Advanced Statistics: NYX Trading System - M
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 | -0.063 | ||||
| SD | 0.030 | ||||
| Sharpe ratio (Glass type estimate) | -2.134 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.086 | ||||
| df | 34.000 | ||||
| t | -3.644 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.375 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.867 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.337 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.836 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.845 | ||||
| Upside Potential Ratio | 0.072 | ||||
| Upside part of mean | 0.002 | ||||
| Downside part of mean | -0.066 | ||||
| Upside SD | 0.003 | ||||
| Downside SD | 0.034 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 35.000 | ||||
| Mean of predictor | 0.533 | ||||
| Mean of criterion | -0.063 | ||||
| SD of predictor | 0.254 | ||||
| SD of criterion | 0.030 | ||||
| Covariance | 0.001 | ||||
| r | 0.180 | ||||
| b (slope, estimate of beta) | 0.021 | ||||
| a (intercept, estimate of alpha) | -0.074 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 33.000 | ||||
| t(b) | 1.050 | ||||
| p(b) | 0.151 | ||||
| t(a) | -3.659 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.020 | ||||
| Upperbound of 95% confidence interval for beta | 0.062 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.116 | ||||
| Upperbound of 95% confidence interval for alpha | -0.033 | ||||
| Treynor index (mean / b) | -3.007 | ||||
| Jensen alpha (a) | -0.074 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.063 | ||||
| SD | 0.030 | ||||
| Sharpe ratio (Glass type estimate) | -2.111 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.064 | ||||
| df | 34.000 | ||||
| t | -3.605 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.350 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.846 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.312 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.816 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.830 | ||||
| Upside Potential Ratio | 0.071 | ||||
| Upside part of mean | 0.002 | ||||
| Downside part of mean | -0.066 | ||||
| Upside SD | 0.003 | ||||
| Downside SD | 0.035 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 35.000 | ||||
| Mean of predictor | 0.491 | ||||
| Mean of criterion | -0.063 | ||||
| SD of predictor | 0.242 | ||||
| SD of criterion | 0.030 | ||||
| Covariance | 0.001 | ||||
| r | 0.181 | ||||
| b (slope, estimate of beta) | 0.023 | ||||
| a (intercept, estimate of alpha) | -0.075 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 33.000 | ||||
| t(b) | 1.056 | ||||
| p(b) | 0.149 | ||||
| t(a) | -3.643 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.021 | ||||
| Upperbound of 95% confidence interval for beta | 0.066 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.116 | ||||
| Upperbound of 95% confidence interval for alpha | -0.033 | ||||
| Treynor index (mean / b) | -2.820 | ||||
| Jensen alpha (a) | -0.075 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.023 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.018 | ||||
| Expected Shortfall on VaR | 0.030 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 35.000 | ||||
| Minimum | 0.964 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.009 | ||||
| Mean of quarter 1 | 0.992 | ||||
| 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 | 0.965 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.057 | ||||
| Mean of outliers high | 1.007 | ||||
| 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) | -5.559 | ||||
| VaR(95%) (regression method) | 0.111 | ||||
| Expected Shortfall (regression method) | 0.116 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.069 | ||||
| Quartile 1 | 0.069 | ||||
| Median | 0.069 | ||||
| Quartile 3 | 0.069 | ||||
| Maximum | 0.069 | ||||
| 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) | -0.019 | ||||
| Compounded annual return (geometric extrapolation) | -0.019 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.280 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.841 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.063 | ||||
| SD | 0.026 | ||||
| Sharpe ratio (Glass type estimate) | -2.369 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.367 | ||||
| df | 780.000 | ||||
| t | -4.091 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.510 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.227 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.508 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.226 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.956 | ||||
| Upside Potential Ratio | 1.366 | ||||
| Upside part of mean | 0.029 | ||||
| Downside part of mean | -0.092 | ||||
| Upside SD | 0.016 | ||||
| Downside SD | 0.021 | ||||
| N nonnegative terms | 19.000 | ||||
| N negative terms | 762.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 781.000 | ||||
| Mean of predictor | 0.575 | ||||
| Mean of criterion | -0.063 | ||||
| SD of predictor | 0.308 | ||||
| SD of criterion | 0.026 | ||||
| Covariance | 0.000 | ||||
| r | 0.013 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | -0.063 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 779.000 | ||||
| t(b) | 0.371 | ||||
| p(b) | 0.355 | ||||
| t(a) | -4.104 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.005 | ||||
| Upperbound of 95% confidence interval for beta | 0.007 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.094 | ||||
| Upperbound of 95% confidence interval for alpha | -0.033 | ||||
| Treynor index (mean / b) | -54.959 | ||||
| Jensen alpha (a) | -0.063 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.063 | ||||
| SD | 0.027 | ||||
| Sharpe ratio (Glass type estimate) | -2.379 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.377 | ||||
| df | 780.000 | ||||
| t | -4.108 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.520 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.237 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.518 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.236 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.954 | ||||
| Upside Potential Ratio | 1.352 | ||||
| Upside part of mean | 0.029 | ||||
| Downside part of mean | -0.092 | ||||
| Upside SD | 0.016 | ||||
| Downside SD | 0.021 | ||||
| N nonnegative terms | 19.000 | ||||
| N negative terms | 762.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 781.000 | ||||
| Mean of predictor | 0.527 | ||||
| Mean of criterion | -0.063 | ||||
| SD of predictor | 0.310 | ||||
| SD of criterion | 0.027 | ||||
| Covariance | 0.000 | ||||
| r | 0.013 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | -0.064 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 779.000 | ||||
| t(b) | 0.362 | ||||
| p(b) | 0.359 | ||||
| t(a) | -4.121 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.005 | ||||
| Upperbound of 95% confidence interval for beta | 0.007 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.094 | ||||
| Upperbound of 95% confidence interval for alpha | -0.033 | ||||
| Treynor index (mean / b) | -56.843 | ||||
| Jensen alpha (a) | -0.064 | ||||
| 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 | 0.004 | ||||
| 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 | 781.000 | ||||
| Minimum | 0.980 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.016 | ||||
| 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 | 28.000 | ||||
| Percentage of outliers low | 0.036 | ||||
| Mean of outliers low | 0.995 | ||||
| Number of outliers high | 19.000 | ||||
| Percentage of outliers high | 0.024 | ||||
| Mean of outliers high | 1.005 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.348 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | 0.183 | ||||
| VaR(95%) (regression method) | 0.000 | ||||
| Expected Shortfall (regression method) | 0.003 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.084 | ||||
| Quartile 1 | 0.084 | ||||
| Median | 0.084 | ||||
| Quartile 3 | 0.084 | ||||
| Maximum | 0.084 | ||||
| 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) | -0.019 | ||||
| Compounded annual return (geometric extrapolation) | -0.019 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.225 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -5.224 | ||||
| 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 | 1.025 | ||||
| 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 | 0.923 | ||||
| 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) | -8729316270596448.000 | ||||
| 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) | 366553745985078443374676126203904.000 | ||||
| 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 | ||||