Advanced Statistics: OdysseusTradingSystem
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 | -0.109 | ||||
| SD | 0.123 | ||||
| Sharpe ratio (Glass type estimate) | -0.890 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.869 | ||||
| df | 32.000 | ||||
| t | -1.476 | ||||
| p | 0.925 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.085 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.318 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.070 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.332 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.001 | ||||
| Upside Potential Ratio | 0.335 | ||||
| Upside part of mean | 0.037 | ||||
| Downside part of mean | -0.146 | ||||
| Upside SD | 0.061 | ||||
| Downside SD | 0.109 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 33.000 | ||||
| Mean of predictor | 0.571 | ||||
| Mean of criterion | -0.109 | ||||
| SD of predictor | 0.254 | ||||
| SD of criterion | 0.123 | ||||
| Covariance | 0.004 | ||||
| r | 0.120 | ||||
| b (slope, estimate of beta) | 0.058 | ||||
| a (intercept, estimate of alpha) | -0.142 | ||||
| Mean Square Error | 0.015 | ||||
| DF error | 31.000 | ||||
| t(b) | 0.676 | ||||
| p(b) | 0.252 | ||||
| t(a) | -1.594 | ||||
| p(a) | 0.939 | ||||
| Lowerbound of 95% confidence interval for beta | -0.117 | ||||
| Upperbound of 95% confidence interval for beta | 0.234 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.324 | ||||
| Upperbound of 95% confidence interval for alpha | 0.040 | ||||
| Treynor index (mean / b) | -1.876 | ||||
| Jensen alpha (a) | -0.142 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.117 | ||||
| SD | 0.127 | ||||
| Sharpe ratio (Glass type estimate) | -0.922 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.900 | ||||
| df | 32.000 | ||||
| t | -1.528 | ||||
| p | 0.932 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.118 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.288 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.102 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.302 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.009 | ||||
| Upside Potential Ratio | 0.300 | ||||
| Upside part of mean | 0.035 | ||||
| Downside part of mean | -0.151 | ||||
| Upside SD | 0.058 | ||||
| Downside SD | 0.116 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 33.000 | ||||
| Mean of predictor | 0.527 | ||||
| Mean of criterion | -0.117 | ||||
| SD of predictor | 0.240 | ||||
| SD of criterion | 0.127 | ||||
| Covariance | 0.004 | ||||
| r | 0.138 | ||||
| b (slope, estimate of beta) | 0.073 | ||||
| a (intercept, estimate of alpha) | -0.155 | ||||
| Mean Square Error | 0.016 | ||||
| DF error | 31.000 | ||||
| t(b) | 0.777 | ||||
| p(b) | 0.222 | ||||
| t(a) | -1.698 | ||||
| p(a) | 0.950 | ||||
| Lowerbound of 95% confidence interval for beta | -0.119 | ||||
| Upperbound of 95% confidence interval for beta | 0.264 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.342 | ||||
| Upperbound of 95% confidence interval for alpha | 0.031 | ||||
| Treynor index (mean / b) | -1.602 | ||||
| Jensen alpha (a) | -0.155 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.068 | ||||
| Expected Shortfall on VaR | 0.082 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.041 | ||||
| Expected Shortfall on VaR | 0.083 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 33.000 | ||||
| Minimum | 0.858 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.104 | ||||
| Mean of quarter 1 | 0.969 | ||||
| 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 | 3.000 | ||||
| Percentage of outliers low | 0.091 | ||||
| Mean of outliers low | 0.906 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.030 | ||||
| Mean of outliers high | 1.104 | ||||
| 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) | -0.750 | ||||
| VaR(95%) (regression method) | 0.080 | ||||
| Expected Shortfall (regression method) | 0.118 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.259 | ||||
| Quartile 1 | 0.259 | ||||
| Median | 0.259 | ||||
| Quartile 3 | 0.259 | ||||
| Maximum | 0.259 | ||||
| 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) | -0.066 | ||||
| Compounded annual return (geometric extrapolation) | -0.070 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.271 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.860 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.111 | ||||
| SD | 0.100 | ||||
| Sharpe ratio (Glass type estimate) | -1.113 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.112 | ||||
| df | 726.000 | ||||
| t | -1.854 | ||||
| p | 0.968 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.291 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.065 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.290 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.066 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.698 | ||||
| Upside Potential Ratio | 1.782 | ||||
| Upside part of mean | 0.117 | ||||
| Downside part of mean | -0.228 | ||||
| Upside SD | 0.076 | ||||
| Downside SD | 0.066 | ||||
| N nonnegative terms | 26.000 | ||||
| N negative terms | 701.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 727.000 | ||||
| Mean of predictor | 0.614 | ||||
| Mean of criterion | -0.111 | ||||
| SD of predictor | 0.328 | ||||
| SD of criterion | 0.100 | ||||
| Covariance | -0.001 | ||||
| r | -0.035 | ||||
| b (slope, estimate of beta) | -0.011 | ||||
| a (intercept, estimate of alpha) | -0.105 | ||||
| Mean Square Error | 0.010 | ||||
| DF error | 725.000 | ||||
| t(b) | -0.951 | ||||
| p(b) | 0.829 | ||||
| t(a) | -1.732 | ||||
| p(a) | 0.958 | ||||
| Lowerbound of 95% confidence interval for beta | -0.033 | ||||
| Upperbound of 95% confidence interval for beta | 0.011 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.223 | ||||
| Upperbound of 95% confidence interval for alpha | 0.014 | ||||
| Treynor index (mean / b) | 10.345 | ||||
| Jensen alpha (a) | -0.105 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.116 | ||||
| SD | 0.098 | ||||
| Sharpe ratio (Glass type estimate) | -1.181 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.180 | ||||
| df | 726.000 | ||||
| t | -1.968 | ||||
| p | 0.975 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.359 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.003 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.358 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.002 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.736 | ||||
| Upside Potential Ratio | 1.704 | ||||
| Upside part of mean | 0.114 | ||||
| Downside part of mean | -0.230 | ||||
| Upside SD | 0.072 | ||||
| Downside SD | 0.067 | ||||
| N nonnegative terms | 26.000 | ||||
| N negative terms | 701.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 727.000 | ||||
| Mean of predictor | 0.559 | ||||
| Mean of criterion | -0.116 | ||||
| SD of predictor | 0.332 | ||||
| SD of criterion | 0.098 | ||||
| Covariance | -0.001 | ||||
| r | -0.035 | ||||
| b (slope, estimate of beta) | -0.010 | ||||
| a (intercept, estimate of alpha) | -0.110 | ||||
| Mean Square Error | 0.010 | ||||
| DF error | 725.000 | ||||
| t(b) | -0.935 | ||||
| p(b) | 0.825 | ||||
| t(a) | -1.860 | ||||
| p(a) | 0.968 | ||||
| Lowerbound of 95% confidence interval for beta | -0.032 | ||||
| Upperbound of 95% confidence interval for beta | 0.011 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.227 | ||||
| Upperbound of 95% confidence interval for alpha | 0.006 | ||||
| Treynor index (mean / b) | 11.295 | ||||
| Jensen alpha (a) | -0.110 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.013 | ||||
| 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 | 727.000 | ||||
| Minimum | 0.932 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.115 | ||||
| Mean of quarter 1 | 0.997 | ||||
| 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 | 47.000 | ||||
| Percentage of outliers low | 0.065 | ||||
| Mean of outliers low | 0.989 | ||||
| Number of outliers high | 26.000 | ||||
| Percentage of outliers high | 0.036 | ||||
| Mean of outliers high | 1.013 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.622 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | 0.056 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | 0.007 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.008 | ||||
| Quartile 3 | 0.018 | ||||
| Maximum | 0.259 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.008 | ||||
| Mean of quarter 3 | 0.018 | ||||
| Mean of quarter 4 | 0.259 | ||||
| Inter Quartile Range | 0.013 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.200 | ||||
| Mean of outliers high | 0.259 | ||||
| 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) | -0.065 | ||||
| Compounded annual return (geometric extrapolation) | -0.070 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.269 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.269 | ||||
| Compounded annual return / Expected Shortfall lognormal | -5.400 | ||||
| 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 | 1.013 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.446 | ||||
| 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 | 0.912 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.448 | ||||
| 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) | -8730438590860116.000 | ||||
| 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) | 153296804453015361056099790749696.000 | ||||
| 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 | ||||