Advanced Statistics: Beetlejuice
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 | 0.109 | ||||
| SD | 1.080 | ||||
| Sharpe ratio (Glass type estimate) | 0.101 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.099 | ||||
| df | 33.000 | ||||
| t | 0.170 | ||||
| p | 0.433 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.064 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.265 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.066 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.263 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.214 | ||||
| Upside Potential Ratio | 1.157 | ||||
| Upside part of mean | 0.592 | ||||
| Downside part of mean | -0.483 | ||||
| Upside SD | 0.934 | ||||
| Downside SD | 0.512 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 25.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.553 | ||||
| Mean of criterion | 0.109 | ||||
| SD of predictor | 0.242 | ||||
| SD of criterion | 1.080 | ||||
| Covariance | 0.019 | ||||
| r | 0.071 | ||||
| b (slope, estimate of beta) | 0.317 | ||||
| a (intercept, estimate of alpha) | -0.066 | ||||
| Mean Square Error | 1.198 | ||||
| DF error | 32.000 | ||||
| t(b) | 0.404 | ||||
| p(b) | 0.345 | ||||
| t(a) | -0.085 | ||||
| p(a) | 0.533 | ||||
| Lowerbound of 95% confidence interval for beta | -1.284 | ||||
| Upperbound of 95% confidence interval for beta | 1.919 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.660 | ||||
| Upperbound of 95% confidence interval for alpha | 1.527 | ||||
| Treynor index (mean / b) | 0.344 | ||||
| Jensen alpha (a) | -0.066 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.373 | ||||
| SD | 1.043 | ||||
| Sharpe ratio (Glass type estimate) | -0.358 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.349 | ||||
| df | 33.000 | ||||
| t | -0.602 | ||||
| p | 0.724 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.522 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.813 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.517 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.818 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.430 | ||||
| Upside Potential Ratio | 0.426 | ||||
| Upside part of mean | 0.370 | ||||
| Downside part of mean | -0.742 | ||||
| Upside SD | 0.560 | ||||
| Downside SD | 0.868 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 25.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.512 | ||||
| Mean of criterion | -0.373 | ||||
| SD of predictor | 0.238 | ||||
| SD of criterion | 1.043 | ||||
| Covariance | 0.016 | ||||
| r | 0.065 | ||||
| b (slope, estimate of beta) | 0.283 | ||||
| a (intercept, estimate of alpha) | -0.518 | ||||
| Mean Square Error | 1.117 | ||||
| DF error | 32.000 | ||||
| t(b) | 0.366 | ||||
| p(b) | 0.358 | ||||
| t(a) | -0.698 | ||||
| p(a) | 0.755 | ||||
| Lowerbound of 95% confidence interval for beta | -1.289 | ||||
| Upperbound of 95% confidence interval for beta | 1.854 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.028 | ||||
| Upperbound of 95% confidence interval for alpha | 0.993 | ||||
| Treynor index (mean / b) | -1.319 | ||||
| Jensen alpha (a) | -0.518 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.409 | ||||
| Expected Shortfall on VaR | 0.476 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.115 | ||||
| Expected Shortfall on VaR | 0.254 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 34.000 | ||||
| Minimum | 0.261 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.003 | ||||
| Maximum | 2.575 | ||||
| Mean of quarter 1 | 0.858 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.190 | ||||
| Inter Quartile Range | 0.003 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.176 | ||||
| Mean of outliers low | 0.787 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.206 | ||||
| Mean of outliers high | 1.243 | ||||
| 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) | 1.455 | ||||
| VaR(95%) (regression method) | 0.138 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.850 | ||||
| Quartile 1 | 0.850 | ||||
| Median | 0.850 | ||||
| Quartile 3 | 0.850 | ||||
| Maximum | 0.850 | ||||
| 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 | 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) | -0.214 | ||||
| Compounded annual return (geometric extrapolation) | -0.280 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.330 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.589 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.109 | ||||
| SD | 0.965 | ||||
| Sharpe ratio (Glass type estimate) | 0.113 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.113 | ||||
| df | 761.000 | ||||
| t | 0.192 | ||||
| p | 0.424 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.037 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.262 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.037 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.262 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.173 | ||||
| Upside Potential Ratio | 2.648 | ||||
| Upside part of mean | 1.664 | ||||
| Downside part of mean | -1.555 | ||||
| Upside SD | 0.731 | ||||
| Downside SD | 0.628 | ||||
| N nonnegative terms | 153.000 | ||||
| N negative terms | 609.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 762.000 | ||||
| Mean of predictor | 0.610 | ||||
| Mean of criterion | 0.109 | ||||
| SD of predictor | 0.332 | ||||
| SD of criterion | 0.965 | ||||
| Covariance | -0.000 | ||||
| r | -0.001 | ||||
| b (slope, estimate of beta) | -0.002 | ||||
| a (intercept, estimate of alpha) | 0.110 | ||||
| Mean Square Error | 0.932 | ||||
| DF error | 760.000 | ||||
| t(b) | -0.019 | ||||
| p(b) | 0.508 | ||||
| t(a) | 0.193 | ||||
| p(a) | 0.424 | ||||
| Lowerbound of 95% confidence interval for beta | -0.209 | ||||
| Upperbound of 95% confidence interval for beta | 0.205 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.008 | ||||
| Upperbound of 95% confidence interval for alpha | 1.228 | ||||
| Treynor index (mean / b) | -54.160 | ||||
| Jensen alpha (a) | 0.110 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.364 | ||||
| SD | 0.995 | ||||
| Sharpe ratio (Glass type estimate) | -0.366 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.366 | ||||
| df | 761.000 | ||||
| t | -0.624 | ||||
| p | 0.734 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.515 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.783 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.515 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.784 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.459 | ||||
| Upside Potential Ratio | 1.838 | ||||
| Upside part of mean | 1.459 | ||||
| Downside part of mean | -1.823 | ||||
| Upside SD | 0.600 | ||||
| Downside SD | 0.794 | ||||
| N nonnegative terms | 153.000 | ||||
| N negative terms | 609.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 762.000 | ||||
| Mean of predictor | 0.554 | ||||
| Mean of criterion | -0.364 | ||||
| SD of predictor | 0.333 | ||||
| SD of criterion | 0.995 | ||||
| Covariance | -0.001 | ||||
| r | -0.002 | ||||
| b (slope, estimate of beta) | -0.007 | ||||
| a (intercept, estimate of alpha) | -0.361 | ||||
| Mean Square Error | 0.992 | ||||
| DF error | 760.000 | ||||
| t(b) | -0.065 | ||||
| p(b) | 0.526 | ||||
| t(a) | -0.614 | ||||
| p(a) | 0.730 | ||||
| Lowerbound of 95% confidence interval for beta | -0.220 | ||||
| Upperbound of 95% confidence interval for beta | 0.206 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.513 | ||||
| Upperbound of 95% confidence interval for alpha | 0.792 | ||||
| Treynor index (mean / b) | 52.016 | ||||
| Jensen alpha (a) | -0.361 | ||||
| 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%) | 0.018 | ||||
| Expected Shortfall on VaR | 0.041 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 762.000 | ||||
| Minimum | 0.485 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.782 | ||||
| Mean of quarter 1 | 0.977 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.025 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 134.000 | ||||
| Percentage of outliers low | 0.176 | ||||
| Mean of outliers low | 0.967 | ||||
| Number of outliers high | 159.000 | ||||
| Percentage of outliers high | 0.209 | ||||
| Mean of outliers high | 1.031 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.844 | ||||
| VaR(95%) (moments method) | 0.006 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.152 | ||||
| VaR(95%) (regression method) | 0.005 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.007 | ||||
| Quartile 1 | 0.014 | ||||
| Median | 0.019 | ||||
| Quartile 3 | 0.255 | ||||
| Maximum | 0.954 | ||||
| Mean of quarter 1 | 0.007 | ||||
| Mean of quarter 2 | 0.017 | ||||
| Mean of quarter 3 | 0.021 | ||||
| Mean of quarter 4 | 0.954 | ||||
| Inter Quartile Range | 0.240 | ||||
| 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 | 0.954 | ||||
| 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) | -0.208 | ||||
| Compounded annual return (geometric extrapolation) | -0.274 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.287 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.287 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.282 | ||||
| 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 | 0.891 | ||||
| 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 | 0.783 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.465 | ||||
| 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) | -8752123059705484.000 | ||||
| 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) | -1566273174056300962777207012327424.000 | ||||
| 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 | ||||