Advanced Statistics: Trinity ETF Growth Portfolio
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 | -0.046 | ||||
| SD | 0.250 | ||||
| Sharpe ratio (Glass type estimate) | -0.184 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.182 | ||||
| df | 49.000 | ||||
| t | -0.376 | ||||
| p | 0.646 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.144 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.777 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.142 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.779 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.248 | ||||
| Upside Potential Ratio | 0.876 | ||||
| Upside part of mean | 0.163 | ||||
| Downside part of mean | -0.209 | ||||
| Upside SD | 0.164 | ||||
| Downside SD | 0.186 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 43.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 50.000 | ||||
| Mean of predictor | 0.400 | ||||
| Mean of criterion | -0.046 | ||||
| SD of predictor | 0.296 | ||||
| SD of criterion | 0.250 | ||||
| Covariance | 0.021 | ||||
| r | 0.281 | ||||
| b (slope, estimate of beta) | 0.238 | ||||
| a (intercept, estimate of alpha) | -0.141 | ||||
| Mean Square Error | 0.059 | ||||
| DF error | 48.000 | ||||
| t(b) | 2.025 | ||||
| p(b) | 0.024 | ||||
| t(a) | -1.104 | ||||
| p(a) | 0.862 | ||||
| Lowerbound of 95% confidence interval for beta | 0.002 | ||||
| Upperbound of 95% confidence interval for beta | 0.473 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.398 | ||||
| Upperbound of 95% confidence interval for alpha | 0.116 | ||||
| Treynor index (mean / b) | -0.194 | ||||
| Jensen alpha (a) | -0.141 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.079 | ||||
| SD | 0.262 | ||||
| Sharpe ratio (Glass type estimate) | -0.300 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.295 | ||||
| df | 49.000 | ||||
| t | -0.612 | ||||
| p | 0.728 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.260 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.664 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.257 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.667 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.367 | ||||
| Upside Potential Ratio | 0.705 | ||||
| Upside part of mean | 0.151 | ||||
| Downside part of mean | -0.229 | ||||
| Upside SD | 0.148 | ||||
| Downside SD | 0.214 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 43.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 50.000 | ||||
| Mean of predictor | 0.353 | ||||
| Mean of criterion | -0.079 | ||||
| SD of predictor | 0.279 | ||||
| SD of criterion | 0.262 | ||||
| Covariance | 0.025 | ||||
| r | 0.341 | ||||
| b (slope, estimate of beta) | 0.320 | ||||
| a (intercept, estimate of alpha) | -0.191 | ||||
| Mean Square Error | 0.062 | ||||
| DF error | 48.000 | ||||
| t(b) | 2.512 | ||||
| p(b) | 0.008 | ||||
| t(a) | -1.474 | ||||
| p(a) | 0.926 | ||||
| Lowerbound of 95% confidence interval for beta | 0.064 | ||||
| Upperbound of 95% confidence interval for beta | 0.575 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.452 | ||||
| Upperbound of 95% confidence interval for alpha | 0.070 | ||||
| Treynor index (mean / b) | -0.246 | ||||
| Jensen alpha (a) | -0.191 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.123 | ||||
| Expected Shortfall on VaR | 0.150 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.055 | ||||
| Expected Shortfall on VaR | 0.117 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 50.000 | ||||
| Minimum | 0.696 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.281 | ||||
| Mean of quarter 1 | 0.945 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.054 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 10.000 | ||||
| Percentage of outliers low | 0.200 | ||||
| Mean of outliers low | 0.929 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.140 | ||||
| Mean of outliers high | 1.101 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.381 | ||||
| VaR(95%) (moments method) | 0.006 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.986 | ||||
| VaR(95%) (regression method) | 0.055 | ||||
| Expected Shortfall (regression method) | 5.342 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.060 | ||||
| Median | 0.120 | ||||
| Quartile 3 | 0.271 | ||||
| Maximum | 0.422 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.120 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.422 | ||||
| Inter Quartile Range | 0.211 | ||||
| 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) | -0.032 | ||||
| Compounded annual return (geometric extrapolation) | -0.034 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.080 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.080 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.227 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.030 | ||||
| SD | 0.303 | ||||
| Sharpe ratio (Glass type estimate) | -0.100 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.100 | ||||
| df | 1111.000 | ||||
| t | -0.205 | ||||
| p | 0.504 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.051 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.852 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.051 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.852 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.130 | ||||
| Upside Potential Ratio | 3.353 | ||||
| Upside part of mean | 0.776 | ||||
| Downside part of mean | -0.806 | ||||
| Upside SD | 0.195 | ||||
| Downside SD | 0.231 | ||||
| N nonnegative terms | 138.000 | ||||
| N negative terms | 974.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1112.000 | ||||
| Mean of predictor | 0.424 | ||||
| Mean of criterion | -0.030 | ||||
| SD of predictor | 0.350 | ||||
| SD of criterion | 0.303 | ||||
| Covariance | 0.023 | ||||
| r | 0.212 | ||||
| b (slope, estimate of beta) | 0.184 | ||||
| a (intercept, estimate of alpha) | -0.108 | ||||
| Mean Square Error | 0.088 | ||||
| DF error | 1110.000 | ||||
| t(b) | 7.242 | ||||
| p(b) | 0.394 | ||||
| t(a) | -0.751 | ||||
| p(a) | 0.511 | ||||
| Lowerbound of 95% confidence interval for beta | 0.134 | ||||
| Upperbound of 95% confidence interval for beta | 0.233 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.391 | ||||
| Upperbound of 95% confidence interval for alpha | 0.174 | ||||
| Treynor index (mean / b) | -0.164 | ||||
| Jensen alpha (a) | -0.108 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.078 | ||||
| SD | 0.313 | ||||
| Sharpe ratio (Glass type estimate) | -0.249 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.249 | ||||
| df | 1111.000 | ||||
| t | -0.513 | ||||
| p | 0.510 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.200 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.702 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.200 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.703 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.312 | ||||
| Upside Potential Ratio | 3.033 | ||||
| Upside part of mean | 0.757 | ||||
| Downside part of mean | -0.835 | ||||
| Upside SD | 0.188 | ||||
| Downside SD | 0.250 | ||||
| N nonnegative terms | 138.000 | ||||
| N negative terms | 974.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1112.000 | ||||
| Mean of predictor | 0.360 | ||||
| Mean of criterion | -0.078 | ||||
| SD of predictor | 0.362 | ||||
| SD of criterion | 0.313 | ||||
| Covariance | 0.024 | ||||
| r | 0.216 | ||||
| b (slope, estimate of beta) | 0.187 | ||||
| a (intercept, estimate of alpha) | -0.145 | ||||
| Mean Square Error | 0.093 | ||||
| DF error | 1110.000 | ||||
| t(b) | 7.367 | ||||
| p(b) | 0.392 | ||||
| t(a) | -0.976 | ||||
| p(a) | 0.515 | ||||
| Lowerbound of 95% confidence interval for beta | 0.137 | ||||
| Upperbound of 95% confidence interval for beta | 0.236 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.437 | ||||
| Upperbound of 95% confidence interval for alpha | 0.146 | ||||
| Treynor index (mean / b) | -0.417 | ||||
| Jensen alpha (a) | -0.145 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.032 | ||||
| Expected Shortfall on VaR | 0.039 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.022 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1112.000 | ||||
| Minimum | 0.742 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.152 | ||||
| Mean of quarter 1 | 0.988 | ||||
| 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 | 125.000 | ||||
| Percentage of outliers low | 0.112 | ||||
| Mean of outliers low | 0.974 | ||||
| Number of outliers high | 139.000 | ||||
| Percentage of outliers high | 0.125 | ||||
| Mean of outliers high | 1.024 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.176 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.007 | ||||
| Extreme Value Index (regression method) | 0.252 | ||||
| VaR(95%) (regression method) | 0.010 | ||||
| Expected Shortfall (regression method) | 0.028 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.029 | ||||
| Quartile 1 | 0.045 | ||||
| Median | 0.063 | ||||
| Quartile 3 | 0.191 | ||||
| Maximum | 0.460 | ||||
| Mean of quarter 1 | 0.029 | ||||
| Mean of quarter 2 | 0.061 | ||||
| Mean of quarter 3 | 0.088 | ||||
| Mean of quarter 4 | 0.377 | ||||
| Inter Quartile Range | 0.147 | ||||
| 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 | 0.460 | ||||
| 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) | -0.032 | ||||
| Compounded annual return (geometric extrapolation) | -0.033 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.072 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.088 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.846 | ||||
| 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 | 1.244 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.401 | ||||
| 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 | 1.160 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.404 | ||||
| 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) | -8663324731752262.000 | ||||
| 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) | -73955249717803566232159278596096.000 | ||||
| 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 | ||||