Advanced Statistics: ETF Timer
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.095 | ||||
| SD | 0.266 | ||||
| Sharpe ratio (Glass type estimate) | 0.357 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.356 | ||||
| df | 202.000 | ||||
| t | 1.469 | ||||
| p | 0.072 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.121 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.834 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.122 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.834 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.461 | ||||
| Upside Potential Ratio | 1.555 | ||||
| Upside part of mean | 0.320 | ||||
| Downside part of mean | -0.225 | ||||
| Upside SD | 0.169 | ||||
| Downside SD | 0.206 | ||||
| N nonnegative terms | 114.000 | ||||
| N negative terms | 89.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 203.000 | ||||
| Mean of predictor | 0.075 | ||||
| Mean of criterion | 0.095 | ||||
| SD of predictor | 0.186 | ||||
| SD of criterion | 0.266 | ||||
| Covariance | 0.018 | ||||
| r | 0.360 | ||||
| b (slope, estimate of beta) | 0.515 | ||||
| a (intercept, estimate of alpha) | 0.056 | ||||
| Mean Square Error | 0.062 | ||||
| DF error | 201.000 | ||||
| t(b) | 5.477 | ||||
| p(b) | 0.276 | ||||
| t(a) | 0.924 | ||||
| p(a) | 0.459 | ||||
| Lowerbound of 95% confidence interval for beta | 0.330 | ||||
| Upperbound of 95% confidence interval for beta | 0.701 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.064 | ||||
| Upperbound of 95% confidence interval for alpha | 0.176 | ||||
| Treynor index (mean / b) | 0.184 | ||||
| Jensen alpha (a) | 0.056 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.045 | ||||
| SD | 0.352 | ||||
| Sharpe ratio (Glass type estimate) | 0.128 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.128 | ||||
| df | 202.000 | ||||
| t | 0.528 | ||||
| p | 0.299 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.349 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.605 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.349 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.605 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.144 | ||||
| Upside Potential Ratio | 0.977 | ||||
| Upside part of mean | 0.306 | ||||
| Downside part of mean | -0.260 | ||||
| Upside SD | 0.159 | ||||
| Downside SD | 0.313 | ||||
| N nonnegative terms | 114.000 | ||||
| N negative terms | 89.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 203.000 | ||||
| Mean of predictor | 0.057 | ||||
| Mean of criterion | 0.045 | ||||
| SD of predictor | 0.188 | ||||
| SD of criterion | 0.352 | ||||
| Covariance | 0.017 | ||||
| r | 0.258 | ||||
| b (slope, estimate of beta) | 0.481 | ||||
| a (intercept, estimate of alpha) | 0.018 | ||||
| Mean Square Error | 0.116 | ||||
| DF error | 201.000 | ||||
| t(b) | 3.784 | ||||
| p(b) | 0.338 | ||||
| t(a) | 0.211 | ||||
| p(a) | 0.491 | ||||
| Lowerbound of 95% confidence interval for beta | 0.231 | ||||
| Upperbound of 95% confidence interval for beta | 0.732 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.146 | ||||
| Upperbound of 95% confidence interval for alpha | 0.181 | ||||
| Treynor index (mean / b) | 0.094 | ||||
| Jensen alpha (a) | 0.018 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.151 | ||||
| Expected Shortfall on VaR | 0.185 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.038 | ||||
| Expected Shortfall on VaR | 0.087 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 203.000 | ||||
| Minimum | 0.309 | ||||
| Quartile 1 | 0.982 | ||||
| Median | 1.010 | ||||
| Quartile 3 | 1.042 | ||||
| Maximum | 1.201 | ||||
| Mean of quarter 1 | 0.935 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.025 | ||||
| Mean of quarter 4 | 1.088 | ||||
| Inter Quartile Range | 0.060 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.025 | ||||
| Mean of outliers low | 0.740 | ||||
| Number of outliers high | 10.000 | ||||
| Percentage of outliers high | 0.049 | ||||
| Mean of outliers high | 1.160 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.468 | ||||
| VaR(95%) (moments method) | 0.059 | ||||
| Expected Shortfall (moments method) | 0.127 | ||||
| Extreme Value Index (regression method) | 0.373 | ||||
| VaR(95%) (regression method) | 0.057 | ||||
| Expected Shortfall (regression method) | 0.109 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 21.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.020 | ||||
| Median | 0.050 | ||||
| Quartile 3 | 0.142 | ||||
| Maximum | 0.691 | ||||
| Mean of quarter 1 | 0.009 | ||||
| Mean of quarter 2 | 0.041 | ||||
| Mean of quarter 3 | 0.102 | ||||
| Mean of quarter 4 | 0.341 | ||||
| Inter Quartile Range | 0.123 | ||||
| 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 | 0.095 | ||||
| Mean of outliers high | 0.517 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.142 | ||||
| VaR(95%) (moments method) | 0.327 | ||||
| Expected Shortfall (moments method) | 0.480 | ||||
| Extreme Value Index (regression method) | 0.527 | ||||
| VaR(95%) (regression method) | 0.437 | ||||
| Expected Shortfall (regression method) | 0.992 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.208 | ||||
| Compounded annual return (geometric extrapolation) | 0.093 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.135 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.274 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.503 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.137 | ||||
| SD | 0.396 | ||||
| Sharpe ratio (Glass type estimate) | 0.345 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.345 | ||||
| df | 4434.000 | ||||
| t | 1.420 | ||||
| p | 0.078 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.131 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.821 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.131 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.821 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.476 | ||||
| Upside Potential Ratio | 4.604 | ||||
| Upside part of mean | 1.320 | ||||
| Downside part of mean | -1.184 | ||||
| Upside SD | 0.273 | ||||
| Downside SD | 0.287 | ||||
| N nonnegative terms | 2184.000 | ||||
| N negative terms | 2251.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 4435.000 | ||||
| Mean of predictor | 0.113 | ||||
| Mean of criterion | 0.137 | ||||
| SD of predictor | 0.335 | ||||
| SD of criterion | 0.396 | ||||
| Covariance | -0.026 | ||||
| r | -0.193 | ||||
| b (slope, estimate of beta) | -0.229 | ||||
| a (intercept, estimate of alpha) | 0.162 | ||||
| Mean Square Error | 0.151 | ||||
| DF error | 4433.000 | ||||
| t(b) | -13.119 | ||||
| p(b) | 1.000 | ||||
| t(a) | 1.720 | ||||
| p(a) | 0.043 | ||||
| Lowerbound of 95% confidence interval for beta | -0.263 | ||||
| Upperbound of 95% confidence interval for beta | -0.194 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.023 | ||||
| Upperbound of 95% confidence interval for alpha | 0.348 | ||||
| Treynor index (mean / b) | -0.598 | ||||
| Jensen alpha (a) | 0.162 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.046 | ||||
| SD | 0.452 | ||||
| Sharpe ratio (Glass type estimate) | 0.101 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.101 | ||||
| df | 4434.000 | ||||
| t | 0.415 | ||||
| p | 0.339 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.376 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.577 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.376 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.577 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.122 | ||||
| Upside Potential Ratio | 3.430 | ||||
| Upside part of mean | 1.286 | ||||
| Downside part of mean | -1.241 | ||||
| Upside SD | 0.252 | ||||
| Downside SD | 0.375 | ||||
| N nonnegative terms | 2184.000 | ||||
| N negative terms | 2251.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 4435.000 | ||||
| Mean of predictor | 0.057 | ||||
| Mean of criterion | 0.046 | ||||
| SD of predictor | 0.335 | ||||
| SD of criterion | 0.452 | ||||
| Covariance | -0.026 | ||||
| r | -0.173 | ||||
| b (slope, estimate of beta) | -0.234 | ||||
| a (intercept, estimate of alpha) | 0.059 | ||||
| Mean Square Error | 0.198 | ||||
| DF error | 4433.000 | ||||
| t(b) | -11.718 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.545 | ||||
| p(a) | 0.293 | ||||
| Lowerbound of 95% confidence interval for beta | -0.273 | ||||
| Upperbound of 95% confidence interval for beta | -0.195 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.153 | ||||
| Upperbound of 95% confidence interval for alpha | 0.271 | ||||
| Treynor index (mean / b) | -0.195 | ||||
| Jensen alpha (a) | 0.059 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.045 | ||||
| Expected Shortfall on VaR | 0.056 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.023 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 4435.000 | ||||
| Minimum | 0.318 | ||||
| Quartile 1 | 0.996 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.005 | ||||
| Maximum | 1.361 | ||||
| Mean of quarter 1 | 0.983 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.018 | ||||
| Inter Quartile Range | 0.009 | ||||
| Number outliers low | 268.000 | ||||
| Percentage of outliers low | 0.060 | ||||
| Mean of outliers low | 0.957 | ||||
| Number of outliers high | 256.000 | ||||
| Percentage of outliers high | 0.058 | ||||
| Mean of outliers high | 1.045 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.636 | ||||
| VaR(95%) (moments method) | 0.015 | ||||
| Expected Shortfall (moments method) | 0.044 | ||||
| Extreme Value Index (regression method) | 0.483 | ||||
| VaR(95%) (regression method) | 0.013 | ||||
| Expected Shortfall (regression method) | 0.028 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 124.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.003 | ||||
| Median | 0.007 | ||||
| Quartile 3 | 0.029 | ||||
| Maximum | 0.697 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.005 | ||||
| Mean of quarter 3 | 0.016 | ||||
| Mean of quarter 4 | 0.127 | ||||
| Inter Quartile Range | 0.026 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 18.000 | ||||
| Percentage of outliers high | 0.145 | ||||
| Mean of outliers high | 0.188 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.645 | ||||
| VaR(95%) (moments method) | 0.120 | ||||
| Expected Shortfall (moments method) | 0.377 | ||||
| Extreme Value Index (regression method) | 0.592 | ||||
| VaR(95%) (regression method) | 0.127 | ||||
| Expected Shortfall (regression method) | 0.356 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.210 | ||||
| Compounded annual return (geometric extrapolation) | 0.094 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.135 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.736 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.681 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.034 | ||||
| SD | 0.206 | ||||
| Sharpe ratio (Glass type estimate) | 0.167 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.166 | ||||
| df | 130.000 | ||||
| t | 0.118 | ||||
| p | 0.495 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.605 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.939 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.606 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.938 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.241 | ||||
| Upside Potential Ratio | 9.185 | ||||
| Upside part of mean | 1.309 | ||||
| Downside part of mean | -1.274 | ||||
| Upside SD | 0.148 | ||||
| Downside SD | 0.142 | ||||
| N nonnegative terms | 70.000 | ||||
| N negative terms | 61.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.121 | ||||
| Mean of criterion | 0.034 | ||||
| SD of predictor | 0.137 | ||||
| SD of criterion | 0.206 | ||||
| Covariance | 0.021 | ||||
| r | 0.757 | ||||
| b (slope, estimate of beta) | 1.137 | ||||
| a (intercept, estimate of alpha) | -0.103 | ||||
| Mean Square Error | 0.018 | ||||
| DF error | 129.000 | ||||
| t(b) | 13.166 | ||||
| p(b) | 0.069 | ||||
| t(a) | -0.539 | ||||
| p(a) | 0.530 | ||||
| Lowerbound of 95% confidence interval for beta | 0.966 | ||||
| Upperbound of 95% confidence interval for beta | 1.307 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.482 | ||||
| Upperbound of 95% confidence interval for alpha | 0.275 | ||||
| Treynor index (mean / b) | 0.030 | ||||
| Jensen alpha (a) | -0.103 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.013 | ||||
| SD | 0.206 | ||||
| Sharpe ratio (Glass type estimate) | 0.065 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.064 | ||||
| df | 130.000 | ||||
| t | 0.046 | ||||
| p | 0.498 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.707 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.836 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.707 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.836 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.093 | ||||
| Upside Potential Ratio | 9.012 | ||||
| Upside part of mean | 1.298 | ||||
| Downside part of mean | -1.284 | ||||
| Upside SD | 0.146 | ||||
| Downside SD | 0.144 | ||||
| N nonnegative terms | 70.000 | ||||
| N negative terms | 61.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.112 | ||||
| Mean of criterion | 0.013 | ||||
| SD of predictor | 0.137 | ||||
| SD of criterion | 0.206 | ||||
| Covariance | 0.021 | ||||
| r | 0.760 | ||||
| b (slope, estimate of beta) | 1.140 | ||||
| a (intercept, estimate of alpha) | -0.114 | ||||
| Mean Square Error | 0.018 | ||||
| DF error | 129.000 | ||||
| t(b) | 13.263 | ||||
| p(b) | 0.068 | ||||
| t(a) | -0.598 | ||||
| p(a) | 0.533 | ||||
| Lowerbound of 95% confidence interval for beta | 0.970 | ||||
| Upperbound of 95% confidence interval for beta | 1.310 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.491 | ||||
| Upperbound of 95% confidence interval for alpha | 0.263 | ||||
| Treynor index (mean / b) | 0.012 | ||||
| Jensen alpha (a) | -0.114 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.026 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.020 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.963 | ||||
| Quartile 1 | 0.992 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.008 | ||||
| Maximum | 1.040 | ||||
| Mean of quarter 1 | 0.985 | ||||
| Mean of quarter 2 | 0.996 | ||||
| Mean of quarter 3 | 1.004 | ||||
| Mean of quarter 4 | 1.016 | ||||
| Inter Quartile Range | 0.016 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.015 | ||||
| Mean of outliers low | 0.964 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.008 | ||||
| Mean of outliers high | 1.040 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.253 | ||||
| VaR(95%) (moments method) | 0.016 | ||||
| Expected Shortfall (moments method) | 0.019 | ||||
| Extreme Value Index (regression method) | -0.119 | ||||
| VaR(95%) (regression method) | 0.015 | ||||
| Expected Shortfall (regression method) | 0.018 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.028 | ||||
| Quartile 3 | 0.056 | ||||
| Maximum | 0.158 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.017 | ||||
| Mean of quarter 3 | 0.040 | ||||
| Mean of quarter 4 | 0.115 | ||||
| Inter Quartile Range | 0.051 | ||||
| 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 | 0.143 | ||||
| Mean of outliers high | 0.158 | ||||
| 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) | 0.058 | ||||
| Compounded annual return (geometric extrapolation) | 0.059 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.374 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.514 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.284 | ||||