Advanced Statistics: Bullchart ETF Timer
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 | 0.130 | ||||
| SD | 0.247 | ||||
| Sharpe ratio (Glass type estimate) | 0.525 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.519 | ||||
| df | 62.000 | ||||
| t | 1.203 | ||||
| p | 0.117 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.337 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.383 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.341 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.379 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.981 | ||||
| Upside Potential Ratio | 2.519 | ||||
| Upside part of mean | 0.333 | ||||
| Downside part of mean | -0.203 | ||||
| Upside SD | 0.210 | ||||
| Downside SD | 0.132 | ||||
| N nonnegative terms | 18.000 | ||||
| N negative terms | 45.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 63.000 | ||||
| Mean of predictor | 0.331 | ||||
| Mean of criterion | 0.130 | ||||
| SD of predictor | 0.232 | ||||
| SD of criterion | 0.247 | ||||
| Covariance | -0.011 | ||||
| r | -0.189 | ||||
| b (slope, estimate of beta) | -0.202 | ||||
| a (intercept, estimate of alpha) | 0.197 | ||||
| Mean Square Error | 0.060 | ||||
| DF error | 61.000 | ||||
| t(b) | -1.504 | ||||
| p(b) | 0.931 | ||||
| t(a) | 1.700 | ||||
| p(a) | 0.047 | ||||
| Lowerbound of 95% confidence interval for beta | -0.470 | ||||
| Upperbound of 95% confidence interval for beta | 0.066 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.035 | ||||
| Upperbound of 95% confidence interval for alpha | 0.428 | ||||
| Treynor index (mean / b) | -0.644 | ||||
| Jensen alpha (a) | 0.197 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.100 | ||||
| SD | 0.240 | ||||
| Sharpe ratio (Glass type estimate) | 0.416 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.411 | ||||
| df | 62.000 | ||||
| t | 0.953 | ||||
| p | 0.172 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.444 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.273 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.448 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.269 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.709 | ||||
| Upside Potential Ratio | 2.213 | ||||
| Upside part of mean | 0.312 | ||||
| Downside part of mean | -0.212 | ||||
| Upside SD | 0.195 | ||||
| Downside SD | 0.141 | ||||
| N nonnegative terms | 18.000 | ||||
| N negative terms | 45.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 63.000 | ||||
| Mean of predictor | 0.301 | ||||
| Mean of criterion | 0.100 | ||||
| SD of predictor | 0.224 | ||||
| SD of criterion | 0.240 | ||||
| Covariance | -0.010 | ||||
| r | -0.183 | ||||
| b (slope, estimate of beta) | -0.196 | ||||
| a (intercept, estimate of alpha) | 0.159 | ||||
| Mean Square Error | 0.057 | ||||
| DF error | 61.000 | ||||
| t(b) | -1.453 | ||||
| p(b) | 0.924 | ||||
| t(a) | 1.423 | ||||
| p(a) | 0.080 | ||||
| Lowerbound of 95% confidence interval for beta | -0.466 | ||||
| Upperbound of 95% confidence interval for beta | 0.074 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.064 | ||||
| Upperbound of 95% confidence interval for alpha | 0.382 | ||||
| Treynor index (mean / b) | -0.510 | ||||
| Jensen alpha (a) | 0.159 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.100 | ||||
| Expected Shortfall on VaR | 0.126 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.048 | ||||
| Expected Shortfall on VaR | 0.095 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 63.000 | ||||
| Minimum | 0.818 | ||||
| Quartile 1 | 0.995 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.033 | ||||
| Maximum | 1.210 | ||||
| Mean of quarter 1 | 0.944 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.111 | ||||
| Inter Quartile Range | 0.038 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.079 | ||||
| Mean of outliers low | 0.886 | ||||
| Number of outliers high | 11.000 | ||||
| Percentage of outliers high | 0.175 | ||||
| Mean of outliers high | 1.138 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.226 | ||||
| VaR(95%) (moments method) | 0.022 | ||||
| Expected Shortfall (moments method) | 0.024 | ||||
| Extreme Value Index (regression method) | 0.000 | ||||
| VaR(95%) (regression method) | 0.070 | ||||
| Expected Shortfall (regression method) | 0.111 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.009 | ||||
| Quartile 1 | 0.021 | ||||
| Median | 0.047 | ||||
| Quartile 3 | 0.090 | ||||
| Maximum | 0.264 | ||||
| Mean of quarter 1 | 0.014 | ||||
| Mean of quarter 2 | 0.028 | ||||
| Mean of quarter 3 | 0.071 | ||||
| Mean of quarter 4 | 0.199 | ||||
| Inter Quartile Range | 0.069 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.200 | ||||
| Mean of outliers high | 0.251 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -197.904 | ||||
| VaR(95%) (moments method) | 0.188 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -3.559 | ||||
| VaR(95%) (regression method) | 0.437 | ||||
| Expected Shortfall (regression method) | 0.438 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.215 | ||||
| Compounded annual return (geometric extrapolation) | 0.155 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.588 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.778 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.230 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.115 | ||||
| SD | 0.180 | ||||
| Sharpe ratio (Glass type estimate) | 0.639 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.639 | ||||
| df | 1385.000 | ||||
| t | 1.470 | ||||
| p | 0.475 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.213 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.492 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.214 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.491 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.039 | ||||
| Upside Potential Ratio | 7.380 | ||||
| Upside part of mean | 0.816 | ||||
| Downside part of mean | -0.701 | ||||
| Upside SD | 0.142 | ||||
| Downside SD | 0.111 | ||||
| N nonnegative terms | 364.000 | ||||
| N negative terms | 1022.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1386.000 | ||||
| Mean of predictor | 0.363 | ||||
| Mean of criterion | 0.115 | ||||
| SD of predictor | 0.307 | ||||
| SD of criterion | 0.180 | ||||
| Covariance | -0.006 | ||||
| r | -0.113 | ||||
| b (slope, estimate of beta) | -0.066 | ||||
| a (intercept, estimate of alpha) | 0.139 | ||||
| Mean Square Error | 0.032 | ||||
| DF error | 1384.000 | ||||
| t(b) | -4.223 | ||||
| p(b) | 0.556 | ||||
| t(a) | 1.783 | ||||
| p(a) | 0.476 | ||||
| Lowerbound of 95% confidence interval for beta | -0.097 | ||||
| Upperbound of 95% confidence interval for beta | -0.035 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.014 | ||||
| Upperbound of 95% confidence interval for alpha | 0.292 | ||||
| Treynor index (mean / b) | -1.742 | ||||
| Jensen alpha (a) | 0.139 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.099 | ||||
| SD | 0.179 | ||||
| Sharpe ratio (Glass type estimate) | 0.553 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.553 | ||||
| df | 1385.000 | ||||
| t | 1.273 | ||||
| p | 0.478 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.299 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.406 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.299 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.406 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.883 | ||||
| Upside Potential Ratio | 7.197 | ||||
| Upside part of mean | 0.806 | ||||
| Downside part of mean | -0.707 | ||||
| Upside SD | 0.139 | ||||
| Downside SD | 0.112 | ||||
| N nonnegative terms | 364.000 | ||||
| N negative terms | 1022.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1386.000 | ||||
| Mean of predictor | 0.314 | ||||
| Mean of criterion | 0.099 | ||||
| SD of predictor | 0.317 | ||||
| SD of criterion | 0.179 | ||||
| Covariance | -0.006 | ||||
| r | -0.110 | ||||
| b (slope, estimate of beta) | -0.062 | ||||
| a (intercept, estimate of alpha) | 0.118 | ||||
| Mean Square Error | 0.032 | ||||
| DF error | 1384.000 | ||||
| t(b) | -4.101 | ||||
| p(b) | 0.555 | ||||
| t(a) | 1.528 | ||||
| p(a) | 0.479 | ||||
| Lowerbound of 95% confidence interval for beta | -0.091 | ||||
| Upperbound of 95% confidence interval for beta | -0.032 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.034 | ||||
| Upperbound of 95% confidence interval for alpha | 0.270 | ||||
| Treynor index (mean / b) | -1.601 | ||||
| Jensen alpha (a) | 0.118 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.018 | ||||
| Expected Shortfall on VaR | 0.022 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.016 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1386.000 | ||||
| Minimum | 0.952 | ||||
| Quartile 1 | 0.999 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.001 | ||||
| Maximum | 1.090 | ||||
| Mean of quarter 1 | 0.990 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.013 | ||||
| Inter Quartile Range | 0.002 | ||||
| Number outliers low | 268.000 | ||||
| Percentage of outliers low | 0.193 | ||||
| Mean of outliers low | 0.987 | ||||
| Number of outliers high | 272.000 | ||||
| Percentage of outliers high | 0.196 | ||||
| Mean of outliers high | 1.016 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.072 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.007 | ||||
| Extreme Value Index (regression method) | 0.044 | ||||
| VaR(95%) (regression method) | 0.009 | ||||
| Expected Shortfall (regression method) | 0.014 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 39.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.011 | ||||
| Median | 0.021 | ||||
| Quartile 3 | 0.054 | ||||
| Maximum | 0.302 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.018 | ||||
| Mean of quarter 3 | 0.034 | ||||
| Mean of quarter 4 | 0.129 | ||||
| Inter Quartile Range | 0.042 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.103 | ||||
| Mean of outliers high | 0.204 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.003 | ||||
| VaR(95%) (moments method) | 0.122 | ||||
| Expected Shortfall (moments method) | 0.165 | ||||
| Extreme Value Index (regression method) | 0.293 | ||||
| VaR(95%) (regression method) | 0.141 | ||||
| Expected Shortfall (regression method) | 0.235 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.214 | ||||
| Compounded annual return (geometric extrapolation) | 0.154 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.509 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.191 | ||||
| Compounded annual return / Expected Shortfall lognormal | 6.940 | ||||
| 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 | 1.169 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.505 | ||||
| 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 | 1.041 | ||||
| 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) | -8727981447498945.000 | ||||
| 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) | 281820813878935620935269314723840.000 | ||||
| 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 | ||||