Advanced Statistics: Z TRADING 3
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 | 0.013 | ||||
| SD | 0.083 | ||||
| Sharpe ratio (Glass type estimate) | 0.160 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.158 | ||||
| df | 44.000 | ||||
| t | 0.310 | ||||
| p | 0.379 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.853 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.172 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.855 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.170 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.324 | ||||
| Upside Potential Ratio | 2.038 | ||||
| Upside part of mean | 0.084 | ||||
| Downside part of mean | -0.070 | ||||
| Upside SD | 0.071 | ||||
| Downside SD | 0.041 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 45.000 | ||||
| Mean of predictor | 0.408 | ||||
| Mean of criterion | 0.013 | ||||
| SD of predictor | 0.266 | ||||
| SD of criterion | 0.083 | ||||
| Covariance | -0.001 | ||||
| r | -0.042 | ||||
| b (slope, estimate of beta) | -0.013 | ||||
| a (intercept, estimate of alpha) | 0.019 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 43.000 | ||||
| t(b) | -0.279 | ||||
| p(b) | 0.609 | ||||
| t(a) | 0.394 | ||||
| p(a) | 0.348 | ||||
| Lowerbound of 95% confidence interval for beta | -0.109 | ||||
| Upperbound of 95% confidence interval for beta | 0.083 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.077 | ||||
| Upperbound of 95% confidence interval for alpha | 0.114 | ||||
| Treynor index (mean / b) | -1.004 | ||||
| Jensen alpha (a) | 0.019 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.010 | ||||
| SD | 0.081 | ||||
| Sharpe ratio (Glass type estimate) | 0.123 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.121 | ||||
| df | 44.000 | ||||
| t | 0.239 | ||||
| p | 0.406 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.890 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.135 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.891 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.134 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.239 | ||||
| Upside Potential Ratio | 1.942 | ||||
| Upside part of mean | 0.081 | ||||
| Downside part of mean | -0.071 | ||||
| Upside SD | 0.068 | ||||
| Downside SD | 0.042 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 45.000 | ||||
| Mean of predictor | 0.369 | ||||
| Mean of criterion | 0.010 | ||||
| SD of predictor | 0.253 | ||||
| SD of criterion | 0.081 | ||||
| Covariance | -0.001 | ||||
| r | -0.036 | ||||
| b (slope, estimate of beta) | -0.012 | ||||
| a (intercept, estimate of alpha) | 0.014 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 43.000 | ||||
| t(b) | -0.239 | ||||
| p(b) | 0.594 | ||||
| t(a) | 0.311 | ||||
| p(a) | 0.379 | ||||
| Lowerbound of 95% confidence interval for beta | -0.110 | ||||
| Upperbound of 95% confidence interval for beta | 0.087 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.078 | ||||
| Upperbound of 95% confidence interval for alpha | 0.107 | ||||
| Treynor index (mean / b) | -0.856 | ||||
| Jensen alpha (a) | 0.014 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.037 | ||||
| Expected Shortfall on VaR | 0.046 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.018 | ||||
| Expected Shortfall on VaR | 0.033 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 45.000 | ||||
| Minimum | 0.956 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.002 | ||||
| Maximum | 1.086 | ||||
| Mean of quarter 1 | 0.988 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.032 | ||||
| Inter Quartile Range | 0.002 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.089 | ||||
| Mean of outliers low | 0.966 | ||||
| Number of outliers high | 8.000 | ||||
| Percentage of outliers high | 0.178 | ||||
| Mean of outliers high | 1.043 | ||||
| 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) | -0.928 | ||||
| VaR(95%) (regression method) | 0.022 | ||||
| Expected Shortfall (regression method) | 0.030 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.032 | ||||
| Quartile 1 | 0.035 | ||||
| Median | 0.038 | ||||
| Quartile 3 | 0.047 | ||||
| Maximum | 0.056 | ||||
| Mean of quarter 1 | 0.032 | ||||
| Mean of quarter 2 | 0.038 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.056 | ||||
| Inter Quartile Range | 0.012 | ||||
| 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) | 0.060 | ||||
| Compounded annual return (geometric extrapolation) | 0.055 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.998 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.998 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.199 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.012 | ||||
| SD | 0.075 | ||||
| Sharpe ratio (Glass type estimate) | 0.156 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.156 | ||||
| df | 1002.000 | ||||
| t | 0.305 | ||||
| p | 0.495 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.846 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.158 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.846 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.158 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.231 | ||||
| Upside Potential Ratio | 3.631 | ||||
| Upside part of mean | 0.184 | ||||
| Downside part of mean | -0.172 | ||||
| Upside SD | 0.055 | ||||
| Downside SD | 0.051 | ||||
| N nonnegative terms | 158.000 | ||||
| N negative terms | 845.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1003.000 | ||||
| Mean of predictor | 0.467 | ||||
| Mean of criterion | 0.012 | ||||
| SD of predictor | 0.345 | ||||
| SD of criterion | 0.075 | ||||
| Covariance | 0.001 | ||||
| r | 0.024 | ||||
| b (slope, estimate of beta) | 0.005 | ||||
| a (intercept, estimate of alpha) | 0.009 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 1001.000 | ||||
| t(b) | 0.748 | ||||
| p(b) | 0.227 | ||||
| t(a) | 0.242 | ||||
| p(a) | 0.405 | ||||
| Lowerbound of 95% confidence interval for beta | -0.008 | ||||
| Upperbound of 95% confidence interval for beta | 0.019 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.066 | ||||
| Upperbound of 95% confidence interval for alpha | 0.085 | ||||
| Treynor index (mean / b) | 2.277 | ||||
| Jensen alpha (a) | 0.009 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.009 | ||||
| SD | 0.075 | ||||
| Sharpe ratio (Glass type estimate) | 0.119 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.119 | ||||
| df | 1002.000 | ||||
| t | 0.232 | ||||
| p | 0.496 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.883 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.121 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.883 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.120 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.173 | ||||
| Upside Potential Ratio | 3.546 | ||||
| Upside part of mean | 0.182 | ||||
| Downside part of mean | -0.173 | ||||
| Upside SD | 0.054 | ||||
| Downside SD | 0.051 | ||||
| N nonnegative terms | 158.000 | ||||
| N negative terms | 845.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1003.000 | ||||
| Mean of predictor | 0.409 | ||||
| Mean of criterion | 0.009 | ||||
| SD of predictor | 0.338 | ||||
| SD of criterion | 0.075 | ||||
| Covariance | 0.001 | ||||
| r | 0.024 | ||||
| b (slope, estimate of beta) | 0.005 | ||||
| a (intercept, estimate of alpha) | 0.007 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 1001.000 | ||||
| t(b) | 0.764 | ||||
| p(b) | 0.222 | ||||
| t(a) | 0.175 | ||||
| p(a) | 0.431 | ||||
| Lowerbound of 95% confidence interval for beta | -0.008 | ||||
| Upperbound of 95% confidence interval for beta | 0.019 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.068 | ||||
| Upperbound of 95% confidence interval for alpha | 0.082 | ||||
| Treynor index (mean / b) | 1.661 | ||||
| Jensen alpha (a) | 0.007 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1003.000 | ||||
| Minimum | 0.954 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.055 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.003 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 73.000 | ||||
| Percentage of outliers low | 0.073 | ||||
| Mean of outliers low | 0.993 | ||||
| Number of outliers high | 159.000 | ||||
| Percentage of outliers high | 0.159 | ||||
| Mean of outliers high | 1.005 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.274 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.004 | ||||
| Extreme Value Index (regression method) | 0.151 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | 0.007 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 11.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.015 | ||||
| Quartile 3 | 0.030 | ||||
| Maximum | 0.072 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.009 | ||||
| Mean of quarter 3 | 0.017 | ||||
| Mean of quarter 4 | 0.059 | ||||
| Inter Quartile Range | 0.025 | ||||
| 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 | 0.091 | ||||
| Mean of outliers high | 0.072 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -20.402 | ||||
| VaR(95%) (moments method) | 0.063 | ||||
| Expected Shortfall (moments method) | 0.063 | ||||
| Extreme Value Index (regression method) | -2.113 | ||||
| VaR(95%) (regression method) | 0.085 | ||||
| Expected Shortfall (regression method) | 0.086 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.059 | ||||
| Compounded annual return (geometric extrapolation) | 0.054 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.760 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.918 | ||||
| Compounded annual return / Expected Shortfall lognormal | 5.752 | ||||
| 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 | 1.043 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.480 | ||||
| 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 | 0.927 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.482 | ||||
| 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) | -8737794639129722.000 | ||||
| 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) | 160288308188094193030151175929856.000 | ||||
| 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 | ||||