Advanced Statistics: mwz
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 | 0.072 | ||||
| SD | 0.433 | ||||
| Sharpe ratio (Glass type estimate) | 0.167 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.166 | ||||
| df | 87.000 | ||||
| t | 0.453 | ||||
| p | 0.326 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.557 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.891 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.558 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.890 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.355 | ||||
| Upside Potential Ratio | 1.485 | ||||
| Upside part of mean | 0.303 | ||||
| Downside part of mean | -0.230 | ||||
| Upside SD | 0.380 | ||||
| Downside SD | 0.204 | ||||
| N nonnegative terms | 14.000 | ||||
| N negative terms | 74.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 88.000 | ||||
| Mean of predictor | 0.125 | ||||
| Mean of criterion | 0.072 | ||||
| SD of predictor | 0.244 | ||||
| SD of criterion | 0.433 | ||||
| Covariance | -0.000 | ||||
| r | -0.002 | ||||
| b (slope, estimate of beta) | -0.003 | ||||
| a (intercept, estimate of alpha) | 0.073 | ||||
| Mean Square Error | 0.190 | ||||
| DF error | 86.000 | ||||
| t(b) | -0.014 | ||||
| p(b) | 0.506 | ||||
| t(a) | 0.447 | ||||
| p(a) | 0.328 | ||||
| Lowerbound of 95% confidence interval for beta | -0.383 | ||||
| Upperbound of 95% confidence interval for beta | 0.377 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.251 | ||||
| Upperbound of 95% confidence interval for alpha | 0.396 | ||||
| Treynor index (mean / b) | -26.319 | ||||
| Jensen alpha (a) | 0.073 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.002 | ||||
| SD | 0.374 | ||||
| Sharpe ratio (Glass type estimate) | -0.006 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.006 | ||||
| df | 87.000 | ||||
| t | -0.015 | ||||
| p | 0.506 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.729 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.718 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.729 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.718 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.009 | ||||
| Upside Potential Ratio | 1.049 | ||||
| Upside part of mean | 0.253 | ||||
| Downside part of mean | -0.256 | ||||
| Upside SD | 0.283 | ||||
| Downside SD | 0.242 | ||||
| N nonnegative terms | 14.000 | ||||
| N negative terms | 74.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 88.000 | ||||
| Mean of predictor | 0.094 | ||||
| Mean of criterion | -0.002 | ||||
| SD of predictor | 0.253 | ||||
| SD of criterion | 0.374 | ||||
| Covariance | 0.001 | ||||
| r | 0.014 | ||||
| b (slope, estimate of beta) | 0.021 | ||||
| a (intercept, estimate of alpha) | -0.004 | ||||
| Mean Square Error | 0.142 | ||||
| DF error | 86.000 | ||||
| t(b) | 0.131 | ||||
| p(b) | 0.448 | ||||
| t(a) | -0.029 | ||||
| p(a) | 0.511 | ||||
| Lowerbound of 95% confidence interval for beta | -0.296 | ||||
| Upperbound of 95% confidence interval for beta | 0.337 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.282 | ||||
| Upperbound of 95% confidence interval for alpha | 0.274 | ||||
| Treynor index (mean / b) | -0.100 | ||||
| Jensen alpha (a) | -0.004 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.163 | ||||
| Expected Shortfall on VaR | 0.199 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.060 | ||||
| Expected Shortfall on VaR | 0.127 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 88.000 | ||||
| Minimum | 0.617 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.945 | ||||
| Mean of quarter 1 | 0.935 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.103 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 19.000 | ||||
| Percentage of outliers low | 0.216 | ||||
| Mean of outliers low | 0.925 | ||||
| Number of outliers high | 19.000 | ||||
| Percentage of outliers high | 0.216 | ||||
| Mean of outliers high | 1.120 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -7.621 | ||||
| VaR(95%) (moments method) | 0.006 | ||||
| Expected Shortfall (moments method) | 0.006 | ||||
| Extreme Value Index (regression method) | 0.036 | ||||
| VaR(95%) (regression method) | 0.099 | ||||
| Expected Shortfall (regression method) | 0.195 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.054 | ||||
| Quartile 1 | 0.075 | ||||
| Median | 0.181 | ||||
| Quartile 3 | 0.271 | ||||
| Maximum | 0.566 | ||||
| Mean of quarter 1 | 0.065 | ||||
| Mean of quarter 2 | 0.181 | ||||
| Mean of quarter 3 | 0.271 | ||||
| Mean of quarter 4 | 0.566 | ||||
| Inter Quartile Range | 0.196 | ||||
| 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 | 0.200 | ||||
| Mean of outliers high | 0.566 | ||||
| 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) | 0.049 | ||||
| Compounded annual return (geometric extrapolation) | 0.043 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.076 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.076 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.215 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.544 | ||||
| SD | 1.100 | ||||
| Sharpe ratio (Glass type estimate) | 0.494 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.494 | ||||
| df | 1930.000 | ||||
| t | 1.342 | ||||
| p | 0.485 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.228 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.216 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.228 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.216 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.911 | ||||
| Upside Potential Ratio | 3.567 | ||||
| Upside part of mean | 2.129 | ||||
| Downside part of mean | -1.586 | ||||
| Upside SD | 0.924 | ||||
| Downside SD | 0.597 | ||||
| N nonnegative terms | 244.000 | ||||
| N negative terms | 1687.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1931.000 | ||||
| Mean of predictor | 0.278 | ||||
| Mean of criterion | 0.544 | ||||
| SD of predictor | 0.631 | ||||
| SD of criterion | 1.100 | ||||
| Covariance | 0.042 | ||||
| r | 0.060 | ||||
| b (slope, estimate of beta) | 0.105 | ||||
| a (intercept, estimate of alpha) | 0.514 | ||||
| Mean Square Error | 1.205 | ||||
| DF error | 1929.000 | ||||
| t(b) | 2.642 | ||||
| p(b) | 0.462 | ||||
| t(a) | 1.272 | ||||
| p(a) | 0.482 | ||||
| Lowerbound of 95% confidence interval for beta | 0.027 | ||||
| Upperbound of 95% confidence interval for beta | 0.182 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.279 | ||||
| Upperbound of 95% confidence interval for alpha | 1.308 | ||||
| Treynor index (mean / b) | 5.193 | ||||
| Jensen alpha (a) | 0.514 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.002 | ||||
| SD | 1.045 | ||||
| Sharpe ratio (Glass type estimate) | -0.002 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.002 | ||||
| df | 1930.000 | ||||
| t | -0.006 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.724 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.720 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.724 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.720 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.003 | ||||
| Upside Potential Ratio | 2.390 | ||||
| Upside part of mean | 1.830 | ||||
| Downside part of mean | -1.832 | ||||
| Upside SD | 0.711 | ||||
| Downside SD | 0.765 | ||||
| N nonnegative terms | 244.000 | ||||
| N negative terms | 1687.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1931.000 | ||||
| Mean of predictor | 0.087 | ||||
| Mean of criterion | -0.002 | ||||
| SD of predictor | 0.616 | ||||
| SD of criterion | 1.045 | ||||
| Covariance | 0.036 | ||||
| r | 0.055 | ||||
| b (slope, estimate of beta) | 0.094 | ||||
| a (intercept, estimate of alpha) | -0.010 | ||||
| Mean Square Error | 1.090 | ||||
| DF error | 1929.000 | ||||
| t(b) | 2.438 | ||||
| p(b) | 0.465 | ||||
| t(a) | -0.027 | ||||
| p(a) | 0.500 | ||||
| Lowerbound of 95% confidence interval for beta | 0.018 | ||||
| Upperbound of 95% confidence interval for beta | 0.170 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.765 | ||||
| Upperbound of 95% confidence interval for alpha | 0.744 | ||||
| Treynor index (mean / b) | -0.024 | ||||
| Jensen alpha (a) | -0.010 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.101 | ||||
| Expected Shortfall on VaR | 0.124 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.044 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1931.000 | ||||
| Minimum | 0.380 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.154 | ||||
| Mean of quarter 1 | 0.976 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.033 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 272.000 | ||||
| Percentage of outliers low | 0.141 | ||||
| Mean of outliers low | 0.958 | ||||
| Number of outliers high | 293.000 | ||||
| Percentage of outliers high | 0.152 | ||||
| Mean of outliers high | 1.054 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.360 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| 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 | 10.000 | ||||
| Minimum | 0.124 | ||||
| Quartile 1 | 0.232 | ||||
| Median | 0.318 | ||||
| Quartile 3 | 0.420 | ||||
| Maximum | 0.666 | ||||
| Mean of quarter 1 | 0.181 | ||||
| Mean of quarter 2 | 0.256 | ||||
| Mean of quarter 3 | 0.395 | ||||
| Mean of quarter 4 | 0.566 | ||||
| Inter Quartile Range | 0.188 | ||||
| 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) | -44.959 | ||||
| VaR(95%) (moments method) | 0.599 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -2.777 | ||||
| VaR(95%) (regression method) | 0.838 | ||||
| Expected Shortfall (regression method) | 0.841 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.049 | ||||
| Compounded annual return (geometric extrapolation) | 0.043 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.064 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.075 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.342 | ||||
| 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 | 0.909 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.564 | ||||
| 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 | 0.742 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.585 | ||||
| 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) | -8772675763203125.000 | ||||
| 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) | 101268695496661500212314898432000.000 | ||||
| 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 | ||||