Advanced Statistics: CogniTraderSP
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 | -0.029 | ||||
| SD | 0.039 | ||||
| Sharpe ratio (Glass type estimate) | -0.740 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.722 | ||||
| df | 31.000 | ||||
| t | -1.208 | ||||
| p | 0.882 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.948 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.480 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.935 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.492 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.343 | ||||
| Upside Potential Ratio | 0.988 | ||||
| Upside part of mean | 0.021 | ||||
| Downside part of mean | -0.049 | ||||
| Upside SD | 0.032 | ||||
| Downside SD | 0.021 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.607 | ||||
| Mean of criterion | -0.029 | ||||
| SD of predictor | 0.267 | ||||
| SD of criterion | 0.039 | ||||
| Covariance | -0.001 | ||||
| r | -0.081 | ||||
| b (slope, estimate of beta) | -0.012 | ||||
| a (intercept, estimate of alpha) | -0.021 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 30.000 | ||||
| t(b) | -0.444 | ||||
| p(b) | 0.670 | ||||
| t(a) | -0.746 | ||||
| p(a) | 0.769 | ||||
| Lowerbound of 95% confidence interval for beta | -0.065 | ||||
| Upperbound of 95% confidence interval for beta | 0.042 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.080 | ||||
| Upperbound of 95% confidence interval for alpha | 0.037 | ||||
| Treynor index (mean / b) | 2.447 | ||||
| Jensen alpha (a) | -0.021 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.029 | ||||
| SD | 0.038 | ||||
| Sharpe ratio (Glass type estimate) | -0.771 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.753 | ||||
| df | 31.000 | ||||
| t | -1.260 | ||||
| p | 0.891 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.981 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.450 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.967 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.462 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.364 | ||||
| Upside Potential Ratio | 0.954 | ||||
| Upside part of mean | 0.020 | ||||
| Downside part of mean | -0.050 | ||||
| Upside SD | 0.032 | ||||
| Downside SD | 0.021 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.559 | ||||
| Mean of criterion | -0.029 | ||||
| SD of predictor | 0.249 | ||||
| SD of criterion | 0.038 | ||||
| Covariance | -0.001 | ||||
| r | -0.079 | ||||
| b (slope, estimate of beta) | -0.012 | ||||
| a (intercept, estimate of alpha) | -0.022 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 30.000 | ||||
| t(b) | -0.433 | ||||
| p(b) | 0.666 | ||||
| t(a) | -0.800 | ||||
| p(a) | 0.785 | ||||
| Lowerbound of 95% confidence interval for beta | -0.068 | ||||
| Upperbound of 95% confidence interval for beta | 0.044 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.080 | ||||
| Upperbound of 95% confidence interval for alpha | 0.035 | ||||
| Treynor index (mean / b) | 2.439 | ||||
| Jensen alpha (a) | -0.022 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.020 | ||||
| Expected Shortfall on VaR | 0.025 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.013 | ||||
| Expected Shortfall on VaR | 0.018 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 32.000 | ||||
| Minimum | 0.975 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.057 | ||||
| Mean of quarter 1 | 0.997 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.008 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.031 | ||||
| Mean of outliers low | 0.975 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.094 | ||||
| Mean of outliers high | 1.022 | ||||
| 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 | 1.000 | ||||
| Minimum | 0.025 | ||||
| Quartile 1 | 0.025 | ||||
| Median | 0.025 | ||||
| Quartile 3 | 0.025 | ||||
| Maximum | 0.025 | ||||
| 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) | 0.015 | ||||
| Compounded annual return (geometric extrapolation) | 0.015 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.600 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.610 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.029 | ||||
| SD | 0.036 | ||||
| Sharpe ratio (Glass type estimate) | -0.793 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.792 | ||||
| df | 713.000 | ||||
| t | -1.309 | ||||
| p | 0.905 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.981 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.395 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.980 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.396 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.144 | ||||
| Upside Potential Ratio | 2.536 | ||||
| Upside part of mean | 0.064 | ||||
| Downside part of mean | -0.093 | ||||
| Upside SD | 0.026 | ||||
| Downside SD | 0.025 | ||||
| N nonnegative terms | 26.000 | ||||
| N negative terms | 688.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 714.000 | ||||
| Mean of predictor | 0.644 | ||||
| Mean of criterion | -0.029 | ||||
| SD of predictor | 0.342 | ||||
| SD of criterion | 0.036 | ||||
| Covariance | 0.001 | ||||
| r | 0.051 | ||||
| b (slope, estimate of beta) | 0.005 | ||||
| a (intercept, estimate of alpha) | -0.032 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 712.000 | ||||
| t(b) | 1.371 | ||||
| p(b) | 0.085 | ||||
| t(a) | -1.460 | ||||
| p(a) | 0.928 | ||||
| Lowerbound of 95% confidence interval for beta | -0.002 | ||||
| Upperbound of 95% confidence interval for beta | 0.013 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.076 | ||||
| Upperbound of 95% confidence interval for alpha | 0.011 | ||||
| Treynor index (mean / b) | -5.292 | ||||
| Jensen alpha (a) | -0.032 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.029 | ||||
| SD | 0.036 | ||||
| Sharpe ratio (Glass type estimate) | -0.811 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.810 | ||||
| df | 713.000 | ||||
| t | -1.339 | ||||
| p | 0.909 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.999 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.377 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.998 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.378 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.161 | ||||
| Upside Potential Ratio | 2.503 | ||||
| Upside part of mean | 0.063 | ||||
| Downside part of mean | -0.093 | ||||
| Upside SD | 0.026 | ||||
| Downside SD | 0.025 | ||||
| N nonnegative terms | 26.000 | ||||
| N negative terms | 688.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 714.000 | ||||
| Mean of predictor | 0.584 | ||||
| Mean of criterion | -0.029 | ||||
| SD of predictor | 0.345 | ||||
| SD of criterion | 0.036 | ||||
| Covariance | 0.001 | ||||
| r | 0.051 | ||||
| b (slope, estimate of beta) | 0.005 | ||||
| a (intercept, estimate of alpha) | -0.033 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 712.000 | ||||
| t(b) | 1.365 | ||||
| p(b) | 0.086 | ||||
| t(a) | -1.474 | ||||
| p(a) | 0.930 | ||||
| Lowerbound of 95% confidence interval for beta | -0.002 | ||||
| Upperbound of 95% confidence interval for beta | 0.013 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.076 | ||||
| Upperbound of 95% confidence interval for alpha | 0.011 | ||||
| Treynor index (mean / b) | -5.474 | ||||
| Jensen alpha (a) | -0.033 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.003 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 714.000 | ||||
| Minimum | 0.977 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.019 | ||||
| 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 | 19.000 | ||||
| Percentage of outliers low | 0.027 | ||||
| Mean of outliers low | 0.993 | ||||
| Number of outliers high | 26.000 | ||||
| Percentage of outliers high | 0.036 | ||||
| Mean of outliers high | 1.007 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.157 | ||||
| VaR(95%) (moments method) | -0.011 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.223 | ||||
| VaR(95%) (regression method) | -0.005 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.010 | ||||
| Quartile 3 | 0.026 | ||||
| Maximum | 0.067 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.010 | ||||
| Mean of quarter 3 | 0.026 | ||||
| Mean of quarter 4 | 0.067 | ||||
| Inter Quartile Range | 0.021 | ||||
| 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 | 0.067 | ||||
| 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) | 0.015 | ||||
| Compounded annual return (geometric extrapolation) | 0.015 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.220 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.220 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.104 | ||||
| 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 | 0.993 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.517 | ||||
| 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 | 0.859 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.516 | ||||
| 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) | -8753337707619828.000 | ||||
| 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) | 249536207749731127583556096753664.000 | ||||
| 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 | ||||