Advanced Statistics: Extreme Trader
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 | -0.131 | ||||
| SD | 0.253 | ||||
| Sharpe ratio (Glass type estimate) | -0.518 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.511 | ||||
| df | 54.000 | ||||
| t | -1.108 | ||||
| p | 0.864 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.436 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.405 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.431 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.410 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.565 | ||||
| Upside Potential Ratio | 0.444 | ||||
| Upside part of mean | 0.103 | ||||
| Downside part of mean | -0.234 | ||||
| Upside SD | 0.102 | ||||
| Downside SD | 0.231 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 49.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 55.000 | ||||
| Mean of predictor | 0.417 | ||||
| Mean of criterion | -0.131 | ||||
| SD of predictor | 0.245 | ||||
| SD of criterion | 0.253 | ||||
| Covariance | -0.001 | ||||
| r | -0.020 | ||||
| b (slope, estimate of beta) | -0.020 | ||||
| a (intercept, estimate of alpha) | -0.122 | ||||
| Mean Square Error | 0.065 | ||||
| DF error | 53.000 | ||||
| t(b) | -0.145 | ||||
| p(b) | 0.557 | ||||
| t(a) | -0.920 | ||||
| p(a) | 0.819 | ||||
| Lowerbound of 95% confidence interval for beta | -0.304 | ||||
| Upperbound of 95% confidence interval for beta | 0.263 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.389 | ||||
| Upperbound of 95% confidence interval for alpha | 0.144 | ||||
| Treynor index (mean / b) | 6.394 | ||||
| Jensen alpha (a) | -0.122 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.169 | ||||
| SD | 0.293 | ||||
| Sharpe ratio (Glass type estimate) | -0.577 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.569 | ||||
| df | 54.000 | ||||
| t | -1.236 | ||||
| p | 0.889 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.496 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.347 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.491 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.353 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.608 | ||||
| Upside Potential Ratio | 0.351 | ||||
| Upside part of mean | 0.098 | ||||
| Downside part of mean | -0.267 | ||||
| Upside SD | 0.096 | ||||
| Downside SD | 0.278 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 49.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 55.000 | ||||
| Mean of predictor | 0.381 | ||||
| Mean of criterion | -0.169 | ||||
| SD of predictor | 0.235 | ||||
| SD of criterion | 0.293 | ||||
| Covariance | 0.001 | ||||
| r | 0.012 | ||||
| b (slope, estimate of beta) | 0.014 | ||||
| a (intercept, estimate of alpha) | -0.175 | ||||
| Mean Square Error | 0.088 | ||||
| DF error | 53.000 | ||||
| t(b) | 0.084 | ||||
| p(b) | 0.467 | ||||
| t(a) | -1.143 | ||||
| p(a) | 0.871 | ||||
| Lowerbound of 95% confidence interval for beta | -0.329 | ||||
| Upperbound of 95% confidence interval for beta | 0.358 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.481 | ||||
| Upperbound of 95% confidence interval for alpha | 0.132 | ||||
| Treynor index (mean / b) | -11.779 | ||||
| Jensen alpha (a) | -0.175 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.142 | ||||
| Expected Shortfall on VaR | 0.172 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.063 | ||||
| Expected Shortfall on VaR | 0.135 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 55.000 | ||||
| Minimum | 0.629 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.152 | ||||
| Mean of quarter 1 | 0.936 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.035 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 9.000 | ||||
| Percentage of outliers low | 0.164 | ||||
| Mean of outliers low | 0.901 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.109 | ||||
| Mean of outliers high | 1.082 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.969 | ||||
| VaR(95%) (moments method) | 0.006 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.303 | ||||
| VaR(95%) (regression method) | 0.047 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.336 | ||||
| Quartile 1 | 0.368 | ||||
| Median | 0.400 | ||||
| Quartile 3 | 0.433 | ||||
| Maximum | 0.465 | ||||
| Mean of quarter 1 | 0.336 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.465 | ||||
| Inter Quartile Range | 0.064 | ||||
| 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) | -0.095 | ||||
| Compounded annual return (geometric extrapolation) | -0.118 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.253 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.253 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.686 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.081 | ||||
| SD | 0.416 | ||||
| Sharpe ratio (Glass type estimate) | -0.194 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.194 | ||||
| df | 1210.000 | ||||
| t | -0.418 | ||||
| p | 0.506 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.106 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.717 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.106 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.717 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.279 | ||||
| Upside Potential Ratio | 3.039 | ||||
| Upside part of mean | 0.883 | ||||
| Downside part of mean | -0.963 | ||||
| Upside SD | 0.298 | ||||
| Downside SD | 0.290 | ||||
| N nonnegative terms | 94.000 | ||||
| N negative terms | 1117.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1211.000 | ||||
| Mean of predictor | 0.468 | ||||
| Mean of criterion | -0.081 | ||||
| SD of predictor | 0.354 | ||||
| SD of criterion | 0.416 | ||||
| Covariance | -0.004 | ||||
| r | -0.030 | ||||
| b (slope, estimate of beta) | -0.035 | ||||
| a (intercept, estimate of alpha) | -0.064 | ||||
| Mean Square Error | 0.173 | ||||
| DF error | 1209.000 | ||||
| t(b) | -1.039 | ||||
| p(b) | 0.519 | ||||
| t(a) | -0.332 | ||||
| p(a) | 0.506 | ||||
| Lowerbound of 95% confidence interval for beta | -0.101 | ||||
| Upperbound of 95% confidence interval for beta | 0.031 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.446 | ||||
| Upperbound of 95% confidence interval for alpha | 0.317 | ||||
| Treynor index (mean / b) | 2.306 | ||||
| Jensen alpha (a) | -0.064 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.168 | ||||
| SD | 0.420 | ||||
| Sharpe ratio (Glass type estimate) | -0.401 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.400 | ||||
| df | 1210.000 | ||||
| t | -0.861 | ||||
| p | 0.512 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.312 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.511 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.312 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.511 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.536 | ||||
| Upside Potential Ratio | 2.684 | ||||
| Upside part of mean | 0.842 | ||||
| Downside part of mean | -1.010 | ||||
| Upside SD | 0.279 | ||||
| Downside SD | 0.314 | ||||
| N nonnegative terms | 94.000 | ||||
| N negative terms | 1117.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1211.000 | ||||
| Mean of predictor | 0.404 | ||||
| Mean of criterion | -0.168 | ||||
| SD of predictor | 0.359 | ||||
| SD of criterion | 0.420 | ||||
| Covariance | -0.004 | ||||
| r | -0.029 | ||||
| b (slope, estimate of beta) | -0.034 | ||||
| a (intercept, estimate of alpha) | -0.154 | ||||
| Mean Square Error | 0.176 | ||||
| DF error | 1209.000 | ||||
| t(b) | -1.022 | ||||
| p(b) | 0.519 | ||||
| t(a) | -0.788 | ||||
| p(a) | 0.514 | ||||
| Lowerbound of 95% confidence interval for beta | -0.100 | ||||
| Upperbound of 95% confidence interval for beta | 0.032 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.538 | ||||
| Upperbound of 95% confidence interval for alpha | 0.230 | ||||
| Treynor index (mean / b) | 4.890 | ||||
| Jensen alpha (a) | -0.154 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.042 | ||||
| Expected Shortfall on VaR | 0.053 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.027 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1211.000 | ||||
| Minimum | 0.739 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.252 | ||||
| Mean of quarter 1 | 0.986 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.014 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 117.000 | ||||
| Percentage of outliers low | 0.097 | ||||
| Mean of outliers low | 0.964 | ||||
| Number of outliers high | 95.000 | ||||
| Percentage of outliers high | 0.078 | ||||
| Mean of outliers high | 1.043 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.250 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.007 | ||||
| Extreme Value Index (regression method) | 0.118 | ||||
| VaR(95%) (regression method) | 0.013 | ||||
| Expected Shortfall (regression method) | 0.041 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.131 | ||||
| Quartile 1 | 0.238 | ||||
| Median | 0.346 | ||||
| Quartile 3 | 0.453 | ||||
| Maximum | 0.561 | ||||
| Mean of quarter 1 | 0.131 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.561 | ||||
| Inter Quartile Range | 0.215 | ||||
| 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) | -0.094 | ||||
| Compounded annual return (geometric extrapolation) | -0.117 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.208 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.208 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.218 | ||||
| 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 | 1.073 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.496 | ||||
| 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 | 0.951 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.492 | ||||
| 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) | -8737292147986388.000 | ||||
| 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) | 759824939614307466769960179597312.000 | ||||
| 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 | ||||