Advanced Statistics: MR T-RADES
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 | -0.036 | ||||
| SD | 0.155 | ||||
| Sharpe ratio (Glass type estimate) | -0.235 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.230 | ||||
| df | 38.000 | ||||
| t | -0.423 | ||||
| p | 0.663 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.321 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.855 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.318 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.859 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.389 | ||||
| Upside Potential Ratio | 0.721 | ||||
| Upside part of mean | 0.068 | ||||
| Downside part of mean | -0.104 | ||||
| Upside SD | 0.122 | ||||
| Downside SD | 0.094 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 38.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.501 | ||||
| Mean of criterion | -0.036 | ||||
| SD of predictor | 0.264 | ||||
| SD of criterion | 0.155 | ||||
| Covariance | 0.004 | ||||
| r | 0.089 | ||||
| b (slope, estimate of beta) | 0.052 | ||||
| a (intercept, estimate of alpha) | -0.063 | ||||
| Mean Square Error | 0.025 | ||||
| DF error | 37.000 | ||||
| t(b) | 0.544 | ||||
| p(b) | 0.295 | ||||
| t(a) | -0.630 | ||||
| p(a) | 0.734 | ||||
| Lowerbound of 95% confidence interval for beta | -0.143 | ||||
| Upperbound of 95% confidence interval for beta | 0.248 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.264 | ||||
| Upperbound of 95% confidence interval for alpha | 0.139 | ||||
| Treynor index (mean / b) | -0.696 | ||||
| Jensen alpha (a) | -0.063 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.048 | ||||
| SD | 0.151 | ||||
| Sharpe ratio (Glass type estimate) | -0.316 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.310 | ||||
| df | 38.000 | ||||
| t | -0.570 | ||||
| p | 0.714 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.404 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.776 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.399 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.780 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.470 | ||||
| Upside Potential Ratio | 0.602 | ||||
| Upside part of mean | 0.061 | ||||
| Downside part of mean | -0.109 | ||||
| Upside SD | 0.110 | ||||
| Downside SD | 0.101 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 38.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.458 | ||||
| Mean of criterion | -0.048 | ||||
| SD of predictor | 0.248 | ||||
| SD of criterion | 0.151 | ||||
| Covariance | 0.004 | ||||
| r | 0.109 | ||||
| b (slope, estimate of beta) | 0.066 | ||||
| a (intercept, estimate of alpha) | -0.078 | ||||
| Mean Square Error | 0.023 | ||||
| DF error | 37.000 | ||||
| t(b) | 0.665 | ||||
| p(b) | 0.255 | ||||
| t(a) | -0.814 | ||||
| p(a) | 0.789 | ||||
| Lowerbound of 95% confidence interval for beta | -0.135 | ||||
| Upperbound of 95% confidence interval for beta | 0.267 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.272 | ||||
| Upperbound of 95% confidence interval for alpha | 0.116 | ||||
| Treynor index (mean / b) | -0.722 | ||||
| Jensen alpha (a) | -0.078 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.073 | ||||
| Expected Shortfall on VaR | 0.089 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.030 | ||||
| Expected Shortfall on VaR | 0.062 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 39.000 | ||||
| Minimum | 0.842 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.223 | ||||
| Mean of quarter 1 | 0.980 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.022 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.051 | ||||
| Mean of outliers low | 0.901 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.026 | ||||
| Mean of outliers high | 1.223 | ||||
| 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) | 0.523 | ||||
| VaR(95%) (regression method) | 0.030 | ||||
| Expected Shortfall (regression method) | 0.201 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.192 | ||||
| Quartile 1 | 0.192 | ||||
| Median | 0.192 | ||||
| Quartile 3 | 0.192 | ||||
| Maximum | 0.192 | ||||
| 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 | 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) | -0.004 | ||||
| Compounded annual return (geometric extrapolation) | -0.004 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.019 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.040 | ||||
| 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 | 0.106 | ||||
| Sharpe ratio (Glass type estimate) | -0.399 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.399 | ||||
| df | 859.000 | ||||
| t | -0.723 | ||||
| p | 0.765 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.481 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.683 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.481 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.683 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.637 | ||||
| Upside Potential Ratio | 1.441 | ||||
| Upside part of mean | 0.095 | ||||
| Downside part of mean | -0.137 | ||||
| Upside SD | 0.082 | ||||
| Downside SD | 0.066 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 851.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 860.000 | ||||
| Mean of predictor | 0.528 | ||||
| Mean of criterion | -0.042 | ||||
| SD of predictor | 0.311 | ||||
| SD of criterion | 0.106 | ||||
| Covariance | 0.001 | ||||
| r | 0.020 | ||||
| b (slope, estimate of beta) | 0.007 | ||||
| a (intercept, estimate of alpha) | -0.046 | ||||
| Mean Square Error | 0.011 | ||||
| DF error | 858.000 | ||||
| t(b) | 0.578 | ||||
| p(b) | 0.282 | ||||
| t(a) | -0.779 | ||||
| p(a) | 0.782 | ||||
| Lowerbound of 95% confidence interval for beta | -0.016 | ||||
| Upperbound of 95% confidence interval for beta | 0.029 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.161 | ||||
| Upperbound of 95% confidence interval for alpha | 0.069 | ||||
| Treynor index (mean / b) | -6.284 | ||||
| Jensen alpha (a) | -0.046 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.048 | ||||
| SD | 0.105 | ||||
| Sharpe ratio (Glass type estimate) | -0.455 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.454 | ||||
| df | 859.000 | ||||
| t | -0.824 | ||||
| p | 0.795 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.537 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.627 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.536 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.628 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.696 | ||||
| Upside Potential Ratio | 1.345 | ||||
| Upside part of mean | 0.092 | ||||
| Downside part of mean | -0.140 | ||||
| Upside SD | 0.079 | ||||
| Downside SD | 0.068 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 851.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 860.000 | ||||
| Mean of predictor | 0.479 | ||||
| Mean of criterion | -0.048 | ||||
| SD of predictor | 0.311 | ||||
| SD of criterion | 0.105 | ||||
| Covariance | 0.001 | ||||
| r | 0.018 | ||||
| b (slope, estimate of beta) | 0.006 | ||||
| a (intercept, estimate of alpha) | -0.050 | ||||
| Mean Square Error | 0.011 | ||||
| DF error | 858.000 | ||||
| t(b) | 0.521 | ||||
| p(b) | 0.301 | ||||
| t(a) | -0.869 | ||||
| p(a) | 0.808 | ||||
| Lowerbound of 95% confidence interval for beta | -0.017 | ||||
| Upperbound of 95% confidence interval for beta | 0.028 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.164 | ||||
| Upperbound of 95% confidence interval for alpha | 0.063 | ||||
| Treynor index (mean / b) | -7.965 | ||||
| Jensen alpha (a) | -0.050 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.013 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 860.000 | ||||
| Minimum | 0.909 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.099 | ||||
| Mean of quarter 1 | 0.999 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.001 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 13.000 | ||||
| Percentage of outliers low | 0.015 | ||||
| Mean of outliers low | 0.976 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.010 | ||||
| Mean of outliers high | 1.035 | ||||
| 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) | 0.109 | ||||
| VaR(95%) (regression method) | -0.016 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.201 | ||||
| Quartile 1 | 0.201 | ||||
| Median | 0.201 | ||||
| Quartile 3 | 0.201 | ||||
| Maximum | 0.201 | ||||
| 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 | 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) | -0.004 | ||||
| Compounded annual return (geometric extrapolation) | -0.004 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.018 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.266 | ||||
| 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 | 1.051 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.488 | ||||
| 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 | 0.931 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.491 | ||||
| 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) | -8739542836594534.000 | ||||
| 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) | -388205662317198108452230977814528.000 | ||||
| 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 | ||||