Advanced Statistics: Delta FX Cross
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 | -0.108 | ||||
| SD | 0.072 | ||||
| Sharpe ratio (Glass type estimate) | -1.489 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.470 | ||||
| df | 57.000 | ||||
| t | -3.274 | ||||
| p | 0.999 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.416 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.551 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.401 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.538 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.386 | ||||
| Upside Potential Ratio | 0.047 | ||||
| Upside part of mean | 0.004 | ||||
| Downside part of mean | -0.111 | ||||
| Upside SD | 0.008 | ||||
| Downside SD | 0.078 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 57.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 58.000 | ||||
| Mean of predictor | 0.385 | ||||
| Mean of criterion | -0.108 | ||||
| SD of predictor | 0.326 | ||||
| SD of criterion | 0.072 | ||||
| Covariance | 0.003 | ||||
| r | 0.109 | ||||
| b (slope, estimate of beta) | 0.024 | ||||
| a (intercept, estimate of alpha) | -0.117 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 56.000 | ||||
| t(b) | 0.818 | ||||
| p(b) | 0.208 | ||||
| t(a) | -3.353 | ||||
| p(a) | 0.999 | ||||
| Lowerbound of 95% confidence interval for beta | -0.035 | ||||
| Upperbound of 95% confidence interval for beta | 0.083 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.187 | ||||
| Upperbound of 95% confidence interval for alpha | -0.047 | ||||
| Treynor index (mean / b) | -4.464 | ||||
| Jensen alpha (a) | -0.117 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.110 | ||||
| SD | 0.076 | ||||
| Sharpe ratio (Glass type estimate) | -1.445 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.426 | ||||
| df | 57.000 | ||||
| t | -3.176 | ||||
| p | 0.999 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.369 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.509 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.355 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.496 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.349 | ||||
| Upside Potential Ratio | 0.044 | ||||
| Upside part of mean | 0.004 | ||||
| Downside part of mean | -0.114 | ||||
| Upside SD | 0.008 | ||||
| Downside SD | 0.082 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 57.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 58.000 | ||||
| Mean of predictor | 0.332 | ||||
| Mean of criterion | -0.110 | ||||
| SD of predictor | 0.302 | ||||
| SD of criterion | 0.076 | ||||
| Covariance | 0.002 | ||||
| r | 0.108 | ||||
| b (slope, estimate of beta) | 0.027 | ||||
| a (intercept, estimate of alpha) | -0.119 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 56.000 | ||||
| t(b) | 0.813 | ||||
| p(b) | 0.210 | ||||
| t(a) | -3.263 | ||||
| p(a) | 0.999 | ||||
| Lowerbound of 95% confidence interval for beta | -0.040 | ||||
| Upperbound of 95% confidence interval for beta | 0.095 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.193 | ||||
| Upperbound of 95% confidence interval for alpha | -0.046 | ||||
| Treynor index (mean / b) | -4.036 | ||||
| Jensen alpha (a) | -0.119 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.044 | ||||
| Expected Shortfall on VaR | 0.053 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.032 | ||||
| Expected Shortfall on VaR | 0.062 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 58.000 | ||||
| Minimum | 0.865 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.021 | ||||
| Mean of quarter 1 | 0.978 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.001 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 10.000 | ||||
| Percentage of outliers low | 0.172 | ||||
| Mean of outliers low | 0.967 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.052 | ||||
| Mean of outliers high | 1.007 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -9.686 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| Extreme Value Index (regression method) | -0.110 | ||||
| VaR(95%) (regression method) | 0.036 | ||||
| Expected Shortfall (regression method) | 0.068 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.275 | ||||
| Quartile 1 | 0.275 | ||||
| Median | 0.275 | ||||
| Quartile 3 | 0.275 | ||||
| Maximum | 0.275 | ||||
| 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) | -0.057 | ||||
| Compounded annual return (geometric extrapolation) | -0.064 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.234 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.207 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.108 | ||||
| SD | 0.054 | ||||
| Sharpe ratio (Glass type estimate) | -1.991 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.990 | ||||
| df | 1280.000 | ||||
| t | -4.402 | ||||
| p | 0.561 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.880 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.101 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.880 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.100 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.404 | ||||
| Upside Potential Ratio | 1.097 | ||||
| Upside part of mean | 0.049 | ||||
| Downside part of mean | -0.158 | ||||
| Upside SD | 0.031 | ||||
| Downside SD | 0.045 | ||||
| N nonnegative terms | 32.000 | ||||
| N negative terms | 1249.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1281.000 | ||||
| Mean of predictor | 0.397 | ||||
| Mean of criterion | -0.108 | ||||
| SD of predictor | 0.326 | ||||
| SD of criterion | 0.054 | ||||
| Covariance | 0.001 | ||||
| r | 0.035 | ||||
| b (slope, estimate of beta) | 0.006 | ||||
| a (intercept, estimate of alpha) | -0.111 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 1279.000 | ||||
| t(b) | 1.267 | ||||
| p(b) | 0.477 | ||||
| t(a) | -4.486 | ||||
| p(a) | 0.579 | ||||
| Lowerbound of 95% confidence interval for beta | -0.003 | ||||
| Upperbound of 95% confidence interval for beta | 0.015 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.159 | ||||
| Upperbound of 95% confidence interval for alpha | -0.062 | ||||
| Treynor index (mean / b) | -18.320 | ||||
| Jensen alpha (a) | -0.111 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.110 | ||||
| SD | 0.055 | ||||
| Sharpe ratio (Glass type estimate) | -2.012 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.011 | ||||
| df | 1280.000 | ||||
| t | -4.448 | ||||
| p | 0.562 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.901 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.122 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.900 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.121 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.411 | ||||
| Upside Potential Ratio | 1.074 | ||||
| Upside part of mean | 0.049 | ||||
| Downside part of mean | -0.159 | ||||
| Upside SD | 0.031 | ||||
| Downside SD | 0.045 | ||||
| N nonnegative terms | 32.000 | ||||
| N negative terms | 1249.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1281.000 | ||||
| Mean of predictor | 0.343 | ||||
| Mean of criterion | -0.110 | ||||
| SD of predictor | 0.325 | ||||
| SD of criterion | 0.055 | ||||
| Covariance | 0.001 | ||||
| r | 0.035 | ||||
| b (slope, estimate of beta) | 0.006 | ||||
| a (intercept, estimate of alpha) | -0.112 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 1279.000 | ||||
| t(b) | 1.242 | ||||
| p(b) | 0.478 | ||||
| t(a) | -4.521 | ||||
| p(a) | 0.580 | ||||
| Lowerbound of 95% confidence interval for beta | -0.003 | ||||
| Upperbound of 95% confidence interval for beta | 0.015 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.160 | ||||
| Upperbound of 95% confidence interval for alpha | -0.063 | ||||
| Treynor index (mean / b) | -18.854 | ||||
| Jensen alpha (a) | -0.112 | ||||
| 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 | 0.007 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1281.000 | ||||
| Minimum | 0.971 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.030 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.001 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 76.000 | ||||
| Percentage of outliers low | 0.059 | ||||
| Mean of outliers low | 0.993 | ||||
| Number of outliers high | 51.000 | ||||
| Percentage of outliers high | 0.040 | ||||
| Mean of outliers high | 1.005 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -3.376 | ||||
| VaR(95%) (moments method) | -0.004 | ||||
| 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 | 2.000 | ||||
| Minimum | 0.029 | ||||
| Quartile 1 | 0.099 | ||||
| Median | 0.168 | ||||
| Quartile 3 | 0.237 | ||||
| Maximum | 0.306 | ||||
| Mean of quarter 1 | 0.029 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.306 | ||||
| Inter Quartile Range | 0.138 | ||||
| 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) | -0.056 | ||||
| Compounded annual return (geometric extrapolation) | -0.064 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.207 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.207 | ||||
| Compounded annual return / Expected Shortfall lognormal | -8.659 | ||||
| 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 | 0.990 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.388 | ||||
| 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 | 0.913 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.389 | ||||
| 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) | -8707761857846692.000 | ||||
| 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) | 2190851633026424330861054728863744.000 | ||||
| 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 | ||||