Advanced Statistics: TT Fdax Trader
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 | -0.065 | ||||
| SD | 0.037 | ||||
| Sharpe ratio (Glass type estimate) | -1.757 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.717 | ||||
| df | 33.000 | ||||
| t | -2.958 | ||||
| p | 0.997 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.984 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.507 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.953 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.481 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.598 | ||||
| Upside Potential Ratio | 0.079 | ||||
| Upside part of mean | 0.003 | ||||
| Downside part of mean | -0.068 | ||||
| Upside SD | 0.005 | ||||
| Downside SD | 0.041 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.592 | ||||
| Mean of criterion | -0.065 | ||||
| SD of predictor | 0.288 | ||||
| SD of criterion | 0.037 | ||||
| Covariance | 0.001 | ||||
| r | 0.121 | ||||
| b (slope, estimate of beta) | 0.015 | ||||
| a (intercept, estimate of alpha) | -0.074 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 32.000 | ||||
| t(b) | 0.688 | ||||
| p(b) | 0.248 | ||||
| t(a) | -2.868 | ||||
| p(a) | 0.996 | ||||
| Lowerbound of 95% confidence interval for beta | -0.030 | ||||
| Upperbound of 95% confidence interval for beta | 0.061 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.127 | ||||
| Upperbound of 95% confidence interval for alpha | -0.021 | ||||
| Treynor index (mean / b) | -4.183 | ||||
| Jensen alpha (a) | -0.074 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.065 | ||||
| SD | 0.038 | ||||
| Sharpe ratio (Glass type estimate) | -1.734 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.695 | ||||
| df | 33.000 | ||||
| t | -2.919 | ||||
| p | 0.997 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.959 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.486 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.929 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.461 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.581 | ||||
| Upside Potential Ratio | 0.077 | ||||
| Upside part of mean | 0.003 | ||||
| Downside part of mean | -0.069 | ||||
| Upside SD | 0.005 | ||||
| Downside SD | 0.041 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.539 | ||||
| Mean of criterion | -0.065 | ||||
| SD of predictor | 0.274 | ||||
| SD of criterion | 0.038 | ||||
| Covariance | 0.001 | ||||
| r | 0.116 | ||||
| b (slope, estimate of beta) | 0.016 | ||||
| a (intercept, estimate of alpha) | -0.074 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 32.000 | ||||
| t(b) | 0.662 | ||||
| p(b) | 0.256 | ||||
| t(a) | -2.838 | ||||
| p(a) | 0.996 | ||||
| Lowerbound of 95% confidence interval for beta | -0.033 | ||||
| Upperbound of 95% confidence interval for beta | 0.065 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.127 | ||||
| Upperbound of 95% confidence interval for alpha | -0.021 | ||||
| Treynor index (mean / b) | -4.087 | ||||
| Jensen alpha (a) | -0.074 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.023 | ||||
| Expected Shortfall on VaR | 0.028 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 34.000 | ||||
| Minimum | 0.946 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.012 | ||||
| Mean of quarter 1 | 0.990 | ||||
| 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 | 7.000 | ||||
| Percentage of outliers low | 0.206 | ||||
| Mean of outliers low | 0.987 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.206 | ||||
| Mean of outliers high | 1.004 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.335 | ||||
| VaR(95%) (moments method) | 0.005 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.619 | ||||
| VaR(95%) (regression method) | 0.010 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.083 | ||||
| Quartile 1 | 0.083 | ||||
| Median | 0.083 | ||||
| Quartile 3 | 0.083 | ||||
| Maximum | 0.083 | ||||
| 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) | -0.021 | ||||
| Compounded annual return (geometric extrapolation) | -0.021 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.257 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.770 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.065 | ||||
| SD | 0.029 | ||||
| Sharpe ratio (Glass type estimate) | -2.208 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.206 | ||||
| df | 753.000 | ||||
| t | -3.746 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.368 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.047 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.367 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.045 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.327 | ||||
| Upside Potential Ratio | 0.839 | ||||
| Upside part of mean | 0.023 | ||||
| Downside part of mean | -0.088 | ||||
| Upside SD | 0.010 | ||||
| Downside SD | 0.028 | ||||
| N nonnegative terms | 110.000 | ||||
| N negative terms | 644.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 754.000 | ||||
| Mean of predictor | 0.620 | ||||
| Mean of criterion | -0.065 | ||||
| SD of predictor | 0.328 | ||||
| SD of criterion | 0.029 | ||||
| Covariance | 0.000 | ||||
| r | 0.023 | ||||
| b (slope, estimate of beta) | 0.002 | ||||
| a (intercept, estimate of alpha) | -0.066 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 752.000 | ||||
| t(b) | 0.619 | ||||
| p(b) | 0.268 | ||||
| t(a) | -3.791 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.004 | ||||
| Upperbound of 95% confidence interval for beta | 0.008 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.100 | ||||
| Upperbound of 95% confidence interval for alpha | -0.032 | ||||
| Treynor index (mean / b) | -32.057 | ||||
| Jensen alpha (a) | -0.066 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.065 | ||||
| SD | 0.030 | ||||
| Sharpe ratio (Glass type estimate) | -2.197 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.194 | ||||
| df | 753.000 | ||||
| t | -3.726 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.356 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.035 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.355 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.034 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.310 | ||||
| Upside Potential Ratio | 0.826 | ||||
| Upside part of mean | 0.023 | ||||
| Downside part of mean | -0.088 | ||||
| Upside SD | 0.010 | ||||
| Downside SD | 0.028 | ||||
| N nonnegative terms | 110.000 | ||||
| N negative terms | 644.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 754.000 | ||||
| Mean of predictor | 0.565 | ||||
| Mean of criterion | -0.065 | ||||
| SD of predictor | 0.329 | ||||
| SD of criterion | 0.030 | ||||
| Covariance | 0.000 | ||||
| r | 0.022 | ||||
| b (slope, estimate of beta) | 0.002 | ||||
| a (intercept, estimate of alpha) | -0.066 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 752.000 | ||||
| t(b) | 0.603 | ||||
| p(b) | 0.273 | ||||
| t(a) | -3.768 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.004 | ||||
| Upperbound of 95% confidence interval for beta | 0.008 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.101 | ||||
| Upperbound of 95% confidence interval for alpha | -0.032 | ||||
| Treynor index (mean / b) | -32.852 | ||||
| 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%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.002 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 754.000 | ||||
| Minimum | 0.963 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.012 | ||||
| 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 | 116.000 | ||||
| Percentage of outliers low | 0.154 | ||||
| Mean of outliers low | 0.999 | ||||
| Number of outliers high | 138.000 | ||||
| Percentage of outliers high | 0.183 | ||||
| Mean of outliers high | 1.001 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.029 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.672 | ||||
| VaR(95%) (regression method) | -0.000 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.084 | ||||
| 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) | -0.020 | ||||
| Compounded annual return (geometric extrapolation) | -0.021 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.250 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -5.198 | ||||
| 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 | 1.042 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.499 | ||||
| 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 | 0.917 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.497 | ||||
| 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) | -8742714715724973.000 | ||||
| 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) | 186177787677911513346125126959104.000 | ||||
| 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 | ||||