Advanced Statistics: (46518146)
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 | -0.042 | ||||
| SD | 0.060 | ||||
| Sharpe ratio (Glass type estimate) | -0.708 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.698 | ||||
| df | 56.000 | ||||
| t | -1.543 | ||||
| p | 0.936 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.614 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.204 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.607 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.210 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.044 | ||||
| Upside Potential Ratio | 0.857 | ||||
| Upside part of mean | 0.035 | ||||
| Downside part of mean | -0.077 | ||||
| Upside SD | 0.045 | ||||
| Downside SD | 0.041 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 52.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 57.000 | ||||
| Mean of predictor | 0.342 | ||||
| Mean of criterion | -0.042 | ||||
| SD of predictor | 0.264 | ||||
| SD of criterion | 0.060 | ||||
| Covariance | -0.001 | ||||
| r | -0.070 | ||||
| b (slope, estimate of beta) | -0.016 | ||||
| a (intercept, estimate of alpha) | -0.037 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 55.000 | ||||
| t(b) | -0.518 | ||||
| p(b) | 0.697 | ||||
| t(a) | -1.251 | ||||
| p(a) | 0.892 | ||||
| Lowerbound of 95% confidence interval for beta | -0.077 | ||||
| Upperbound of 95% confidence interval for beta | 0.045 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.096 | ||||
| Upperbound of 95% confidence interval for alpha | 0.022 | ||||
| Treynor index (mean / b) | 2.682 | ||||
| Jensen alpha (a) | -0.037 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.059 | ||||
| Sharpe ratio (Glass type estimate) | -0.746 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.736 | ||||
| df | 56.000 | ||||
| t | -1.627 | ||||
| p | 0.945 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.653 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.167 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.646 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.173 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.068 | ||||
| Upside Potential Ratio | 0.818 | ||||
| Upside part of mean | 0.034 | ||||
| Downside part of mean | -0.078 | ||||
| Upside SD | 0.043 | ||||
| Downside SD | 0.041 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 52.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 57.000 | ||||
| Mean of predictor | 0.303 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.258 | ||||
| SD of criterion | 0.059 | ||||
| Covariance | -0.001 | ||||
| r | -0.084 | ||||
| b (slope, estimate of beta) | -0.019 | ||||
| a (intercept, estimate of alpha) | -0.038 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 55.000 | ||||
| t(b) | -0.626 | ||||
| p(b) | 0.733 | ||||
| t(a) | -1.328 | ||||
| p(a) | 0.905 | ||||
| Lowerbound of 95% confidence interval for beta | -0.081 | ||||
| Upperbound of 95% confidence interval for beta | 0.042 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.096 | ||||
| Upperbound of 95% confidence interval for alpha | 0.019 | ||||
| Treynor index (mean / b) | 2.288 | ||||
| Jensen alpha (a) | -0.038 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.031 | ||||
| Expected Shortfall on VaR | 0.038 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 57.000 | ||||
| Minimum | 0.953 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.085 | ||||
| Mean of quarter 1 | 0.988 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.013 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.123 | ||||
| Mean of outliers low | 0.975 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.088 | ||||
| Mean of outliers high | 1.037 | ||||
| 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) | -0.748 | ||||
| VaR(95%) (regression method) | 0.026 | ||||
| Expected Shortfall (regression method) | 0.036 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.067 | ||||
| Quartile 1 | 0.074 | ||||
| Median | 0.081 | ||||
| Quartile 3 | 0.088 | ||||
| Maximum | 0.095 | ||||
| Mean of quarter 1 | 0.067 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.095 | ||||
| Inter Quartile Range | 0.014 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.000 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.042 | ||||
| SD | 0.070 | ||||
| Sharpe ratio (Glass type estimate) | -0.596 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.596 | ||||
| df | 1253.000 | ||||
| t | -1.304 | ||||
| p | 0.523 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.492 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.300 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.492 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.300 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.824 | ||||
| Upside Potential Ratio | 2.970 | ||||
| Upside part of mean | 0.150 | ||||
| Downside part of mean | -0.191 | ||||
| Upside SD | 0.048 | ||||
| Downside SD | 0.050 | ||||
| N nonnegative terms | 93.000 | ||||
| N negative terms | 1161.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1254.000 | ||||
| Mean of predictor | 0.369 | ||||
| Mean of criterion | -0.042 | ||||
| SD of predictor | 0.312 | ||||
| SD of criterion | 0.070 | ||||
| Covariance | -0.001 | ||||
| r | -0.056 | ||||
| b (slope, estimate of beta) | -0.012 | ||||
| a (intercept, estimate of alpha) | -0.037 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 1252.000 | ||||
| t(b) | -1.977 | ||||
| p(b) | 0.528 | ||||
| t(a) | -1.158 | ||||
| p(a) | 0.516 | ||||
| Lowerbound of 95% confidence interval for beta | -0.025 | ||||
| Upperbound of 95% confidence interval for beta | -0.000 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.100 | ||||
| Upperbound of 95% confidence interval for alpha | 0.026 | ||||
| Treynor index (mean / b) | 3.332 | ||||
| Jensen alpha (a) | -0.037 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.070 | ||||
| Sharpe ratio (Glass type estimate) | -0.631 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.630 | ||||
| df | 1253.000 | ||||
| t | -1.380 | ||||
| p | 0.525 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.527 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.266 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.527 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.266 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.862 | ||||
| Upside Potential Ratio | 2.911 | ||||
| Upside part of mean | 0.149 | ||||
| Downside part of mean | -0.193 | ||||
| Upside SD | 0.048 | ||||
| Downside SD | 0.051 | ||||
| N nonnegative terms | 93.000 | ||||
| N negative terms | 1161.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1254.000 | ||||
| Mean of predictor | 0.319 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.314 | ||||
| SD of criterion | 0.070 | ||||
| Covariance | -0.001 | ||||
| r | -0.055 | ||||
| b (slope, estimate of beta) | -0.012 | ||||
| a (intercept, estimate of alpha) | -0.040 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 1252.000 | ||||
| t(b) | -1.962 | ||||
| p(b) | 0.528 | ||||
| t(a) | -1.256 | ||||
| p(a) | 0.518 | ||||
| Lowerbound of 95% confidence interval for beta | -0.025 | ||||
| Upperbound of 95% confidence interval for beta | -0.000 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.103 | ||||
| Upperbound of 95% confidence interval for alpha | 0.023 | ||||
| Treynor index (mean / b) | 3.579 | ||||
| Jensen alpha (a) | -0.040 | ||||
| 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 | 0.009 | ||||
| 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 | 1254.000 | ||||
| Minimum | 0.957 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.045 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.002 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 89.000 | ||||
| Percentage of outliers low | 0.071 | ||||
| Mean of outliers low | 0.992 | ||||
| Number of outliers high | 98.000 | ||||
| Percentage of outliers high | 0.078 | ||||
| Mean of outliers high | 1.007 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.886 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| 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 | 9.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.006 | ||||
| Median | 0.024 | ||||
| Quartile 3 | 0.035 | ||||
| Maximum | 0.103 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.015 | ||||
| Mean of quarter 3 | 0.032 | ||||
| Mean of quarter 4 | 0.093 | ||||
| Inter Quartile Range | 0.029 | ||||
| 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 | 0.222 | ||||
| Mean of outliers high | 0.093 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -32.931 | ||||
| VaR(95%) (moments method) | 0.070 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -2.127 | ||||
| VaR(95%) (regression method) | 0.137 | ||||
| Expected Shortfall (regression method) | 0.139 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.000 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| 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 | 1.093 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.440 | ||||
| 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 | 0.994 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.441 | ||||
| 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) | -8714914444473211.000 | ||||
| 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) | 5638308925470407807281463627350016.000 | ||||
| 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 | ||||