Advanced Statistics: The Cleaner Fish
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 | -0.051 | ||||
| SD | 0.549 | ||||
| Sharpe ratio (Glass type estimate) | -0.093 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.092 | ||||
| df | 69.000 | ||||
| t | -0.224 | ||||
| p | 0.588 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.904 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.719 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.904 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.720 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.109 | ||||
| Upside Potential Ratio | 1.063 | ||||
| Upside part of mean | 0.496 | ||||
| Downside part of mean | -0.547 | ||||
| Upside SD | 0.282 | ||||
| Downside SD | 0.466 | ||||
| N nonnegative terms | 35.000 | ||||
| N negative terms | 35.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 70.000 | ||||
| Mean of predictor | 0.268 | ||||
| Mean of criterion | -0.051 | ||||
| SD of predictor | 0.331 | ||||
| SD of criterion | 0.549 | ||||
| Covariance | 0.057 | ||||
| r | 0.315 | ||||
| b (slope, estimate of beta) | 0.522 | ||||
| a (intercept, estimate of alpha) | -0.191 | ||||
| Mean Square Error | 0.275 | ||||
| DF error | 68.000 | ||||
| t(b) | 2.738 | ||||
| p(b) | 0.004 | ||||
| t(a) | -0.856 | ||||
| p(a) | 0.802 | ||||
| Lowerbound of 95% confidence interval for beta | 0.142 | ||||
| Upperbound of 95% confidence interval for beta | 0.903 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.636 | ||||
| Upperbound of 95% confidence interval for alpha | 0.254 | ||||
| Treynor index (mean / b) | -0.098 | ||||
| Jensen alpha (a) | -0.191 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -1.861 | ||||
| SD | 4.658 | ||||
| Sharpe ratio (Glass type estimate) | -0.400 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.395 | ||||
| df | 69.000 | ||||
| t | -0.965 | ||||
| p | 0.831 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.212 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.416 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.209 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.419 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.400 | ||||
| Upside Potential Ratio | 0.099 | ||||
| Upside part of mean | 0.460 | ||||
| Downside part of mean | -2.321 | ||||
| Upside SD | 0.253 | ||||
| Downside SD | 4.649 | ||||
| N nonnegative terms | 35.000 | ||||
| N negative terms | 35.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 70.000 | ||||
| Mean of predictor | 0.215 | ||||
| Mean of criterion | -1.861 | ||||
| SD of predictor | 0.313 | ||||
| SD of criterion | 4.658 | ||||
| Covariance | 0.016 | ||||
| r | 0.011 | ||||
| b (slope, estimate of beta) | 0.168 | ||||
| a (intercept, estimate of alpha) | -1.897 | ||||
| Mean Square Error | 22.013 | ||||
| DF error | 68.000 | ||||
| t(b) | 0.093 | ||||
| p(b) | 0.463 | ||||
| t(a) | -0.958 | ||||
| p(a) | 0.829 | ||||
| Lowerbound of 95% confidence interval for beta | -3.438 | ||||
| Upperbound of 95% confidence interval for beta | 3.773 | ||||
| Lowerbound of 95% confidence interval for alpha | -5.850 | ||||
| Upperbound of 95% confidence interval for alpha | 2.056 | ||||
| Treynor index (mean / b) | -11.099 | ||||
| Jensen alpha (a) | -1.897 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.906 | ||||
| Expected Shortfall on VaR | 0.941 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.102 | ||||
| Expected Shortfall on VaR | 0.226 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 70.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.944 | ||||
| Median | 1.007 | ||||
| Quartile 3 | 1.062 | ||||
| Maximum | 1.335 | ||||
| Mean of quarter 1 | 0.839 | ||||
| Mean of quarter 2 | 0.990 | ||||
| Mean of quarter 3 | 1.038 | ||||
| Mean of quarter 4 | 1.132 | ||||
| Inter Quartile Range | 0.118 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.029 | ||||
| Mean of outliers low | 0.382 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.043 | ||||
| Mean of outliers high | 1.306 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.487 | ||||
| VaR(95%) (moments method) | 0.163 | ||||
| Expected Shortfall (moments method) | 0.348 | ||||
| Extreme Value Index (regression method) | 0.461 | ||||
| VaR(95%) (regression method) | 0.147 | ||||
| Expected Shortfall (regression method) | 0.291 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.107 | ||||
| Quartile 1 | 0.116 | ||||
| Median | 0.336 | ||||
| Quartile 3 | 0.665 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.107 | ||||
| Mean of quarter 2 | 0.119 | ||||
| Mean of quarter 3 | 0.553 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.549 | ||||
| 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) | -0.171 | ||||
| Compounded annual return (geometric extrapolation) | -0.837 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.837 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.837 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.890 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.195 | ||||
| SD | 0.878 | ||||
| Sharpe ratio (Glass type estimate) | 0.223 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.222 | ||||
| df | 1538.000 | ||||
| t | 0.539 | ||||
| p | 0.493 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.586 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.031 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.586 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.031 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.303 | ||||
| Upside Potential Ratio | 5.107 | ||||
| Upside part of mean | 3.288 | ||||
| Downside part of mean | -3.093 | ||||
| Upside SD | 0.596 | ||||
| Downside SD | 0.644 | ||||
| N nonnegative terms | 672.000 | ||||
| N negative terms | 867.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1539.000 | ||||
| Mean of predictor | 0.379 | ||||
| Mean of criterion | 0.195 | ||||
| SD of predictor | 0.547 | ||||
| SD of criterion | 0.878 | ||||
| Covariance | 0.310 | ||||
| r | 0.645 | ||||
| b (slope, estimate of beta) | 1.035 | ||||
| a (intercept, estimate of alpha) | -0.197 | ||||
| Mean Square Error | 0.450 | ||||
| DF error | 1537.000 | ||||
| t(b) | 33.128 | ||||
| p(b) | 0.120 | ||||
| t(a) | -0.710 | ||||
| p(a) | 0.512 | ||||
| Lowerbound of 95% confidence interval for beta | 0.974 | ||||
| Upperbound of 95% confidence interval for beta | 1.096 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.740 | ||||
| Upperbound of 95% confidence interval for alpha | 0.347 | ||||
| Treynor index (mean / b) | 0.189 | ||||
| Jensen alpha (a) | -0.197 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -1.848 | ||||
| SD | 4.720 | ||||
| Sharpe ratio (Glass type estimate) | -0.392 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.391 | ||||
| df | 1538.000 | ||||
| t | -0.949 | ||||
| p | 0.512 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.200 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.417 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.200 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.417 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.394 | ||||
| Upside Potential Ratio | 0.668 | ||||
| Upside part of mean | 3.132 | ||||
| Downside part of mean | -4.980 | ||||
| Upside SD | 0.541 | ||||
| Downside SD | 4.688 | ||||
| N nonnegative terms | 672.000 | ||||
| N negative terms | 867.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1539.000 | ||||
| Mean of predictor | 0.230 | ||||
| Mean of criterion | -1.848 | ||||
| SD of predictor | 0.546 | ||||
| SD of criterion | 4.720 | ||||
| Covariance | 0.303 | ||||
| r | 0.118 | ||||
| b (slope, estimate of beta) | 1.015 | ||||
| a (intercept, estimate of alpha) | -2.081 | ||||
| Mean Square Error | 21.981 | ||||
| DF error | 1537.000 | ||||
| t(b) | 4.641 | ||||
| p(b) | 0.425 | ||||
| t(a) | -1.076 | ||||
| p(a) | 0.517 | ||||
| Lowerbound of 95% confidence interval for beta | 0.586 | ||||
| Upperbound of 95% confidence interval for beta | 1.445 | ||||
| Lowerbound of 95% confidence interval for alpha | -5.877 | ||||
| Upperbound of 95% confidence interval for alpha | 1.714 | ||||
| Treynor index (mean / b) | -1.820 | ||||
| Jensen alpha (a) | -2.081 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.385 | ||||
| Expected Shortfall on VaR | 0.453 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.064 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1539.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.990 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.012 | ||||
| Maximum | 1.470 | ||||
| Mean of quarter 1 | 0.956 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.004 | ||||
| Mean of quarter 4 | 1.046 | ||||
| Inter Quartile Range | 0.021 | ||||
| Number outliers low | 116.000 | ||||
| Percentage of outliers low | 0.075 | ||||
| Mean of outliers low | 0.902 | ||||
| Number of outliers high | 106.000 | ||||
| Percentage of outliers high | 0.069 | ||||
| Mean of outliers high | 1.108 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.611 | ||||
| VaR(95%) (moments method) | 0.040 | ||||
| Expected Shortfall (moments method) | 0.115 | ||||
| Extreme Value Index (regression method) | 0.346 | ||||
| VaR(95%) (regression method) | 0.036 | ||||
| Expected Shortfall (regression method) | 0.069 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 21.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.009 | ||||
| Median | 0.022 | ||||
| Quartile 3 | 0.133 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | 0.016 | ||||
| Mean of quarter 3 | 0.052 | ||||
| Mean of quarter 4 | 0.427 | ||||
| Inter Quartile Range | 0.124 | ||||
| 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 | 0.095 | ||||
| Mean of outliers high | 0.819 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.772 | ||||
| VaR(95%) (moments method) | 0.473 | ||||
| Expected Shortfall (moments method) | 2.114 | ||||
| Extreme Value Index (regression method) | 1.408 | ||||
| VaR(95%) (regression method) | 0.476 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.170 | ||||
| Compounded annual return (geometric extrapolation) | -0.835 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.835 | ||||
| Compounded annual return / average of 25% largest draw downs | -1.958 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.845 | ||||
| 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 | 1.364 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.481 | ||||
| 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 | 1.245 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.483 | ||||
| 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) | -8689546418343754.000 | ||||
| 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) | 199344813371014908912195111747584.000 | ||||
| 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 | ||||