Advanced Statistics: ziggy
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 | 0.009 | ||||
| SD | 0.491 | ||||
| Sharpe ratio (Glass type estimate) | 0.018 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.018 | ||||
| df | 82.000 | ||||
| t | 0.048 | ||||
| p | 0.481 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.727 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.763 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.727 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.763 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.027 | ||||
| Upside Potential Ratio | 1.974 | ||||
| Upside part of mean | 0.653 | ||||
| Downside part of mean | -0.645 | ||||
| Upside SD | 0.358 | ||||
| Downside SD | 0.331 | ||||
| N nonnegative terms | 38.000 | ||||
| N negative terms | 45.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 83.000 | ||||
| Mean of predictor | 0.203 | ||||
| Mean of criterion | 0.009 | ||||
| SD of predictor | 0.211 | ||||
| SD of criterion | 0.491 | ||||
| Covariance | 0.031 | ||||
| r | 0.297 | ||||
| b (slope, estimate of beta) | 0.690 | ||||
| a (intercept, estimate of alpha) | -0.131 | ||||
| Mean Square Error | 0.222 | ||||
| DF error | 81.000 | ||||
| t(b) | 2.795 | ||||
| p(b) | 0.003 | ||||
| t(a) | -0.705 | ||||
| p(a) | 0.759 | ||||
| Lowerbound of 95% confidence interval for beta | 0.199 | ||||
| Upperbound of 95% confidence interval for beta | 1.182 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.501 | ||||
| Upperbound of 95% confidence interval for alpha | 0.239 | ||||
| Treynor index (mean / b) | 0.013 | ||||
| Jensen alpha (a) | -0.131 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.110 | ||||
| SD | 0.494 | ||||
| Sharpe ratio (Glass type estimate) | -0.223 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.221 | ||||
| df | 82.000 | ||||
| t | -0.586 | ||||
| p | 0.720 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.968 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.524 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.967 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.525 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.293 | ||||
| Upside Potential Ratio | 1.587 | ||||
| Upside part of mean | 0.597 | ||||
| Downside part of mean | -0.707 | ||||
| Upside SD | 0.317 | ||||
| Downside SD | 0.376 | ||||
| N nonnegative terms | 38.000 | ||||
| N negative terms | 45.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 83.000 | ||||
| Mean of predictor | 0.181 | ||||
| Mean of criterion | -0.110 | ||||
| SD of predictor | 0.196 | ||||
| SD of criterion | 0.494 | ||||
| Covariance | 0.029 | ||||
| r | 0.299 | ||||
| b (slope, estimate of beta) | 0.752 | ||||
| a (intercept, estimate of alpha) | -0.246 | ||||
| Mean Square Error | 0.225 | ||||
| DF error | 81.000 | ||||
| t(b) | 2.822 | ||||
| p(b) | 0.003 | ||||
| t(a) | -1.319 | ||||
| p(a) | 0.905 | ||||
| Lowerbound of 95% confidence interval for beta | 0.222 | ||||
| Upperbound of 95% confidence interval for beta | 1.283 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.617 | ||||
| Upperbound of 95% confidence interval for alpha | 0.125 | ||||
| Treynor index (mean / b) | -0.146 | ||||
| Jensen alpha (a) | -0.246 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.216 | ||||
| Expected Shortfall on VaR | 0.260 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.131 | ||||
| Expected Shortfall on VaR | 0.233 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 83.000 | ||||
| Minimum | 0.623 | ||||
| Quartile 1 | 0.920 | ||||
| Median | 0.993 | ||||
| Quartile 3 | 1.095 | ||||
| Maximum | 1.478 | ||||
| Mean of quarter 1 | 0.835 | ||||
| Mean of quarter 2 | 0.960 | ||||
| Mean of quarter 3 | 1.042 | ||||
| Mean of quarter 4 | 1.182 | ||||
| Inter Quartile Range | 0.174 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.012 | ||||
| Mean of outliers low | 0.623 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.024 | ||||
| Mean of outliers high | 1.420 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.190 | ||||
| VaR(95%) (moments method) | 0.166 | ||||
| Expected Shortfall (moments method) | 0.205 | ||||
| Extreme Value Index (regression method) | 0.070 | ||||
| VaR(95%) (regression method) | 0.170 | ||||
| Expected Shortfall (regression method) | 0.233 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.044 | ||||
| Quartile 1 | 0.136 | ||||
| Median | 0.403 | ||||
| Quartile 3 | 0.409 | ||||
| Maximum | 0.662 | ||||
| Mean of quarter 1 | 0.090 | ||||
| Mean of quarter 2 | 0.403 | ||||
| Mean of quarter 3 | 0.409 | ||||
| Mean of quarter 4 | 0.662 | ||||
| Inter Quartile Range | 0.273 | ||||
| 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) | -0.053 | ||||
| Compounded annual return (geometric extrapolation) | -0.064 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.097 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.097 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.245 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.039 | ||||
| SD | 0.478 | ||||
| Sharpe ratio (Glass type estimate) | 0.081 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.081 | ||||
| df | 1825.000 | ||||
| t | 0.213 | ||||
| p | 0.497 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.662 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.823 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.662 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.823 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.114 | ||||
| Upside Potential Ratio | 7.043 | ||||
| Upside part of mean | 2.378 | ||||
| Downside part of mean | -2.340 | ||||
| Upside SD | 0.338 | ||||
| Downside SD | 0.338 | ||||
| N nonnegative terms | 918.000 | ||||
| N negative terms | 908.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1826.000 | ||||
| Mean of predictor | 0.231 | ||||
| Mean of criterion | 0.039 | ||||
| SD of predictor | 0.243 | ||||
| SD of criterion | 0.478 | ||||
| Covariance | 0.032 | ||||
| r | 0.276 | ||||
| b (slope, estimate of beta) | 0.542 | ||||
| a (intercept, estimate of alpha) | -0.086 | ||||
| Mean Square Error | 0.211 | ||||
| DF error | 1824.000 | ||||
| t(b) | 12.248 | ||||
| p(b) | 0.362 | ||||
| t(a) | -0.496 | ||||
| p(a) | 0.506 | ||||
| Lowerbound of 95% confidence interval for beta | 0.455 | ||||
| Upperbound of 95% confidence interval for beta | 0.629 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.428 | ||||
| Upperbound of 95% confidence interval for alpha | 0.255 | ||||
| Treynor index (mean / b) | 0.071 | ||||
| Jensen alpha (a) | -0.086 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.075 | ||||
| SD | 0.478 | ||||
| Sharpe ratio (Glass type estimate) | -0.158 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.157 | ||||
| df | 1825.000 | ||||
| t | -0.416 | ||||
| p | 0.506 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.900 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.585 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.900 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.585 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.212 | ||||
| Upside Potential Ratio | 6.555 | ||||
| Upside part of mean | 2.325 | ||||
| Downside part of mean | -2.400 | ||||
| Upside SD | 0.320 | ||||
| Downside SD | 0.355 | ||||
| N nonnegative terms | 918.000 | ||||
| N negative terms | 908.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1826.000 | ||||
| Mean of predictor | 0.201 | ||||
| Mean of criterion | -0.075 | ||||
| SD of predictor | 0.243 | ||||
| SD of criterion | 0.478 | ||||
| Covariance | 0.032 | ||||
| r | 0.278 | ||||
| b (slope, estimate of beta) | 0.547 | ||||
| a (intercept, estimate of alpha) | -0.185 | ||||
| Mean Square Error | 0.211 | ||||
| DF error | 1824.000 | ||||
| t(b) | 12.383 | ||||
| p(b) | 0.361 | ||||
| t(a) | -1.065 | ||||
| p(a) | 0.512 | ||||
| Lowerbound of 95% confidence interval for beta | 0.461 | ||||
| Upperbound of 95% confidence interval for beta | 0.634 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.527 | ||||
| Upperbound of 95% confidence interval for alpha | 0.156 | ||||
| Treynor index (mean / b) | -0.138 | ||||
| Jensen alpha (a) | -0.185 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.048 | ||||
| Expected Shortfall on VaR | 0.059 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.020 | ||||
| Expected Shortfall on VaR | 0.042 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1826.000 | ||||
| Minimum | 0.761 | ||||
| Quartile 1 | 0.990 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.012 | ||||
| Maximum | 1.373 | ||||
| Mean of quarter 1 | 0.969 | ||||
| Mean of quarter 2 | 0.995 | ||||
| Mean of quarter 3 | 1.005 | ||||
| Mean of quarter 4 | 1.031 | ||||
| Inter Quartile Range | 0.022 | ||||
| Number outliers low | 84.000 | ||||
| Percentage of outliers low | 0.046 | ||||
| Mean of outliers low | 0.923 | ||||
| Number of outliers high | 80.000 | ||||
| Percentage of outliers high | 0.044 | ||||
| Mean of outliers high | 1.073 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.481 | ||||
| VaR(95%) (moments method) | 0.032 | ||||
| Expected Shortfall (moments method) | 0.068 | ||||
| Extreme Value Index (regression method) | 0.337 | ||||
| VaR(95%) (regression method) | 0.027 | ||||
| Expected Shortfall (regression method) | 0.047 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 23.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.014 | ||||
| Median | 0.055 | ||||
| Quartile 3 | 0.137 | ||||
| Maximum | 0.701 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.039 | ||||
| Mean of quarter 3 | 0.104 | ||||
| Mean of quarter 4 | 0.356 | ||||
| Inter Quartile Range | 0.123 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.130 | ||||
| Mean of outliers high | 0.541 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.190 | ||||
| VaR(95%) (moments method) | 0.359 | ||||
| Expected Shortfall (moments method) | 0.564 | ||||
| Extreme Value Index (regression method) | 0.220 | ||||
| VaR(95%) (regression method) | 0.376 | ||||
| Expected Shortfall (regression method) | 0.593 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.028 | ||||
| Compounded annual return (geometric extrapolation) | -0.031 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.044 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.087 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.519 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.521 | ||||
| SD | 1.182 | ||||
| Sharpe ratio (Glass type estimate) | 0.440 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.438 | ||||
| df | 130.000 | ||||
| t | 0.311 | ||||
| p | 0.486 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.333 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.212 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.335 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.210 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.668 | ||||
| Upside Potential Ratio | 9.432 | ||||
| Upside part of mean | 7.350 | ||||
| Downside part of mean | -6.829 | ||||
| Upside SD | 0.884 | ||||
| Downside SD | 0.779 | ||||
| N nonnegative terms | 66.000 | ||||
| N negative terms | 65.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.674 | ||||
| Mean of criterion | 0.521 | ||||
| SD of predictor | 0.561 | ||||
| SD of criterion | 1.182 | ||||
| Covariance | 0.194 | ||||
| r | 0.292 | ||||
| b (slope, estimate of beta) | 0.616 | ||||
| a (intercept, estimate of alpha) | -0.511 | ||||
| Mean Square Error | 1.288 | ||||
| DF error | 129.000 | ||||
| t(b) | 3.474 | ||||
| p(b) | 0.316 | ||||
| t(a) | -0.313 | ||||
| p(a) | 0.518 | ||||
| Lowerbound of 95% confidence interval for beta | 0.265 | ||||
| Upperbound of 95% confidence interval for beta | 0.968 | ||||
| Lowerbound of 95% confidence interval for alpha | -3.741 | ||||
| Upperbound of 95% confidence interval for alpha | 2.718 | ||||
| Treynor index (mean / b) | 0.844 | ||||
| Jensen alpha (a) | -0.511 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.155 | ||||
| SD | 1.161 | ||||
| Sharpe ratio (Glass type estimate) | -0.133 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.133 | ||||
| df | 130.000 | ||||
| t | -0.094 | ||||
| p | 0.504 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.905 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.639 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.905 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.639 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.188 | ||||
| Upside Potential Ratio | 8.492 | ||||
| Upside part of mean | 7.000 | ||||
| Downside part of mean | -7.155 | ||||
| Upside SD | 0.812 | ||||
| Downside SD | 0.824 | ||||
| N nonnegative terms | 66.000 | ||||
| N negative terms | 65.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.516 | ||||
| Mean of criterion | -0.155 | ||||
| SD of predictor | 0.554 | ||||
| SD of criterion | 1.161 | ||||
| Covariance | 0.193 | ||||
| r | 0.300 | ||||
| b (slope, estimate of beta) | 0.629 | ||||
| a (intercept, estimate of alpha) | -1.108 | ||||
| Mean Square Error | 1.237 | ||||
| DF error | 129.000 | ||||
| t(b) | 3.570 | ||||
| p(b) | 0.312 | ||||
| t(a) | -0.695 | ||||
| p(a) | 0.539 | ||||
| Lowerbound of 95% confidence interval for beta | 0.280 | ||||
| Upperbound of 95% confidence interval for beta | 0.978 | ||||
| Lowerbound of 95% confidence interval for alpha | -4.265 | ||||
| Upperbound of 95% confidence interval for alpha | 2.049 | ||||
| Treynor index (mean / b) | -0.246 | ||||
| Jensen alpha (a) | -1.108 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.112 | ||||
| Expected Shortfall on VaR | 0.138 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.060 | ||||
| Expected Shortfall on VaR | 0.111 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.845 | ||||
| Quartile 1 | 0.957 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.044 | ||||
| Maximum | 1.373 | ||||
| Mean of quarter 1 | 0.912 | ||||
| Mean of quarter 2 | 0.985 | ||||
| Mean of quarter 3 | 1.024 | ||||
| Mean of quarter 4 | 1.089 | ||||
| Inter Quartile Range | 0.088 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.015 | ||||
| Mean of outliers high | 1.283 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.356 | ||||
| VaR(95%) (moments method) | 0.090 | ||||
| Expected Shortfall (moments method) | 0.106 | ||||
| Extreme Value Index (regression method) | -0.358 | ||||
| VaR(95%) (regression method) | 0.091 | ||||
| Expected Shortfall (regression method) | 0.107 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.044 | ||||
| Quartile 1 | 0.056 | ||||
| Median | 0.062 | ||||
| Quartile 3 | 0.186 | ||||
| Maximum | 0.552 | ||||
| Mean of quarter 1 | 0.044 | ||||
| Mean of quarter 2 | 0.060 | ||||
| Mean of quarter 3 | 0.063 | ||||
| Mean of quarter 4 | 0.552 | ||||
| Inter Quartile Range | 0.130 | ||||
| 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 | 0.250 | ||||
| Mean of outliers high | 0.552 | ||||
| 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) | -0.108 | ||||
| Compounded annual return (geometric extrapolation) | -0.105 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.190 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.190 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.762 | ||||