Advanced Statistics: Prudentius Praemium FX
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 | -0.012 | ||||
| SD | 0.118 | ||||
| Sharpe ratio (Glass type estimate) | -0.103 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.101 | ||||
| df | 34.000 | ||||
| t | -0.176 | ||||
| p | 0.569 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.250 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.046 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.248 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.047 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.181 | ||||
| Upside Potential Ratio | 1.167 | ||||
| Upside part of mean | 0.078 | ||||
| Downside part of mean | -0.090 | ||||
| Upside SD | 0.095 | ||||
| Downside SD | 0.067 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 35.000 | ||||
| Mean of predictor | 0.568 | ||||
| Mean of criterion | -0.012 | ||||
| SD of predictor | 0.308 | ||||
| SD of criterion | 0.118 | ||||
| Covariance | -0.003 | ||||
| r | -0.072 | ||||
| b (slope, estimate of beta) | -0.028 | ||||
| a (intercept, estimate of alpha) | 0.004 | ||||
| Mean Square Error | 0.014 | ||||
| DF error | 33.000 | ||||
| t(b) | -0.415 | ||||
| p(b) | 0.660 | ||||
| t(a) | 0.045 | ||||
| p(a) | 0.482 | ||||
| Lowerbound of 95% confidence interval for beta | -0.163 | ||||
| Upperbound of 95% confidence interval for beta | 0.108 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.158 | ||||
| Upperbound of 95% confidence interval for alpha | 0.165 | ||||
| Treynor index (mean / b) | 0.439 | ||||
| Jensen alpha (a) | 0.004 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.019 | ||||
| SD | 0.115 | ||||
| Sharpe ratio (Glass type estimate) | -0.162 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.158 | ||||
| df | 34.000 | ||||
| t | -0.276 | ||||
| p | 0.608 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.309 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.988 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.306 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.990 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.266 | ||||
| Upside Potential Ratio | 1.052 | ||||
| Upside part of mean | 0.074 | ||||
| Downside part of mean | -0.092 | ||||
| Upside SD | 0.090 | ||||
| Downside SD | 0.070 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 35.000 | ||||
| Mean of predictor | 0.514 | ||||
| Mean of criterion | -0.019 | ||||
| SD of predictor | 0.279 | ||||
| SD of criterion | 0.115 | ||||
| Covariance | -0.002 | ||||
| r | -0.069 | ||||
| b (slope, estimate of beta) | -0.028 | ||||
| a (intercept, estimate of alpha) | -0.004 | ||||
| Mean Square Error | 0.014 | ||||
| DF error | 33.000 | ||||
| t(b) | -0.397 | ||||
| p(b) | 0.653 | ||||
| t(a) | -0.051 | ||||
| p(a) | 0.520 | ||||
| Lowerbound of 95% confidence interval for beta | -0.175 | ||||
| Upperbound of 95% confidence interval for beta | 0.118 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.162 | ||||
| Upperbound of 95% confidence interval for alpha | 0.154 | ||||
| Treynor index (mean / b) | 0.654 | ||||
| Jensen alpha (a) | -0.004 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.055 | ||||
| Expected Shortfall on VaR | 0.068 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.025 | ||||
| Expected Shortfall on VaR | 0.050 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 35.000 | ||||
| Minimum | 0.899 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.133 | ||||
| Mean of quarter 1 | 0.984 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.026 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.086 | ||||
| Mean of outliers low | 0.953 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.057 | ||||
| Mean of outliers high | 1.117 | ||||
| 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) | 1.376 | ||||
| VaR(95%) (regression method) | 0.018 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.137 | ||||
| Quartile 1 | 0.137 | ||||
| Median | 0.137 | ||||
| Quartile 3 | 0.137 | ||||
| Maximum | 0.137 | ||||
| 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) | 0.026 | ||||
| Compounded annual return (geometric extrapolation) | 0.026 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.187 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.380 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.017 | ||||
| SD | 0.063 | ||||
| Sharpe ratio (Glass type estimate) | -0.268 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.268 | ||||
| df | 775.000 | ||||
| t | -0.462 | ||||
| p | 0.678 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.407 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.871 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.407 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.871 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.342 | ||||
| Upside Potential Ratio | 1.952 | ||||
| Upside part of mean | 0.097 | ||||
| Downside part of mean | -0.114 | ||||
| Upside SD | 0.039 | ||||
| Downside SD | 0.050 | ||||
| N nonnegative terms | 42.000 | ||||
| N negative terms | 734.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 776.000 | ||||
| Mean of predictor | 0.603 | ||||
| Mean of criterion | -0.017 | ||||
| SD of predictor | 0.360 | ||||
| SD of criterion | 0.063 | ||||
| Covariance | -0.000 | ||||
| r | -0.006 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | -0.016 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 774.000 | ||||
| t(b) | -0.160 | ||||
| p(b) | 0.564 | ||||
| t(a) | -0.443 | ||||
| p(a) | 0.671 | ||||
| Lowerbound of 95% confidence interval for beta | -0.013 | ||||
| Upperbound of 95% confidence interval for beta | 0.011 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.089 | ||||
| Upperbound of 95% confidence interval for alpha | 0.056 | ||||
| Treynor index (mean / b) | 16.753 | ||||
| Jensen alpha (a) | -0.016 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.019 | ||||
| SD | 0.064 | ||||
| Sharpe ratio (Glass type estimate) | -0.297 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.296 | ||||
| df | 775.000 | ||||
| t | -0.511 | ||||
| p | 0.695 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.436 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.842 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.435 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.843 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.372 | ||||
| Upside Potential Ratio | 1.883 | ||||
| Upside part of mean | 0.096 | ||||
| Downside part of mean | -0.115 | ||||
| Upside SD | 0.039 | ||||
| Downside SD | 0.051 | ||||
| N nonnegative terms | 42.000 | ||||
| N negative terms | 734.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 776.000 | ||||
| Mean of predictor | 0.540 | ||||
| Mean of criterion | -0.019 | ||||
| SD of predictor | 0.351 | ||||
| SD of criterion | 0.064 | ||||
| Covariance | -0.000 | ||||
| r | -0.005 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | -0.019 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 774.000 | ||||
| t(b) | -0.138 | ||||
| p(b) | 0.555 | ||||
| t(a) | -0.495 | ||||
| p(a) | 0.690 | ||||
| Lowerbound of 95% confidence interval for beta | -0.014 | ||||
| Upperbound of 95% confidence interval for beta | 0.012 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.092 | ||||
| Upperbound of 95% confidence interval for alpha | 0.055 | ||||
| Treynor index (mean / b) | 21.029 | ||||
| Jensen alpha (a) | -0.019 | ||||
| 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%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.003 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 776.000 | ||||
| Minimum | 0.930 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.038 | ||||
| Mean of quarter 1 | 0.999 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.002 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 21.000 | ||||
| Percentage of outliers low | 0.027 | ||||
| Mean of outliers low | 0.990 | ||||
| Number of outliers high | 44.000 | ||||
| Percentage of outliers high | 0.057 | ||||
| Mean of outliers high | 1.007 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.156 | ||||
| VaR(95%) (moments method) | -0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.386 | ||||
| VaR(95%) (regression method) | -0.003 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.005 | ||||
| Quartile 3 | 0.015 | ||||
| Maximum | 0.147 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.004 | ||||
| Mean of quarter 3 | 0.013 | ||||
| Mean of quarter 4 | 0.082 | ||||
| Inter Quartile Range | 0.013 | ||||
| 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 | 0.143 | ||||
| Mean of outliers high | 0.147 | ||||
| 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) | 0.026 | ||||
| Compounded annual return (geometric extrapolation) | 0.025 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.172 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.309 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.087 | ||||
| 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 | 0.962 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.439 | ||||
| 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 | 0.864 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.439 | ||||
| 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) | -8735003922917795.000 | ||||
| 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) | 133359935079999101472667393327104.000 | ||||
| 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 | ||||