Advanced Statistics: Intensive Care
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 | -0.044 | ||||
| SD | 0.007 | ||||
| Sharpe ratio (Glass type estimate) | -6.588 | ||||
| Sharpe ratio (Hedges UMVUE) | -6.518 | ||||
| df | 71.000 | ||||
| t | -16.137 | ||||
| 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) | -7.856 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -5.180 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.150 | ||||
| Upside Potential Ratio | 0.093 | ||||
| Upside part of mean | 0.001 | ||||
| Downside part of mean | -0.045 | ||||
| Upside SD | 0.003 | ||||
| Downside SD | 0.014 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 71.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 72.000 | ||||
| Mean of predictor | 0.257 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.269 | ||||
| SD of criterion | 0.007 | ||||
| Covariance | -0.000 | ||||
| r | -0.033 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 70.000 | ||||
| t(b) | -0.278 | ||||
| p(b) | 0.609 | ||||
| t(a) | -15.370 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.007 | ||||
| Upperbound of 95% confidence interval for beta | 0.005 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.050 | ||||
| Upperbound of 95% confidence interval for alpha | -0.038 | ||||
| Treynor index (mean / b) | 53.276 | ||||
| Jensen alpha (a) | -0.044 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.007 | ||||
| Sharpe ratio (Glass type estimate) | -6.580 | ||||
| Sharpe ratio (Hedges UMVUE) | -6.510 | ||||
| df | 71.000 | ||||
| t | -16.117 | ||||
| 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) | -7.846 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -5.173 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.148 | ||||
| Upside Potential Ratio | 0.092 | ||||
| Upside part of mean | 0.001 | ||||
| Downside part of mean | -0.045 | ||||
| Upside SD | 0.003 | ||||
| Downside SD | 0.014 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 71.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 72.000 | ||||
| Mean of predictor | 0.220 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.263 | ||||
| SD of criterion | 0.007 | ||||
| Covariance | -0.000 | ||||
| r | -0.033 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 70.000 | ||||
| t(b) | -0.280 | ||||
| p(b) | 0.610 | ||||
| t(a) | -15.496 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.007 | ||||
| Upperbound of 95% confidence interval for beta | 0.005 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.049 | ||||
| Upperbound of 95% confidence interval for alpha | -0.038 | ||||
| Treynor index (mean / b) | 51.833 | ||||
| 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%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.008 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 72.000 | ||||
| Minimum | 0.989 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.011 | ||||
| Mean of quarter 1 | 0.999 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.001 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.042 | ||||
| Mean of outliers low | 0.996 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.042 | ||||
| Mean of outliers high | 1.004 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.015 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 3.091 | ||||
| VaR(95%) (regression method) | 0.001 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.004 | ||||
| Median | 0.007 | ||||
| Quartile 3 | 0.009 | ||||
| Maximum | 0.011 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.011 | ||||
| Inter Quartile Range | 0.005 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.000 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.199 | ||||
| SD | 0.737 | ||||
| Sharpe ratio (Glass type estimate) | 0.269 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.269 | ||||
| df | 1572.000 | ||||
| t | 0.660 | ||||
| p | 0.492 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.531 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.069 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.531 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.069 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.506 | ||||
| Upside Potential Ratio | 2.222 | ||||
| Upside part of mean | 0.873 | ||||
| Downside part of mean | -0.674 | ||||
| Upside SD | 0.624 | ||||
| Downside SD | 0.393 | ||||
| N nonnegative terms | 56.000 | ||||
| N negative terms | 1517.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1573.000 | ||||
| Mean of predictor | 0.406 | ||||
| Mean of criterion | 0.199 | ||||
| SD of predictor | 0.583 | ||||
| SD of criterion | 0.737 | ||||
| Covariance | -0.103 | ||||
| r | -0.240 | ||||
| b (slope, estimate of beta) | -0.304 | ||||
| a (intercept, estimate of alpha) | 0.322 | ||||
| Mean Square Error | 0.513 | ||||
| DF error | 1571.000 | ||||
| t(b) | -9.792 | ||||
| p(b) | 0.651 | ||||
| t(a) | 1.100 | ||||
| p(a) | 0.482 | ||||
| Lowerbound of 95% confidence interval for beta | -0.364 | ||||
| Upperbound of 95% confidence interval for beta | -0.243 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.252 | ||||
| Upperbound of 95% confidence interval for alpha | 0.896 | ||||
| Treynor index (mean / b) | -0.654 | ||||
| Jensen alpha (a) | 0.322 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.686 | ||||
| Sharpe ratio (Glass type estimate) | -0.064 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.064 | ||||
| df | 1572.000 | ||||
| t | -0.157 | ||||
| p | 0.502 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.864 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.736 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.864 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.736 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.094 | ||||
| Upside Potential Ratio | 1.549 | ||||
| Upside part of mean | 0.728 | ||||
| Downside part of mean | -0.772 | ||||
| Upside SD | 0.500 | ||||
| Downside SD | 0.470 | ||||
| N nonnegative terms | 56.000 | ||||
| N negative terms | 1517.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1573.000 | ||||
| Mean of predictor | 0.238 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.580 | ||||
| SD of criterion | 0.686 | ||||
| Covariance | -0.100 | ||||
| r | -0.251 | ||||
| b (slope, estimate of beta) | -0.298 | ||||
| a (intercept, estimate of alpha) | 0.027 | ||||
| Mean Square Error | 0.442 | ||||
| DF error | 1571.000 | ||||
| t(b) | -10.293 | ||||
| p(b) | 0.658 | ||||
| t(a) | 0.099 | ||||
| p(a) | 0.498 | ||||
| Lowerbound of 95% confidence interval for beta | -0.354 | ||||
| Upperbound of 95% confidence interval for beta | -0.241 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.505 | ||||
| Upperbound of 95% confidence interval for alpha | 0.559 | ||||
| Treynor index (mean / b) | 0.148 | ||||
| Jensen alpha (a) | 0.027 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.068 | ||||
| Expected Shortfall on VaR | 0.084 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.020 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1573.000 | ||||
| Minimum | 0.641 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.792 | ||||
| Mean of quarter 1 | 0.990 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.013 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 57.000 | ||||
| Percentage of outliers low | 0.036 | ||||
| Mean of outliers low | 0.933 | ||||
| Number of outliers high | 56.000 | ||||
| Percentage of outliers high | 0.036 | ||||
| Mean of outliers high | 1.094 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.682 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| 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 | 13.000 | ||||
| Minimum | 0.045 | ||||
| Quartile 1 | 0.169 | ||||
| Median | 0.245 | ||||
| Quartile 3 | 0.350 | ||||
| Maximum | 0.442 | ||||
| Mean of quarter 1 | 0.111 | ||||
| Mean of quarter 2 | 0.203 | ||||
| Mean of quarter 3 | 0.344 | ||||
| Mean of quarter 4 | 0.384 | ||||
| Inter Quartile Range | 0.181 | ||||
| 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) | 0.238 | ||||
| VaR(95%) (moments method) | 0.406 | ||||
| Expected Shortfall (moments method) | 0.464 | ||||
| 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) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.000 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| 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 | 1.129 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.502 | ||||
| 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 | 1.000 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.506 | ||||
| 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) | -8734457713465651.000 | ||||
| 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) | -206544206730044879952067866656768.000 | ||||
| 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 | ||||