Advanced Statistics: FUREX Blue
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 | -0.062 | ||||
| SD | 0.181 | ||||
| Sharpe ratio (Glass type estimate) | -0.343 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.339 | ||||
| df | 57.000 | ||||
| t | -0.755 | ||||
| p | 0.773 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.236 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.552 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.232 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.555 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.492 | ||||
| Upside Potential Ratio | 1.006 | ||||
| Upside part of mean | 0.127 | ||||
| Downside part of mean | -0.189 | ||||
| Upside SD | 0.129 | ||||
| Downside SD | 0.126 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 50.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 58.000 | ||||
| Mean of predictor | 0.371 | ||||
| Mean of criterion | -0.062 | ||||
| SD of predictor | 0.271 | ||||
| SD of criterion | 0.181 | ||||
| Covariance | -0.001 | ||||
| r | -0.020 | ||||
| b (slope, estimate of beta) | -0.013 | ||||
| a (intercept, estimate of alpha) | -0.057 | ||||
| Mean Square Error | 0.033 | ||||
| DF error | 56.000 | ||||
| t(b) | -0.149 | ||||
| p(b) | 0.559 | ||||
| t(a) | -0.640 | ||||
| p(a) | 0.738 | ||||
| Lowerbound of 95% confidence interval for beta | -0.192 | ||||
| Upperbound of 95% confidence interval for beta | 0.165 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.236 | ||||
| Upperbound of 95% confidence interval for alpha | 0.122 | ||||
| Treynor index (mean / b) | 4.674 | ||||
| Jensen alpha (a) | -0.057 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.078 | ||||
| SD | 0.178 | ||||
| Sharpe ratio (Glass type estimate) | -0.436 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.430 | ||||
| df | 57.000 | ||||
| t | -0.958 | ||||
| p | 0.829 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.329 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.461 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.325 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.465 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.581 | ||||
| Upside Potential Ratio | 0.889 | ||||
| Upside part of mean | 0.119 | ||||
| Downside part of mean | -0.197 | ||||
| Upside SD | 0.118 | ||||
| Downside SD | 0.134 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 50.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 58.000 | ||||
| Mean of predictor | 0.331 | ||||
| Mean of criterion | -0.078 | ||||
| SD of predictor | 0.260 | ||||
| SD of criterion | 0.178 | ||||
| Covariance | -0.001 | ||||
| r | -0.019 | ||||
| b (slope, estimate of beta) | -0.013 | ||||
| a (intercept, estimate of alpha) | -0.073 | ||||
| Mean Square Error | 0.032 | ||||
| DF error | 56.000 | ||||
| t(b) | -0.144 | ||||
| p(b) | 0.557 | ||||
| t(a) | -0.841 | ||||
| p(a) | 0.798 | ||||
| Lowerbound of 95% confidence interval for beta | -0.197 | ||||
| Upperbound of 95% confidence interval for beta | 0.171 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.248 | ||||
| Upperbound of 95% confidence interval for alpha | 0.102 | ||||
| Treynor index (mean / b) | 5.891 | ||||
| Jensen alpha (a) | -0.073 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.087 | ||||
| Expected Shortfall on VaR | 0.106 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.050 | ||||
| Expected Shortfall on VaR | 0.097 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 58.000 | ||||
| Minimum | 0.838 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.240 | ||||
| Mean of quarter 1 | 0.951 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.043 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 10.000 | ||||
| Percentage of outliers low | 0.172 | ||||
| Mean of outliers low | 0.927 | ||||
| Number of outliers high | 8.000 | ||||
| Percentage of outliers high | 0.138 | ||||
| Mean of outliers high | 1.080 | ||||
| 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) | -0.402 | ||||
| VaR(95%) (regression method) | 0.068 | ||||
| Expected Shortfall (regression method) | 0.096 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.088 | ||||
| Quartile 1 | 0.166 | ||||
| Median | 0.244 | ||||
| Quartile 3 | 0.321 | ||||
| Maximum | 0.399 | ||||
| Mean of quarter 1 | 0.088 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.399 | ||||
| Inter Quartile Range | 0.156 | ||||
| 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) | -0.031 | ||||
| Compounded annual return (geometric extrapolation) | -0.033 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.083 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.083 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.312 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.040 | ||||
| SD | 0.276 | ||||
| Sharpe ratio (Glass type estimate) | -0.147 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.147 | ||||
| df | 1275.000 | ||||
| t | -0.324 | ||||
| p | 0.506 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.035 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.742 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.035 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.742 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.242 | ||||
| Upside Potential Ratio | 4.245 | ||||
| Upside part of mean | 0.709 | ||||
| Downside part of mean | -0.750 | ||||
| Upside SD | 0.219 | ||||
| Downside SD | 0.167 | ||||
| N nonnegative terms | 156.000 | ||||
| N negative terms | 1120.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1276.000 | ||||
| Mean of predictor | 0.408 | ||||
| Mean of criterion | -0.040 | ||||
| SD of predictor | 0.322 | ||||
| SD of criterion | 0.276 | ||||
| Covariance | -0.001 | ||||
| r | -0.017 | ||||
| b (slope, estimate of beta) | -0.014 | ||||
| a (intercept, estimate of alpha) | -0.035 | ||||
| Mean Square Error | 0.076 | ||||
| DF error | 1274.000 | ||||
| t(b) | -0.595 | ||||
| p(b) | 0.508 | ||||
| t(a) | -0.276 | ||||
| p(a) | 0.504 | ||||
| Lowerbound of 95% confidence interval for beta | -0.061 | ||||
| Upperbound of 95% confidence interval for beta | 0.033 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.281 | ||||
| Upperbound of 95% confidence interval for alpha | 0.211 | ||||
| Treynor index (mean / b) | 2.836 | ||||
| Jensen alpha (a) | -0.035 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.078 | ||||
| SD | 0.271 | ||||
| Sharpe ratio (Glass type estimate) | -0.286 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.286 | ||||
| df | 1275.000 | ||||
| t | -0.631 | ||||
| p | 0.511 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.174 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.602 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.174 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.602 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.447 | ||||
| Upside Potential Ratio | 3.962 | ||||
| Upside part of mean | 0.687 | ||||
| Downside part of mean | -0.764 | ||||
| Upside SD | 0.208 | ||||
| Downside SD | 0.173 | ||||
| N nonnegative terms | 156.000 | ||||
| N negative terms | 1120.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1276.000 | ||||
| Mean of predictor | 0.356 | ||||
| Mean of criterion | -0.078 | ||||
| SD of predictor | 0.323 | ||||
| SD of criterion | 0.271 | ||||
| Covariance | -0.001 | ||||
| r | -0.017 | ||||
| b (slope, estimate of beta) | -0.014 | ||||
| a (intercept, estimate of alpha) | -0.072 | ||||
| Mean Square Error | 0.073 | ||||
| DF error | 1274.000 | ||||
| t(b) | -0.606 | ||||
| p(b) | 0.508 | ||||
| t(a) | -0.589 | ||||
| p(a) | 0.508 | ||||
| Lowerbound of 95% confidence interval for beta | -0.060 | ||||
| Upperbound of 95% confidence interval for beta | 0.032 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.314 | ||||
| Upperbound of 95% confidence interval for alpha | 0.169 | ||||
| Treynor index (mean / b) | 5.450 | ||||
| Jensen alpha (a) | -0.072 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.027 | ||||
| Expected Shortfall on VaR | 0.034 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.020 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1276.000 | ||||
| Minimum | 0.882 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.180 | ||||
| Mean of quarter 1 | 0.989 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.011 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 210.000 | ||||
| Percentage of outliers low | 0.165 | ||||
| Mean of outliers low | 0.984 | ||||
| Number of outliers high | 160.000 | ||||
| Percentage of outliers high | 0.125 | ||||
| Mean of outliers high | 1.022 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.620 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.005 | ||||
| Extreme Value Index (regression method) | 0.029 | ||||
| VaR(95%) (regression method) | 0.010 | ||||
| Expected Shortfall (regression method) | 0.019 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.008 | ||||
| Quartile 1 | 0.091 | ||||
| Median | 0.123 | ||||
| Quartile 3 | 0.210 | ||||
| Maximum | 0.456 | ||||
| Mean of quarter 1 | 0.008 | ||||
| Mean of quarter 2 | 0.118 | ||||
| Mean of quarter 3 | 0.128 | ||||
| Mean of quarter 4 | 0.456 | ||||
| Inter Quartile Range | 0.120 | ||||
| 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 | 0.250 | ||||
| Mean of outliers high | 0.456 | ||||
| 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) | -0.031 | ||||
| Compounded annual return (geometric extrapolation) | -0.033 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.072 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.072 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.963 | ||||
| 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 | 1.022 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.390 | ||||
| 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 | 0.944 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.391 | ||||
| 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) | -8702939358641660.000 | ||||
| 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) | -80855647968571594712538352189440.000 | ||||
| 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 | ||||