Advanced Statistics: FFX Limited
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 | 0.019 | ||||
| SD | 0.067 | ||||
| Sharpe ratio (Glass type estimate) | 0.283 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.277 | ||||
| df | 34.000 | ||||
| t | 0.484 | ||||
| p | 0.316 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.868 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.431 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.872 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.427 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.015 | ||||
| Upside Potential Ratio | 3.545 | ||||
| Upside part of mean | 0.066 | ||||
| Downside part of mean | -0.047 | ||||
| Upside SD | 0.063 | ||||
| Downside SD | 0.019 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 35.000 | ||||
| Mean of predictor | 0.556 | ||||
| Mean of criterion | 0.019 | ||||
| SD of predictor | 0.309 | ||||
| SD of criterion | 0.067 | ||||
| Covariance | -0.003 | ||||
| r | -0.161 | ||||
| b (slope, estimate of beta) | -0.035 | ||||
| a (intercept, estimate of alpha) | 0.038 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 33.000 | ||||
| t(b) | -0.936 | ||||
| p(b) | 0.822 | ||||
| t(a) | 0.864 | ||||
| p(a) | 0.197 | ||||
| Lowerbound of 95% confidence interval for beta | -0.110 | ||||
| Upperbound of 95% confidence interval for beta | 0.041 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.052 | ||||
| Upperbound of 95% confidence interval for alpha | 0.128 | ||||
| Treynor index (mean / b) | -0.544 | ||||
| Jensen alpha (a) | 0.038 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.017 | ||||
| SD | 0.065 | ||||
| Sharpe ratio (Glass type estimate) | 0.259 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.253 | ||||
| df | 34.000 | ||||
| t | 0.442 | ||||
| p | 0.331 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.892 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.406 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.896 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.402 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.896 | ||||
| Upside Potential Ratio | 3.416 | ||||
| Upside part of mean | 0.064 | ||||
| Downside part of mean | -0.047 | ||||
| Upside SD | 0.061 | ||||
| Downside SD | 0.019 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 35.000 | ||||
| Mean of predictor | 0.501 | ||||
| Mean of criterion | 0.017 | ||||
| SD of predictor | 0.287 | ||||
| SD of criterion | 0.065 | ||||
| Covariance | -0.003 | ||||
| r | -0.159 | ||||
| b (slope, estimate of beta) | -0.036 | ||||
| a (intercept, estimate of alpha) | 0.035 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 33.000 | ||||
| t(b) | -0.927 | ||||
| p(b) | 0.820 | ||||
| t(a) | 0.815 | ||||
| p(a) | 0.210 | ||||
| Lowerbound of 95% confidence interval for beta | -0.115 | ||||
| Upperbound of 95% confidence interval for beta | 0.043 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.052 | ||||
| Upperbound of 95% confidence interval for alpha | 0.121 | ||||
| Treynor index (mean / b) | -0.466 | ||||
| Jensen alpha (a) | 0.035 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.029 | ||||
| Expected Shortfall on VaR | 0.036 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.014 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 35.000 | ||||
| Minimum | 0.980 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.068 | ||||
| Mean of quarter 1 | 0.997 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.023 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.057 | ||||
| Mean of outliers low | 0.988 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.114 | ||||
| Mean of outliers high | 1.052 | ||||
| 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) | 1.531 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.007 | ||||
| Median | 0.012 | ||||
| Quartile 3 | 0.016 | ||||
| Maximum | 0.020 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.020 | ||||
| Inter Quartile Range | 0.009 | ||||
| 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) | 0.066 | ||||
| Compounded annual return (geometric extrapolation) | 0.063 | ||||
| Calmar ratio (compounded annual return / max draw down) | 3.096 | ||||
| Compounded annual return / average of 25% largest draw downs | 3.096 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.722 | ||||
| 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 | 0.062 | ||||
| Sharpe ratio (Glass type estimate) | 0.279 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.279 | ||||
| df | 779.000 | ||||
| t | 0.482 | ||||
| p | 0.315 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.857 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.415 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.857 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.415 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.446 | ||||
| Upside Potential Ratio | 4.365 | ||||
| Upside part of mean | 0.170 | ||||
| Downside part of mean | -0.153 | ||||
| Upside SD | 0.049 | ||||
| Downside SD | 0.039 | ||||
| N nonnegative terms | 63.000 | ||||
| N negative terms | 717.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 780.000 | ||||
| Mean of predictor | 0.594 | ||||
| Mean of criterion | 0.017 | ||||
| SD of predictor | 0.354 | ||||
| SD of criterion | 0.062 | ||||
| Covariance | -0.000 | ||||
| r | -0.014 | ||||
| b (slope, estimate of beta) | -0.002 | ||||
| a (intercept, estimate of alpha) | 0.019 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 778.000 | ||||
| t(b) | -0.394 | ||||
| p(b) | 0.653 | ||||
| t(a) | 0.519 | ||||
| p(a) | 0.302 | ||||
| Lowerbound of 95% confidence interval for beta | -0.015 | ||||
| Upperbound of 95% confidence interval for beta | 0.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.053 | ||||
| Upperbound of 95% confidence interval for alpha | 0.090 | ||||
| Treynor index (mean / b) | -7.005 | ||||
| Jensen alpha (a) | 0.019 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.015 | ||||
| SD | 0.062 | ||||
| Sharpe ratio (Glass type estimate) | 0.248 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.248 | ||||
| df | 779.000 | ||||
| t | 0.429 | ||||
| p | 0.334 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.888 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.384 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.888 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.384 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.393 | ||||
| Upside Potential Ratio | 4.292 | ||||
| Upside part of mean | 0.169 | ||||
| Downside part of mean | -0.154 | ||||
| Upside SD | 0.048 | ||||
| Downside SD | 0.039 | ||||
| N nonnegative terms | 63.000 | ||||
| N negative terms | 717.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 780.000 | ||||
| Mean of predictor | 0.532 | ||||
| Mean of criterion | 0.015 | ||||
| SD of predictor | 0.351 | ||||
| SD of criterion | 0.062 | ||||
| Covariance | -0.000 | ||||
| r | -0.014 | ||||
| b (slope, estimate of beta) | -0.002 | ||||
| a (intercept, estimate of alpha) | 0.017 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 778.000 | ||||
| t(b) | -0.382 | ||||
| p(b) | 0.649 | ||||
| t(a) | 0.462 | ||||
| p(a) | 0.322 | ||||
| Lowerbound of 95% confidence interval for beta | -0.015 | ||||
| Upperbound of 95% confidence interval for beta | 0.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.054 | ||||
| Upperbound of 95% confidence interval for alpha | 0.088 | ||||
| Treynor index (mean / b) | -6.372 | ||||
| Jensen alpha (a) | 0.017 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.006 | ||||
| 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 | 780.000 | ||||
| Minimum | 0.965 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.027 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.003 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 50.000 | ||||
| Percentage of outliers low | 0.064 | ||||
| Mean of outliers low | 0.993 | ||||
| Number of outliers high | 63.000 | ||||
| Percentage of outliers high | 0.081 | ||||
| Mean of outliers high | 1.008 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.050 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| Extreme Value Index (regression method) | 0.156 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | 0.005 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.007 | ||||
| Median | 0.016 | ||||
| Quartile 3 | 0.034 | ||||
| Maximum | 0.063 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.012 | ||||
| Mean of quarter 3 | 0.018 | ||||
| Mean of quarter 4 | 0.051 | ||||
| Inter Quartile Range | 0.027 | ||||
| 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) | -7.040 | ||||
| VaR(95%) (moments method) | 0.056 | ||||
| Expected Shortfall (moments method) | 0.056 | ||||
| Extreme Value Index (regression method) | -1.225 | ||||
| VaR(95%) (regression method) | 0.069 | ||||
| Expected Shortfall (regression method) | 0.072 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.065 | ||||
| Compounded annual return (geometric extrapolation) | 0.061 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.978 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.206 | ||||
| Compounded annual return / Expected Shortfall lognormal | 7.808 | ||||
| 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 | 1.033 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.449 | ||||
| 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 | 0.931 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.451 | ||||
| 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) | -8728594788494403.000 | ||||
| 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) | -79758600044065281001972836597760.000 | ||||
| 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 | ||||