Advanced Statistics: NYX Trading System - W
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 | -0.058 | ||||
| SD | 0.027 | ||||
| Sharpe ratio (Glass type estimate) | -2.129 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.082 | ||||
| df | 34.000 | ||||
| t | -3.636 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.369 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.862 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.331 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.832 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.906 | ||||
| Upside Potential Ratio | 0.167 | ||||
| Upside part of mean | 0.005 | ||||
| Downside part of mean | -0.063 | ||||
| Upside SD | 0.009 | ||||
| Downside SD | 0.030 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 35.000 | ||||
| Mean of predictor | 0.574 | ||||
| Mean of criterion | -0.058 | ||||
| SD of predictor | 0.352 | ||||
| SD of criterion | 0.027 | ||||
| Covariance | 0.001 | ||||
| r | 0.106 | ||||
| b (slope, estimate of beta) | 0.008 | ||||
| a (intercept, estimate of alpha) | -0.062 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 33.000 | ||||
| t(b) | 0.611 | ||||
| p(b) | 0.273 | ||||
| t(a) | -3.514 | ||||
| p(a) | 0.999 | ||||
| Lowerbound of 95% confidence interval for beta | -0.019 | ||||
| Upperbound of 95% confidence interval for beta | 0.035 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.099 | ||||
| Upperbound of 95% confidence interval for alpha | -0.026 | ||||
| Treynor index (mean / b) | -7.088 | ||||
| Jensen alpha (a) | -0.062 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.058 | ||||
| SD | 0.027 | ||||
| Sharpe ratio (Glass type estimate) | -2.116 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.069 | ||||
| df | 34.000 | ||||
| t | -3.613 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.355 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.850 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.317 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.820 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.894 | ||||
| Upside Potential Ratio | 0.163 | ||||
| Upside part of mean | 0.005 | ||||
| Downside part of mean | -0.063 | ||||
| Upside SD | 0.009 | ||||
| Downside SD | 0.031 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 35.000 | ||||
| Mean of predictor | 0.506 | ||||
| Mean of criterion | -0.058 | ||||
| SD of predictor | 0.329 | ||||
| SD of criterion | 0.027 | ||||
| Covariance | 0.001 | ||||
| r | 0.107 | ||||
| b (slope, estimate of beta) | 0.009 | ||||
| a (intercept, estimate of alpha) | -0.063 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 33.000 | ||||
| t(b) | 0.616 | ||||
| p(b) | 0.271 | ||||
| t(a) | -3.517 | ||||
| p(a) | 0.999 | ||||
| Lowerbound of 95% confidence interval for beta | -0.020 | ||||
| Upperbound of 95% confidence interval for beta | 0.038 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.099 | ||||
| Upperbound of 95% confidence interval for alpha | -0.026 | ||||
| Treynor index (mean / b) | -6.535 | ||||
| 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%) | 0.018 | ||||
| Expected Shortfall on VaR | 0.021 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.027 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 35.000 | ||||
| Minimum | 0.967 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.018 | ||||
| Mean of quarter 1 | 0.993 | ||||
| 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 | 2.000 | ||||
| Percentage of outliers low | 0.057 | ||||
| Mean of outliers low | 0.970 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.057 | ||||
| Mean of outliers high | 1.010 | ||||
| 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) | -2.855 | ||||
| VaR(95%) (regression method) | 0.045 | ||||
| Expected Shortfall (regression method) | 0.055 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.059 | ||||
| Quartile 1 | 0.059 | ||||
| Median | 0.059 | ||||
| Quartile 3 | 0.059 | ||||
| Maximum | 0.059 | ||||
| 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) | -0.014 | ||||
| Compounded annual return (geometric extrapolation) | -0.014 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.238 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.664 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.058 | ||||
| SD | 0.025 | ||||
| Sharpe ratio (Glass type estimate) | -2.347 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.345 | ||||
| df | 769.000 | ||||
| t | -4.024 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.496 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.197 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.494 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.196 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.967 | ||||
| Upside Potential Ratio | 1.470 | ||||
| Upside part of mean | 0.029 | ||||
| Downside part of mean | -0.086 | ||||
| Upside SD | 0.015 | ||||
| Downside SD | 0.019 | ||||
| N nonnegative terms | 22.000 | ||||
| N negative terms | 748.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 770.000 | ||||
| Mean of predictor | 0.587 | ||||
| Mean of criterion | -0.058 | ||||
| SD of predictor | 0.317 | ||||
| SD of criterion | 0.025 | ||||
| Covariance | 0.000 | ||||
| r | 0.012 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | -0.058 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 768.000 | ||||
| t(b) | 0.341 | ||||
| p(b) | 0.367 | ||||
| t(a) | -4.035 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.005 | ||||
| Upperbound of 95% confidence interval for beta | 0.006 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.086 | ||||
| Upperbound of 95% confidence interval for alpha | -0.030 | ||||
| Treynor index (mean / b) | -60.552 | ||||
| Jensen alpha (a) | -0.058 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.058 | ||||
| SD | 0.025 | ||||
| Sharpe ratio (Glass type estimate) | -2.357 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.355 | ||||
| df | 769.000 | ||||
| t | -4.041 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.506 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.207 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.504 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.206 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.967 | ||||
| Upside Potential Ratio | 1.456 | ||||
| Upside part of mean | 0.028 | ||||
| Downside part of mean | -0.086 | ||||
| Upside SD | 0.015 | ||||
| Downside SD | 0.020 | ||||
| N nonnegative terms | 22.000 | ||||
| N negative terms | 748.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 770.000 | ||||
| Mean of predictor | 0.535 | ||||
| Mean of criterion | -0.058 | ||||
| SD of predictor | 0.320 | ||||
| SD of criterion | 0.025 | ||||
| Covariance | 0.000 | ||||
| r | 0.012 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | -0.058 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 768.000 | ||||
| t(b) | 0.332 | ||||
| p(b) | 0.370 | ||||
| t(a) | -4.052 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.005 | ||||
| Upperbound of 95% confidence interval for beta | 0.006 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.087 | ||||
| Upperbound of 95% confidence interval for alpha | -0.030 | ||||
| Treynor index (mean / b) | -62.959 | ||||
| Jensen alpha (a) | -0.058 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.003 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.002 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 770.000 | ||||
| Minimum | 0.983 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.015 | ||||
| Mean of quarter 1 | 0.999 | ||||
| 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 | 25.000 | ||||
| Percentage of outliers low | 0.032 | ||||
| Mean of outliers low | 0.995 | ||||
| Number of outliers high | 22.000 | ||||
| Percentage of outliers high | 0.029 | ||||
| Mean of outliers high | 1.004 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.662 | ||||
| VaR(95%) (moments method) | -0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.090 | ||||
| VaR(95%) (regression method) | -0.000 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.073 | ||||
| Quartile 1 | 0.073 | ||||
| Median | 0.073 | ||||
| Quartile 3 | 0.073 | ||||
| Maximum | 0.073 | ||||
| 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) | -0.014 | ||||
| Compounded annual return (geometric extrapolation) | -0.014 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.189 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -4.123 | ||||
| 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 | 0.987 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.447 | ||||
| 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 | 0.885 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.449 | ||||
| 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) | -8734885633693877.000 | ||||
| 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) | -837594057924798032713418411081728.000 | ||||
| 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 | ||||