Advanced Statistics: Prolific Turbo Trading System
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.046 | ||||
| SD | 0.039 | ||||
| Sharpe ratio (Glass type estimate) | -1.178 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.163 | ||||
| df | 60.000 | ||||
| t | -2.656 | ||||
| p | 0.995 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.068 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.279 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.057 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.269 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.306 | ||||
| Upside Potential Ratio | 0.419 | ||||
| Upside part of mean | 0.015 | ||||
| Downside part of mean | -0.060 | ||||
| Upside SD | 0.021 | ||||
| Downside SD | 0.035 | ||||
| N nonnegative terms | 11.000 | ||||
| N negative terms | 50.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.383 | ||||
| Mean of criterion | -0.046 | ||||
| SD of predictor | 0.332 | ||||
| SD of criterion | 0.039 | ||||
| Covariance | 0.006 | ||||
| r | 0.448 | ||||
| b (slope, estimate of beta) | 0.052 | ||||
| a (intercept, estimate of alpha) | -0.065 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 59.000 | ||||
| t(b) | 3.845 | ||||
| p(b) | 0.000 | ||||
| t(a) | -4.017 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | 0.025 | ||||
| Upperbound of 95% confidence interval for beta | 0.079 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.098 | ||||
| Upperbound of 95% confidence interval for alpha | -0.033 | ||||
| Treynor index (mean / b) | -0.873 | ||||
| Jensen alpha (a) | -0.065 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.046 | ||||
| SD | 0.039 | ||||
| Sharpe ratio (Glass type estimate) | -1.183 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.168 | ||||
| df | 60.000 | ||||
| t | -2.667 | ||||
| p | 0.995 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.073 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.284 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.062 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.274 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.296 | ||||
| Upside Potential Ratio | 0.402 | ||||
| Upside part of mean | 0.014 | ||||
| Downside part of mean | -0.061 | ||||
| Upside SD | 0.020 | ||||
| Downside SD | 0.036 | ||||
| N nonnegative terms | 11.000 | ||||
| N negative terms | 50.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.326 | ||||
| Mean of criterion | -0.046 | ||||
| SD of predictor | 0.315 | ||||
| SD of criterion | 0.039 | ||||
| Covariance | 0.006 | ||||
| r | 0.489 | ||||
| b (slope, estimate of beta) | 0.061 | ||||
| a (intercept, estimate of alpha) | -0.066 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 59.000 | ||||
| t(b) | 4.309 | ||||
| p(b) | 0.000 | ||||
| t(a) | -4.149 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | 0.032 | ||||
| Upperbound of 95% confidence interval for beta | 0.089 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.098 | ||||
| Upperbound of 95% confidence interval for alpha | -0.034 | ||||
| Treynor index (mean / b) | -0.761 | ||||
| Jensen alpha (a) | -0.066 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.022 | ||||
| Expected Shortfall on VaR | 0.027 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.015 | ||||
| Expected Shortfall on VaR | 0.028 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 61.000 | ||||
| Minimum | 0.937 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.003 | ||||
| Maximum | 1.048 | ||||
| Mean of quarter 1 | 0.991 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.009 | ||||
| Inter Quartile Range | 0.005 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.033 | ||||
| Mean of outliers low | 0.961 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.033 | ||||
| Mean of outliers high | 1.031 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.771 | ||||
| VaR(95%) (moments method) | 0.008 | ||||
| Expected Shortfall (moments method) | 0.038 | ||||
| Extreme Value Index (regression method) | 1.029 | ||||
| VaR(95%) (regression method) | 0.007 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.007 | ||||
| Median | 0.016 | ||||
| Quartile 3 | 0.028 | ||||
| Maximum | 0.063 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.016 | ||||
| Mean of quarter 3 | 0.028 | ||||
| Mean of quarter 4 | 0.063 | ||||
| Inter Quartile Range | 0.022 | ||||
| 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 | 0.063 | ||||
| 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) | -0.002 | ||||
| Compounded annual return (geometric extrapolation) | -0.002 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.034 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.034 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.080 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.069 | ||||
| Sharpe ratio (Glass type estimate) | -0.630 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.630 | ||||
| df | 1335.000 | ||||
| t | -1.423 | ||||
| p | 0.525 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.498 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.238 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.498 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.238 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.820 | ||||
| Upside Potential Ratio | 2.574 | ||||
| Upside part of mean | 0.137 | ||||
| Downside part of mean | -0.181 | ||||
| Upside SD | 0.044 | ||||
| Downside SD | 0.053 | ||||
| N nonnegative terms | 550.000 | ||||
| N negative terms | 786.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1336.000 | ||||
| Mean of predictor | 0.410 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.389 | ||||
| SD of criterion | 0.069 | ||||
| Covariance | 0.007 | ||||
| r | 0.277 | ||||
| b (slope, estimate of beta) | 0.049 | ||||
| a (intercept, estimate of alpha) | -0.064 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 1334.000 | ||||
| t(b) | 10.534 | ||||
| p(b) | 0.361 | ||||
| t(a) | -2.161 | ||||
| p(a) | 0.530 | ||||
| Lowerbound of 95% confidence interval for beta | 0.040 | ||||
| Upperbound of 95% confidence interval for beta | 0.059 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.122 | ||||
| Upperbound of 95% confidence interval for alpha | -0.006 | ||||
| Treynor index (mean / b) | -0.885 | ||||
| Jensen alpha (a) | -0.064 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.046 | ||||
| SD | 0.070 | ||||
| Sharpe ratio (Glass type estimate) | -0.659 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.658 | ||||
| df | 1335.000 | ||||
| t | -1.487 | ||||
| p | 0.526 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.527 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.210 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.527 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.210 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.841 | ||||
| Upside Potential Ratio | 2.485 | ||||
| Upside part of mean | 0.136 | ||||
| Downside part of mean | -0.183 | ||||
| Upside SD | 0.044 | ||||
| Downside SD | 0.055 | ||||
| N nonnegative terms | 550.000 | ||||
| N negative terms | 786.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1336.000 | ||||
| Mean of predictor | 0.334 | ||||
| Mean of criterion | -0.046 | ||||
| SD of predictor | 0.388 | ||||
| SD of criterion | 0.070 | ||||
| Covariance | 0.008 | ||||
| r | 0.292 | ||||
| b (slope, estimate of beta) | 0.053 | ||||
| a (intercept, estimate of alpha) | -0.064 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 1334.000 | ||||
| t(b) | 11.144 | ||||
| p(b) | 0.354 | ||||
| t(a) | -2.145 | ||||
| p(a) | 0.529 | ||||
| Lowerbound of 95% confidence interval for beta | 0.043 | ||||
| Upperbound of 95% confidence interval for beta | 0.062 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.122 | ||||
| Upperbound of 95% confidence interval for alpha | -0.005 | ||||
| Treynor index (mean / b) | -0.875 | ||||
| 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%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| 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 | 1336.000 | ||||
| Minimum | 0.920 | ||||
| Quartile 1 | 0.999 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.001 | ||||
| Maximum | 1.054 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.002 | ||||
| Inter Quartile Range | 0.001 | ||||
| Number outliers low | 51.000 | ||||
| Percentage of outliers low | 0.038 | ||||
| Mean of outliers low | 0.991 | ||||
| Number of outliers high | 54.000 | ||||
| Percentage of outliers high | 0.040 | ||||
| Mean of outliers high | 1.008 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.819 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.010 | ||||
| Extreme Value Index (regression method) | 0.942 | ||||
| VaR(95%) (regression method) | 0.001 | ||||
| Expected Shortfall (regression method) | 0.013 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.001 | ||||
| Median | 0.019 | ||||
| Quartile 3 | 0.028 | ||||
| Maximum | 0.092 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.006 | ||||
| Mean of quarter 3 | 0.026 | ||||
| Mean of quarter 4 | 0.061 | ||||
| Inter Quartile Range | 0.027 | ||||
| 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 | 0.125 | ||||
| Mean of outliers high | 0.092 | ||||
| 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) | -0.002 | ||||
| Compounded annual return (geometric extrapolation) | -0.002 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.023 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.035 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.236 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.055 | ||||
| SD | 0.013 | ||||
| Sharpe ratio (Glass type estimate) | -4.142 | ||||
| Sharpe ratio (Hedges UMVUE) | -4.118 | ||||
| df | 130.000 | ||||
| t | -2.929 | ||||
| p | 0.624 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -6.952 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.317 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -6.935 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.302 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -4.830 | ||||
| Upside Potential Ratio | 4.887 | ||||
| Upside part of mean | 0.056 | ||||
| Downside part of mean | -0.111 | ||||
| Upside SD | 0.008 | ||||
| Downside SD | 0.011 | ||||
| N nonnegative terms | 46.000 | ||||
| N negative terms | 85.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.288 | ||||
| Mean of criterion | -0.055 | ||||
| SD of predictor | 0.371 | ||||
| SD of criterion | 0.013 | ||||
| Covariance | 0.002 | ||||
| r | 0.316 | ||||
| b (slope, estimate of beta) | 0.011 | ||||
| a (intercept, estimate of alpha) | -0.070 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | 3.785 | ||||
| p(b) | 0.302 | ||||
| t(a) | -3.802 | ||||
| p(a) | 0.699 | ||||
| Lowerbound of 95% confidence interval for beta | 0.005 | ||||
| Upperbound of 95% confidence interval for beta | 0.017 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.107 | ||||
| Upperbound of 95% confidence interval for alpha | -0.034 | ||||
| Treynor index (mean / b) | -4.867 | ||||
| Jensen alpha (a) | -0.070 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.056 | ||||
| SD | 0.013 | ||||
| Sharpe ratio (Glass type estimate) | -4.148 | ||||
| Sharpe ratio (Hedges UMVUE) | -4.124 | ||||
| df | 130.000 | ||||
| t | -2.933 | ||||
| p | 0.625 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -6.957 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.323 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -6.941 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.307 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -4.834 | ||||
| Upside Potential Ratio | 4.880 | ||||
| Upside part of mean | 0.056 | ||||
| Downside part of mean | -0.112 | ||||
| Upside SD | 0.008 | ||||
| Downside SD | 0.011 | ||||
| N nonnegative terms | 46.000 | ||||
| N negative terms | 85.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.217 | ||||
| Mean of criterion | -0.056 | ||||
| SD of predictor | 0.372 | ||||
| SD of criterion | 0.013 | ||||
| Covariance | 0.002 | ||||
| r | 0.316 | ||||
| b (slope, estimate of beta) | 0.011 | ||||
| a (intercept, estimate of alpha) | -0.069 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | 3.777 | ||||
| p(b) | 0.303 | ||||
| t(a) | -3.769 | ||||
| p(a) | 0.697 | ||||
| Lowerbound of 95% confidence interval for beta | 0.005 | ||||
| Upperbound of 95% confidence interval for beta | 0.017 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.106 | ||||
| Upperbound of 95% confidence interval for alpha | -0.033 | ||||
| Treynor index (mean / b) | -4.884 | ||||
| Jensen alpha (a) | -0.069 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.002 | ||||
| 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 | 131.000 | ||||
| Minimum | 0.997 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.002 | ||||
| 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 | 0.001 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.015 | ||||
| Mean of outliers low | 0.997 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.008 | ||||
| Mean of outliers high | 1.002 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.092 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | 0.288 | ||||
| VaR(95%) (regression method) | 0.001 | ||||
| Expected Shortfall (regression method) | 0.002 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.008 | ||||
| Quartile 1 | 0.008 | ||||
| Median | 0.008 | ||||
| Quartile 3 | 0.008 | ||||
| Maximum | 0.008 | ||||
| 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) | -0.011 | ||||
| Compounded annual return (geometric extrapolation) | -0.011 | ||||
| Calmar ratio (compounded annual return / max draw down) | -1.385 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -5.962 | ||||