Advanced Statistics: Jaypex
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 | 0.059 | ||||
| SD | 0.385 | ||||
| Sharpe ratio (Glass type estimate) | 0.152 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.151 | ||||
| df | 64.000 | ||||
| t | 0.355 | ||||
| p | 0.362 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.691 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.994 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.692 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.993 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.207 | ||||
| Upside Potential Ratio | 0.794 | ||||
| Upside part of mean | 0.224 | ||||
| Downside part of mean | -0.166 | ||||
| Upside SD | 0.257 | ||||
| Downside SD | 0.283 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 59.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 65.000 | ||||
| Mean of predictor | 0.337 | ||||
| Mean of criterion | 0.059 | ||||
| SD of predictor | 0.301 | ||||
| SD of criterion | 0.385 | ||||
| Covariance | -0.041 | ||||
| r | -0.350 | ||||
| b (slope, estimate of beta) | -0.447 | ||||
| a (intercept, estimate of alpha) | 0.209 | ||||
| Mean Square Error | 0.132 | ||||
| DF error | 63.000 | ||||
| t(b) | -2.965 | ||||
| p(b) | 0.998 | ||||
| t(a) | 1.274 | ||||
| p(a) | 0.104 | ||||
| Lowerbound of 95% confidence interval for beta | -0.748 | ||||
| Upperbound of 95% confidence interval for beta | -0.146 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.119 | ||||
| Upperbound of 95% confidence interval for alpha | 0.537 | ||||
| Treynor index (mean / b) | -0.131 | ||||
| Jensen alpha (a) | 0.209 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.512 | ||||
| Sharpe ratio (Glass type estimate) | -0.086 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.085 | ||||
| df | 64.000 | ||||
| t | -0.201 | ||||
| p | 0.579 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.928 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.756 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.928 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.757 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.097 | ||||
| Upside Potential Ratio | 0.430 | ||||
| Upside part of mean | 0.196 | ||||
| Downside part of mean | -0.241 | ||||
| Upside SD | 0.222 | ||||
| Downside SD | 0.457 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 59.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 65.000 | ||||
| Mean of predictor | 0.288 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.299 | ||||
| SD of criterion | 0.512 | ||||
| Covariance | -0.047 | ||||
| r | -0.304 | ||||
| b (slope, estimate of beta) | -0.519 | ||||
| a (intercept, estimate of alpha) | 0.105 | ||||
| Mean Square Error | 0.241 | ||||
| DF error | 63.000 | ||||
| t(b) | -2.530 | ||||
| p(b) | 0.993 | ||||
| t(a) | 0.479 | ||||
| p(a) | 0.317 | ||||
| Lowerbound of 95% confidence interval for beta | -0.929 | ||||
| Upperbound of 95% confidence interval for beta | -0.109 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.333 | ||||
| Upperbound of 95% confidence interval for alpha | 0.543 | ||||
| Treynor index (mean / b) | 0.085 | ||||
| Jensen alpha (a) | 0.105 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.219 | ||||
| Expected Shortfall on VaR | 0.264 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.045 | ||||
| Expected Shortfall on VaR | 0.102 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 65.000 | ||||
| Minimum | 0.347 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.374 | ||||
| Mean of quarter 1 | 0.960 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.077 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 13.000 | ||||
| Percentage of outliers low | 0.200 | ||||
| Mean of outliers low | 0.947 | ||||
| Number of outliers high | 11.000 | ||||
| Percentage of outliers high | 0.169 | ||||
| Mean of outliers high | 1.113 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.437 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 2.646 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.029 | ||||
| Quartile 1 | 0.185 | ||||
| Median | 0.341 | ||||
| Quartile 3 | 0.497 | ||||
| Maximum | 0.653 | ||||
| Mean of quarter 1 | 0.029 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.653 | ||||
| Inter Quartile Range | 0.312 | ||||
| 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 | 0.440 | ||||
| SD | 1.008 | ||||
| Sharpe ratio (Glass type estimate) | 0.437 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.436 | ||||
| df | 1420.000 | ||||
| t | 1.017 | ||||
| p | 0.487 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.405 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.278 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.405 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.278 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.774 | ||||
| Upside Potential Ratio | 2.661 | ||||
| Upside part of mean | 1.513 | ||||
| Downside part of mean | -1.073 | ||||
| Upside SD | 0.833 | ||||
| Downside SD | 0.568 | ||||
| N nonnegative terms | 105.000 | ||||
| N negative terms | 1316.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1421.000 | ||||
| Mean of predictor | 0.432 | ||||
| Mean of criterion | 0.440 | ||||
| SD of predictor | 0.546 | ||||
| SD of criterion | 1.008 | ||||
| Covariance | -0.249 | ||||
| r | -0.452 | ||||
| b (slope, estimate of beta) | -0.836 | ||||
| a (intercept, estimate of alpha) | 0.801 | ||||
| Mean Square Error | 0.809 | ||||
| DF error | 1419.000 | ||||
| t(b) | -19.110 | ||||
| p(b) | 0.778 | ||||
| t(a) | 2.071 | ||||
| p(a) | 0.465 | ||||
| Lowerbound of 95% confidence interval for beta | -0.922 | ||||
| Upperbound of 95% confidence interval for beta | -0.750 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.042 | ||||
| Upperbound of 95% confidence interval for alpha | 1.560 | ||||
| Treynor index (mean / b) | -0.526 | ||||
| Jensen alpha (a) | 0.801 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 1.001 | ||||
| Sharpe ratio (Glass type estimate) | -0.044 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.044 | ||||
| df | 1420.000 | ||||
| t | -0.103 | ||||
| p | 0.501 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.886 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.797 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.886 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.798 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.058 | ||||
| Upside Potential Ratio | 1.659 | ||||
| Upside part of mean | 1.265 | ||||
| Downside part of mean | -1.309 | ||||
| Upside SD | 0.648 | ||||
| Downside SD | 0.762 | ||||
| N nonnegative terms | 105.000 | ||||
| N negative terms | 1316.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1421.000 | ||||
| Mean of predictor | 0.281 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.551 | ||||
| SD of criterion | 1.001 | ||||
| Covariance | -0.250 | ||||
| r | -0.453 | ||||
| b (slope, estimate of beta) | -0.823 | ||||
| a (intercept, estimate of alpha) | 0.187 | ||||
| Mean Square Error | 0.798 | ||||
| DF error | 1419.000 | ||||
| t(b) | -19.122 | ||||
| p(b) | 0.778 | ||||
| t(a) | 0.488 | ||||
| p(a) | 0.492 | ||||
| Lowerbound of 95% confidence interval for beta | -0.907 | ||||
| Upperbound of 95% confidence interval for beta | -0.738 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.565 | ||||
| Upperbound of 95% confidence interval for alpha | 0.940 | ||||
| Treynor index (mean / b) | 0.054 | ||||
| Jensen alpha (a) | 0.187 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.097 | ||||
| Expected Shortfall on VaR | 0.120 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1421.000 | ||||
| Minimum | 0.353 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.001 | ||||
| Mean of quarter 1 | 0.984 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.023 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 148.000 | ||||
| Percentage of outliers low | 0.104 | ||||
| Mean of outliers low | 0.962 | ||||
| Number of outliers high | 139.000 | ||||
| Percentage of outliers high | 0.098 | ||||
| Mean of outliers high | 1.059 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.870 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.968 | ||||
| VaR(95%) (regression method) | -0.002 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.011 | ||||
| Quartile 1 | 0.034 | ||||
| Median | 0.069 | ||||
| Quartile 3 | 0.236 | ||||
| Maximum | 0.658 | ||||
| Mean of quarter 1 | 0.011 | ||||
| Mean of quarter 2 | 0.042 | ||||
| Mean of quarter 3 | 0.096 | ||||
| Mean of quarter 4 | 0.658 | ||||
| Inter Quartile Range | 0.202 | ||||
| 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 | 0.658 | ||||
| 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 | -0.001 | ||||
| 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 | 0.948 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.462 | ||||
| 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 | 0.840 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.462 | ||||
| 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) | -8744467189039925.000 | ||||
| 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) | -443390344461989635515701759311872.000 | ||||
| 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 | ||||