Advanced Statistics: ETF Quickie
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 | 0.001 | ||||
| SD | 0.129 | ||||
| Sharpe ratio (Glass type estimate) | 0.007 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.007 | ||||
| df | 51.000 | ||||
| t | 0.014 | ||||
| p | 0.495 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.935 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.948 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.935 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.948 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.016 | ||||
| Upside Potential Ratio | 1.590 | ||||
| Upside part of mean | 0.085 | ||||
| Downside part of mean | -0.084 | ||||
| Upside SD | 0.117 | ||||
| Downside SD | 0.053 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 42.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 52.000 | ||||
| Mean of predictor | 0.338 | ||||
| Mean of criterion | 0.001 | ||||
| SD of predictor | 0.232 | ||||
| SD of criterion | 0.129 | ||||
| Covariance | 0.000 | ||||
| r | 0.012 | ||||
| b (slope, estimate of beta) | 0.007 | ||||
| a (intercept, estimate of alpha) | -0.001 | ||||
| Mean Square Error | 0.017 | ||||
| DF error | 50.000 | ||||
| t(b) | 0.084 | ||||
| p(b) | 0.467 | ||||
| t(a) | -0.020 | ||||
| p(a) | 0.508 | ||||
| Lowerbound of 95% confidence interval for beta | -0.152 | ||||
| Upperbound of 95% confidence interval for beta | 0.165 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.138 | ||||
| Upperbound of 95% confidence interval for alpha | 0.136 | ||||
| Treynor index (mean / b) | 0.129 | ||||
| Jensen alpha (a) | -0.001 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.007 | ||||
| SD | 0.120 | ||||
| Sharpe ratio (Glass type estimate) | -0.054 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.054 | ||||
| df | 51.000 | ||||
| t | -0.113 | ||||
| p | 0.545 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.996 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.887 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.995 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.888 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.119 | ||||
| Upside Potential Ratio | 1.430 | ||||
| Upside part of mean | 0.078 | ||||
| Downside part of mean | -0.085 | ||||
| Upside SD | 0.105 | ||||
| Downside SD | 0.055 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 42.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 52.000 | ||||
| Mean of predictor | 0.307 | ||||
| Mean of criterion | -0.007 | ||||
| SD of predictor | 0.224 | ||||
| SD of criterion | 0.120 | ||||
| Covariance | 0.000 | ||||
| r | 0.015 | ||||
| b (slope, estimate of beta) | 0.008 | ||||
| a (intercept, estimate of alpha) | -0.009 | ||||
| Mean Square Error | 0.015 | ||||
| DF error | 50.000 | ||||
| t(b) | 0.107 | ||||
| p(b) | 0.457 | ||||
| t(a) | -0.144 | ||||
| p(a) | 0.557 | ||||
| Lowerbound of 95% confidence interval for beta | -0.144 | ||||
| Upperbound of 95% confidence interval for beta | 0.160 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.135 | ||||
| Upperbound of 95% confidence interval for alpha | 0.117 | ||||
| Treynor index (mean / b) | -0.802 | ||||
| Jensen alpha (a) | -0.009 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.056 | ||||
| Expected Shortfall on VaR | 0.069 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.041 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 52.000 | ||||
| Minimum | 0.917 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.239 | ||||
| Mean of quarter 1 | 0.984 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.031 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 9.000 | ||||
| Percentage of outliers low | 0.173 | ||||
| Mean of outliers low | 0.977 | ||||
| Number of outliers high | 11.000 | ||||
| Percentage of outliers high | 0.212 | ||||
| Mean of outliers high | 1.037 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -8.465 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| Extreme Value Index (regression method) | 0.291 | ||||
| VaR(95%) (regression method) | 0.024 | ||||
| Expected Shortfall (regression method) | 0.057 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.014 | ||||
| Quartile 1 | 0.044 | ||||
| Median | 0.073 | ||||
| Quartile 3 | 0.102 | ||||
| Maximum | 0.131 | ||||
| Mean of quarter 1 | 0.014 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.131 | ||||
| Inter Quartile Range | 0.059 | ||||
| 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) | 0.041 | ||||
| Compounded annual return (geometric extrapolation) | 0.038 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.291 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.291 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.553 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.003 | ||||
| SD | 0.143 | ||||
| Sharpe ratio (Glass type estimate) | 0.020 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.020 | ||||
| df | 1155.000 | ||||
| t | 0.042 | ||||
| p | 0.499 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.913 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.953 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.913 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.953 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.032 | ||||
| Upside Potential Ratio | 3.296 | ||||
| Upside part of mean | 0.287 | ||||
| Downside part of mean | -0.284 | ||||
| Upside SD | 0.113 | ||||
| Downside SD | 0.087 | ||||
| N nonnegative terms | 154.000 | ||||
| N negative terms | 1002.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1156.000 | ||||
| Mean of predictor | 0.391 | ||||
| Mean of criterion | 0.003 | ||||
| SD of predictor | 0.313 | ||||
| SD of criterion | 0.143 | ||||
| Covariance | -0.001 | ||||
| r | -0.018 | ||||
| b (slope, estimate of beta) | -0.008 | ||||
| a (intercept, estimate of alpha) | 0.006 | ||||
| Mean Square Error | 0.020 | ||||
| DF error | 1154.000 | ||||
| t(b) | -0.620 | ||||
| p(b) | 0.509 | ||||
| t(a) | 0.089 | ||||
| p(a) | 0.499 | ||||
| Lowerbound of 95% confidence interval for beta | -0.035 | ||||
| Upperbound of 95% confidence interval for beta | 0.018 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.128 | ||||
| Upperbound of 95% confidence interval for alpha | 0.140 | ||||
| Treynor index (mean / b) | -0.340 | ||||
| Jensen alpha (a) | 0.006 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.007 | ||||
| SD | 0.141 | ||||
| Sharpe ratio (Glass type estimate) | -0.051 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.051 | ||||
| df | 1155.000 | ||||
| t | -0.107 | ||||
| p | 0.502 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.984 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.882 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.984 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.882 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.080 | ||||
| Upside Potential Ratio | 3.147 | ||||
| Upside part of mean | 0.281 | ||||
| Downside part of mean | -0.288 | ||||
| Upside SD | 0.109 | ||||
| Downside SD | 0.089 | ||||
| N nonnegative terms | 154.000 | ||||
| N negative terms | 1002.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1156.000 | ||||
| Mean of predictor | 0.342 | ||||
| Mean of criterion | -0.007 | ||||
| SD of predictor | 0.311 | ||||
| SD of criterion | 0.141 | ||||
| Covariance | -0.001 | ||||
| r | -0.018 | ||||
| b (slope, estimate of beta) | -0.008 | ||||
| a (intercept, estimate of alpha) | -0.004 | ||||
| Mean Square Error | 0.020 | ||||
| DF error | 1154.000 | ||||
| t(b) | -0.602 | ||||
| p(b) | 0.509 | ||||
| t(a) | -0.066 | ||||
| p(a) | 0.501 | ||||
| Lowerbound of 95% confidence interval for beta | -0.034 | ||||
| Upperbound of 95% confidence interval for beta | 0.018 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.136 | ||||
| Upperbound of 95% confidence interval for alpha | 0.128 | ||||
| Treynor index (mean / b) | 0.894 | ||||
| Jensen alpha (a) | -0.004 | ||||
| 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 | 0.018 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.008 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1156.000 | ||||
| Minimum | 0.921 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.126 | ||||
| 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 | 164.000 | ||||
| Percentage of outliers low | 0.142 | ||||
| Mean of outliers low | 0.993 | ||||
| Number of outliers high | 168.000 | ||||
| Percentage of outliers high | 0.145 | ||||
| Mean of outliers high | 1.008 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.053 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.716 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | 0.011 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 14.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.004 | ||||
| Quartile 3 | 0.014 | ||||
| Maximum | 0.244 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.003 | ||||
| Mean of quarter 3 | 0.007 | ||||
| Mean of quarter 4 | 0.108 | ||||
| Inter Quartile Range | 0.012 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.214 | ||||
| Mean of outliers high | 0.139 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -6.352 | ||||
| VaR(95%) (moments method) | 0.052 | ||||
| Expected Shortfall (moments method) | 0.052 | ||||
| Extreme Value Index (regression method) | 0.273 | ||||
| VaR(95%) (regression method) | 0.115 | ||||
| Expected Shortfall (regression method) | 0.216 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.040 | ||||
| Compounded annual return (geometric extrapolation) | 0.038 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.154 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.348 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.106 | ||||
| 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 | 1.135 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.562 | ||||
| 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 | 0.978 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.558 | ||||
| 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) | -8748217546883332.000 | ||||
| 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) | 340936205171822757541390896332800.000 | ||||
| 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 | ||||