Advanced Statistics: choice trading
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 | -0.051 | ||||
| SD | 0.122 | ||||
| Sharpe ratio (Glass type estimate) | -0.416 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.408 | ||||
| df | 36.000 | ||||
| t | -0.731 | ||||
| p | 0.765 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.534 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.707 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.528 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.712 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.597 | ||||
| Upside Potential Ratio | 0.718 | ||||
| Upside part of mean | 0.061 | ||||
| Downside part of mean | -0.112 | ||||
| Upside SD | 0.087 | ||||
| Downside SD | 0.085 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 37.000 | ||||
| Mean of predictor | 0.523 | ||||
| Mean of criterion | -0.051 | ||||
| SD of predictor | 0.301 | ||||
| SD of criterion | 0.122 | ||||
| Covariance | 0.004 | ||||
| r | 0.105 | ||||
| b (slope, estimate of beta) | 0.043 | ||||
| a (intercept, estimate of alpha) | -0.073 | ||||
| Mean Square Error | 0.015 | ||||
| DF error | 35.000 | ||||
| t(b) | 0.626 | ||||
| p(b) | 0.268 | ||||
| t(a) | -0.930 | ||||
| p(a) | 0.821 | ||||
| Lowerbound of 95% confidence interval for beta | -0.096 | ||||
| Upperbound of 95% confidence interval for beta | 0.181 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.233 | ||||
| Upperbound of 95% confidence interval for alpha | 0.087 | ||||
| Treynor index (mean / b) | -1.192 | ||||
| Jensen alpha (a) | -0.073 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.058 | ||||
| SD | 0.122 | ||||
| Sharpe ratio (Glass type estimate) | -0.478 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.468 | ||||
| df | 36.000 | ||||
| t | -0.839 | ||||
| p | 0.796 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.596 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.647 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.589 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.654 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.642 | ||||
| Upside Potential Ratio | 0.638 | ||||
| Upside part of mean | 0.058 | ||||
| Downside part of mean | -0.116 | ||||
| Upside SD | 0.081 | ||||
| Downside SD | 0.090 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 37.000 | ||||
| Mean of predictor | 0.472 | ||||
| Mean of criterion | -0.058 | ||||
| SD of predictor | 0.277 | ||||
| SD of criterion | 0.122 | ||||
| Covariance | 0.004 | ||||
| r | 0.116 | ||||
| b (slope, estimate of beta) | 0.051 | ||||
| a (intercept, estimate of alpha) | -0.082 | ||||
| Mean Square Error | 0.015 | ||||
| DF error | 35.000 | ||||
| t(b) | 0.689 | ||||
| p(b) | 0.248 | ||||
| t(a) | -1.053 | ||||
| p(a) | 0.850 | ||||
| Lowerbound of 95% confidence interval for beta | -0.099 | ||||
| Upperbound of 95% confidence interval for beta | 0.201 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.240 | ||||
| Upperbound of 95% confidence interval for alpha | 0.076 | ||||
| Treynor index (mean / b) | -1.142 | ||||
| Jensen alpha (a) | -0.082 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.061 | ||||
| Expected Shortfall on VaR | 0.074 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.031 | ||||
| Expected Shortfall on VaR | 0.062 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 37.000 | ||||
| Minimum | 0.869 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.153 | ||||
| Mean of quarter 1 | 0.978 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.022 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.108 | ||||
| Mean of outliers low | 0.945 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.081 | ||||
| Mean of outliers high | 1.067 | ||||
| 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) | 0.426 | ||||
| VaR(95%) (regression method) | 0.042 | ||||
| Expected Shortfall (regression method) | 0.134 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.207 | ||||
| Quartile 1 | 0.207 | ||||
| Median | 0.207 | ||||
| Quartile 3 | 0.207 | ||||
| Maximum | 0.207 | ||||
| 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) | -0.014 | ||||
| Compounded annual return (geometric extrapolation) | -0.014 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.067 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.188 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.049 | ||||
| SD | 0.135 | ||||
| Sharpe ratio (Glass type estimate) | -0.360 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.360 | ||||
| df | 825.000 | ||||
| t | -0.640 | ||||
| p | 0.739 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.464 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.744 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.464 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.744 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.469 | ||||
| Upside Potential Ratio | 2.764 | ||||
| Upside part of mean | 0.286 | ||||
| Downside part of mean | -0.335 | ||||
| Upside SD | 0.086 | ||||
| Downside SD | 0.104 | ||||
| N nonnegative terms | 58.000 | ||||
| N negative terms | 768.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 826.000 | ||||
| Mean of predictor | 0.584 | ||||
| Mean of criterion | -0.049 | ||||
| SD of predictor | 0.314 | ||||
| SD of criterion | 0.135 | ||||
| Covariance | 0.000 | ||||
| r | 0.003 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | -0.049 | ||||
| Mean Square Error | 0.018 | ||||
| DF error | 824.000 | ||||
| t(b) | 0.076 | ||||
| p(b) | 0.470 | ||||
| t(a) | -0.644 | ||||
| p(a) | 0.740 | ||||
| Lowerbound of 95% confidence interval for beta | -0.028 | ||||
| Upperbound of 95% confidence interval for beta | 0.030 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.199 | ||||
| Upperbound of 95% confidence interval for alpha | 0.101 | ||||
| Treynor index (mean / b) | -42.932 | ||||
| Jensen alpha (a) | -0.049 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.058 | ||||
| SD | 0.136 | ||||
| Sharpe ratio (Glass type estimate) | -0.424 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.423 | ||||
| df | 825.000 | ||||
| t | -0.752 | ||||
| p | 0.774 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.527 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.681 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.527 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.681 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.540 | ||||
| Upside Potential Ratio | 2.644 | ||||
| Upside part of mean | 0.283 | ||||
| Downside part of mean | -0.340 | ||||
| Upside SD | 0.085 | ||||
| Downside SD | 0.107 | ||||
| N nonnegative terms | 58.000 | ||||
| N negative terms | 768.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 826.000 | ||||
| Mean of predictor | 0.534 | ||||
| Mean of criterion | -0.058 | ||||
| SD of predictor | 0.316 | ||||
| SD of criterion | 0.136 | ||||
| Covariance | 0.000 | ||||
| r | 0.003 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | -0.058 | ||||
| Mean Square Error | 0.019 | ||||
| DF error | 824.000 | ||||
| t(b) | 0.085 | ||||
| p(b) | 0.466 | ||||
| t(a) | -0.756 | ||||
| p(a) | 0.775 | ||||
| Lowerbound of 95% confidence interval for beta | -0.028 | ||||
| Upperbound of 95% confidence interval for beta | 0.031 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.210 | ||||
| Upperbound of 95% confidence interval for alpha | 0.093 | ||||
| Treynor index (mean / b) | -45.423 | ||||
| Jensen alpha (a) | -0.058 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.017 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 826.000 | ||||
| Minimum | 0.894 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.065 | ||||
| Mean of quarter 1 | 0.996 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.004 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 57.000 | ||||
| Percentage of outliers low | 0.069 | ||||
| Mean of outliers low | 0.984 | ||||
| Number of outliers high | 58.000 | ||||
| Percentage of outliers high | 0.070 | ||||
| Mean of outliers high | 1.016 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.535 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| Extreme Value Index (regression method) | 0.222 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | 0.012 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.034 | ||||
| Median | 0.056 | ||||
| Quartile 3 | 0.082 | ||||
| Maximum | 0.245 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | 0.043 | ||||
| Mean of quarter 3 | 0.074 | ||||
| Mean of quarter 4 | 0.169 | ||||
| Inter Quartile Range | 0.049 | ||||
| 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 | 0.125 | ||||
| Mean of outliers high | 0.245 | ||||
| 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) | -0.013 | ||||
| Compounded annual return (geometric extrapolation) | -0.014 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.056 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.081 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.782 | ||||
| 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 | 1.134 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.497 | ||||
| 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 | 1.007 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.502 | ||||
| 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) | -8732447480437412.000 | ||||
| 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) | 914882711204036757005943571480576.000 | ||||
| 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 | ||||