Advanced Statistics: TrendFX
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 | 0.271 | ||||
| Sharpe ratio (Glass type estimate) | 0.400 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.394 | ||||
| df | 45.000 | ||||
| t | 0.784 | ||||
| p | 0.219 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.606 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.403 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.611 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.398 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.849 | ||||
| Upside Potential Ratio | 2.047 | ||||
| Upside part of mean | 0.261 | ||||
| Downside part of mean | -0.153 | ||||
| Upside SD | 0.238 | ||||
| Downside SD | 0.128 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 46.000 | ||||
| Mean of predictor | 0.428 | ||||
| Mean of criterion | 0.108 | ||||
| SD of predictor | 0.262 | ||||
| SD of criterion | 0.271 | ||||
| Covariance | -0.009 | ||||
| r | -0.132 | ||||
| b (slope, estimate of beta) | -0.137 | ||||
| a (intercept, estimate of alpha) | 0.167 | ||||
| Mean Square Error | 0.074 | ||||
| DF error | 44.000 | ||||
| t(b) | -0.886 | ||||
| p(b) | 0.810 | ||||
| t(a) | 1.087 | ||||
| p(a) | 0.141 | ||||
| Lowerbound of 95% confidence interval for beta | -0.449 | ||||
| Upperbound of 95% confidence interval for beta | 0.175 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.143 | ||||
| Upperbound of 95% confidence interval for alpha | 0.477 | ||||
| Treynor index (mean / b) | -0.791 | ||||
| Jensen alpha (a) | 0.167 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.075 | ||||
| SD | 0.254 | ||||
| Sharpe ratio (Glass type estimate) | 0.295 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.290 | ||||
| df | 45.000 | ||||
| t | 0.578 | ||||
| p | 0.283 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.709 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.296 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.713 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.293 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.543 | ||||
| Upside Potential Ratio | 1.711 | ||||
| Upside part of mean | 0.236 | ||||
| Downside part of mean | -0.161 | ||||
| Upside SD | 0.211 | ||||
| Downside SD | 0.138 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 46.000 | ||||
| Mean of predictor | 0.389 | ||||
| Mean of criterion | 0.075 | ||||
| SD of predictor | 0.242 | ||||
| SD of criterion | 0.254 | ||||
| Covariance | -0.008 | ||||
| r | -0.127 | ||||
| b (slope, estimate of beta) | -0.134 | ||||
| a (intercept, estimate of alpha) | 0.127 | ||||
| Mean Square Error | 0.065 | ||||
| DF error | 44.000 | ||||
| t(b) | -0.851 | ||||
| p(b) | 0.800 | ||||
| t(a) | 0.883 | ||||
| p(a) | 0.191 | ||||
| Lowerbound of 95% confidence interval for beta | -0.450 | ||||
| Upperbound of 95% confidence interval for beta | 0.183 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.163 | ||||
| Upperbound of 95% confidence interval for alpha | 0.417 | ||||
| Treynor index (mean / b) | -0.561 | ||||
| Jensen alpha (a) | 0.127 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.108 | ||||
| Expected Shortfall on VaR | 0.135 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.038 | ||||
| Expected Shortfall on VaR | 0.080 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 46.000 | ||||
| Minimum | 0.827 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.311 | ||||
| Mean of quarter 1 | 0.962 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.087 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.174 | ||||
| Mean of outliers low | 0.943 | ||||
| Number of outliers high | 10.000 | ||||
| Percentage of outliers high | 0.217 | ||||
| Mean of outliers high | 1.104 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.948 | ||||
| VaR(95%) (moments method) | 0.005 | ||||
| Expected Shortfall (moments method) | 0.006 | ||||
| Extreme Value Index (regression method) | -0.172 | ||||
| VaR(95%) (regression method) | 0.070 | ||||
| Expected Shortfall (regression method) | 0.118 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.069 | ||||
| Quartile 1 | 0.110 | ||||
| Median | 0.150 | ||||
| Quartile 3 | 0.162 | ||||
| Maximum | 0.173 | ||||
| Mean of quarter 1 | 0.069 | ||||
| Mean of quarter 2 | 0.150 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.173 | ||||
| Inter Quartile Range | 0.052 | ||||
| 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) | 0.151 | ||||
| Compounded annual return (geometric extrapolation) | 0.126 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.730 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.730 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.938 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.092 | ||||
| SD | 0.198 | ||||
| Sharpe ratio (Glass type estimate) | 0.464 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.464 | ||||
| df | 1022.000 | ||||
| t | 0.917 | ||||
| p | 0.486 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.528 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.456 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.528 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.456 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.845 | ||||
| Upside Potential Ratio | 5.507 | ||||
| Upside part of mean | 0.599 | ||||
| Downside part of mean | -0.507 | ||||
| Upside SD | 0.165 | ||||
| Downside SD | 0.109 | ||||
| N nonnegative terms | 178.000 | ||||
| N negative terms | 845.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1023.000 | ||||
| Mean of predictor | 0.465 | ||||
| Mean of criterion | 0.092 | ||||
| SD of predictor | 0.294 | ||||
| SD of criterion | 0.198 | ||||
| Covariance | -0.001 | ||||
| r | -0.014 | ||||
| b (slope, estimate of beta) | -0.010 | ||||
| a (intercept, estimate of alpha) | 0.096 | ||||
| Mean Square Error | 0.039 | ||||
| DF error | 1021.000 | ||||
| t(b) | -0.456 | ||||
| p(b) | 0.509 | ||||
| t(a) | 0.957 | ||||
| p(a) | 0.481 | ||||
| Lowerbound of 95% confidence interval for beta | -0.051 | ||||
| Upperbound of 95% confidence interval for beta | 0.032 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.101 | ||||
| Upperbound of 95% confidence interval for alpha | 0.294 | ||||
| Treynor index (mean / b) | -9.576 | ||||
| Jensen alpha (a) | 0.096 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.073 | ||||
| SD | 0.194 | ||||
| Sharpe ratio (Glass type estimate) | 0.375 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.375 | ||||
| df | 1022.000 | ||||
| t | 0.741 | ||||
| p | 0.488 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.617 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.367 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.617 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.367 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.656 | ||||
| Upside Potential Ratio | 5.282 | ||||
| Upside part of mean | 0.586 | ||||
| Downside part of mean | -0.513 | ||||
| Upside SD | 0.159 | ||||
| Downside SD | 0.111 | ||||
| N nonnegative terms | 178.000 | ||||
| N negative terms | 845.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1023.000 | ||||
| Mean of predictor | 0.420 | ||||
| Mean of criterion | 0.073 | ||||
| SD of predictor | 0.297 | ||||
| SD of criterion | 0.194 | ||||
| Covariance | -0.001 | ||||
| r | -0.012 | ||||
| b (slope, estimate of beta) | -0.008 | ||||
| a (intercept, estimate of alpha) | 0.076 | ||||
| Mean Square Error | 0.038 | ||||
| DF error | 1021.000 | ||||
| t(b) | -0.392 | ||||
| p(b) | 0.508 | ||||
| t(a) | 0.772 | ||||
| p(a) | 0.485 | ||||
| Lowerbound of 95% confidence interval for beta | -0.048 | ||||
| Upperbound of 95% confidence interval for beta | 0.032 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.117 | ||||
| Upperbound of 95% confidence interval for alpha | 0.270 | ||||
| Treynor index (mean / b) | -9.098 | ||||
| Jensen alpha (a) | 0.076 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.024 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.013 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1023.000 | ||||
| Minimum | 0.932 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.134 | ||||
| Mean of quarter 1 | 0.993 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.009 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 189.000 | ||||
| Percentage of outliers low | 0.185 | ||||
| Mean of outliers low | 0.990 | ||||
| Number of outliers high | 184.000 | ||||
| Percentage of outliers high | 0.180 | ||||
| Mean of outliers high | 1.013 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.422 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.009 | ||||
| Extreme Value Index (regression method) | 0.066 | ||||
| VaR(95%) (regression method) | 0.007 | ||||
| Expected Shortfall (regression method) | 0.014 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 11.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.009 | ||||
| Median | 0.036 | ||||
| Quartile 3 | 0.121 | ||||
| Maximum | 0.242 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | 0.022 | ||||
| Mean of quarter 3 | 0.058 | ||||
| Mean of quarter 4 | 0.220 | ||||
| Inter Quartile Range | 0.112 | ||||
| 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) | -25762.290 | ||||
| VaR(95%) (moments method) | 0.232 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -7.602 | ||||
| VaR(95%) (regression method) | 0.544 | ||||
| Expected Shortfall (regression method) | 0.544 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.148 | ||||
| Compounded annual return (geometric extrapolation) | 0.124 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.512 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.562 | ||||
| Compounded annual return / Expected Shortfall lognormal | 5.129 | ||||
| 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 | 0.973 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.472 | ||||
| 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 | 0.859 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.475 | ||||
| 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) | -8744894235750811.000 | ||||
| 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) | -770407965300698593418655310020608.000 | ||||
| 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 | ||||