Advanced Statistics: Pegasi 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 | -0.035 | ||||
| SD | 0.066 | ||||
| Sharpe ratio (Glass type estimate) | -0.531 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.519 | ||||
| df | 34.000 | ||||
| t | -0.907 | ||||
| p | 0.815 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.682 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.627 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.674 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.635 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.719 | ||||
| Upside Potential Ratio | 0.888 | ||||
| Upside part of mean | 0.043 | ||||
| Downside part of mean | -0.079 | ||||
| Upside SD | 0.044 | ||||
| Downside SD | 0.049 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 35.000 | ||||
| Mean of predictor | 0.581 | ||||
| Mean of criterion | -0.035 | ||||
| SD of predictor | 0.342 | ||||
| SD of criterion | 0.066 | ||||
| Covariance | -0.003 | ||||
| r | -0.150 | ||||
| b (slope, estimate of beta) | -0.029 | ||||
| a (intercept, estimate of alpha) | -0.018 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 33.000 | ||||
| t(b) | -0.872 | ||||
| p(b) | 0.805 | ||||
| t(a) | -0.421 | ||||
| p(a) | 0.662 | ||||
| Lowerbound of 95% confidence interval for beta | -0.097 | ||||
| Upperbound of 95% confidence interval for beta | 0.039 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.107 | ||||
| Upperbound of 95% confidence interval for alpha | 0.070 | ||||
| Treynor index (mean / b) | 1.210 | ||||
| Jensen alpha (a) | -0.018 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.037 | ||||
| SD | 0.066 | ||||
| Sharpe ratio (Glass type estimate) | -0.562 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.549 | ||||
| df | 34.000 | ||||
| t | -0.959 | ||||
| p | 0.828 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.713 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.598 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.704 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.606 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.741 | ||||
| Upside Potential Ratio | 0.843 | ||||
| Upside part of mean | 0.042 | ||||
| Downside part of mean | -0.080 | ||||
| Upside SD | 0.043 | ||||
| Downside SD | 0.050 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 35.000 | ||||
| Mean of predictor | 0.515 | ||||
| Mean of criterion | -0.037 | ||||
| SD of predictor | 0.323 | ||||
| SD of criterion | 0.066 | ||||
| Covariance | -0.003 | ||||
| r | -0.149 | ||||
| b (slope, estimate of beta) | -0.031 | ||||
| a (intercept, estimate of alpha) | -0.021 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 33.000 | ||||
| t(b) | -0.866 | ||||
| p(b) | 0.804 | ||||
| t(a) | -0.500 | ||||
| p(a) | 0.690 | ||||
| Lowerbound of 95% confidence interval for beta | -0.103 | ||||
| Upperbound of 95% confidence interval for beta | 0.041 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.109 | ||||
| Upperbound of 95% confidence interval for alpha | 0.066 | ||||
| Treynor index (mean / b) | 1.217 | ||||
| Jensen alpha (a) | -0.021 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.034 | ||||
| Expected Shortfall on VaR | 0.042 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.022 | ||||
| Expected Shortfall on VaR | 0.040 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 35.000 | ||||
| Minimum | 0.935 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.061 | ||||
| Mean of quarter 1 | 0.988 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.015 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.086 | ||||
| Mean of outliers low | 0.963 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.086 | ||||
| Mean of outliers high | 1.046 | ||||
| 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) | -0.110 | ||||
| VaR(95%) (regression method) | 0.029 | ||||
| Expected Shortfall (regression method) | 0.061 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.009 | ||||
| Quartile 1 | 0.023 | ||||
| Median | 0.038 | ||||
| Quartile 3 | 0.051 | ||||
| Maximum | 0.065 | ||||
| Mean of quarter 1 | 0.009 | ||||
| Mean of quarter 2 | 0.038 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.065 | ||||
| Inter Quartile Range | 0.028 | ||||
| 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) | 0.007 | ||||
| Compounded annual return (geometric extrapolation) | 0.007 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.104 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.104 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.163 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.036 | ||||
| SD | 0.047 | ||||
| Sharpe ratio (Glass type estimate) | -0.765 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.764 | ||||
| df | 774.000 | ||||
| t | -1.316 | ||||
| p | 0.906 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.905 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.375 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.905 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.376 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.096 | ||||
| Upside Potential Ratio | 2.657 | ||||
| Upside part of mean | 0.088 | ||||
| Downside part of mean | -0.124 | ||||
| Upside SD | 0.034 | ||||
| Downside SD | 0.033 | ||||
| N nonnegative terms | 31.000 | ||||
| N negative terms | 744.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 775.000 | ||||
| Mean of predictor | 0.614 | ||||
| Mean of criterion | -0.036 | ||||
| SD of predictor | 0.367 | ||||
| SD of criterion | 0.047 | ||||
| Covariance | 0.000 | ||||
| r | 0.021 | ||||
| b (slope, estimate of beta) | 0.003 | ||||
| a (intercept, estimate of alpha) | -0.038 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 773.000 | ||||
| t(b) | 0.588 | ||||
| p(b) | 0.278 | ||||
| t(a) | -1.369 | ||||
| p(a) | 0.914 | ||||
| Lowerbound of 95% confidence interval for beta | -0.006 | ||||
| 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 | 0.016 | ||||
| Treynor index (mean / b) | -13.299 | ||||
| Jensen alpha (a) | -0.038 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.037 | ||||
| SD | 0.047 | ||||
| Sharpe ratio (Glass type estimate) | -0.789 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.788 | ||||
| df | 774.000 | ||||
| t | -1.357 | ||||
| p | 0.912 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.929 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.352 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.928 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.352 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.120 | ||||
| Upside Potential Ratio | 2.617 | ||||
| Upside part of mean | 0.087 | ||||
| Downside part of mean | -0.125 | ||||
| Upside SD | 0.034 | ||||
| Downside SD | 0.033 | ||||
| N nonnegative terms | 31.000 | ||||
| N negative terms | 744.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 775.000 | ||||
| Mean of predictor | 0.541 | ||||
| Mean of criterion | -0.037 | ||||
| SD of predictor | 0.388 | ||||
| SD of criterion | 0.047 | ||||
| Covariance | 0.000 | ||||
| r | 0.020 | ||||
| b (slope, estimate of beta) | 0.002 | ||||
| a (intercept, estimate of alpha) | -0.039 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 773.000 | ||||
| t(b) | 0.555 | ||||
| p(b) | 0.290 | ||||
| t(a) | -1.399 | ||||
| p(a) | 0.919 | ||||
| Lowerbound of 95% confidence interval for beta | -0.006 | ||||
| Upperbound of 95% confidence interval for beta | 0.011 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.093 | ||||
| Upperbound of 95% confidence interval for alpha | 0.016 | ||||
| Treynor index (mean / b) | -15.355 | ||||
| Jensen alpha (a) | -0.039 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.006 | ||||
| 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 | 775.000 | ||||
| Minimum | 0.977 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.024 | ||||
| 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 | 35.000 | ||||
| Percentage of outliers low | 0.045 | ||||
| Mean of outliers low | 0.993 | ||||
| Number of outliers high | 32.000 | ||||
| Percentage of outliers high | 0.041 | ||||
| Mean of outliers high | 1.008 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.365 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | -0.081 | ||||
| VaR(95%) (regression method) | 0.000 | ||||
| Expected Shortfall (regression method) | 0.003 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.001 | ||||
| Median | 0.003 | ||||
| Quartile 3 | 0.041 | ||||
| Maximum | 0.067 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.002 | ||||
| Mean of quarter 3 | 0.018 | ||||
| Mean of quarter 4 | 0.066 | ||||
| Inter Quartile Range | 0.040 | ||||
| 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) | 0.007 | ||||
| Compounded annual return (geometric extrapolation) | 0.007 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.100 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.101 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.086 | ||||
| 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 | 1.016 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.452 | ||||
| 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 | 0.912 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.454 | ||||
| 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) | -8732259080171024.000 | ||||
| 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) | -75772273987537325053636815880192.000 | ||||
| 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 | ||||