Advanced Statistics: AzureFX
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 | 0.656 | ||||
| SD | 1.724 | ||||
| Sharpe ratio (Glass type estimate) | 0.381 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.373 | ||||
| df | 40.000 | ||||
| t | 0.704 | ||||
| p | 0.243 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.685 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.442 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.690 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.437 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.906 | ||||
| Upside Potential Ratio | 3.037 | ||||
| Upside part of mean | 2.201 | ||||
| Downside part of mean | -1.545 | ||||
| Upside SD | 1.553 | ||||
| Downside SD | 0.725 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 24.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 41.000 | ||||
| Mean of predictor | 0.487 | ||||
| Mean of criterion | 0.656 | ||||
| SD of predictor | 0.298 | ||||
| SD of criterion | 1.724 | ||||
| Covariance | 0.096 | ||||
| r | 0.187 | ||||
| b (slope, estimate of beta) | 1.083 | ||||
| a (intercept, estimate of alpha) | 0.129 | ||||
| Mean Square Error | 2.943 | ||||
| DF error | 39.000 | ||||
| t(b) | 1.190 | ||||
| p(b) | 0.121 | ||||
| t(a) | 0.125 | ||||
| p(a) | 0.451 | ||||
| Lowerbound of 95% confidence interval for beta | -0.758 | ||||
| Upperbound of 95% confidence interval for beta | 2.925 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.952 | ||||
| Upperbound of 95% confidence interval for alpha | 2.209 | ||||
| Treynor index (mean / b) | 0.606 | ||||
| Jensen alpha (a) | 0.129 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.422 | ||||
| SD | 1.456 | ||||
| Sharpe ratio (Glass type estimate) | -0.290 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.284 | ||||
| df | 40.000 | ||||
| t | -0.536 | ||||
| p | 0.702 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.350 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.774 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.346 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.778 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.402 | ||||
| Upside Potential Ratio | 1.464 | ||||
| Upside part of mean | 1.536 | ||||
| Downside part of mean | -1.958 | ||||
| Upside SD | 0.992 | ||||
| Downside SD | 1.049 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 24.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 41.000 | ||||
| Mean of predictor | 0.436 | ||||
| Mean of criterion | -0.422 | ||||
| SD of predictor | 0.287 | ||||
| SD of criterion | 1.456 | ||||
| Covariance | 0.141 | ||||
| r | 0.337 | ||||
| b (slope, estimate of beta) | 1.707 | ||||
| a (intercept, estimate of alpha) | -1.166 | ||||
| Mean Square Error | 1.929 | ||||
| DF error | 39.000 | ||||
| t(b) | 2.234 | ||||
| p(b) | 0.016 | ||||
| t(a) | -1.419 | ||||
| p(a) | 0.918 | ||||
| Lowerbound of 95% confidence interval for beta | 0.162 | ||||
| Upperbound of 95% confidence interval for beta | 3.252 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.828 | ||||
| Upperbound of 95% confidence interval for alpha | 0.496 | ||||
| Treynor index (mean / b) | -0.247 | ||||
| Jensen alpha (a) | -1.166 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.517 | ||||
| Expected Shortfall on VaR | 0.590 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.327 | ||||
| Expected Shortfall on VaR | 0.535 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 41.000 | ||||
| Minimum | 0.242 | ||||
| Quartile 1 | 0.778 | ||||
| Median | 0.966 | ||||
| Quartile 3 | 1.122 | ||||
| Maximum | 2.901 | ||||
| Mean of quarter 1 | 0.657 | ||||
| Mean of quarter 2 | 0.860 | ||||
| Mean of quarter 3 | 1.035 | ||||
| Mean of quarter 4 | 1.721 | ||||
| Inter Quartile Range | 0.344 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.024 | ||||
| Mean of outliers low | 0.242 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.122 | ||||
| Mean of outliers high | 2.183 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.159 | ||||
| VaR(95%) (moments method) | 0.384 | ||||
| Expected Shortfall (moments method) | 0.522 | ||||
| Extreme Value Index (regression method) | 0.856 | ||||
| VaR(95%) (regression method) | 0.336 | ||||
| Expected Shortfall (regression method) | 1.229 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.214 | ||||
| Quartile 1 | 0.394 | ||||
| Median | 0.574 | ||||
| Quartile 3 | 0.754 | ||||
| Maximum | 0.935 | ||||
| Mean of quarter 1 | 0.214 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.935 | ||||
| Inter Quartile Range | 0.360 | ||||
| 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) | -0.212 | ||||
| Compounded annual return (geometric extrapolation) | -0.315 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.337 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.337 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.534 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1014.982 | ||||
| SD | 1878.916 | ||||
| Sharpe ratio (Glass type estimate) | 0.540 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.540 | ||||
| df | 900.000 | ||||
| t | 1.002 | ||||
| p | 0.158 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.517 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.597 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.517 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.597 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 790.350 | ||||
| Upside Potential Ratio | 796.630 | ||||
| Upside part of mean | 1023.047 | ||||
| Downside part of mean | -8.066 | ||||
| Upside SD | 1878.920 | ||||
| Downside SD | 1.284 | ||||
| N nonnegative terms | 412.000 | ||||
| N negative terms | 489.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 901.000 | ||||
| Mean of predictor | 0.490 | ||||
| Mean of criterion | 1014.982 | ||||
| SD of predictor | 0.330 | ||||
| SD of criterion | 1878.916 | ||||
| Covariance | -34.123 | ||||
| r | -0.055 | ||||
| b (slope, estimate of beta) | -313.198 | ||||
| a (intercept, estimate of alpha) | 1168.605 | ||||
| Mean Square Error | 3523554.987 | ||||
| DF error | 899.000 | ||||
| t(b) | -1.652 | ||||
| p(b) | 0.951 | ||||
| t(a) | 1.150 | ||||
| p(a) | 0.125 | ||||
| Lowerbound of 95% confidence interval for beta | -685.237 | ||||
| Upperbound of 95% confidence interval for beta | 58.842 | ||||
| Lowerbound of 95% confidence interval for alpha | -826.366 | ||||
| Upperbound of 95% confidence interval for alpha | 3163.576 | ||||
| Treynor index (mean / b) | -3.241 | ||||
| Jensen alpha (a) | 1168.605 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.420 | ||||
| SD | 6.480 | ||||
| Sharpe ratio (Glass type estimate) | -0.065 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.065 | ||||
| df | 900.000 | ||||
| t | -0.120 | ||||
| p | 0.548 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.122 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.992 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.122 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.992 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.093 | ||||
| Upside Potential Ratio | 2.387 | ||||
| Upside part of mean | 10.748 | ||||
| Downside part of mean | -11.167 | ||||
| Upside SD | 4.656 | ||||
| Downside SD | 4.502 | ||||
| N nonnegative terms | 412.000 | ||||
| N negative terms | 489.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 901.000 | ||||
| Mean of predictor | 0.435 | ||||
| Mean of criterion | -0.420 | ||||
| SD of predictor | 0.331 | ||||
| SD of criterion | 6.480 | ||||
| Covariance | 0.245 | ||||
| r | 0.114 | ||||
| b (slope, estimate of beta) | 2.234 | ||||
| a (intercept, estimate of alpha) | -1.392 | ||||
| Mean Square Error | 41.493 | ||||
| DF error | 899.000 | ||||
| t(b) | 3.448 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.399 | ||||
| p(a) | 0.655 | ||||
| Lowerbound of 95% confidence interval for beta | 0.962 | ||||
| Upperbound of 95% confidence interval for beta | 3.505 | ||||
| Lowerbound of 95% confidence interval for alpha | -8.232 | ||||
| Upperbound of 95% confidence interval for alpha | 5.448 | ||||
| Treynor index (mean / b) | -0.188 | ||||
| Jensen alpha (a) | -1.392 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.483 | ||||
| Expected Shortfall on VaR | 0.558 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.073 | ||||
| Expected Shortfall on VaR | 0.156 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 901.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.964 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.028 | ||||
| Maximum | 3485.333 | ||||
| Mean of quarter 1 | 0.894 | ||||
| Mean of quarter 2 | 0.983 | ||||
| Mean of quarter 3 | 1.010 | ||||
| Mean of quarter 4 | 16.627 | ||||
| Inter Quartile Range | 0.064 | ||||
| Number outliers low | 50.000 | ||||
| Percentage of outliers low | 0.055 | ||||
| Mean of outliers low | 0.755 | ||||
| Number of outliers high | 60.000 | ||||
| Percentage of outliers high | 0.067 | ||||
| Mean of outliers high | 59.418 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.484 | ||||
| VaR(95%) (moments method) | 0.108 | ||||
| Expected Shortfall (moments method) | 0.232 | ||||
| Extreme Value Index (regression method) | 0.403 | ||||
| VaR(95%) (regression method) | 0.092 | ||||
| Expected Shortfall (regression method) | 0.171 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.011 | ||||
| Median | 0.071 | ||||
| Quartile 3 | 0.203 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.032 | ||||
| Mean of quarter 3 | 0.110 | ||||
| Mean of quarter 4 | 0.617 | ||||
| Inter Quartile Range | 0.192 | ||||
| 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 | 0.167 | ||||
| Mean of outliers high | 1.000 | ||||
| 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) | -0.211 | ||||
| Compounded annual return (geometric extrapolation) | -0.313 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.313 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.507 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.561 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 6976.014 | ||||
| SD | 4927.554 | ||||
| Sharpe ratio (Glass type estimate) | 1.416 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.408 | ||||
| df | 130.000 | ||||
| t | 1.001 | ||||
| p | 0.456 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.364 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.190 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.370 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.185 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2814.824 | ||||
| Upside Potential Ratio | 2821.624 | ||||
| Upside part of mean | 6992.866 | ||||
| Downside part of mean | -16.852 | ||||
| Upside SD | 4927.593 | ||||
| Downside SD | 2.478 | ||||
| N nonnegative terms | 51.000 | ||||
| N negative terms | 80.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.071 | ||||
| Mean of criterion | 6976.014 | ||||
| SD of predictor | 0.467 | ||||
| SD of criterion | 4927.554 | ||||
| Covariance | -252.725 | ||||
| r | -0.110 | ||||
| b (slope, estimate of beta) | -1158.338 | ||||
| a (intercept, estimate of alpha) | 8216.048 | ||||
| Mean Square Error | 24174001.771 | ||||
| DF error | 129.000 | ||||
| t(b) | -1.255 | ||||
| p(b) | 0.570 | ||||
| t(a) | 1.170 | ||||
| p(a) | 0.435 | ||||
| Lowerbound of 95% confidence interval for beta | -2984.915 | ||||
| Upperbound of 95% confidence interval for beta | 668.239 | ||||
| Lowerbound of 95% confidence interval for alpha | -5679.446 | ||||
| Upperbound of 95% confidence interval for alpha | 22111.543 | ||||
| Treynor index (mean / b) | -6.022 | ||||
| Jensen alpha (a) | 8216.048 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.264 | ||||
| SD | 16.549 | ||||
| Sharpe ratio (Glass type estimate) | 0.016 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.016 | ||||
| df | 130.000 | ||||
| t | 0.011 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.756 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.788 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.756 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.788 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.023 | ||||
| Upside Potential Ratio | 3.042 | ||||
| Upside part of mean | 34.665 | ||||
| Downside part of mean | -34.401 | ||||
| Upside SD | 11.911 | ||||
| Downside SD | 11.397 | ||||
| N nonnegative terms | 51.000 | ||||
| N negative terms | 80.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.959 | ||||
| Mean of criterion | 0.264 | ||||
| SD of predictor | 0.472 | ||||
| SD of criterion | 16.549 | ||||
| Covariance | 0.893 | ||||
| r | 0.114 | ||||
| b (slope, estimate of beta) | 4.016 | ||||
| a (intercept, estimate of alpha) | -3.587 | ||||
| Mean Square Error | 272.362 | ||||
| DF error | 129.000 | ||||
| t(b) | 1.308 | ||||
| p(b) | 0.427 | ||||
| t(a) | -0.152 | ||||
| p(a) | 0.509 | ||||
| Lowerbound of 95% confidence interval for beta | -2.057 | ||||
| Upperbound of 95% confidence interval for beta | 10.088 | ||||
| Lowerbound of 95% confidence interval for alpha | -50.130 | ||||
| Upperbound of 95% confidence interval for alpha | 42.956 | ||||
| Treynor index (mean / b) | 0.066 | ||||
| Jensen alpha (a) | -3.587 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.814 | ||||
| Expected Shortfall on VaR | 0.871 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.166 | ||||
| Expected Shortfall on VaR | 0.338 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.924 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.087 | ||||
| Maximum | 3485.333 | ||||
| Mean of quarter 1 | 0.775 | ||||
| Mean of quarter 2 | 0.970 | ||||
| Mean of quarter 3 | 1.021 | ||||
| Mean of quarter 4 | 106.933 | ||||
| Inter Quartile Range | 0.162 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.046 | ||||
| Mean of outliers low | 0.448 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.069 | ||||
| Mean of outliers high | 389.004 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.322 | ||||
| VaR(95%) (moments method) | 0.214 | ||||
| Expected Shortfall (moments method) | 0.377 | ||||
| Extreme Value Index (regression method) | 0.290 | ||||
| VaR(95%) (regression method) | 0.190 | ||||
| Expected Shortfall (regression method) | 0.316 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.058 | ||||
| Quartile 1 | 0.084 | ||||
| Median | 0.110 | ||||
| Quartile 3 | 0.555 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.058 | ||||
| Mean of quarter 2 | 0.110 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.471 | ||||
| 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) | 0.333 | ||||
| Compounded annual return (geometric extrapolation) | 0.360 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.360 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.360 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.414 | ||||