Advanced Statistics: ETF MKT 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 | -0.008 | ||||
| SD | 0.074 | ||||
| Sharpe ratio (Glass type estimate) | -0.108 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.105 | ||||
| df | 35.000 | ||||
| t | -0.186 | ||||
| p | 0.573 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.239 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.025 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.237 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.027 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.178 | ||||
| Upside Potential Ratio | 1.314 | ||||
| Upside part of mean | 0.058 | ||||
| Downside part of mean | -0.066 | ||||
| Upside SD | 0.057 | ||||
| Downside SD | 0.044 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.516 | ||||
| Mean of criterion | -0.008 | ||||
| SD of predictor | 0.285 | ||||
| SD of criterion | 0.074 | ||||
| Covariance | -0.003 | ||||
| r | -0.157 | ||||
| b (slope, estimate of beta) | -0.040 | ||||
| a (intercept, estimate of alpha) | 0.013 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 34.000 | ||||
| t(b) | -0.926 | ||||
| p(b) | 0.820 | ||||
| t(a) | 0.269 | ||||
| p(a) | 0.395 | ||||
| Lowerbound of 95% confidence interval for beta | -0.129 | ||||
| Upperbound of 95% confidence interval for beta | 0.048 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.085 | ||||
| Upperbound of 95% confidence interval for alpha | 0.111 | ||||
| Treynor index (mean / b) | 0.196 | ||||
| Jensen alpha (a) | 0.013 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.010 | ||||
| SD | 0.073 | ||||
| Sharpe ratio (Glass type estimate) | -0.144 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.141 | ||||
| df | 35.000 | ||||
| t | -0.250 | ||||
| p | 0.598 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.275 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.989 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.273 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.991 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.229 | ||||
| Upside Potential Ratio | 1.240 | ||||
| Upside part of mean | 0.057 | ||||
| Downside part of mean | -0.067 | ||||
| Upside SD | 0.055 | ||||
| Downside SD | 0.046 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.468 | ||||
| Mean of criterion | -0.010 | ||||
| SD of predictor | 0.267 | ||||
| SD of criterion | 0.073 | ||||
| Covariance | -0.003 | ||||
| r | -0.159 | ||||
| b (slope, estimate of beta) | -0.043 | ||||
| a (intercept, estimate of alpha) | 0.010 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 34.000 | ||||
| t(b) | -0.942 | ||||
| p(b) | 0.824 | ||||
| t(a) | 0.208 | ||||
| p(a) | 0.418 | ||||
| Lowerbound of 95% confidence interval for beta | -0.137 | ||||
| Upperbound of 95% confidence interval for beta | 0.050 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.086 | ||||
| Upperbound of 95% confidence interval for alpha | 0.106 | ||||
| Treynor index (mean / b) | 0.242 | ||||
| Jensen alpha (a) | 0.010 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.035 | ||||
| Expected Shortfall on VaR | 0.043 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.034 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 36.000 | ||||
| Minimum | 0.934 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.093 | ||||
| Mean of quarter 1 | 0.990 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.022 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.056 | ||||
| Mean of outliers low | 0.956 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.167 | ||||
| Mean of outliers high | 1.033 | ||||
| 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) | -0.090 | ||||
| VaR(95%) (regression method) | 0.022 | ||||
| Expected Shortfall (regression method) | 0.064 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.087 | ||||
| Quartile 1 | 0.087 | ||||
| Median | 0.087 | ||||
| Quartile 3 | 0.087 | ||||
| Maximum | 0.087 | ||||
| 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 | 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) | 0.035 | ||||
| Compounded annual return (geometric extrapolation) | 0.034 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.390 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.790 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.009 | ||||
| SD | 0.065 | ||||
| Sharpe ratio (Glass type estimate) | -0.139 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.139 | ||||
| df | 802.000 | ||||
| t | -0.244 | ||||
| p | 0.596 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.259 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.980 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.259 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.980 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.205 | ||||
| Upside Potential Ratio | 3.799 | ||||
| Upside part of mean | 0.168 | ||||
| Downside part of mean | -0.177 | ||||
| Upside SD | 0.048 | ||||
| Downside SD | 0.044 | ||||
| N nonnegative terms | 87.000 | ||||
| N negative terms | 716.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 803.000 | ||||
| Mean of predictor | 0.518 | ||||
| Mean of criterion | -0.009 | ||||
| SD of predictor | 0.308 | ||||
| SD of criterion | 0.065 | ||||
| Covariance | -0.002 | ||||
| r | -0.086 | ||||
| b (slope, estimate of beta) | -0.018 | ||||
| a (intercept, estimate of alpha) | 0.000 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 801.000 | ||||
| t(b) | -2.429 | ||||
| p(b) | 0.992 | ||||
| t(a) | 0.008 | ||||
| p(a) | 0.497 | ||||
| Lowerbound of 95% confidence interval for beta | -0.033 | ||||
| Upperbound of 95% confidence interval for beta | -0.003 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.073 | ||||
| Upperbound of 95% confidence interval for alpha | 0.074 | ||||
| Treynor index (mean / b) | 0.501 | ||||
| Jensen alpha (a) | 0.000 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.011 | ||||
| SD | 0.065 | ||||
| Sharpe ratio (Glass type estimate) | -0.172 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.172 | ||||
| df | 802.000 | ||||
| t | -0.301 | ||||
| p | 0.618 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.291 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.948 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.291 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.948 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.251 | ||||
| Upside Potential Ratio | 3.738 | ||||
| Upside part of mean | 0.167 | ||||
| Downside part of mean | -0.178 | ||||
| Upside SD | 0.047 | ||||
| Downside SD | 0.045 | ||||
| N nonnegative terms | 87.000 | ||||
| N negative terms | 716.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 803.000 | ||||
| Mean of predictor | 0.470 | ||||
| Mean of criterion | -0.011 | ||||
| SD of predictor | 0.310 | ||||
| SD of criterion | 0.065 | ||||
| Covariance | -0.002 | ||||
| r | -0.084 | ||||
| b (slope, estimate of beta) | -0.018 | ||||
| a (intercept, estimate of alpha) | -0.003 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 801.000 | ||||
| t(b) | -2.396 | ||||
| p(b) | 0.992 | ||||
| t(a) | -0.077 | ||||
| p(a) | 0.531 | ||||
| Lowerbound of 95% confidence interval for beta | -0.032 | ||||
| Upperbound of 95% confidence interval for beta | -0.003 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.076 | ||||
| Upperbound of 95% confidence interval for alpha | 0.070 | ||||
| Treynor index (mean / b) | 0.632 | ||||
| Jensen alpha (a) | -0.003 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.008 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 803.000 | ||||
| Minimum | 0.972 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.038 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.003 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 56.000 | ||||
| Percentage of outliers low | 0.070 | ||||
| Mean of outliers low | 0.992 | ||||
| Number of outliers high | 90.000 | ||||
| Percentage of outliers high | 0.112 | ||||
| Mean of outliers high | 1.006 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.384 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| Extreme Value Index (regression method) | -0.235 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | 0.007 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.003 | ||||
| Median | 0.007 | ||||
| Quartile 3 | 0.026 | ||||
| Maximum | 0.104 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.006 | ||||
| Mean of quarter 3 | 0.012 | ||||
| Mean of quarter 4 | 0.063 | ||||
| Inter Quartile Range | 0.022 | ||||
| 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 | 0.100 | ||||
| Mean of outliers high | 0.104 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -3.031 | ||||
| VaR(95%) (moments method) | 0.065 | ||||
| Expected Shortfall (moments method) | 0.066 | ||||
| Extreme Value Index (regression method) | -0.077 | ||||
| VaR(95%) (regression method) | 0.114 | ||||
| Expected Shortfall (regression method) | 0.158 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.035 | ||||
| Compounded annual return (geometric extrapolation) | 0.033 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.321 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.532 | ||||
| Compounded annual return / Expected Shortfall lognormal | 4.018 | ||||
| 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 | 0.901 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.471 | ||||
| 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 | 0.787 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.478 | ||||
| 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) | -8754249361620766.000 | ||||
| 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) | -2791239261011828232532881806721024.000 | ||||
| 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 | ||||