Advanced Statistics: Turquoise IXFN M
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 | 0.006 | ||||
| SD | 0.224 | ||||
| Sharpe ratio (Glass type estimate) | 0.026 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.026 | ||||
| df | 76.000 | ||||
| t | 0.066 | ||||
| p | 0.474 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.748 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.800 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.748 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.800 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.047 | ||||
| Upside Potential Ratio | 1.089 | ||||
| Upside part of mean | 0.137 | ||||
| Downside part of mean | -0.132 | ||||
| Upside SD | 0.184 | ||||
| Downside SD | 0.126 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 70.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 77.000 | ||||
| Mean of predictor | 0.222 | ||||
| Mean of criterion | 0.006 | ||||
| SD of predictor | 0.276 | ||||
| SD of criterion | 0.224 | ||||
| Covariance | -0.006 | ||||
| r | -0.103 | ||||
| b (slope, estimate of beta) | -0.084 | ||||
| a (intercept, estimate of alpha) | 0.024 | ||||
| Mean Square Error | 0.051 | ||||
| DF error | 75.000 | ||||
| t(b) | -0.896 | ||||
| p(b) | 0.813 | ||||
| t(a) | 0.268 | ||||
| p(a) | 0.395 | ||||
| Lowerbound of 95% confidence interval for beta | -0.270 | ||||
| Upperbound of 95% confidence interval for beta | 0.102 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.157 | ||||
| Upperbound of 95% confidence interval for alpha | 0.206 | ||||
| Treynor index (mean / b) | -0.070 | ||||
| Jensen alpha (a) | 0.024 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.017 | ||||
| SD | 0.215 | ||||
| Sharpe ratio (Glass type estimate) | -0.081 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.080 | ||||
| df | 76.000 | ||||
| t | -0.205 | ||||
| p | 0.581 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.855 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.693 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.854 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.694 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.125 | ||||
| Upside Potential Ratio | 0.882 | ||||
| Upside part of mean | 0.123 | ||||
| Downside part of mean | -0.140 | ||||
| Upside SD | 0.162 | ||||
| Downside SD | 0.139 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 70.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 77.000 | ||||
| Mean of predictor | 0.181 | ||||
| Mean of criterion | -0.017 | ||||
| SD of predictor | 0.278 | ||||
| SD of criterion | 0.215 | ||||
| Covariance | -0.005 | ||||
| r | -0.091 | ||||
| b (slope, estimate of beta) | -0.070 | ||||
| a (intercept, estimate of alpha) | -0.005 | ||||
| Mean Square Error | 0.046 | ||||
| DF error | 75.000 | ||||
| t(b) | -0.790 | ||||
| p(b) | 0.784 | ||||
| t(a) | -0.054 | ||||
| p(a) | 0.522 | ||||
| Lowerbound of 95% confidence interval for beta | -0.246 | ||||
| Upperbound of 95% confidence interval for beta | 0.106 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.177 | ||||
| Upperbound of 95% confidence interval for alpha | 0.167 | ||||
| Treynor index (mean / b) | 0.248 | ||||
| Jensen alpha (a) | -0.005 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.098 | ||||
| Expected Shortfall on VaR | 0.121 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.036 | ||||
| Expected Shortfall on VaR | 0.076 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 77.000 | ||||
| Minimum | 0.783 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.315 | ||||
| Mean of quarter 1 | 0.970 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.048 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 13.000 | ||||
| Percentage of outliers low | 0.169 | ||||
| Mean of outliers low | 0.955 | ||||
| Number of outliers high | 12.000 | ||||
| Percentage of outliers high | 0.156 | ||||
| Mean of outliers high | 1.076 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.638 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.006 | ||||
| Extreme Value Index (regression method) | -0.266 | ||||
| VaR(95%) (regression method) | 0.037 | ||||
| Expected Shortfall (regression method) | 0.098 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.008 | ||||
| Quartile 1 | 0.108 | ||||
| Median | 0.209 | ||||
| Quartile 3 | 0.251 | ||||
| Maximum | 0.292 | ||||
| Mean of quarter 1 | 0.008 | ||||
| Mean of quarter 2 | 0.209 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.292 | ||||
| Inter Quartile Range | 0.142 | ||||
| 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) | 0.029 | ||||
| Compounded annual return (geometric extrapolation) | 0.027 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.092 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.092 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.223 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.320 | ||||
| SD | 0.863 | ||||
| Sharpe ratio (Glass type estimate) | 0.370 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.370 | ||||
| df | 1681.000 | ||||
| t | 0.939 | ||||
| p | 0.485 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.403 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.144 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.403 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.144 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.673 | ||||
| Upside Potential Ratio | 3.119 | ||||
| Upside part of mean | 1.481 | ||||
| Downside part of mean | -1.161 | ||||
| Upside SD | 0.721 | ||||
| Downside SD | 0.475 | ||||
| N nonnegative terms | 141.000 | ||||
| N negative terms | 1541.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1682.000 | ||||
| Mean of predictor | 0.349 | ||||
| Mean of criterion | 0.320 | ||||
| SD of predictor | 0.584 | ||||
| SD of criterion | 0.863 | ||||
| Covariance | -0.074 | ||||
| r | -0.147 | ||||
| b (slope, estimate of beta) | -0.217 | ||||
| a (intercept, estimate of alpha) | 0.396 | ||||
| Mean Square Error | 0.730 | ||||
| DF error | 1680.000 | ||||
| t(b) | -6.087 | ||||
| p(b) | 0.573 | ||||
| t(a) | 1.173 | ||||
| p(a) | 0.486 | ||||
| Lowerbound of 95% confidence interval for beta | -0.287 | ||||
| Upperbound of 95% confidence interval for beta | -0.147 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.266 | ||||
| Upperbound of 95% confidence interval for alpha | 1.057 | ||||
| Treynor index (mean / b) | -1.474 | ||||
| Jensen alpha (a) | 0.396 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.017 | ||||
| SD | 0.811 | ||||
| Sharpe ratio (Glass type estimate) | -0.021 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.021 | ||||
| df | 1681.000 | ||||
| t | -0.054 | ||||
| p | 0.501 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.795 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.752 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.795 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.752 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.031 | ||||
| Upside Potential Ratio | 2.288 | ||||
| Upside part of mean | 1.285 | ||||
| Downside part of mean | -1.302 | ||||
| Upside SD | 0.586 | ||||
| Downside SD | 0.561 | ||||
| N nonnegative terms | 141.000 | ||||
| N negative terms | 1541.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1682.000 | ||||
| Mean of predictor | 0.182 | ||||
| Mean of criterion | -0.017 | ||||
| SD of predictor | 0.578 | ||||
| SD of criterion | 0.811 | ||||
| Covariance | -0.069 | ||||
| r | -0.147 | ||||
| b (slope, estimate of beta) | -0.207 | ||||
| a (intercept, estimate of alpha) | 0.020 | ||||
| Mean Square Error | 0.644 | ||||
| DF error | 1680.000 | ||||
| t(b) | -6.110 | ||||
| p(b) | 0.574 | ||||
| t(a) | 0.064 | ||||
| p(a) | 0.499 | ||||
| Lowerbound of 95% confidence interval for beta | -0.273 | ||||
| Upperbound of 95% confidence interval for beta | -0.141 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.601 | ||||
| Upperbound of 95% confidence interval for alpha | 0.642 | ||||
| Treynor index (mean / b) | 0.084 | ||||
| Jensen alpha (a) | 0.020 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.079 | ||||
| Expected Shortfall on VaR | 0.098 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.015 | ||||
| Expected Shortfall on VaR | 0.033 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1682.000 | ||||
| Minimum | 0.600 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.747 | ||||
| Mean of quarter 1 | 0.983 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.023 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 155.000 | ||||
| Percentage of outliers low | 0.092 | ||||
| Mean of outliers low | 0.954 | ||||
| Number of outliers high | 160.000 | ||||
| Percentage of outliers high | 0.095 | ||||
| Mean of outliers high | 1.060 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.508 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.609 | ||||
| VaR(95%) (regression method) | 0.007 | ||||
| Expected Shortfall (regression method) | 0.057 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.247 | ||||
| Median | 0.346 | ||||
| Quartile 3 | 0.404 | ||||
| Maximum | 0.452 | ||||
| Mean of quarter 1 | 0.054 | ||||
| Mean of quarter 2 | 0.299 | ||||
| Mean of quarter 3 | 0.394 | ||||
| Mean of quarter 4 | 0.433 | ||||
| Inter Quartile Range | 0.157 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.125 | ||||
| Mean of outliers low | 0.002 | ||||
| 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) | 0.029 | ||||
| Compounded annual return (geometric extrapolation) | 0.027 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.060 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.062 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.275 | ||||
| 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 | 0.846 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.464 | ||||
| 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 | 0.736 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.470 | ||||
| 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) | -8758666996320440.000 | ||||
| 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) | -8559056932768996203614341678759936.000 | ||||
| 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 | ||||