Advanced Statistics: Discretionary FDAX trading
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 | -0.003 | ||||
| SD | 0.069 | ||||
| Sharpe ratio (Glass type estimate) | -0.042 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.041 | ||||
| df | 31.000 | ||||
| t | -0.069 | ||||
| p | 0.527 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.242 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.158 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.241 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.159 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.135 | ||||
| Upside Potential Ratio | 2.484 | ||||
| Upside part of mean | 0.054 | ||||
| Downside part of mean | -0.057 | ||||
| Upside SD | 0.065 | ||||
| Downside SD | 0.022 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 27.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.604 | ||||
| Mean of criterion | -0.003 | ||||
| SD of predictor | 0.284 | ||||
| SD of criterion | 0.069 | ||||
| Covariance | -0.003 | ||||
| r | -0.135 | ||||
| b (slope, estimate of beta) | -0.033 | ||||
| a (intercept, estimate of alpha) | 0.017 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 30.000 | ||||
| t(b) | -0.745 | ||||
| p(b) | 0.769 | ||||
| t(a) | 0.336 | ||||
| p(a) | 0.369 | ||||
| Lowerbound of 95% confidence interval for beta | -0.123 | ||||
| Upperbound of 95% confidence interval for beta | 0.057 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.086 | ||||
| Upperbound of 95% confidence interval for alpha | 0.120 | ||||
| Treynor index (mean / b) | 0.089 | ||||
| Jensen alpha (a) | 0.017 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.005 | ||||
| SD | 0.066 | ||||
| Sharpe ratio (Glass type estimate) | -0.077 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.075 | ||||
| df | 31.000 | ||||
| t | -0.125 | ||||
| p | 0.550 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.277 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.124 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.275 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.125 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.235 | ||||
| Upside Potential Ratio | 2.378 | ||||
| Upside part of mean | 0.052 | ||||
| Downside part of mean | -0.057 | ||||
| Upside SD | 0.062 | ||||
| Downside SD | 0.022 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 27.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.552 | ||||
| Mean of criterion | -0.005 | ||||
| SD of predictor | 0.272 | ||||
| SD of criterion | 0.066 | ||||
| Covariance | -0.002 | ||||
| r | -0.129 | ||||
| b (slope, estimate of beta) | -0.031 | ||||
| a (intercept, estimate of alpha) | 0.012 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 30.000 | ||||
| t(b) | -0.710 | ||||
| p(b) | 0.758 | ||||
| t(a) | 0.256 | ||||
| p(a) | 0.400 | ||||
| Lowerbound of 95% confidence interval for beta | -0.122 | ||||
| Upperbound of 95% confidence interval for beta | 0.059 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.085 | ||||
| Upperbound of 95% confidence interval for alpha | 0.110 | ||||
| Treynor index (mean / b) | 0.163 | ||||
| Jensen alpha (a) | 0.012 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.031 | ||||
| Expected Shortfall on VaR | 0.039 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.015 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 32.000 | ||||
| Minimum | 0.982 | ||||
| Quartile 1 | 0.999 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.102 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.020 | ||||
| Inter Quartile Range | 0.001 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.219 | ||||
| Mean of outliers low | 0.993 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.156 | ||||
| Mean of outliers high | 1.032 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.314 | ||||
| VaR(95%) (moments method) | 0.006 | ||||
| Expected Shortfall (moments method) | 0.011 | ||||
| Extreme Value Index (regression method) | 0.768 | ||||
| VaR(95%) (regression method) | 0.008 | ||||
| Expected Shortfall (regression method) | 0.032 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.018 | ||||
| Quartile 1 | 0.020 | ||||
| Median | 0.022 | ||||
| Quartile 3 | 0.025 | ||||
| Maximum | 0.027 | ||||
| Mean of quarter 1 | 0.018 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.027 | ||||
| Inter Quartile Range | 0.005 | ||||
| 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) | 0.041 | ||||
| Compounded annual return (geometric extrapolation) | 0.040 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.479 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.479 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.012 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.001 | ||||
| SD | 0.096 | ||||
| Sharpe ratio (Glass type estimate) | -0.010 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.010 | ||||
| df | 703.000 | ||||
| t | -0.017 | ||||
| p | 0.507 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.206 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.186 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.206 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.186 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.028 | ||||
| Upside Potential Ratio | 4.899 | ||||
| Upside part of mean | 0.173 | ||||
| Downside part of mean | -0.174 | ||||
| Upside SD | 0.090 | ||||
| Downside SD | 0.035 | ||||
| N nonnegative terms | 106.000 | ||||
| N negative terms | 598.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 704.000 | ||||
| Mean of predictor | 0.632 | ||||
| Mean of criterion | -0.001 | ||||
| SD of predictor | 0.336 | ||||
| SD of criterion | 0.096 | ||||
| Covariance | -0.001 | ||||
| r | -0.021 | ||||
| b (slope, estimate of beta) | -0.006 | ||||
| a (intercept, estimate of alpha) | 0.003 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 702.000 | ||||
| t(b) | -0.548 | ||||
| p(b) | 0.708 | ||||
| t(a) | 0.047 | ||||
| p(a) | 0.481 | ||||
| Lowerbound of 95% confidence interval for beta | -0.027 | ||||
| Upperbound of 95% confidence interval for beta | 0.015 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.113 | ||||
| Upperbound of 95% confidence interval for alpha | 0.119 | ||||
| Treynor index (mean / b) | 0.164 | ||||
| Jensen alpha (a) | 0.003 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.005 | ||||
| SD | 0.093 | ||||
| Sharpe ratio (Glass type estimate) | -0.058 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.058 | ||||
| df | 703.000 | ||||
| t | -0.095 | ||||
| p | 0.538 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.254 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.138 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.254 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.138 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.152 | ||||
| Upside Potential Ratio | 4.758 | ||||
| Upside part of mean | 0.169 | ||||
| Downside part of mean | -0.174 | ||||
| Upside SD | 0.086 | ||||
| Downside SD | 0.035 | ||||
| N nonnegative terms | 106.000 | ||||
| N negative terms | 598.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 704.000 | ||||
| Mean of predictor | 0.574 | ||||
| Mean of criterion | -0.005 | ||||
| SD of predictor | 0.338 | ||||
| SD of criterion | 0.093 | ||||
| Covariance | -0.001 | ||||
| r | -0.021 | ||||
| b (slope, estimate of beta) | -0.006 | ||||
| a (intercept, estimate of alpha) | -0.002 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 702.000 | ||||
| t(b) | -0.553 | ||||
| p(b) | 0.710 | ||||
| t(a) | -0.037 | ||||
| p(a) | 0.515 | ||||
| Lowerbound of 95% confidence interval for beta | -0.026 | ||||
| Upperbound of 95% confidence interval for beta | 0.015 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.114 | ||||
| Upperbound of 95% confidence interval for alpha | 0.110 | ||||
| Treynor index (mean / b) | 0.939 | ||||
| Jensen alpha (a) | -0.002 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.012 | ||||
| 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 | 704.000 | ||||
| Minimum | 0.977 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.098 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.003 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 164.000 | ||||
| Percentage of outliers low | 0.233 | ||||
| Mean of outliers low | 0.998 | ||||
| Number of outliers high | 129.000 | ||||
| Percentage of outliers high | 0.183 | ||||
| Mean of outliers high | 1.004 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.852 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.015 | ||||
| Extreme Value Index (regression method) | 0.702 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | 0.006 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.031 | ||||
| Quartile 1 | 0.046 | ||||
| Median | 0.062 | ||||
| Quartile 3 | 0.078 | ||||
| Maximum | 0.094 | ||||
| Mean of quarter 1 | 0.031 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.094 | ||||
| Inter Quartile Range | 0.032 | ||||
| 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) | 0.041 | ||||
| Compounded annual return (geometric extrapolation) | 0.039 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.421 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.421 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.330 | ||||
| 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 | 1.150 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.504 | ||||
| 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 | 1.022 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.504 | ||||
| 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) | -8731043370496946.000 | ||||
| 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) | 614809174934251933850541093814272.000 | ||||
| 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 | ||||