Advanced Statistics: German Index Future (FDAX) - Timezone -
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 | 0.143 | ||||
| Sharpe ratio (Glass type estimate) | 0.024 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.024 | ||||
| df | 48.000 | ||||
| t | 0.049 | ||||
| p | 0.480 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.946 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.994 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.946 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.994 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.040 | ||||
| Upside Potential Ratio | 1.710 | ||||
| Upside part of mean | 0.150 | ||||
| Downside part of mean | -0.147 | ||||
| Upside SD | 0.110 | ||||
| Downside SD | 0.088 | ||||
| N nonnegative terms | 15.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 49.000 | ||||
| Mean of predictor | 0.392 | ||||
| Mean of criterion | 0.003 | ||||
| SD of predictor | 0.247 | ||||
| SD of criterion | 0.143 | ||||
| Covariance | -0.004 | ||||
| r | -0.111 | ||||
| b (slope, estimate of beta) | -0.064 | ||||
| a (intercept, estimate of alpha) | 0.029 | ||||
| Mean Square Error | 0.021 | ||||
| DF error | 47.000 | ||||
| t(b) | -0.764 | ||||
| p(b) | 0.776 | ||||
| t(a) | 0.365 | ||||
| p(a) | 0.358 | ||||
| Lowerbound of 95% confidence interval for beta | -0.232 | ||||
| Upperbound of 95% confidence interval for beta | 0.104 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.129 | ||||
| Upperbound of 95% confidence interval for alpha | 0.186 | ||||
| Treynor index (mean / b) | -0.054 | ||||
| Jensen alpha (a) | 0.029 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.006 | ||||
| SD | 0.140 | ||||
| Sharpe ratio (Glass type estimate) | -0.044 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.044 | ||||
| df | 48.000 | ||||
| t | -0.090 | ||||
| p | 0.536 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.014 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.926 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.014 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.926 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.069 | ||||
| Upside Potential Ratio | 1.586 | ||||
| Upside part of mean | 0.144 | ||||
| Downside part of mean | -0.150 | ||||
| Upside SD | 0.105 | ||||
| Downside SD | 0.091 | ||||
| N nonnegative terms | 15.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 49.000 | ||||
| Mean of predictor | 0.356 | ||||
| Mean of criterion | -0.006 | ||||
| SD of predictor | 0.237 | ||||
| SD of criterion | 0.140 | ||||
| Covariance | -0.004 | ||||
| r | -0.107 | ||||
| b (slope, estimate of beta) | -0.063 | ||||
| a (intercept, estimate of alpha) | 0.016 | ||||
| Mean Square Error | 0.020 | ||||
| DF error | 47.000 | ||||
| t(b) | -0.737 | ||||
| p(b) | 0.768 | ||||
| t(a) | 0.214 | ||||
| p(a) | 0.416 | ||||
| Lowerbound of 95% confidence interval for beta | -0.235 | ||||
| Upperbound of 95% confidence interval for beta | 0.109 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.137 | ||||
| Upperbound of 95% confidence interval for alpha | 0.169 | ||||
| Treynor index (mean / b) | 0.099 | ||||
| Jensen alpha (a) | 0.016 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.065 | ||||
| Expected Shortfall on VaR | 0.080 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.034 | ||||
| Expected Shortfall on VaR | 0.065 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 49.000 | ||||
| Minimum | 0.917 | ||||
| Quartile 1 | 0.994 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.008 | ||||
| Maximum | 1.146 | ||||
| Mean of quarter 1 | 0.965 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.054 | ||||
| Inter Quartile Range | 0.014 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.122 | ||||
| Mean of outliers low | 0.935 | ||||
| Number of outliers high | 8.000 | ||||
| Percentage of outliers high | 0.163 | ||||
| Mean of outliers high | 1.072 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.867 | ||||
| VaR(95%) (moments method) | 0.036 | ||||
| Expected Shortfall (moments method) | 0.294 | ||||
| Extreme Value Index (regression method) | -0.016 | ||||
| VaR(95%) (regression method) | 0.031 | ||||
| Expected Shortfall (regression method) | 0.045 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.071 | ||||
| Quartile 1 | 0.080 | ||||
| Median | 0.090 | ||||
| Quartile 3 | 0.164 | ||||
| Maximum | 0.238 | ||||
| Mean of quarter 1 | 0.071 | ||||
| Mean of quarter 2 | 0.090 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.238 | ||||
| Inter Quartile Range | 0.084 | ||||
| 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) | 0.162 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.162 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.479 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.003 | ||||
| SD | 0.092 | ||||
| Sharpe ratio (Glass type estimate) | -0.027 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.027 | ||||
| df | 1086.000 | ||||
| t | -0.056 | ||||
| p | 0.501 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.990 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.935 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.990 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.935 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.035 | ||||
| Upside Potential Ratio | 4.884 | ||||
| Upside part of mean | 0.349 | ||||
| Downside part of mean | -0.351 | ||||
| Upside SD | 0.059 | ||||
| Downside SD | 0.071 | ||||
| N nonnegative terms | 308.000 | ||||
| N negative terms | 779.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1087.000 | ||||
| Mean of predictor | 0.428 | ||||
| Mean of criterion | -0.003 | ||||
| SD of predictor | 0.275 | ||||
| SD of criterion | 0.092 | ||||
| Covariance | -0.001 | ||||
| r | -0.035 | ||||
| b (slope, estimate of beta) | -0.012 | ||||
| a (intercept, estimate of alpha) | 0.002 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 1085.000 | ||||
| t(b) | -1.150 | ||||
| p(b) | 0.522 | ||||
| t(a) | 0.055 | ||||
| p(a) | 0.499 | ||||
| Lowerbound of 95% confidence interval for beta | -0.032 | ||||
| Upperbound of 95% confidence interval for beta | 0.008 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.087 | ||||
| Upperbound of 95% confidence interval for alpha | 0.092 | ||||
| Treynor index (mean / b) | 0.216 | ||||
| Jensen alpha (a) | 0.002 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.007 | ||||
| SD | 0.093 | ||||
| Sharpe ratio (Glass type estimate) | -0.073 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.073 | ||||
| df | 1086.000 | ||||
| t | -0.150 | ||||
| p | 0.502 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.036 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.889 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.036 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.889 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.094 | ||||
| Upside Potential Ratio | 4.801 | ||||
| Upside part of mean | 0.347 | ||||
| Downside part of mean | -0.354 | ||||
| Upside SD | 0.058 | ||||
| Downside SD | 0.072 | ||||
| N nonnegative terms | 308.000 | ||||
| N negative terms | 779.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1087.000 | ||||
| Mean of predictor | 0.389 | ||||
| Mean of criterion | -0.007 | ||||
| SD of predictor | 0.280 | ||||
| SD of criterion | 0.093 | ||||
| Covariance | -0.001 | ||||
| r | -0.034 | ||||
| b (slope, estimate of beta) | -0.011 | ||||
| a (intercept, estimate of alpha) | -0.002 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 1085.000 | ||||
| t(b) | -1.118 | ||||
| p(b) | 0.522 | ||||
| t(a) | -0.054 | ||||
| p(a) | 0.501 | ||||
| Lowerbound of 95% confidence interval for beta | -0.031 | ||||
| Upperbound of 95% confidence interval for beta | 0.008 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.092 | ||||
| Upperbound of 95% confidence interval for alpha | 0.087 | ||||
| Treynor index (mean / b) | 0.607 | ||||
| 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%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.008 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1087.000 | ||||
| Minimum | 0.949 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.031 | ||||
| Mean of quarter 1 | 0.995 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.005 | ||||
| Inter Quartile Range | 0.001 | ||||
| Number outliers low | 171.000 | ||||
| Percentage of outliers low | 0.157 | ||||
| Mean of outliers low | 0.992 | ||||
| Number of outliers high | 232.000 | ||||
| Percentage of outliers high | 0.213 | ||||
| Mean of outliers high | 1.006 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.806 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.024 | ||||
| Extreme Value Index (regression method) | 0.302 | ||||
| VaR(95%) (regression method) | 0.005 | ||||
| Expected Shortfall (regression method) | 0.010 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.007 | ||||
| Median | 0.016 | ||||
| Quartile 3 | 0.077 | ||||
| Maximum | 0.287 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.010 | ||||
| Mean of quarter 3 | 0.035 | ||||
| Mean of quarter 4 | 0.176 | ||||
| Inter Quartile Range | 0.070 | ||||
| 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 | 0.100 | ||||
| Mean of outliers high | 0.287 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.824 | ||||
| VaR(95%) (moments method) | 0.189 | ||||
| Expected Shortfall (moments method) | 0.190 | ||||
| Extreme Value Index (regression method) | -0.063 | ||||
| VaR(95%) (regression method) | 0.313 | ||||
| Expected Shortfall (regression method) | 0.432 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.040 | ||||
| Compounded annual return (geometric extrapolation) | 0.038 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.132 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.215 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.214 | ||||
| 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 | 0.001 | ||||
| Sharpe ratio (Glass type estimate) | -40.639 | ||||
| Sharpe ratio (Hedges UMVUE) | -40.404 | ||||
| df | 130.000 | ||||
| t | -28.736 | ||||
| p | 0.965 | ||||
| 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) | -46.043 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -34.765 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -15.047 | ||||
| Upside Potential Ratio | 0.026 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 129.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.004 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.428 | ||||
| SD of criterion | 0.001 | ||||
| Covariance | -0.000 | ||||
| r | -0.295 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | -3.507 | ||||
| p(b) | 0.685 | ||||
| t(a) | -29.141 | ||||
| p(a) | 0.989 | ||||
| Lowerbound of 95% confidence interval for beta | -0.001 | ||||
| Upperbound of 95% confidence interval for beta | -0.000 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.046 | ||||
| Upperbound of 95% confidence interval for alpha | -0.041 | ||||
| Treynor index (mean / b) | 58.978 | ||||
| Jensen alpha (a) | -0.044 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.001 | ||||
| Sharpe ratio (Glass type estimate) | -40.636 | ||||
| Sharpe ratio (Hedges UMVUE) | -40.401 | ||||
| df | 130.000 | ||||
| t | -28.734 | ||||
| p | 0.965 | ||||
| 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) | -46.040 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -34.762 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -15.047 | ||||
| Upside Potential Ratio | 0.026 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 129.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.911 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.430 | ||||
| SD of criterion | 0.001 | ||||
| Covariance | -0.000 | ||||
| r | -0.295 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | -3.503 | ||||
| p(b) | 0.685 | ||||
| t(a) | -29.242 | ||||
| p(a) | 0.990 | ||||
| Lowerbound of 95% confidence interval for beta | -0.001 | ||||
| Upperbound of 95% confidence interval for beta | -0.000 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.047 | ||||
| Upperbound of 95% confidence interval for alpha | -0.041 | ||||
| Treynor index (mean / b) | 59.313 | ||||
| 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 | 3.000 | ||||
| Percentage of outliers low | 0.023 | ||||
| Mean of outliers low | 1.000 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.015 | ||||
| Mean of outliers high | 1.000 | ||||
| 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 | 5.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.000 | ||||
| Quartile 3 | 0.000 | ||||
| Maximum | 0.001 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.000 | ||||
| Mean of quarter 3 | 0.000 | ||||
| Mean of quarter 4 | 0.001 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.200 | ||||
| Mean of outliers low | 0.000 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.200 | ||||
| Mean of outliers high | 0.001 | ||||
| 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) | -0.234 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.234 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.766 | ||||