Advanced Statistics: FX investment
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 | -0.161 | ||||
| SD | 0.213 | ||||
| Sharpe ratio (Glass type estimate) | -0.758 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.750 | ||||
| df | 70.000 | ||||
| t | -1.845 | ||||
| p | 0.965 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.571 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.060 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.566 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.065 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.747 | ||||
| Upside Potential Ratio | 0.022 | ||||
| Upside part of mean | 0.005 | ||||
| Downside part of mean | -0.166 | ||||
| Upside SD | 0.012 | ||||
| Downside SD | 0.216 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 70.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 71.000 | ||||
| Mean of predictor | 0.168 | ||||
| Mean of criterion | -0.161 | ||||
| SD of predictor | 0.291 | ||||
| SD of criterion | 0.213 | ||||
| Covariance | -0.000 | ||||
| r | -0.008 | ||||
| b (slope, estimate of beta) | -0.006 | ||||
| a (intercept, estimate of alpha) | -0.160 | ||||
| Mean Square Error | 0.046 | ||||
| DF error | 69.000 | ||||
| t(b) | -0.063 | ||||
| p(b) | 0.525 | ||||
| t(a) | -1.796 | ||||
| p(a) | 0.962 | ||||
| Lowerbound of 95% confidence interval for beta | -0.181 | ||||
| Upperbound of 95% confidence interval for beta | 0.170 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.339 | ||||
| Upperbound of 95% confidence interval for alpha | 0.018 | ||||
| Treynor index (mean / b) | 28.968 | ||||
| Jensen alpha (a) | -0.160 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.192 | ||||
| SD | 0.268 | ||||
| Sharpe ratio (Glass type estimate) | -0.718 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.711 | ||||
| df | 70.000 | ||||
| t | -1.748 | ||||
| p | 0.958 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.530 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.099 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.525 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.104 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.709 | ||||
| Upside Potential Ratio | 0.017 | ||||
| Upside part of mean | 0.005 | ||||
| Downside part of mean | -0.197 | ||||
| Upside SD | 0.011 | ||||
| Downside SD | 0.271 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 70.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 71.000 | ||||
| Mean of predictor | 0.124 | ||||
| Mean of criterion | -0.192 | ||||
| SD of predictor | 0.299 | ||||
| SD of criterion | 0.268 | ||||
| Covariance | -0.001 | ||||
| r | -0.011 | ||||
| b (slope, estimate of beta) | -0.010 | ||||
| a (intercept, estimate of alpha) | -0.191 | ||||
| Mean Square Error | 0.073 | ||||
| DF error | 69.000 | ||||
| t(b) | -0.094 | ||||
| p(b) | 0.537 | ||||
| t(a) | -1.712 | ||||
| p(a) | 0.954 | ||||
| Lowerbound of 95% confidence interval for beta | -0.225 | ||||
| Upperbound of 95% confidence interval for beta | 0.205 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.414 | ||||
| Upperbound of 95% confidence interval for alpha | 0.032 | ||||
| Treynor index (mean / b) | 18.968 | ||||
| Jensen alpha (a) | -0.191 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.133 | ||||
| Expected Shortfall on VaR | 0.161 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.048 | ||||
| Expected Shortfall on VaR | 0.105 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 71.000 | ||||
| Minimum | 0.584 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.032 | ||||
| Mean of quarter 1 | 0.960 | ||||
| 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 | 3.000 | ||||
| Percentage of outliers low | 0.042 | ||||
| Mean of outliers low | 0.758 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.042 | ||||
| Mean of outliers high | 1.011 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1721.316 | ||||
| VaR(95%) (moments method) | -inf | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -2.574 | ||||
| VaR(95%) (regression method) | -0.411 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.598 | ||||
| Quartile 1 | 0.598 | ||||
| Median | 0.598 | ||||
| Quartile 3 | 0.598 | ||||
| Maximum | 0.598 | ||||
| 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) | -0.099 | ||||
| Compounded annual return (geometric extrapolation) | -0.138 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.231 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.858 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.169 | ||||
| SD | 0.196 | ||||
| Sharpe ratio (Glass type estimate) | -0.863 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.862 | ||||
| df | 1557.000 | ||||
| t | -2.104 | ||||
| p | 0.534 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.667 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.058 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.667 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.058 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.931 | ||||
| Upside Potential Ratio | 0.337 | ||||
| Upside part of mean | 0.061 | ||||
| Downside part of mean | -0.231 | ||||
| Upside SD | 0.074 | ||||
| Downside SD | 0.182 | ||||
| N nonnegative terms | 18.000 | ||||
| N negative terms | 1540.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1558.000 | ||||
| Mean of predictor | 0.373 | ||||
| Mean of criterion | -0.169 | ||||
| SD of predictor | 0.615 | ||||
| SD of criterion | 0.196 | ||||
| Covariance | -0.001 | ||||
| r | -0.007 | ||||
| b (slope, estimate of beta) | -0.002 | ||||
| a (intercept, estimate of alpha) | -0.168 | ||||
| Mean Square Error | 0.039 | ||||
| DF error | 1556.000 | ||||
| t(b) | -0.291 | ||||
| p(b) | 0.504 | ||||
| t(a) | -2.091 | ||||
| p(a) | 0.526 | ||||
| Lowerbound of 95% confidence interval for beta | -0.018 | ||||
| Upperbound of 95% confidence interval for beta | 0.014 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.327 | ||||
| Upperbound of 95% confidence interval for alpha | -0.010 | ||||
| Treynor index (mean / b) | 71.896 | ||||
| Jensen alpha (a) | -0.168 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.192 | ||||
| SD | 0.219 | ||||
| Sharpe ratio (Glass type estimate) | -0.877 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.876 | ||||
| df | 1557.000 | ||||
| t | -2.138 | ||||
| p | 0.534 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.681 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.072 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.681 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.072 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.924 | ||||
| Upside Potential Ratio | 0.283 | ||||
| Upside part of mean | 0.059 | ||||
| Downside part of mean | -0.250 | ||||
| Upside SD | 0.070 | ||||
| Downside SD | 0.207 | ||||
| N nonnegative terms | 18.000 | ||||
| N negative terms | 1540.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1558.000 | ||||
| Mean of predictor | 0.188 | ||||
| Mean of criterion | -0.192 | ||||
| SD of predictor | 0.607 | ||||
| SD of criterion | 0.219 | ||||
| Covariance | -0.001 | ||||
| r | -0.009 | ||||
| b (slope, estimate of beta) | -0.003 | ||||
| a (intercept, estimate of alpha) | -0.191 | ||||
| Mean Square Error | 0.048 | ||||
| DF error | 1556.000 | ||||
| t(b) | -0.336 | ||||
| p(b) | 0.504 | ||||
| t(a) | -2.130 | ||||
| p(a) | 0.527 | ||||
| Lowerbound of 95% confidence interval for beta | -0.021 | ||||
| Upperbound of 95% confidence interval for beta | 0.015 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.367 | ||||
| Upperbound of 95% confidence interval for alpha | -0.015 | ||||
| Treynor index (mean / b) | 62.450 | ||||
| Jensen alpha (a) | -0.191 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.023 | ||||
| Expected Shortfall on VaR | 0.028 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1558.000 | ||||
| Minimum | 0.731 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.157 | ||||
| Mean of quarter 1 | 0.997 | ||||
| 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 | 44.000 | ||||
| Percentage of outliers low | 0.028 | ||||
| Mean of outliers low | 0.975 | ||||
| Number of outliers high | 45.000 | ||||
| Percentage of outliers high | 0.029 | ||||
| Mean of outliers high | 1.008 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.664 | ||||
| VaR(95%) (moments method) | -0.019 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.337 | ||||
| VaR(95%) (regression method) | -0.026 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.061 | ||||
| Quartile 1 | 0.209 | ||||
| Median | 0.356 | ||||
| Quartile 3 | 0.504 | ||||
| Maximum | 0.652 | ||||
| Mean of quarter 1 | 0.061 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.652 | ||||
| Inter Quartile Range | 0.295 | ||||
| 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) | -0.098 | ||||
| Compounded annual return (geometric extrapolation) | -0.137 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.211 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.211 | ||||
| Compounded annual return / Expected Shortfall lognormal | -4.871 | ||||
| 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 | 1.682 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.693 | ||||
| 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 | 1.446 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.679 | ||||
| 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) | -8724123480343123.000 | ||||
| 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) | -279062905064392683419413493317632.000 | ||||
| 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 | ||||