Advanced Statistics: FX managed accounts
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 | -0.344 | ||||
| SD | 0.351 | ||||
| Sharpe ratio (Glass type estimate) | -0.979 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.961 | ||||
| df | 43.000 | ||||
| t | -1.874 | ||||
| p | 0.966 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.017 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.071 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.005 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.082 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.952 | ||||
| Upside Potential Ratio | 0.002 | ||||
| Upside part of mean | 0.001 | ||||
| Downside part of mean | -0.344 | ||||
| Upside SD | 0.001 | ||||
| Downside SD | 0.361 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 43.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 44.000 | ||||
| Mean of predictor | 0.501 | ||||
| Mean of criterion | -0.344 | ||||
| SD of predictor | 0.272 | ||||
| SD of criterion | 0.351 | ||||
| Covariance | 0.019 | ||||
| r | 0.196 | ||||
| b (slope, estimate of beta) | 0.253 | ||||
| a (intercept, estimate of alpha) | -0.471 | ||||
| Mean Square Error | 0.122 | ||||
| DF error | 42.000 | ||||
| t(b) | 1.297 | ||||
| p(b) | 0.101 | ||||
| t(a) | -2.278 | ||||
| p(a) | 0.986 | ||||
| Lowerbound of 95% confidence interval for beta | -0.141 | ||||
| Upperbound of 95% confidence interval for beta | 0.648 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.888 | ||||
| Upperbound of 95% confidence interval for alpha | -0.054 | ||||
| Treynor index (mean / b) | -1.357 | ||||
| Jensen alpha (a) | -0.471 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.441 | ||||
| SD | 0.481 | ||||
| Sharpe ratio (Glass type estimate) | -0.917 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.901 | ||||
| df | 43.000 | ||||
| t | -1.755 | ||||
| p | 0.957 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.953 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.130 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.942 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.141 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.896 | ||||
| Upside Potential Ratio | 0.001 | ||||
| Upside part of mean | 0.001 | ||||
| Downside part of mean | -0.441 | ||||
| Upside SD | 0.001 | ||||
| Downside SD | 0.492 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 43.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 44.000 | ||||
| Mean of predictor | 0.456 | ||||
| Mean of criterion | -0.441 | ||||
| SD of predictor | 0.260 | ||||
| SD of criterion | 0.481 | ||||
| Covariance | 0.023 | ||||
| r | 0.186 | ||||
| b (slope, estimate of beta) | 0.343 | ||||
| a (intercept, estimate of alpha) | -0.597 | ||||
| Mean Square Error | 0.228 | ||||
| DF error | 42.000 | ||||
| t(b) | 1.225 | ||||
| p(b) | 0.114 | ||||
| t(a) | -2.130 | ||||
| p(a) | 0.980 | ||||
| Lowerbound of 95% confidence interval for beta | -0.222 | ||||
| Upperbound of 95% confidence interval for beta | 0.908 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.162 | ||||
| Upperbound of 95% confidence interval for alpha | -0.031 | ||||
| Treynor index (mean / b) | -1.285 | ||||
| Jensen alpha (a) | -0.597 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.233 | ||||
| Expected Shortfall on VaR | 0.275 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.099 | ||||
| Expected Shortfall on VaR | 0.211 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 44.000 | ||||
| Minimum | 0.457 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.006 | ||||
| Mean of quarter 1 | 0.899 | ||||
| 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 | 4.000 | ||||
| Percentage of outliers low | 0.091 | ||||
| Mean of outliers low | 0.723 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.045 | ||||
| Mean of outliers high | 1.004 | ||||
| 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) | 1.354 | ||||
| VaR(95%) (regression method) | 0.063 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.768 | ||||
| Quartile 1 | 0.768 | ||||
| Median | 0.768 | ||||
| Quartile 3 | 0.768 | ||||
| Maximum | 0.768 | ||||
| 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) | -0.209 | ||||
| Compounded annual return (geometric extrapolation) | -0.327 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.426 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.190 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.093 | ||||
| SD | 1.219 | ||||
| Sharpe ratio (Glass type estimate) | 0.076 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.076 | ||||
| df | 960.000 | ||||
| t | 0.146 | ||||
| p | 0.442 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.947 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.100 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.947 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.100 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.175 | ||||
| Upside Potential Ratio | 2.039 | ||||
| Upside part of mean | 1.083 | ||||
| Downside part of mean | -0.990 | ||||
| Upside SD | 1.096 | ||||
| Downside SD | 0.531 | ||||
| N nonnegative terms | 45.000 | ||||
| N negative terms | 916.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 961.000 | ||||
| Mean of predictor | 0.510 | ||||
| Mean of criterion | 0.093 | ||||
| SD of predictor | 0.326 | ||||
| SD of criterion | 1.219 | ||||
| Covariance | -0.057 | ||||
| r | -0.144 | ||||
| b (slope, estimate of beta) | -0.539 | ||||
| a (intercept, estimate of alpha) | 0.368 | ||||
| Mean Square Error | 1.457 | ||||
| DF error | 959.000 | ||||
| t(b) | -4.513 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.581 | ||||
| p(a) | 0.281 | ||||
| Lowerbound of 95% confidence interval for beta | -0.774 | ||||
| Upperbound of 95% confidence interval for beta | -0.305 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.874 | ||||
| Upperbound of 95% confidence interval for alpha | 1.611 | ||||
| Treynor index (mean / b) | -0.173 | ||||
| Jensen alpha (a) | 0.368 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.440 | ||||
| SD | 1.003 | ||||
| Sharpe ratio (Glass type estimate) | -0.439 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.439 | ||||
| df | 960.000 | ||||
| t | -0.841 | ||||
| p | 0.800 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.462 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.585 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.462 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.585 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.598 | ||||
| Upside Potential Ratio | 1.040 | ||||
| Upside part of mean | 0.766 | ||||
| Downside part of mean | -1.206 | ||||
| Upside SD | 0.682 | ||||
| Downside SD | 0.736 | ||||
| N nonnegative terms | 45.000 | ||||
| N negative terms | 916.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 961.000 | ||||
| Mean of predictor | 0.456 | ||||
| Mean of criterion | -0.440 | ||||
| SD of predictor | 0.328 | ||||
| SD of criterion | 1.003 | ||||
| Covariance | -0.048 | ||||
| r | -0.146 | ||||
| b (slope, estimate of beta) | -0.448 | ||||
| a (intercept, estimate of alpha) | -0.236 | ||||
| Mean Square Error | 0.986 | ||||
| DF error | 959.000 | ||||
| t(b) | -4.574 | ||||
| p(b) | 1.000 | ||||
| t(a) | -0.454 | ||||
| p(a) | 0.675 | ||||
| Lowerbound of 95% confidence interval for beta | -0.640 | ||||
| Upperbound of 95% confidence interval for beta | -0.256 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.258 | ||||
| Upperbound of 95% confidence interval for alpha | 0.785 | ||||
| Treynor index (mean / b) | 0.984 | ||||
| Jensen alpha (a) | -0.236 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.098 | ||||
| Expected Shortfall on VaR | 0.121 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.013 | ||||
| Expected Shortfall on VaR | 0.029 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 961.000 | ||||
| Minimum | 0.372 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.696 | ||||
| Mean of quarter 1 | 0.986 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.017 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 51.000 | ||||
| Percentage of outliers low | 0.053 | ||||
| Mean of outliers low | 0.932 | ||||
| Number of outliers high | 45.000 | ||||
| Percentage of outliers high | 0.047 | ||||
| Mean of outliers high | 1.088 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.426 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| 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 | 2.000 | ||||
| Minimum | 0.144 | ||||
| Quartile 1 | 0.311 | ||||
| Median | 0.477 | ||||
| Quartile 3 | 0.644 | ||||
| Maximum | 0.811 | ||||
| Mean of quarter 1 | 0.144 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.811 | ||||
| Inter Quartile Range | 0.334 | ||||
| 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) | -0.209 | ||||
| Compounded annual return (geometric extrapolation) | -0.327 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.403 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.403 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.698 | ||||
| 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 | 0.974 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.469 | ||||
| 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 | 0.862 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.475 | ||||
| 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) | -8744542716987766.000 | ||||
| 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) | 125823673148503942205298272370688.000 | ||||
| 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 | ||||