Advanced Statistics: VTD Call Box
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 | 0.169 | ||||
| SD | 0.563 | ||||
| Sharpe ratio (Glass type estimate) | 0.301 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.296 | ||||
| df | 52.000 | ||||
| t | 0.632 | ||||
| p | 0.265 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.635 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.233 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.638 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.231 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.543 | ||||
| Upside Potential Ratio | 1.839 | ||||
| Upside part of mean | 0.573 | ||||
| Downside part of mean | -0.404 | ||||
| Upside SD | 0.465 | ||||
| Downside SD | 0.312 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 43.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 53.000 | ||||
| Mean of predictor | 0.422 | ||||
| Mean of criterion | 0.169 | ||||
| SD of predictor | 0.278 | ||||
| SD of criterion | 0.563 | ||||
| Covariance | 0.038 | ||||
| r | 0.241 | ||||
| b (slope, estimate of beta) | 0.488 | ||||
| a (intercept, estimate of alpha) | -0.037 | ||||
| Mean Square Error | 0.304 | ||||
| DF error | 51.000 | ||||
| t(b) | 1.773 | ||||
| p(b) | 0.041 | ||||
| t(a) | -0.128 | ||||
| p(a) | 0.551 | ||||
| Lowerbound of 95% confidence interval for beta | -0.065 | ||||
| Upperbound of 95% confidence interval for beta | 1.040 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.613 | ||||
| Upperbound of 95% confidence interval for alpha | 0.539 | ||||
| Treynor index (mean / b) | 0.347 | ||||
| Jensen alpha (a) | -0.037 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.026 | ||||
| SD | 0.533 | ||||
| Sharpe ratio (Glass type estimate) | 0.049 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.048 | ||||
| df | 52.000 | ||||
| t | 0.103 | ||||
| p | 0.459 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.884 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.981 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.885 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.981 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.071 | ||||
| Upside Potential Ratio | 1.334 | ||||
| Upside part of mean | 0.489 | ||||
| Downside part of mean | -0.462 | ||||
| Upside SD | 0.381 | ||||
| Downside SD | 0.366 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 43.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 53.000 | ||||
| Mean of predictor | 0.380 | ||||
| Mean of criterion | 0.026 | ||||
| SD of predictor | 0.261 | ||||
| SD of criterion | 0.533 | ||||
| Covariance | 0.040 | ||||
| r | 0.286 | ||||
| b (slope, estimate of beta) | 0.585 | ||||
| a (intercept, estimate of alpha) | -0.196 | ||||
| Mean Square Error | 0.266 | ||||
| DF error | 51.000 | ||||
| t(b) | 2.135 | ||||
| p(b) | 0.019 | ||||
| t(a) | -0.735 | ||||
| p(a) | 0.767 | ||||
| Lowerbound of 95% confidence interval for beta | 0.035 | ||||
| Upperbound of 95% confidence interval for beta | 1.135 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.731 | ||||
| Upperbound of 95% confidence interval for alpha | 0.339 | ||||
| Treynor index (mean / b) | 0.045 | ||||
| Jensen alpha (a) | -0.196 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.222 | ||||
| Expected Shortfall on VaR | 0.269 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.103 | ||||
| Expected Shortfall on VaR | 0.211 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 53.000 | ||||
| Minimum | 0.635 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.681 | ||||
| Mean of quarter 1 | 0.884 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.198 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.151 | ||||
| Mean of outliers low | 0.797 | ||||
| Number of outliers high | 12.000 | ||||
| Percentage of outliers high | 0.226 | ||||
| Mean of outliers high | 1.214 | ||||
| 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) | -0.852 | ||||
| VaR(95%) (regression method) | 0.194 | ||||
| Expected Shortfall (regression method) | 0.244 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.417 | ||||
| Quartile 1 | 0.461 | ||||
| Median | 0.504 | ||||
| Quartile 3 | 0.548 | ||||
| Maximum | 0.591 | ||||
| Mean of quarter 1 | 0.417 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.591 | ||||
| Inter Quartile Range | 0.087 | ||||
| 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) | 0.082 | ||||
| Compounded annual return (geometric extrapolation) | 0.073 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.123 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.123 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.269 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.176 | ||||
| SD | 0.564 | ||||
| Sharpe ratio (Glass type estimate) | 0.313 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.312 | ||||
| df | 1162.000 | ||||
| t | 0.659 | ||||
| p | 0.490 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.618 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.243 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.618 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.243 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.520 | ||||
| Upside Potential Ratio | 5.255 | ||||
| Upside part of mean | 1.780 | ||||
| Downside part of mean | -1.603 | ||||
| Upside SD | 0.450 | ||||
| Downside SD | 0.339 | ||||
| N nonnegative terms | 184.000 | ||||
| N negative terms | 979.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1163.000 | ||||
| Mean of predictor | 0.436 | ||||
| Mean of criterion | 0.176 | ||||
| SD of predictor | 0.313 | ||||
| SD of criterion | 0.564 | ||||
| Covariance | 0.031 | ||||
| r | 0.174 | ||||
| b (slope, estimate of beta) | 0.314 | ||||
| a (intercept, estimate of alpha) | 0.040 | ||||
| Mean Square Error | 0.308 | ||||
| DF error | 1161.000 | ||||
| t(b) | 6.023 | ||||
| p(b) | 0.390 | ||||
| t(a) | 0.149 | ||||
| p(a) | 0.497 | ||||
| Lowerbound of 95% confidence interval for beta | 0.212 | ||||
| Upperbound of 95% confidence interval for beta | 0.416 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.480 | ||||
| Upperbound of 95% confidence interval for alpha | 0.559 | ||||
| Treynor index (mean / b) | 0.562 | ||||
| Jensen alpha (a) | 0.040 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.026 | ||||
| SD | 0.543 | ||||
| Sharpe ratio (Glass type estimate) | 0.047 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.047 | ||||
| df | 1162.000 | ||||
| t | 0.100 | ||||
| p | 0.499 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.883 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.978 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.883 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.978 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.072 | ||||
| Upside Potential Ratio | 4.717 | ||||
| Upside part of mean | 1.691 | ||||
| Downside part of mean | -1.665 | ||||
| Upside SD | 0.408 | ||||
| Downside SD | 0.358 | ||||
| N nonnegative terms | 184.000 | ||||
| N negative terms | 979.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1163.000 | ||||
| Mean of predictor | 0.386 | ||||
| Mean of criterion | 0.026 | ||||
| SD of predictor | 0.316 | ||||
| SD of criterion | 0.543 | ||||
| Covariance | 0.029 | ||||
| r | 0.171 | ||||
| b (slope, estimate of beta) | 0.294 | ||||
| a (intercept, estimate of alpha) | -0.088 | ||||
| Mean Square Error | 0.287 | ||||
| DF error | 1161.000 | ||||
| t(b) | 5.918 | ||||
| p(b) | 0.392 | ||||
| t(a) | -0.345 | ||||
| p(a) | 0.506 | ||||
| Lowerbound of 95% confidence interval for beta | 0.197 | ||||
| Upperbound of 95% confidence interval for beta | 0.392 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.588 | ||||
| Upperbound of 95% confidence interval for alpha | 0.412 | ||||
| Treynor index (mean / b) | 0.087 | ||||
| Jensen alpha (a) | -0.088 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.054 | ||||
| Expected Shortfall on VaR | 0.067 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.041 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1163.000 | ||||
| Minimum | 0.805 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.455 | ||||
| Mean of quarter 1 | 0.976 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.027 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 187.000 | ||||
| Percentage of outliers low | 0.161 | ||||
| Mean of outliers low | 0.963 | ||||
| Number of outliers high | 186.000 | ||||
| Percentage of outliers high | 0.160 | ||||
| Mean of outliers high | 1.043 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -6.562 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| Extreme Value Index (regression method) | 0.125 | ||||
| VaR(95%) (regression method) | 0.023 | ||||
| Expected Shortfall (regression method) | 0.046 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 15.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.012 | ||||
| Median | 0.114 | ||||
| Quartile 3 | 0.159 | ||||
| Maximum | 0.639 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | 0.085 | ||||
| Mean of quarter 3 | 0.132 | ||||
| Mean of quarter 4 | 0.370 | ||||
| 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 | 2.000 | ||||
| Percentage of outliers high | 0.133 | ||||
| Mean of outliers high | 0.559 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.072 | ||||
| VaR(95%) (moments method) | 0.368 | ||||
| Expected Shortfall (moments method) | 0.497 | ||||
| Extreme Value Index (regression method) | 0.309 | ||||
| VaR(95%) (regression method) | 0.490 | ||||
| Expected Shortfall (regression method) | 0.858 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.082 | ||||
| Compounded annual return (geometric extrapolation) | 0.072 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.113 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.195 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.082 | ||||
| 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 | 1.001 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.376 | ||||
| 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 | 0.928 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.382 | ||||
| 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) | -8701350925432871.000 | ||||
| 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) | 169044902512564028368587851825152.000 | ||||
| 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 | ||||