Advanced Statistics: Daily Batch
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 | 0.147 | ||||
| SD | 0.282 | ||||
| Sharpe ratio (Glass type estimate) | 0.522 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.516 | ||||
| df | 70.000 | ||||
| t | 1.270 | ||||
| p | 0.104 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.290 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.330 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.294 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.327 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.046 | ||||
| Upside Potential Ratio | 3.756 | ||||
| Upside part of mean | 0.270 | ||||
| Downside part of mean | -0.123 | ||||
| Upside SD | 0.274 | ||||
| Downside SD | 0.072 | ||||
| N nonnegative terms | 25.000 | ||||
| N negative terms | 46.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 71.000 | ||||
| Mean of predictor | 0.267 | ||||
| Mean of criterion | 0.147 | ||||
| SD of predictor | 0.282 | ||||
| SD of criterion | 0.282 | ||||
| Covariance | -0.005 | ||||
| r | -0.068 | ||||
| b (slope, estimate of beta) | -0.068 | ||||
| a (intercept, estimate of alpha) | 0.165 | ||||
| Mean Square Error | 0.080 | ||||
| DF error | 69.000 | ||||
| t(b) | -0.564 | ||||
| p(b) | 0.713 | ||||
| t(a) | 1.368 | ||||
| p(a) | 0.088 | ||||
| Lowerbound of 95% confidence interval for beta | -0.307 | ||||
| Upperbound of 95% confidence interval for beta | 0.172 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.076 | ||||
| Upperbound of 95% confidence interval for alpha | 0.406 | ||||
| Treynor index (mean / b) | -2.175 | ||||
| Jensen alpha (a) | 0.165 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.115 | ||||
| SD | 0.236 | ||||
| Sharpe ratio (Glass type estimate) | 0.487 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.482 | ||||
| df | 70.000 | ||||
| t | 1.185 | ||||
| p | 0.120 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.324 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.295 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.328 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.292 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.561 | ||||
| Upside Potential Ratio | 3.257 | ||||
| Upside part of mean | 0.240 | ||||
| Downside part of mean | -0.125 | ||||
| Upside SD | 0.225 | ||||
| Downside SD | 0.074 | ||||
| N nonnegative terms | 25.000 | ||||
| N negative terms | 46.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 71.000 | ||||
| Mean of predictor | 0.229 | ||||
| Mean of criterion | 0.115 | ||||
| SD of predictor | 0.256 | ||||
| SD of criterion | 0.236 | ||||
| Covariance | -0.004 | ||||
| r | -0.068 | ||||
| b (slope, estimate of beta) | -0.063 | ||||
| a (intercept, estimate of alpha) | 0.130 | ||||
| Mean Square Error | 0.056 | ||||
| DF error | 69.000 | ||||
| t(b) | -0.566 | ||||
| p(b) | 0.713 | ||||
| t(a) | 1.284 | ||||
| p(a) | 0.102 | ||||
| Lowerbound of 95% confidence interval for beta | -0.284 | ||||
| Upperbound of 95% confidence interval for beta | 0.158 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.072 | ||||
| Upperbound of 95% confidence interval for alpha | 0.331 | ||||
| Treynor index (mean / b) | -1.836 | ||||
| Jensen alpha (a) | 0.130 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.098 | ||||
| Expected Shortfall on VaR | 0.123 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.052 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 71.000 | ||||
| Minimum | 0.918 | ||||
| Quartile 1 | 0.999 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.017 | ||||
| Maximum | 1.578 | ||||
| Mean of quarter 1 | 0.969 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.004 | ||||
| Mean of quarter 4 | 1.090 | ||||
| Inter Quartile Range | 0.019 | ||||
| Number outliers low | 10.000 | ||||
| Percentage of outliers low | 0.141 | ||||
| Mean of outliers low | 0.952 | ||||
| Number of outliers high | 8.000 | ||||
| Percentage of outliers high | 0.113 | ||||
| Mean of outliers high | 1.163 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.178 | ||||
| VaR(95%) (moments method) | 0.011 | ||||
| Expected Shortfall (moments method) | 0.012 | ||||
| Extreme Value Index (regression method) | -0.143 | ||||
| VaR(95%) (regression method) | 0.033 | ||||
| Expected Shortfall (regression method) | 0.048 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.032 | ||||
| Quartile 1 | 0.082 | ||||
| Median | 0.131 | ||||
| Quartile 3 | 0.176 | ||||
| Maximum | 0.222 | ||||
| Mean of quarter 1 | 0.032 | ||||
| Mean of quarter 2 | 0.131 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.222 | ||||
| Inter Quartile Range | 0.095 | ||||
| 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) | 0.265 | ||||
| Compounded annual return (geometric extrapolation) | 0.173 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.778 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.778 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.407 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.205 | ||||
| SD | 0.441 | ||||
| Sharpe ratio (Glass type estimate) | 0.465 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.465 | ||||
| df | 1564.000 | ||||
| t | 1.137 | ||||
| p | 0.486 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.337 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.267 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.337 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.267 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.864 | ||||
| Upside Potential Ratio | 3.143 | ||||
| Upside part of mean | 0.747 | ||||
| Downside part of mean | -0.542 | ||||
| Upside SD | 0.372 | ||||
| Downside SD | 0.238 | ||||
| N nonnegative terms | 310.000 | ||||
| N negative terms | 1255.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1565.000 | ||||
| Mean of predictor | 0.279 | ||||
| Mean of criterion | 0.205 | ||||
| SD of predictor | 0.263 | ||||
| SD of criterion | 0.441 | ||||
| Covariance | -0.009 | ||||
| r | -0.079 | ||||
| b (slope, estimate of beta) | -0.132 | ||||
| a (intercept, estimate of alpha) | 0.242 | ||||
| Mean Square Error | 0.194 | ||||
| DF error | 1563.000 | ||||
| t(b) | -3.114 | ||||
| p(b) | 0.550 | ||||
| t(a) | 1.341 | ||||
| p(a) | 0.478 | ||||
| Lowerbound of 95% confidence interval for beta | -0.214 | ||||
| Upperbound of 95% confidence interval for beta | -0.049 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.112 | ||||
| Upperbound of 95% confidence interval for alpha | 0.596 | ||||
| Treynor index (mean / b) | -1.560 | ||||
| Jensen alpha (a) | 0.242 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.114 | ||||
| SD | 0.426 | ||||
| Sharpe ratio (Glass type estimate) | 0.267 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.267 | ||||
| df | 1564.000 | ||||
| t | 0.652 | ||||
| p | 0.492 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.535 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.069 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.535 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.069 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.398 | ||||
| Upside Potential Ratio | 2.417 | ||||
| Upside part of mean | 0.691 | ||||
| Downside part of mean | -0.578 | ||||
| Upside SD | 0.316 | ||||
| Downside SD | 0.286 | ||||
| N nonnegative terms | 310.000 | ||||
| N negative terms | 1255.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1565.000 | ||||
| Mean of predictor | 0.245 | ||||
| Mean of criterion | 0.114 | ||||
| SD of predictor | 0.261 | ||||
| SD of criterion | 0.426 | ||||
| Covariance | -0.009 | ||||
| r | -0.077 | ||||
| b (slope, estimate of beta) | -0.126 | ||||
| a (intercept, estimate of alpha) | 0.144 | ||||
| Mean Square Error | 0.181 | ||||
| DF error | 1563.000 | ||||
| t(b) | -3.058 | ||||
| p(b) | 0.549 | ||||
| t(a) | 0.829 | ||||
| p(a) | 0.487 | ||||
| Lowerbound of 95% confidence interval for beta | -0.206 | ||||
| Upperbound of 95% confidence interval for beta | -0.045 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.197 | ||||
| Upperbound of 95% confidence interval for alpha | 0.486 | ||||
| Treynor index (mean / b) | -0.904 | ||||
| Jensen alpha (a) | 0.144 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.042 | ||||
| Expected Shortfall on VaR | 0.052 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.014 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1565.000 | ||||
| Minimum | 0.584 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.558 | ||||
| Mean of quarter 1 | 0.992 | ||||
| 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 | 320.000 | ||||
| Percentage of outliers low | 0.204 | ||||
| Mean of outliers low | 0.991 | ||||
| Number of outliers high | 319.000 | ||||
| Percentage of outliers high | 0.204 | ||||
| Mean of outliers high | 1.014 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.820 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.029 | ||||
| Extreme Value Index (regression method) | 0.599 | ||||
| VaR(95%) (regression method) | 0.005 | ||||
| Expected Shortfall (regression method) | 0.016 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 32.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.004 | ||||
| Median | 0.016 | ||||
| Quartile 3 | 0.056 | ||||
| Maximum | 0.423 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.009 | ||||
| Mean of quarter 3 | 0.035 | ||||
| Mean of quarter 4 | 0.215 | ||||
| Inter Quartile Range | 0.052 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.188 | ||||
| Mean of outliers high | 0.262 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.410 | ||||
| VaR(95%) (moments method) | 0.179 | ||||
| Expected Shortfall (moments method) | 0.189 | ||||
| Extreme Value Index (regression method) | -0.628 | ||||
| VaR(95%) (regression method) | 0.258 | ||||
| Expected Shortfall (regression method) | 0.302 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.262 | ||||
| Compounded annual return (geometric extrapolation) | 0.171 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.403 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.796 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.260 | ||||
| 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 | 1.160 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.440 | ||||
| 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 | 1.061 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.442 | ||||
| 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) | -8703931101162496.000 | ||||
| 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) | -3244383069027348350828165069799424.000 | ||||
| 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 | ||||