Advanced Statistics: Iris 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 | 0.097 | ||||
| SD | 0.298 | ||||
| Sharpe ratio (Glass type estimate) | 0.325 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.318 | ||||
| df | 34.000 | ||||
| t | 0.555 | ||||
| p | 0.291 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.828 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.473 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.832 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.468 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.943 | ||||
| Upside Potential Ratio | 1.951 | ||||
| Upside part of mean | 0.200 | ||||
| Downside part of mean | -0.103 | ||||
| Upside SD | 0.276 | ||||
| Downside SD | 0.103 | ||||
| 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 | 0.552 | ||||
| Mean of criterion | 0.097 | ||||
| SD of predictor | 0.311 | ||||
| SD of criterion | 0.298 | ||||
| Covariance | -0.012 | ||||
| r | -0.132 | ||||
| b (slope, estimate of beta) | -0.126 | ||||
| a (intercept, estimate of alpha) | 0.166 | ||||
| Mean Square Error | 0.090 | ||||
| DF error | 33.000 | ||||
| t(b) | -0.765 | ||||
| p(b) | 0.775 | ||||
| t(a) | 0.842 | ||||
| p(a) | 0.203 | ||||
| Lowerbound of 95% confidence interval for beta | -0.462 | ||||
| Upperbound of 95% confidence interval for beta | 0.210 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.236 | ||||
| Upperbound of 95% confidence interval for alpha | 0.568 | ||||
| Treynor index (mean / b) | -0.766 | ||||
| Jensen alpha (a) | 0.166 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.061 | ||||
| SD | 0.259 | ||||
| Sharpe ratio (Glass type estimate) | 0.235 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.230 | ||||
| df | 34.000 | ||||
| t | 0.401 | ||||
| p | 0.345 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.916 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.382 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.919 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.379 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.542 | ||||
| Upside Potential Ratio | 1.514 | ||||
| Upside part of mean | 0.170 | ||||
| Downside part of mean | -0.109 | ||||
| Upside SD | 0.230 | ||||
| Downside SD | 0.112 | ||||
| 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 | 0.496 | ||||
| Mean of criterion | 0.061 | ||||
| SD of predictor | 0.293 | ||||
| SD of criterion | 0.259 | ||||
| Covariance | -0.010 | ||||
| r | -0.126 | ||||
| b (slope, estimate of beta) | -0.111 | ||||
| a (intercept, estimate of alpha) | 0.116 | ||||
| Mean Square Error | 0.068 | ||||
| DF error | 33.000 | ||||
| t(b) | -0.727 | ||||
| p(b) | 0.764 | ||||
| t(a) | 0.680 | ||||
| p(a) | 0.251 | ||||
| Lowerbound of 95% confidence interval for beta | -0.421 | ||||
| Upperbound of 95% confidence interval for beta | 0.199 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.231 | ||||
| Upperbound of 95% confidence interval for alpha | 0.462 | ||||
| Treynor index (mean / b) | -0.548 | ||||
| Jensen alpha (a) | 0.116 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.111 | ||||
| Expected Shortfall on VaR | 0.138 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.029 | ||||
| Expected Shortfall on VaR | 0.062 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 35.000 | ||||
| Minimum | 0.830 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.457 | ||||
| Mean of quarter 1 | 0.980 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.066 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.057 | ||||
| Mean of outliers low | 0.910 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.057 | ||||
| Mean of outliers high | 1.296 | ||||
| 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) | 2.909 | ||||
| VaR(95%) (regression method) | 0.008 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.179 | ||||
| Quartile 1 | 0.179 | ||||
| Median | 0.179 | ||||
| Quartile 3 | 0.179 | ||||
| Maximum | 0.179 | ||||
| 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) | 0.123 | ||||
| Compounded annual return (geometric extrapolation) | 0.110 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.619 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.800 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.073 | ||||
| SD | 0.174 | ||||
| Sharpe ratio (Glass type estimate) | 0.419 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.419 | ||||
| df | 782.000 | ||||
| t | 0.724 | ||||
| p | 0.235 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.715 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.553 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.715 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.553 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.804 | ||||
| Upside Potential Ratio | 3.882 | ||||
| Upside part of mean | 0.351 | ||||
| Downside part of mean | -0.279 | ||||
| Upside SD | 0.148 | ||||
| Downside SD | 0.091 | ||||
| N nonnegative terms | 32.000 | ||||
| N negative terms | 751.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 783.000 | ||||
| Mean of predictor | 0.606 | ||||
| Mean of criterion | 0.073 | ||||
| SD of predictor | 0.361 | ||||
| SD of criterion | 0.174 | ||||
| Covariance | -0.002 | ||||
| r | -0.026 | ||||
| b (slope, estimate of beta) | -0.013 | ||||
| a (intercept, estimate of alpha) | 0.080 | ||||
| Mean Square Error | 0.030 | ||||
| DF error | 781.000 | ||||
| t(b) | -0.734 | ||||
| p(b) | 0.768 | ||||
| t(a) | 0.796 | ||||
| p(a) | 0.213 | ||||
| Lowerbound of 95% confidence interval for beta | -0.046 | ||||
| Upperbound of 95% confidence interval for beta | 0.021 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.118 | ||||
| Upperbound of 95% confidence interval for alpha | 0.279 | ||||
| Treynor index (mean / b) | -5.757 | ||||
| Jensen alpha (a) | 0.080 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.058 | ||||
| SD | 0.170 | ||||
| Sharpe ratio (Glass type estimate) | 0.343 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.343 | ||||
| df | 782.000 | ||||
| t | 0.594 | ||||
| p | 0.276 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.791 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.477 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.791 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.477 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.629 | ||||
| Upside Potential Ratio | 3.685 | ||||
| Upside part of mean | 0.341 | ||||
| Downside part of mean | -0.283 | ||||
| Upside SD | 0.142 | ||||
| Downside SD | 0.093 | ||||
| N nonnegative terms | 32.000 | ||||
| N negative terms | 751.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 783.000 | ||||
| Mean of predictor | 0.537 | ||||
| Mean of criterion | 0.058 | ||||
| SD of predictor | 0.375 | ||||
| SD of criterion | 0.170 | ||||
| Covariance | -0.002 | ||||
| r | -0.024 | ||||
| b (slope, estimate of beta) | -0.011 | ||||
| a (intercept, estimate of alpha) | 0.064 | ||||
| Mean Square Error | 0.029 | ||||
| DF error | 781.000 | ||||
| t(b) | -0.681 | ||||
| p(b) | 0.752 | ||||
| t(a) | 0.651 | ||||
| p(a) | 0.258 | ||||
| Lowerbound of 95% confidence interval for beta | -0.043 | ||||
| Upperbound of 95% confidence interval for beta | 0.021 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.129 | ||||
| Upperbound of 95% confidence interval for alpha | 0.257 | ||||
| Treynor index (mean / b) | -5.292 | ||||
| Jensen alpha (a) | 0.064 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.021 | ||||
| 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 | 783.000 | ||||
| Minimum | 0.936 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.148 | ||||
| Mean of quarter 1 | 0.996 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.005 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 35.000 | ||||
| Percentage of outliers low | 0.045 | ||||
| Mean of outliers low | 0.980 | ||||
| Number of outliers high | 32.000 | ||||
| Percentage of outliers high | 0.041 | ||||
| Mean of outliers high | 1.033 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -4.315 | ||||
| VaR(95%) (moments method) | -0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.059 | ||||
| VaR(95%) (regression method) | -0.001 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.007 | ||||
| Quartile 1 | 0.017 | ||||
| Median | 0.042 | ||||
| Quartile 3 | 0.075 | ||||
| Maximum | 0.179 | ||||
| Mean of quarter 1 | 0.009 | ||||
| Mean of quarter 2 | 0.024 | ||||
| Mean of quarter 3 | 0.063 | ||||
| Mean of quarter 4 | 0.136 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers high | 0.125 | ||||
| Mean of outliers high | 0.179 | ||||
| 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) | 0.120 | ||||
| Compounded annual return (geometric extrapolation) | 0.108 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.603 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.794 | ||||
| Compounded annual return / Expected Shortfall lognormal | 5.090 | ||||
| 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 | 1.045 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.458 | ||||
| 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 | 0.938 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.460 | ||||
| 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) | -8730113635732495.000 | ||||
| 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) | -510901646730822629771928146018304.000 | ||||
| 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 | ||||