Advanced Statistics: Omega TF System
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 | -0.053 | ||||
| SD | 0.096 | ||||
| Sharpe ratio (Glass type estimate) | -0.559 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.547 | ||||
| df | 37.000 | ||||
| t | -0.994 | ||||
| p | 0.837 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.664 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.554 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.656 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.561 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.650 | ||||
| Upside Potential Ratio | 0.602 | ||||
| Upside part of mean | 0.049 | ||||
| Downside part of mean | -0.103 | ||||
| Upside SD | 0.049 | ||||
| Downside SD | 0.082 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 38.000 | ||||
| Mean of predictor | 0.524 | ||||
| Mean of criterion | -0.053 | ||||
| SD of predictor | 0.259 | ||||
| SD of criterion | 0.096 | ||||
| Covariance | 0.003 | ||||
| r | 0.106 | ||||
| b (slope, estimate of beta) | 0.039 | ||||
| a (intercept, estimate of alpha) | -0.074 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 36.000 | ||||
| t(b) | 0.643 | ||||
| p(b) | 0.262 | ||||
| t(a) | -1.176 | ||||
| p(a) | 0.876 | ||||
| Lowerbound of 95% confidence interval for beta | -0.085 | ||||
| Upperbound of 95% confidence interval for beta | 0.163 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.202 | ||||
| Upperbound of 95% confidence interval for alpha | 0.054 | ||||
| Treynor index (mean / b) | -1.360 | ||||
| Jensen alpha (a) | -0.074 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.058 | ||||
| SD | 0.099 | ||||
| Sharpe ratio (Glass type estimate) | -0.585 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.573 | ||||
| df | 37.000 | ||||
| t | -1.042 | ||||
| p | 0.848 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.691 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.528 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.683 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.536 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.666 | ||||
| Upside Potential Ratio | 0.553 | ||||
| Upside part of mean | 0.048 | ||||
| Downside part of mean | -0.106 | ||||
| Upside SD | 0.048 | ||||
| Downside SD | 0.087 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 38.000 | ||||
| Mean of predictor | 0.482 | ||||
| Mean of criterion | -0.058 | ||||
| SD of predictor | 0.245 | ||||
| SD of criterion | 0.099 | ||||
| Covariance | 0.003 | ||||
| r | 0.121 | ||||
| b (slope, estimate of beta) | 0.049 | ||||
| a (intercept, estimate of alpha) | -0.082 | ||||
| Mean Square Error | 0.010 | ||||
| DF error | 36.000 | ||||
| t(b) | 0.734 | ||||
| p(b) | 0.234 | ||||
| t(a) | -1.264 | ||||
| p(a) | 0.893 | ||||
| Lowerbound of 95% confidence interval for beta | -0.087 | ||||
| Upperbound of 95% confidence interval for beta | 0.185 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.213 | ||||
| Upperbound of 95% confidence interval for alpha | 0.049 | ||||
| Treynor index (mean / b) | -1.180 | ||||
| Jensen alpha (a) | -0.082 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.051 | ||||
| Expected Shortfall on VaR | 0.062 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.057 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 38.000 | ||||
| Minimum | 0.871 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.054 | ||||
| Mean of quarter 1 | 0.980 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.017 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.079 | ||||
| Mean of outliers low | 0.933 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.105 | ||||
| Mean of outliers high | 1.043 | ||||
| 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) | 0.170 | ||||
| VaR(95%) (regression method) | 0.042 | ||||
| Expected Shortfall (regression method) | 0.118 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.026 | ||||
| Quartile 1 | 0.062 | ||||
| Median | 0.098 | ||||
| Quartile 3 | 0.133 | ||||
| Maximum | 0.169 | ||||
| Mean of quarter 1 | 0.026 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.169 | ||||
| Inter Quartile Range | 0.071 | ||||
| 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) | -0.014 | ||||
| Compounded annual return (geometric extrapolation) | -0.014 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.083 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.083 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.225 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.052 | ||||
| SD | 0.112 | ||||
| Sharpe ratio (Glass type estimate) | -0.462 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.461 | ||||
| df | 833.000 | ||||
| t | -0.824 | ||||
| p | 0.795 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.560 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.637 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.560 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.637 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.654 | ||||
| Upside Potential Ratio | 2.466 | ||||
| Upside part of mean | 0.195 | ||||
| Downside part of mean | -0.247 | ||||
| Upside SD | 0.079 | ||||
| Downside SD | 0.079 | ||||
| N nonnegative terms | 33.000 | ||||
| N negative terms | 801.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 834.000 | ||||
| Mean of predictor | 0.575 | ||||
| Mean of criterion | -0.052 | ||||
| SD of predictor | 0.329 | ||||
| SD of criterion | 0.112 | ||||
| Covariance | 0.001 | ||||
| r | 0.031 | ||||
| b (slope, estimate of beta) | 0.011 | ||||
| a (intercept, estimate of alpha) | -0.058 | ||||
| Mean Square Error | 0.013 | ||||
| DF error | 832.000 | ||||
| t(b) | 0.894 | ||||
| p(b) | 0.186 | ||||
| t(a) | -0.915 | ||||
| p(a) | 0.820 | ||||
| Lowerbound of 95% confidence interval for beta | -0.013 | ||||
| Upperbound of 95% confidence interval for beta | 0.034 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.182 | ||||
| Upperbound of 95% confidence interval for alpha | 0.066 | ||||
| Treynor index (mean / b) | -4.900 | ||||
| Jensen alpha (a) | -0.058 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.058 | ||||
| SD | 0.112 | ||||
| Sharpe ratio (Glass type estimate) | -0.518 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.518 | ||||
| df | 833.000 | ||||
| t | -0.925 | ||||
| p | 0.822 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.617 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.581 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.617 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.581 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.719 | ||||
| Upside Potential Ratio | 2.380 | ||||
| Upside part of mean | 0.192 | ||||
| Downside part of mean | -0.250 | ||||
| Upside SD | 0.077 | ||||
| Downside SD | 0.081 | ||||
| N nonnegative terms | 33.000 | ||||
| N negative terms | 801.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 834.000 | ||||
| Mean of predictor | 0.519 | ||||
| Mean of criterion | -0.058 | ||||
| SD of predictor | 0.332 | ||||
| SD of criterion | 0.112 | ||||
| Covariance | 0.001 | ||||
| r | 0.031 | ||||
| b (slope, estimate of beta) | 0.010 | ||||
| a (intercept, estimate of alpha) | -0.063 | ||||
| Mean Square Error | 0.013 | ||||
| DF error | 832.000 | ||||
| t(b) | 0.888 | ||||
| p(b) | 0.187 | ||||
| t(a) | -1.006 | ||||
| p(a) | 0.843 | ||||
| Lowerbound of 95% confidence interval for beta | -0.013 | ||||
| Upperbound of 95% confidence interval for beta | 0.033 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.187 | ||||
| Upperbound of 95% confidence interval for alpha | 0.060 | ||||
| Treynor index (mean / b) | -5.582 | ||||
| Jensen alpha (a) | -0.063 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.014 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 834.000 | ||||
| Minimum | 0.937 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.071 | ||||
| Mean of quarter 1 | 0.997 | ||||
| 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 | 36.000 | ||||
| Percentage of outliers low | 0.043 | ||||
| Mean of outliers low | 0.982 | ||||
| Number of outliers high | 33.000 | ||||
| Percentage of outliers high | 0.040 | ||||
| Mean of outliers high | 1.019 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.535 | ||||
| VaR(95%) (moments method) | -0.002 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.214 | ||||
| VaR(95%) (regression method) | -0.002 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.008 | ||||
| Median | 0.050 | ||||
| Quartile 3 | 0.108 | ||||
| Maximum | 0.234 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | 0.030 | ||||
| Mean of quarter 3 | 0.067 | ||||
| Mean of quarter 4 | 0.191 | ||||
| Inter Quartile Range | 0.099 | ||||
| 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) | -0.014 | ||||
| Compounded annual return (geometric extrapolation) | -0.014 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.059 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.072 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.965 | ||||
| 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 | 1.188 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.501 | ||||
| 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 | 1.060 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.504 | ||||
| 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) | -8725877893244091.000 | ||||
| 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) | 1229754263666372423343942515294208.000 | ||||
| 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 | ||||