Advanced Statistics: ETF Basket-Trader (Closed)
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 | -0.036 | ||||
| SD | 0.145 | ||||
| Sharpe ratio (Glass type estimate) | -0.246 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.244 | ||||
| df | 85.000 | ||||
| t | -0.659 | ||||
| p | 0.744 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.978 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.488 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.977 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.489 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.368 | ||||
| Upside Potential Ratio | 0.882 | ||||
| Upside part of mean | 0.085 | ||||
| Downside part of mean | -0.121 | ||||
| Upside SD | 0.107 | ||||
| Downside SD | 0.097 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 77.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 86.000 | ||||
| Mean of predictor | 0.106 | ||||
| Mean of criterion | -0.036 | ||||
| SD of predictor | 0.209 | ||||
| SD of criterion | 0.145 | ||||
| Covariance | 0.006 | ||||
| r | 0.196 | ||||
| b (slope, estimate of beta) | 0.136 | ||||
| a (intercept, estimate of alpha) | -0.050 | ||||
| Mean Square Error | 0.020 | ||||
| DF error | 84.000 | ||||
| t(b) | 1.834 | ||||
| p(b) | 0.035 | ||||
| t(a) | -0.929 | ||||
| p(a) | 0.822 | ||||
| Lowerbound of 95% confidence interval for beta | -0.011 | ||||
| Upperbound of 95% confidence interval for beta | 0.284 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.158 | ||||
| Upperbound of 95% confidence interval for alpha | 0.057 | ||||
| Treynor index (mean / b) | -0.262 | ||||
| Jensen alpha (a) | -0.050 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.046 | ||||
| SD | 0.143 | ||||
| Sharpe ratio (Glass type estimate) | -0.320 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.318 | ||||
| df | 85.000 | ||||
| t | -0.858 | ||||
| p | 0.803 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.053 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.414 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.051 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.416 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.444 | ||||
| Upside Potential Ratio | 0.776 | ||||
| Upside part of mean | 0.080 | ||||
| Downside part of mean | -0.126 | ||||
| Upside SD | 0.099 | ||||
| Downside SD | 0.103 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 77.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 86.000 | ||||
| Mean of predictor | 0.084 | ||||
| Mean of criterion | -0.046 | ||||
| SD of predictor | 0.212 | ||||
| SD of criterion | 0.143 | ||||
| Covariance | 0.008 | ||||
| r | 0.253 | ||||
| b (slope, estimate of beta) | 0.170 | ||||
| a (intercept, estimate of alpha) | -0.060 | ||||
| Mean Square Error | 0.019 | ||||
| DF error | 84.000 | ||||
| t(b) | 2.396 | ||||
| p(b) | 0.009 | ||||
| t(a) | -1.148 | ||||
| p(a) | 0.873 | ||||
| Lowerbound of 95% confidence interval for beta | 0.029 | ||||
| Upperbound of 95% confidence interval for beta | 0.311 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.164 | ||||
| Upperbound of 95% confidence interval for alpha | 0.044 | ||||
| Treynor index (mean / b) | -0.269 | ||||
| Jensen alpha (a) | -0.060 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.069 | ||||
| Expected Shortfall on VaR | 0.085 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.033 | ||||
| Expected Shortfall on VaR | 0.067 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 86.000 | ||||
| Minimum | 0.845 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.228 | ||||
| Mean of quarter 1 | 0.973 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.029 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 13.000 | ||||
| Percentage of outliers low | 0.151 | ||||
| Mean of outliers low | 0.955 | ||||
| Number of outliers high | 15.000 | ||||
| Percentage of outliers high | 0.174 | ||||
| Mean of outliers high | 1.043 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -5.036 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | -0.219 | ||||
| VaR(95%) (regression method) | 0.054 | ||||
| Expected Shortfall (regression method) | 0.103 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.056 | ||||
| Quartile 1 | 0.103 | ||||
| Median | 0.150 | ||||
| Quartile 3 | 0.198 | ||||
| Maximum | 0.245 | ||||
| Mean of quarter 1 | 0.056 | ||||
| Mean of quarter 2 | 0.150 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.245 | ||||
| Inter Quartile Range | 0.094 | ||||
| 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) | -0.002 | ||||
| Compounded annual return (geometric extrapolation) | -0.002 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.007 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.007 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.020 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.032 | ||||
| SD | 0.396 | ||||
| Sharpe ratio (Glass type estimate) | 0.081 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.080 | ||||
| df | 1894.000 | ||||
| t | 0.217 | ||||
| p | 0.498 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.648 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.809 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.648 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.809 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.124 | ||||
| Upside Potential Ratio | 3.003 | ||||
| Upside part of mean | 0.774 | ||||
| Downside part of mean | -0.742 | ||||
| Upside SD | 0.301 | ||||
| Downside SD | 0.258 | ||||
| N nonnegative terms | 159.000 | ||||
| N negative terms | 1736.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1895.000 | ||||
| Mean of predictor | 0.321 | ||||
| Mean of criterion | 0.032 | ||||
| SD of predictor | 0.609 | ||||
| SD of criterion | 0.396 | ||||
| Covariance | 0.029 | ||||
| r | 0.120 | ||||
| b (slope, estimate of beta) | 0.078 | ||||
| a (intercept, estimate of alpha) | 0.007 | ||||
| Mean Square Error | 0.155 | ||||
| DF error | 1893.000 | ||||
| t(b) | 5.248 | ||||
| p(b) | 0.424 | ||||
| t(a) | 0.047 | ||||
| p(a) | 0.499 | ||||
| Lowerbound of 95% confidence interval for beta | 0.049 | ||||
| Upperbound of 95% confidence interval for beta | 0.107 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.280 | ||||
| Upperbound of 95% confidence interval for alpha | 0.294 | ||||
| Treynor index (mean / b) | 0.409 | ||||
| Jensen alpha (a) | 0.007 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.046 | ||||
| SD | 0.394 | ||||
| Sharpe ratio (Glass type estimate) | -0.116 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.116 | ||||
| df | 1894.000 | ||||
| t | -0.312 | ||||
| p | 0.504 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.845 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.613 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.845 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.613 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.165 | ||||
| Upside Potential Ratio | 2.636 | ||||
| Upside part of mean | 0.732 | ||||
| Downside part of mean | -0.778 | ||||
| Upside SD | 0.279 | ||||
| Downside SD | 0.278 | ||||
| N nonnegative terms | 159.000 | ||||
| N negative terms | 1736.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1895.000 | ||||
| Mean of predictor | 0.139 | ||||
| Mean of criterion | -0.046 | ||||
| SD of predictor | 0.601 | ||||
| SD of criterion | 0.394 | ||||
| Covariance | 0.028 | ||||
| r | 0.118 | ||||
| b (slope, estimate of beta) | 0.077 | ||||
| a (intercept, estimate of alpha) | -0.056 | ||||
| Mean Square Error | 0.153 | ||||
| DF error | 1893.000 | ||||
| t(b) | 5.153 | ||||
| p(b) | 0.425 | ||||
| t(a) | -0.388 | ||||
| p(a) | 0.506 | ||||
| Lowerbound of 95% confidence interval for beta | 0.048 | ||||
| Upperbound of 95% confidence interval for beta | 0.106 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.342 | ||||
| Upperbound of 95% confidence interval for alpha | 0.229 | ||||
| Treynor index (mean / b) | -0.593 | ||||
| Jensen alpha (a) | -0.056 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.039 | ||||
| Expected Shortfall on VaR | 0.049 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.021 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1895.000 | ||||
| Minimum | 0.775 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.287 | ||||
| Mean of quarter 1 | 0.989 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.012 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 198.000 | ||||
| Percentage of outliers low | 0.104 | ||||
| Mean of outliers low | 0.974 | ||||
| Number of outliers high | 209.000 | ||||
| Percentage of outliers high | 0.110 | ||||
| Mean of outliers high | 1.027 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.938 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.063 | ||||
| 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 | 5.000 | ||||
| Minimum | 0.208 | ||||
| Quartile 1 | 0.225 | ||||
| Median | 0.229 | ||||
| Quartile 3 | 0.283 | ||||
| Maximum | 0.295 | ||||
| Mean of quarter 1 | 0.217 | ||||
| Mean of quarter 2 | 0.229 | ||||
| Mean of quarter 3 | 0.283 | ||||
| Mean of quarter 4 | 0.295 | ||||
| Inter Quartile Range | 0.058 | ||||
| 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) | -0.002 | ||||
| Compounded annual return (geometric extrapolation) | -0.002 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.006 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.006 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.035 | ||||
| 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 | 1.763 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.696 | ||||
| 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 | 1.526 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.680 | ||||
| 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) | -8715782100889575.000 | ||||
| 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) | -335547260701380333967293630382080.000 | ||||
| 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 | ||||