Advanced Statistics: Bodhi Forex
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 | 0.040 | ||||
| SD | 0.194 | ||||
| Sharpe ratio (Glass type estimate) | 0.209 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.205 | ||||
| df | 39.000 | ||||
| t | 0.381 | ||||
| p | 0.353 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.867 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.282 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.870 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.279 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.460 | ||||
| Upside Potential Ratio | 2.011 | ||||
| Upside part of mean | 0.177 | ||||
| Downside part of mean | -0.136 | ||||
| Upside SD | 0.171 | ||||
| Downside SD | 0.088 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 40.000 | ||||
| Mean of predictor | 0.441 | ||||
| Mean of criterion | 0.040 | ||||
| SD of predictor | 0.240 | ||||
| SD of criterion | 0.194 | ||||
| Covariance | -0.002 | ||||
| r | -0.052 | ||||
| b (slope, estimate of beta) | -0.042 | ||||
| a (intercept, estimate of alpha) | 0.059 | ||||
| Mean Square Error | 0.038 | ||||
| DF error | 38.000 | ||||
| t(b) | -0.320 | ||||
| p(b) | 0.625 | ||||
| t(a) | 0.483 | ||||
| p(a) | 0.316 | ||||
| Lowerbound of 95% confidence interval for beta | -0.307 | ||||
| Upperbound of 95% confidence interval for beta | 0.223 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.188 | ||||
| Upperbound of 95% confidence interval for alpha | 0.306 | ||||
| Treynor index (mean / b) | -0.967 | ||||
| Jensen alpha (a) | 0.059 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.024 | ||||
| SD | 0.181 | ||||
| Sharpe ratio (Glass type estimate) | 0.131 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.128 | ||||
| df | 39.000 | ||||
| t | 0.239 | ||||
| p | 0.406 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.944 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.204 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.946 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.202 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.259 | ||||
| Upside Potential Ratio | 1.789 | ||||
| Upside part of mean | 0.164 | ||||
| Downside part of mean | -0.140 | ||||
| Upside SD | 0.154 | ||||
| Downside SD | 0.091 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 40.000 | ||||
| Mean of predictor | 0.406 | ||||
| Mean of criterion | 0.024 | ||||
| SD of predictor | 0.228 | ||||
| SD of criterion | 0.181 | ||||
| Covariance | -0.002 | ||||
| r | -0.049 | ||||
| b (slope, estimate of beta) | -0.039 | ||||
| a (intercept, estimate of alpha) | 0.040 | ||||
| Mean Square Error | 0.034 | ||||
| DF error | 38.000 | ||||
| t(b) | -0.303 | ||||
| p(b) | 0.618 | ||||
| t(a) | 0.349 | ||||
| p(a) | 0.364 | ||||
| Lowerbound of 95% confidence interval for beta | -0.300 | ||||
| Upperbound of 95% confidence interval for beta | 0.222 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.189 | ||||
| Upperbound of 95% confidence interval for alpha | 0.269 | ||||
| Treynor index (mean / b) | -0.605 | ||||
| Jensen alpha (a) | 0.040 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.081 | ||||
| Expected Shortfall on VaR | 0.100 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.036 | ||||
| Expected Shortfall on VaR | 0.069 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 40.000 | ||||
| Minimum | 0.897 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.273 | ||||
| Mean of quarter 1 | 0.967 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.061 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.150 | ||||
| Mean of outliers low | 0.945 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.150 | ||||
| Mean of outliers high | 1.102 | ||||
| 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) | -0.514 | ||||
| VaR(95%) (regression method) | 0.045 | ||||
| Expected Shortfall (regression method) | 0.062 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.246 | ||||
| Quartile 1 | 0.246 | ||||
| Median | 0.246 | ||||
| Quartile 3 | 0.246 | ||||
| Maximum | 0.246 | ||||
| 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) | 0.076 | ||||
| Compounded annual return (geometric extrapolation) | 0.070 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.284 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.699 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.029 | ||||
| SD | 0.120 | ||||
| Sharpe ratio (Glass type estimate) | 0.244 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.244 | ||||
| df | 892.000 | ||||
| t | 0.451 | ||||
| p | 0.326 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.818 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.306 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.818 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.306 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.400 | ||||
| Upside Potential Ratio | 4.891 | ||||
| Upside part of mean | 0.358 | ||||
| Downside part of mean | -0.329 | ||||
| Upside SD | 0.095 | ||||
| Downside SD | 0.073 | ||||
| N nonnegative terms | 113.000 | ||||
| N negative terms | 780.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 893.000 | ||||
| Mean of predictor | 0.496 | ||||
| Mean of criterion | 0.029 | ||||
| SD of predictor | 0.294 | ||||
| SD of criterion | 0.120 | ||||
| Covariance | -0.000 | ||||
| r | -0.008 | ||||
| b (slope, estimate of beta) | -0.003 | ||||
| a (intercept, estimate of alpha) | 0.031 | ||||
| Mean Square Error | 0.014 | ||||
| DF error | 891.000 | ||||
| t(b) | -0.241 | ||||
| p(b) | 0.595 | ||||
| t(a) | 0.473 | ||||
| p(a) | 0.318 | ||||
| Lowerbound of 95% confidence interval for beta | -0.030 | ||||
| Upperbound of 95% confidence interval for beta | 0.024 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.098 | ||||
| Upperbound of 95% confidence interval for alpha | 0.159 | ||||
| Treynor index (mean / b) | -8.888 | ||||
| Jensen alpha (a) | 0.031 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.022 | ||||
| SD | 0.119 | ||||
| Sharpe ratio (Glass type estimate) | 0.186 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.186 | ||||
| df | 892.000 | ||||
| t | 0.343 | ||||
| p | 0.366 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.876 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.247 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.876 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.247 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.299 | ||||
| Upside Potential Ratio | 4.767 | ||||
| Upside part of mean | 0.354 | ||||
| Downside part of mean | -0.332 | ||||
| Upside SD | 0.093 | ||||
| Downside SD | 0.074 | ||||
| N nonnegative terms | 113.000 | ||||
| N negative terms | 780.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 893.000 | ||||
| Mean of predictor | 0.452 | ||||
| Mean of criterion | 0.022 | ||||
| SD of predictor | 0.295 | ||||
| SD of criterion | 0.119 | ||||
| Covariance | -0.000 | ||||
| r | -0.007 | ||||
| b (slope, estimate of beta) | -0.003 | ||||
| a (intercept, estimate of alpha) | 0.024 | ||||
| Mean Square Error | 0.014 | ||||
| DF error | 891.000 | ||||
| t(b) | -0.221 | ||||
| p(b) | 0.587 | ||||
| t(a) | 0.362 | ||||
| p(a) | 0.359 | ||||
| Lowerbound of 95% confidence interval for beta | -0.030 | ||||
| Upperbound of 95% confidence interval for beta | 0.024 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.104 | ||||
| Upperbound of 95% confidence interval for alpha | 0.151 | ||||
| Treynor index (mean / b) | -7.391 | ||||
| Jensen alpha (a) | 0.024 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.015 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 893.000 | ||||
| Minimum | 0.952 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.065 | ||||
| Mean of quarter 1 | 0.996 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.006 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 108.000 | ||||
| Percentage of outliers low | 0.121 | ||||
| Mean of outliers low | 0.991 | ||||
| Number of outliers high | 116.000 | ||||
| Percentage of outliers high | 0.130 | ||||
| Mean of outliers high | 1.011 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.982 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| Extreme Value Index (regression method) | 0.012 | ||||
| VaR(95%) (regression method) | 0.005 | ||||
| Expected Shortfall (regression method) | 0.011 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.004 | ||||
| Median | 0.009 | ||||
| Quartile 3 | 0.040 | ||||
| Maximum | 0.272 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.007 | ||||
| Mean of quarter 3 | 0.031 | ||||
| Mean of quarter 4 | 0.163 | ||||
| Inter Quartile Range | 0.035 | ||||
| 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 | 0.111 | ||||
| Mean of outliers high | 0.272 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.675 | ||||
| VaR(95%) (moments method) | 0.153 | ||||
| Expected Shortfall (moments method) | 0.526 | ||||
| Extreme Value Index (regression method) | 2.976 | ||||
| VaR(95%) (regression method) | 0.615 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.074 | ||||
| Compounded annual return (geometric extrapolation) | 0.068 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.251 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.420 | ||||
| Compounded annual return / Expected Shortfall lognormal | 4.559 | ||||
| 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 | 0.988 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.450 | ||||
| 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 | 0.885 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.451 | ||||
| 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) | -8735414477814399.000 | ||||
| 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) | -115918768679446467327262000676864.000 | ||||
| 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 | ||||