Advanced Statistics: Traders Trust TACTICAL
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 | -0.043 | ||||
| SD | 0.050 | ||||
| Sharpe ratio (Glass type estimate) | -0.853 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.842 | ||||
| df | 60.000 | ||||
| t | -1.923 | ||||
| p | 0.970 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.732 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.033 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.725 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.040 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.967 | ||||
| Upside Potential Ratio | 0.512 | ||||
| Upside part of mean | 0.023 | ||||
| Downside part of mean | -0.065 | ||||
| Upside SD | 0.026 | ||||
| Downside SD | 0.044 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 56.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.343 | ||||
| Mean of criterion | -0.043 | ||||
| SD of predictor | 0.284 | ||||
| SD of criterion | 0.050 | ||||
| Covariance | 0.000 | ||||
| r | 0.035 | ||||
| b (slope, estimate of beta) | 0.006 | ||||
| a (intercept, estimate of alpha) | -0.045 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 59.000 | ||||
| t(b) | 0.266 | ||||
| p(b) | 0.396 | ||||
| t(a) | -1.888 | ||||
| p(a) | 0.968 | ||||
| Lowerbound of 95% confidence interval for beta | -0.040 | ||||
| Upperbound of 95% confidence interval for beta | 0.052 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.092 | ||||
| Upperbound of 95% confidence interval for alpha | 0.003 | ||||
| Treynor index (mean / b) | -6.993 | ||||
| Jensen alpha (a) | -0.045 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.051 | ||||
| Sharpe ratio (Glass type estimate) | -0.862 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.851 | ||||
| df | 60.000 | ||||
| t | -1.943 | ||||
| p | 0.972 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.741 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.025 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.733 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.032 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.964 | ||||
| Upside Potential Ratio | 0.488 | ||||
| Upside part of mean | 0.022 | ||||
| Downside part of mean | -0.066 | ||||
| Upside SD | 0.025 | ||||
| Downside SD | 0.046 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 56.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.298 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.281 | ||||
| SD of criterion | 0.051 | ||||
| Covariance | 0.000 | ||||
| r | 0.028 | ||||
| b (slope, estimate of beta) | 0.005 | ||||
| a (intercept, estimate of alpha) | -0.045 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 59.000 | ||||
| t(b) | 0.211 | ||||
| p(b) | 0.417 | ||||
| t(a) | -1.904 | ||||
| p(a) | 0.969 | ||||
| Lowerbound of 95% confidence interval for beta | -0.042 | ||||
| Upperbound of 95% confidence interval for beta | 0.052 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.093 | ||||
| Upperbound of 95% confidence interval for alpha | 0.002 | ||||
| Treynor index (mean / b) | -8.796 | ||||
| Jensen alpha (a) | -0.045 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.033 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.018 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 61.000 | ||||
| Minimum | 0.927 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.040 | ||||
| Mean of quarter 1 | 0.992 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.009 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.066 | ||||
| Mean of outliers low | 0.968 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.148 | ||||
| Mean of outliers high | 1.015 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1386.052 | ||||
| VaR(95%) (moments method) | -16503834615044019704101773874941390975573196698256975729849159940722609450540009687060760021739954215721091559715438961835762744804434553923252387026897465820120666730306056785870728387056426968366235310911281621177846357912412962025494668310852141056.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -2.481 | ||||
| VaR(95%) (regression method) | -0.010 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.123 | ||||
| Quartile 1 | 0.123 | ||||
| Median | 0.123 | ||||
| Quartile 3 | 0.123 | ||||
| Maximum | 0.123 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.001 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.031 | ||||
| SD | 0.162 | ||||
| Sharpe ratio (Glass type estimate) | -0.192 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.192 | ||||
| df | 1346.000 | ||||
| t | -0.436 | ||||
| p | 0.506 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.057 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.672 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.057 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.672 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.297 | ||||
| Upside Potential Ratio | 2.300 | ||||
| Upside part of mean | 0.241 | ||||
| Downside part of mean | -0.272 | ||||
| Upside SD | 0.123 | ||||
| Downside SD | 0.105 | ||||
| N nonnegative terms | 52.000 | ||||
| N negative terms | 1295.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1347.000 | ||||
| Mean of predictor | 0.393 | ||||
| Mean of criterion | -0.031 | ||||
| SD of predictor | 0.400 | ||||
| SD of criterion | 0.162 | ||||
| Covariance | -0.003 | ||||
| r | -0.047 | ||||
| b (slope, estimate of beta) | -0.019 | ||||
| a (intercept, estimate of alpha) | -0.024 | ||||
| Mean Square Error | 0.026 | ||||
| DF error | 1345.000 | ||||
| t(b) | -1.709 | ||||
| p(b) | 0.530 | ||||
| t(a) | -0.332 | ||||
| p(a) | 0.506 | ||||
| Lowerbound of 95% confidence interval for beta | -0.040 | ||||
| Upperbound of 95% confidence interval for beta | 0.003 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.164 | ||||
| Upperbound of 95% confidence interval for alpha | 0.116 | ||||
| Treynor index (mean / b) | 1.653 | ||||
| Jensen alpha (a) | -0.024 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.160 | ||||
| Sharpe ratio (Glass type estimate) | -0.275 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.275 | ||||
| df | 1346.000 | ||||
| t | -0.624 | ||||
| p | 0.509 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.140 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.589 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.139 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.589 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.406 | ||||
| Upside Potential Ratio | 2.160 | ||||
| Upside part of mean | 0.234 | ||||
| Downside part of mean | -0.278 | ||||
| Upside SD | 0.117 | ||||
| Downside SD | 0.108 | ||||
| N nonnegative terms | 52.000 | ||||
| N negative terms | 1295.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1347.000 | ||||
| Mean of predictor | 0.312 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.404 | ||||
| SD of criterion | 0.160 | ||||
| Covariance | -0.003 | ||||
| r | -0.047 | ||||
| b (slope, estimate of beta) | -0.019 | ||||
| a (intercept, estimate of alpha) | -0.038 | ||||
| Mean Square Error | 0.026 | ||||
| DF error | 1345.000 | ||||
| t(b) | -1.731 | ||||
| p(b) | 0.530 | ||||
| t(a) | -0.541 | ||||
| p(a) | 0.509 | ||||
| Lowerbound of 95% confidence interval for beta | -0.040 | ||||
| Upperbound of 95% confidence interval for beta | 0.002 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.177 | ||||
| Upperbound of 95% confidence interval for alpha | 0.100 | ||||
| Treynor index (mean / b) | 2.358 | ||||
| Jensen alpha (a) | -0.038 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.020 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.008 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1347.000 | ||||
| Minimum | 0.896 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.154 | ||||
| Mean of quarter 1 | 0.996 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.004 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 76.000 | ||||
| Percentage of outliers low | 0.056 | ||||
| Mean of outliers low | 0.984 | ||||
| Number of outliers high | 77.000 | ||||
| Percentage of outliers high | 0.057 | ||||
| Mean of outliers high | 1.016 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.104 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| Extreme Value Index (regression method) | 0.191 | ||||
| VaR(95%) (regression method) | -0.003 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.047 | ||||
| Quartile 1 | 0.086 | ||||
| Median | 0.103 | ||||
| Quartile 3 | 0.119 | ||||
| Maximum | 0.154 | ||||
| Mean of quarter 1 | 0.047 | ||||
| Mean of quarter 2 | 0.099 | ||||
| Mean of quarter 3 | 0.108 | ||||
| Mean of quarter 4 | 0.154 | ||||
| Inter Quartile Range | 0.033 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.000 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.001 | ||||
| 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 | 1.048 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.471 | ||||
| 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 | 0.934 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.477 | ||||
| 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) | -8735536013042249.000 | ||||
| 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) | 82463470818222016869247720882176.000 | ||||
| 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 | ||||