Advanced Statistics: fxtrend2
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 | 0.086 | ||||
| SD | 0.287 | ||||
| Sharpe ratio (Glass type estimate) | 0.300 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.296 | ||||
| df | 47.000 | ||||
| t | 0.601 | ||||
| p | 0.275 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.683 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.281 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.686 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.277 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.985 | ||||
| Upside Potential Ratio | 2.086 | ||||
| Upside part of mean | 0.182 | ||||
| Downside part of mean | -0.096 | ||||
| Upside SD | 0.271 | ||||
| Downside SD | 0.087 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 42.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 48.000 | ||||
| Mean of predictor | 0.456 | ||||
| Mean of criterion | 0.086 | ||||
| SD of predictor | 0.280 | ||||
| SD of criterion | 0.287 | ||||
| Covariance | 0.005 | ||||
| r | 0.068 | ||||
| b (slope, estimate of beta) | 0.070 | ||||
| a (intercept, estimate of alpha) | 0.054 | ||||
| Mean Square Error | 0.083 | ||||
| DF error | 46.000 | ||||
| t(b) | 0.466 | ||||
| p(b) | 0.322 | ||||
| t(a) | 0.338 | ||||
| p(a) | 0.368 | ||||
| Lowerbound of 95% confidence interval for beta | -0.233 | ||||
| Upperbound of 95% confidence interval for beta | 0.373 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.268 | ||||
| Upperbound of 95% confidence interval for alpha | 0.376 | ||||
| Treynor index (mean / b) | 1.228 | ||||
| Jensen alpha (a) | 0.054 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.054 | ||||
| SD | 0.239 | ||||
| Sharpe ratio (Glass type estimate) | 0.226 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.223 | ||||
| df | 47.000 | ||||
| t | 0.453 | ||||
| p | 0.326 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.756 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.206 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.758 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.204 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.581 | ||||
| Upside Potential Ratio | 1.653 | ||||
| Upside part of mean | 0.154 | ||||
| Downside part of mean | -0.100 | ||||
| Upside SD | 0.218 | ||||
| Downside SD | 0.093 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 42.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 48.000 | ||||
| Mean of predictor | 0.411 | ||||
| Mean of criterion | 0.054 | ||||
| SD of predictor | 0.266 | ||||
| SD of criterion | 0.239 | ||||
| Covariance | 0.006 | ||||
| r | 0.086 | ||||
| b (slope, estimate of beta) | 0.078 | ||||
| a (intercept, estimate of alpha) | 0.022 | ||||
| Mean Square Error | 0.058 | ||||
| DF error | 46.000 | ||||
| t(b) | 0.588 | ||||
| p(b) | 0.280 | ||||
| t(a) | 0.169 | ||||
| p(a) | 0.433 | ||||
| Lowerbound of 95% confidence interval for beta | -0.188 | ||||
| Upperbound of 95% confidence interval for beta | 0.343 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.244 | ||||
| Upperbound of 95% confidence interval for alpha | 0.288 | ||||
| Treynor index (mean / b) | 0.698 | ||||
| Jensen alpha (a) | 0.022 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.103 | ||||
| Expected Shortfall on VaR | 0.129 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.026 | ||||
| Expected Shortfall on VaR | 0.054 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 48.000 | ||||
| Minimum | 0.855 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.536 | ||||
| Mean of quarter 1 | 0.981 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.063 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.042 | ||||
| Mean of outliers low | 0.885 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.125 | ||||
| Mean of outliers high | 1.125 | ||||
| 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) | -1.537 | ||||
| VaR(95%) (regression method) | 0.056 | ||||
| Expected Shortfall (regression method) | 0.148 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.086 | ||||
| Quartile 1 | 0.100 | ||||
| Median | 0.115 | ||||
| Quartile 3 | 0.130 | ||||
| Maximum | 0.145 | ||||
| Mean of quarter 1 | 0.086 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.145 | ||||
| Inter Quartile Range | 0.030 | ||||
| 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) | 0.120 | ||||
| Compounded annual return (geometric extrapolation) | 0.103 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.713 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.713 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.802 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.279 | ||||
| SD | 0.703 | ||||
| Sharpe ratio (Glass type estimate) | 0.397 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.397 | ||||
| df | 1064.000 | ||||
| t | 0.800 | ||||
| p | 0.488 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.575 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.369 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.576 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.369 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.723 | ||||
| Upside Potential Ratio | 3.219 | ||||
| Upside part of mean | 1.243 | ||||
| Downside part of mean | -0.963 | ||||
| Upside SD | 0.588 | ||||
| Downside SD | 0.386 | ||||
| N nonnegative terms | 75.000 | ||||
| N negative terms | 990.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1065.000 | ||||
| Mean of predictor | 0.474 | ||||
| Mean of criterion | 0.279 | ||||
| SD of predictor | 0.325 | ||||
| SD of criterion | 0.703 | ||||
| Covariance | 0.012 | ||||
| r | 0.053 | ||||
| b (slope, estimate of beta) | 0.114 | ||||
| a (intercept, estimate of alpha) | 0.225 | ||||
| Mean Square Error | 0.494 | ||||
| DF error | 1063.000 | ||||
| t(b) | 1.719 | ||||
| p(b) | 0.466 | ||||
| t(a) | 0.644 | ||||
| p(a) | 0.487 | ||||
| Lowerbound of 95% confidence interval for beta | -0.016 | ||||
| Upperbound of 95% confidence interval for beta | 0.244 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.461 | ||||
| Upperbound of 95% confidence interval for alpha | 0.912 | ||||
| Treynor index (mean / b) | 2.452 | ||||
| Jensen alpha (a) | 0.225 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.053 | ||||
| SD | 0.666 | ||||
| Sharpe ratio (Glass type estimate) | 0.079 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.079 | ||||
| df | 1064.000 | ||||
| t | 0.159 | ||||
| p | 0.498 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.893 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.051 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.893 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.051 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.117 | ||||
| Upside Potential Ratio | 2.454 | ||||
| Upside part of mean | 1.107 | ||||
| Downside part of mean | -1.055 | ||||
| Upside SD | 0.490 | ||||
| Downside SD | 0.451 | ||||
| N nonnegative terms | 75.000 | ||||
| N negative terms | 990.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1065.000 | ||||
| Mean of predictor | 0.420 | ||||
| Mean of criterion | 0.053 | ||||
| SD of predictor | 0.328 | ||||
| SD of criterion | 0.666 | ||||
| Covariance | 0.012 | ||||
| r | 0.053 | ||||
| b (slope, estimate of beta) | 0.108 | ||||
| a (intercept, estimate of alpha) | 0.007 | ||||
| Mean Square Error | 0.443 | ||||
| DF error | 1063.000 | ||||
| t(b) | 1.726 | ||||
| p(b) | 0.466 | ||||
| t(a) | 0.023 | ||||
| p(a) | 0.500 | ||||
| Lowerbound of 95% confidence interval for beta | -0.015 | ||||
| Upperbound of 95% confidence interval for beta | 0.230 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.642 | ||||
| Upperbound of 95% confidence interval for alpha | 0.657 | ||||
| Treynor index (mean / b) | 0.489 | ||||
| Jensen alpha (a) | 0.007 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.065 | ||||
| Expected Shortfall on VaR | 0.081 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.028 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1065.000 | ||||
| Minimum | 0.580 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.686 | ||||
| Mean of quarter 1 | 0.986 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.019 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 70.000 | ||||
| Percentage of outliers low | 0.066 | ||||
| Mean of outliers low | 0.946 | ||||
| Number of outliers high | 75.000 | ||||
| Percentage of outliers high | 0.070 | ||||
| Mean of outliers high | 1.068 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.064 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.004 | ||||
| Extreme Value Index (regression method) | 0.520 | ||||
| VaR(95%) (regression method) | 0.006 | ||||
| Expected Shortfall (regression method) | 0.053 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 17.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.030 | ||||
| Median | 0.033 | ||||
| Quartile 3 | 0.056 | ||||
| Maximum | 0.478 | ||||
| Mean of quarter 1 | 0.015 | ||||
| Mean of quarter 2 | 0.032 | ||||
| Mean of quarter 3 | 0.047 | ||||
| Mean of quarter 4 | 0.287 | ||||
| Inter Quartile Range | 0.026 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.176 | ||||
| Mean of outliers high | 0.354 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.277 | ||||
| VaR(95%) (moments method) | 0.205 | ||||
| Expected Shortfall (moments method) | 0.368 | ||||
| Extreme Value Index (regression method) | -1.107 | ||||
| VaR(95%) (regression method) | 0.280 | ||||
| Expected Shortfall (regression method) | 0.301 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.118 | ||||
| Compounded annual return (geometric extrapolation) | 0.101 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.212 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.354 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.251 | ||||
| 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 | 1.277 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.408 | ||||
| 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 | 1.191 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.409 | ||||
| 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) | -8659930676307547.000 | ||||
| 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) | -64837335633267974422065611538432.000 | ||||
| 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 | ||||