Advanced Statistics: Bund PRO
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 | -0.042 | ||||
| SD | 0.089 | ||||
| Sharpe ratio (Glass type estimate) | -0.471 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.467 | ||||
| df | 94.000 | ||||
| t | -1.325 | ||||
| p | 0.906 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.170 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.230 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.167 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.233 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.627 | ||||
| Upside Potential Ratio | 0.461 | ||||
| Upside part of mean | 0.031 | ||||
| Downside part of mean | -0.072 | ||||
| Upside SD | 0.059 | ||||
| Downside SD | 0.067 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 91.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 95.000 | ||||
| Mean of predictor | 0.186 | ||||
| Mean of criterion | -0.042 | ||||
| SD of predictor | 0.259 | ||||
| SD of criterion | 0.089 | ||||
| Covariance | 0.005 | ||||
| r | 0.203 | ||||
| b (slope, estimate of beta) | 0.070 | ||||
| a (intercept, estimate of alpha) | -0.055 | ||||
| Mean Square Error | 0.008 | ||||
| DF error | 93.000 | ||||
| t(b) | 2.002 | ||||
| p(b) | 0.024 | ||||
| t(a) | -1.727 | ||||
| p(a) | 0.956 | ||||
| Lowerbound of 95% confidence interval for beta | 0.001 | ||||
| Upperbound of 95% confidence interval for beta | 0.139 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.118 | ||||
| Upperbound of 95% confidence interval for alpha | 0.008 | ||||
| Treynor index (mean / b) | -0.600 | ||||
| Jensen alpha (a) | -0.055 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.046 | ||||
| SD | 0.091 | ||||
| Sharpe ratio (Glass type estimate) | -0.503 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.499 | ||||
| df | 94.000 | ||||
| t | -1.417 | ||||
| p | 0.920 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.202 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.198 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.200 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.201 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.632 | ||||
| Upside Potential Ratio | 0.401 | ||||
| Upside part of mean | 0.029 | ||||
| Downside part of mean | -0.075 | ||||
| Upside SD | 0.056 | ||||
| Downside SD | 0.072 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 91.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 95.000 | ||||
| Mean of predictor | 0.151 | ||||
| Mean of criterion | -0.046 | ||||
| SD of predictor | 0.262 | ||||
| SD of criterion | 0.091 | ||||
| Covariance | 0.005 | ||||
| r | 0.230 | ||||
| b (slope, estimate of beta) | 0.080 | ||||
| a (intercept, estimate of alpha) | -0.058 | ||||
| Mean Square Error | 0.008 | ||||
| DF error | 93.000 | ||||
| t(b) | 2.278 | ||||
| p(b) | 0.013 | ||||
| t(a) | -1.803 | ||||
| p(a) | 0.963 | ||||
| Lowerbound of 95% confidence interval for beta | 0.010 | ||||
| Upperbound of 95% confidence interval for beta | 0.149 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.121 | ||||
| Upperbound of 95% confidence interval for alpha | 0.006 | ||||
| Treynor index (mean / b) | -0.574 | ||||
| Jensen alpha (a) | -0.058 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.046 | ||||
| Expected Shortfall on VaR | 0.056 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.020 | ||||
| Expected Shortfall on VaR | 0.043 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 95.000 | ||||
| Minimum | 0.828 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.138 | ||||
| Mean of quarter 1 | 0.989 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.011 | ||||
| Inter Quartile Range | 0.001 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.074 | ||||
| Mean of outliers low | 0.965 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.063 | ||||
| Mean of outliers high | 1.044 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.507 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 2.654 | ||||
| VaR(95%) (regression method) | 0.001 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.054 | ||||
| Quartile 1 | 0.083 | ||||
| Median | 0.113 | ||||
| Quartile 3 | 0.143 | ||||
| Maximum | 0.172 | ||||
| Mean of quarter 1 | 0.054 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.172 | ||||
| Inter Quartile Range | 0.059 | ||||
| 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) | -0.002 | ||||
| Compounded annual return (geometric extrapolation) | -0.002 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.010 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.010 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.029 | ||||
| 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 | 0.063 | ||||
| Sharpe ratio (Glass type estimate) | -0.696 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.696 | ||||
| df | 2081.000 | ||||
| t | -1.963 | ||||
| p | 0.975 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.392 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.001 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.392 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.001 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.962 | ||||
| Upside Potential Ratio | 1.881 | ||||
| Upside part of mean | 0.085 | ||||
| Downside part of mean | -0.129 | ||||
| Upside SD | 0.043 | ||||
| Downside SD | 0.045 | ||||
| N nonnegative terms | 207.000 | ||||
| N negative terms | 1875.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2082.000 | ||||
| Mean of predictor | 0.310 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.554 | ||||
| SD of criterion | 0.063 | ||||
| Covariance | 0.003 | ||||
| r | 0.097 | ||||
| b (slope, estimate of beta) | 0.011 | ||||
| a (intercept, estimate of alpha) | -0.047 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 2080.000 | ||||
| t(b) | 4.464 | ||||
| p(b) | 0.000 | ||||
| t(a) | -2.125 | ||||
| p(a) | 0.983 | ||||
| Lowerbound of 95% confidence interval for beta | 0.006 | ||||
| Upperbound of 95% confidence interval for beta | 0.016 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.091 | ||||
| Upperbound of 95% confidence interval for alpha | -0.004 | ||||
| Treynor index (mean / b) | -3.959 | ||||
| Jensen alpha (a) | -0.047 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.046 | ||||
| SD | 0.063 | ||||
| Sharpe ratio (Glass type estimate) | -0.727 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.726 | ||||
| df | 2081.000 | ||||
| t | -2.048 | ||||
| p | 0.980 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.422 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.031 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.422 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.031 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.989 | ||||
| Upside Potential Ratio | 1.831 | ||||
| Upside part of mean | 0.084 | ||||
| Downside part of mean | -0.130 | ||||
| Upside SD | 0.043 | ||||
| Downside SD | 0.046 | ||||
| N nonnegative terms | 207.000 | ||||
| N negative terms | 1875.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2082.000 | ||||
| Mean of predictor | 0.157 | ||||
| Mean of criterion | -0.046 | ||||
| SD of predictor | 0.554 | ||||
| SD of criterion | 0.063 | ||||
| Covariance | 0.003 | ||||
| r | 0.098 | ||||
| b (slope, estimate of beta) | 0.011 | ||||
| a (intercept, estimate of alpha) | -0.047 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 2080.000 | ||||
| t(b) | 4.508 | ||||
| p(b) | 0.000 | ||||
| t(a) | -2.136 | ||||
| p(a) | 0.984 | ||||
| Lowerbound of 95% confidence interval for beta | 0.006 | ||||
| Upperbound of 95% confidence interval for beta | 0.016 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.091 | ||||
| Upperbound of 95% confidence interval for alpha | -0.004 | ||||
| Treynor index (mean / b) | -4.090 | ||||
| Jensen alpha (a) | -0.047 | ||||
| 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 | 0.008 | ||||
| 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 | 2082.000 | ||||
| Minimum | 0.945 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.047 | ||||
| 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 | 0.000 | ||||
| Number outliers low | 225.000 | ||||
| Percentage of outliers low | 0.108 | ||||
| Mean of outliers low | 0.997 | ||||
| Number of outliers high | 213.000 | ||||
| Percentage of outliers high | 0.102 | ||||
| Mean of outliers high | 1.003 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.061 | ||||
| VaR(95%) (moments method) | -0.000 | ||||
| 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 | 4.000 | ||||
| Minimum | 0.033 | ||||
| Quartile 1 | 0.049 | ||||
| Median | 0.063 | ||||
| Quartile 3 | 0.097 | ||||
| Maximum | 0.172 | ||||
| Mean of quarter 1 | 0.033 | ||||
| Mean of quarter 2 | 0.055 | ||||
| Mean of quarter 3 | 0.072 | ||||
| Mean of quarter 4 | 0.172 | ||||
| Inter Quartile Range | 0.048 | ||||
| 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 | 0.250 | ||||
| Mean of outliers high | 0.172 | ||||
| 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) | -0.009 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.009 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.197 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.045 | ||||
| SD | 0.002 | ||||
| Sharpe ratio (Glass type estimate) | -19.053 | ||||
| Sharpe ratio (Hedges UMVUE) | -18.943 | ||||
| df | 130.000 | ||||
| t | -13.472 | ||||
| p | 0.882 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -15.420 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -22.546 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -15.339 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -12.442 | ||||
| Upside Potential Ratio | 0.429 | ||||
| Upside part of mean | 0.002 | ||||
| Downside part of mean | -0.046 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.004 | ||||
| N nonnegative terms | 12.000 | ||||
| N negative terms | 119.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.057 | ||||
| Mean of criterion | -0.045 | ||||
| SD of predictor | 0.480 | ||||
| SD of criterion | 0.002 | ||||
| Covariance | -0.000 | ||||
| r | -0.330 | ||||
| b (slope, estimate of beta) | -0.002 | ||||
| a (intercept, estimate of alpha) | -0.043 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | -3.973 | ||||
| p(b) | 0.706 | ||||
| t(a) | -13.550 | ||||
| p(a) | 0.935 | ||||
| Lowerbound of 95% confidence interval for beta | -0.002 | ||||
| Upperbound of 95% confidence interval for beta | -0.001 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.049 | ||||
| Upperbound of 95% confidence interval for alpha | -0.037 | ||||
| Treynor index (mean / b) | 27.708 | ||||
| Jensen alpha (a) | -0.043 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.045 | ||||
| SD | 0.002 | ||||
| Sharpe ratio (Glass type estimate) | -19.052 | ||||
| Sharpe ratio (Hedges UMVUE) | -18.942 | ||||
| df | 130.000 | ||||
| t | -13.472 | ||||
| p | 0.882 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -15.419 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -22.545 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -15.339 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -12.442 | ||||
| Upside Potential Ratio | 0.429 | ||||
| Upside part of mean | 0.002 | ||||
| Downside part of mean | -0.046 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.004 | ||||
| N nonnegative terms | 12.000 | ||||
| N negative terms | 119.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.941 | ||||
| Mean of criterion | -0.045 | ||||
| SD of predictor | 0.479 | ||||
| SD of criterion | 0.002 | ||||
| Covariance | -0.000 | ||||
| r | -0.328 | ||||
| b (slope, estimate of beta) | -0.002 | ||||
| a (intercept, estimate of alpha) | -0.043 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | -3.947 | ||||
| p(b) | 0.705 | ||||
| t(a) | -13.626 | ||||
| p(a) | 0.935 | ||||
| Lowerbound of 95% confidence interval for beta | -0.002 | ||||
| Upperbound of 95% confidence interval for beta | -0.001 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.049 | ||||
| Upperbound of 95% confidence interval for alpha | -0.037 | ||||
| Treynor index (mean / b) | 27.790 | ||||
| Jensen alpha (a) | -0.043 | ||||
| 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 | 6.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.000 | ||||
| Quartile 3 | 0.000 | ||||
| Maximum | 0.002 | ||||
| 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 | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.167 | ||||
| Mean of outliers high | 0.002 | ||||
| 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) | -0.001 | ||||
| Compounded annual return (geometric extrapolation) | -0.001 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.297 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.541 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.439 | ||||