Advanced Statistics: CityBeatersFX-Income
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 | -0.025 | ||||
| SD | 0.082 | ||||
| Sharpe ratio (Glass type estimate) | -0.307 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.300 | ||||
| df | 35.000 | ||||
| t | -0.532 | ||||
| p | 0.701 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.439 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.829 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.434 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.833 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.654 | ||||
| Upside Potential Ratio | 1.107 | ||||
| Upside part of mean | 0.043 | ||||
| Downside part of mean | -0.068 | ||||
| Upside SD | 0.072 | ||||
| Downside SD | 0.039 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.565 | ||||
| Mean of criterion | -0.025 | ||||
| SD of predictor | 0.268 | ||||
| SD of criterion | 0.082 | ||||
| Covariance | 0.001 | ||||
| r | 0.047 | ||||
| b (slope, estimate of beta) | 0.014 | ||||
| a (intercept, estimate of alpha) | -0.033 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 34.000 | ||||
| t(b) | 0.272 | ||||
| p(b) | 0.394 | ||||
| t(a) | -0.589 | ||||
| p(a) | 0.720 | ||||
| Lowerbound of 95% confidence interval for beta | -0.093 | ||||
| Upperbound of 95% confidence interval for beta | 0.121 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.148 | ||||
| Upperbound of 95% confidence interval for alpha | 0.081 | ||||
| Treynor index (mean / b) | -1.765 | ||||
| Jensen alpha (a) | -0.033 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.028 | ||||
| SD | 0.079 | ||||
| Sharpe ratio (Glass type estimate) | -0.359 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.352 | ||||
| df | 35.000 | ||||
| t | -0.622 | ||||
| p | 0.731 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.492 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.778 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.486 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.783 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.718 | ||||
| Upside Potential Ratio | 1.021 | ||||
| Upside part of mean | 0.040 | ||||
| Downside part of mean | -0.068 | ||||
| Upside SD | 0.067 | ||||
| Downside SD | 0.039 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.519 | ||||
| Mean of criterion | -0.028 | ||||
| SD of predictor | 0.252 | ||||
| SD of criterion | 0.079 | ||||
| Covariance | 0.001 | ||||
| r | 0.053 | ||||
| b (slope, estimate of beta) | 0.017 | ||||
| a (intercept, estimate of alpha) | -0.037 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 34.000 | ||||
| t(b) | 0.312 | ||||
| p(b) | 0.379 | ||||
| t(a) | -0.687 | ||||
| p(a) | 0.752 | ||||
| Lowerbound of 95% confidence interval for beta | -0.092 | ||||
| Upperbound of 95% confidence interval for beta | 0.125 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.146 | ||||
| Upperbound of 95% confidence interval for alpha | 0.072 | ||||
| Treynor index (mean / b) | -1.698 | ||||
| Jensen alpha (a) | -0.037 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.039 | ||||
| Expected Shortfall on VaR | 0.048 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.034 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 36.000 | ||||
| Minimum | 0.948 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.128 | ||||
| Mean of quarter 1 | 0.991 | ||||
| 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 | 0.083 | ||||
| Mean of outliers low | 0.974 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.056 | ||||
| Mean of outliers high | 1.068 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -136.896 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| Extreme Value Index (regression method) | -1.012 | ||||
| VaR(95%) (regression method) | 0.030 | ||||
| Expected Shortfall (regression method) | 0.054 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.077 | ||||
| Quartile 1 | 0.077 | ||||
| Median | 0.077 | ||||
| Quartile 3 | 0.077 | ||||
| Maximum | 0.077 | ||||
| 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) | 0.016 | ||||
| Compounded annual return (geometric extrapolation) | 0.016 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.206 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.332 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.026 | ||||
| SD | 0.067 | ||||
| Sharpe ratio (Glass type estimate) | -0.393 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.393 | ||||
| df | 794.000 | ||||
| t | -0.685 | ||||
| p | 0.753 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.518 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.732 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.518 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.732 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.555 | ||||
| Upside Potential Ratio | 2.627 | ||||
| Upside part of mean | 0.124 | ||||
| Downside part of mean | -0.150 | ||||
| Upside SD | 0.047 | ||||
| Downside SD | 0.047 | ||||
| N nonnegative terms | 35.000 | ||||
| N negative terms | 760.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 795.000 | ||||
| Mean of predictor | 0.596 | ||||
| Mean of criterion | -0.026 | ||||
| SD of predictor | 0.351 | ||||
| SD of criterion | 0.067 | ||||
| Covariance | 0.000 | ||||
| r | 0.015 | ||||
| b (slope, estimate of beta) | 0.003 | ||||
| a (intercept, estimate of alpha) | -0.028 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 793.000 | ||||
| t(b) | 0.414 | ||||
| p(b) | 0.340 | ||||
| t(a) | -0.724 | ||||
| p(a) | 0.765 | ||||
| Lowerbound of 95% confidence interval for beta | -0.010 | ||||
| Upperbound of 95% confidence interval for beta | 0.016 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.103 | ||||
| Upperbound of 95% confidence interval for alpha | 0.048 | ||||
| Treynor index (mean / b) | -9.387 | ||||
| Jensen alpha (a) | -0.028 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.028 | ||||
| SD | 0.067 | ||||
| Sharpe ratio (Glass type estimate) | -0.426 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.426 | ||||
| df | 794.000 | ||||
| t | -0.742 | ||||
| p | 0.771 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.551 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.699 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.551 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.700 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.594 | ||||
| Upside Potential Ratio | 2.569 | ||||
| Upside part of mean | 0.123 | ||||
| Downside part of mean | -0.151 | ||||
| Upside SD | 0.046 | ||||
| Downside SD | 0.048 | ||||
| N nonnegative terms | 35.000 | ||||
| N negative terms | 760.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 795.000 | ||||
| Mean of predictor | 0.534 | ||||
| Mean of criterion | -0.028 | ||||
| SD of predictor | 0.348 | ||||
| SD of criterion | 0.067 | ||||
| Covariance | 0.000 | ||||
| r | 0.015 | ||||
| b (slope, estimate of beta) | 0.003 | ||||
| a (intercept, estimate of alpha) | -0.030 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 793.000 | ||||
| t(b) | 0.427 | ||||
| p(b) | 0.335 | ||||
| t(a) | -0.779 | ||||
| p(a) | 0.782 | ||||
| Lowerbound of 95% confidence interval for beta | -0.010 | ||||
| Upperbound of 95% confidence interval for beta | 0.016 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.105 | ||||
| Upperbound of 95% confidence interval for alpha | 0.046 | ||||
| Treynor index (mean / b) | -9.777 | ||||
| Jensen alpha (a) | -0.030 | ||||
| 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 | 0.009 | ||||
| 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 | 795.000 | ||||
| Minimum | 0.961 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.033 | ||||
| Mean of quarter 1 | 0.998 | ||||
| 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 | 32.000 | ||||
| Percentage of outliers low | 0.040 | ||||
| Mean of outliers low | 0.990 | ||||
| Number of outliers high | 37.000 | ||||
| Percentage of outliers high | 0.047 | ||||
| Mean of outliers high | 1.010 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.134 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | -0.329 | ||||
| VaR(95%) (regression method) | -0.002 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.022 | ||||
| Quartile 1 | 0.036 | ||||
| Median | 0.050 | ||||
| Quartile 3 | 0.099 | ||||
| Maximum | 0.149 | ||||
| Mean of quarter 1 | 0.022 | ||||
| Mean of quarter 2 | 0.050 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.149 | ||||
| Inter Quartile Range | 0.063 | ||||
| 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) | 0.016 | ||||
| Compounded annual return (geometric extrapolation) | 0.016 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.106 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.106 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.836 | ||||
| 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 | 0.980 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.494 | ||||
| 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 | 0.857 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.492 | ||||
| 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) | -8748875976723757.000 | ||||
| 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) | 104186443099774071765874033819648.000 | ||||
| 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 | ||||