 0.180 | ||||
| Maximum | 0.585 | ||||
| Mean of quarter 1 | 0.040 | ||||
| Mean of quarter 2 | 0.152 | ||||
| Mean of quarter 3 | 0.175 | ||||
| Mean of quarter 4 | 0.335 | ||||
| Inter Quartile Range | 0.059 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.182 | ||||
| Mean of outliers low | 0.010 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.091 | ||||
| Mean of outliers high | 0.585 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.002 | ||||
| VaR(95%) (moments method) | 0.350 | ||||
| Expected Shortfall (moments method) | 0.479 | ||||
| Extreme Value Index (regression method) | 1.732 | ||||
| VaR(95%) (regression method) | 0.642 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.085 | ||||
| Compounded annual return (geometric extrapolation) | -0.111 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.190 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.333 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.372 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -1.387 | ||||
| SD | 0.482 | ||||
| Sharpe ratio (Glass type estimate) | -2.877 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.860 | ||||
| df | 130.000 | ||||
| t | -2.034 | ||||
| p | 0.588 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -5.665 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.078 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -5.654 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.067 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.155 | ||||
| Upside Potential Ratio | 2.919 | ||||
| Upside part of mean | 1.283 | ||||
| Downside part of mean | -2.670 | ||||
| Upside SD | 0.212 | ||||
| Downside SD | 0.440 | ||||
| N nonnegative terms | 53.000 | ||||
| N negative terms | 78.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.066 | ||||
| Mean of criterion | -1.387 | ||||
| SD of predictor | 0.501 | ||||
| SD of criterion | 0.482 | ||||
| Covariance | -0.085 | ||||
| r | -0.353 | ||||
| b (slope, estimate of beta) | -0.340 | ||||
| a (intercept, estimate of alpha) | -1.025 | ||||
| Mean Square Error | 0.205 | ||||
| DF error | 129.000 | ||||
| t(b) | -4.289 | ||||
| p(b) | 0.720 | ||||
| t(a) | -1.587 | ||||
| p(a) | 0.588 | ||||
| Lowerbound of 95% confidence interval for beta | -0.497 | ||||
| Upperbound of 95% confidence interval for beta | -0.183 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.303 | ||||
| Upperbound of 95% confidence interval for alpha | 0.253 | ||||
| Treynor index (mean / b) | 4.082 | ||||
| Jensen alpha (a) | -1.025 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -1.515 | ||||
| SD | 0.511 | ||||
| Sharpe ratio (Glass type estimate) | -2.968 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.951 | ||||
| df | 130.000 | ||||
| t | -2.099 | ||||
| p | 0.591 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -5.758 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.167 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -5.746 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.156 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.195 | ||||
| Upside Potential Ratio | 2.660 | ||||
| Upside part of mean | 1.261 | ||||
| Downside part of mean | -2.777 | ||||
| Upside SD | 0.206 | ||||
| Downside SD | 0.474 | ||||
| N nonnegative terms | 53.000 | ||||
| N negative terms | 78.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.937 | ||||
| Mean of criterion | -1.515 | ||||
| SD of predictor | 0.506 | ||||
| SD of criterion | 0.511 | ||||
| Covariance | -0.087 | ||||
| r | -0.338 | ||||
| b (slope, estimate of beta) | -0.341 | ||||
| a (intercept, estimate of alpha) | -1.196 | ||||
| Mean Square Error | 0.233 | ||||
| DF error | 129.000 | ||||
| t(b) | -4.081 | ||||
| p(b) | 0.711 | ||||
| t(a) | -1.742 | ||||
| p(a) | 0.596 | ||||
| Lowerbound of 95% confidence interval for beta | -0.506 | ||||
| Upperbound of 95% confidence interval for beta | -0.176 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.554 | ||||
| Upperbound of 95% confidence interval for alpha | 0.163 | ||||
| Treynor index (mean / b) | 4.445 | ||||
| Jensen alpha (a) | -1.196 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.056 | ||||
| Expected Shortfall on VaR | 0.068 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.026 | ||||
| Expected Shortfall on VaR | 0.054 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.788 | ||||
| Quartile 1 | 0.993 | ||||
| Median | 0.999 | ||||
| Quartile 3 | 1.003 | ||||
| Maximum | 1.081 | ||||
| Mean of quarter 1 | 0.963 | ||||
| Mean of quarter 2 | 0.997 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.019 | ||||
| Inter Quartile Range | 0.011 | ||||
| Number outliers low | 17.000 | ||||
| Percentage of outliers low | 0.130 | ||||
| Mean of outliers low | 0.942 | ||||
| Number of outliers high | 10.000 | ||||
| Percentage of outliers high | 0.076 | ||||
| Mean of outliers high | 1.041 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.371 | ||||
| VaR(95%) (moments method) | 0.028 | ||||
| Expected Shortfall (moments method) | 0.056 | ||||
| Extreme Value Index (regression method) | 0.040 | ||||
| VaR(95%) (regression method) | 0.035 | ||||
| Expected Shortfall (regression method) | 0.054 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.521 | ||||
| Quartile 1 | 0.521 | ||||
| Median | 0.521 | ||||
| Quartile 3 | 0.521 | ||||
| Maximum | 0.521 | ||||
| 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) | -1.042 | ||||
| Compounded annual return (geometric extrapolation) | -0.770 | ||||
| Calmar ratio (compounded annual return / max draw down) | -1.479 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -11.274 | ||||