Advanced Statistics: Discontinued, please see new system
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 | 0.103 | ||||
| SD | 0.320 | ||||
| Sharpe ratio (Glass type estimate) | 0.322 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.316 | ||||
| df | 38.000 | ||||
| t | 0.581 | ||||
| p | 0.282 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.769 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.410 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.774 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.405 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.600 | ||||
| Upside Potential Ratio | 2.001 | ||||
| Upside part of mean | 0.344 | ||||
| Downside part of mean | -0.241 | ||||
| Upside SD | 0.267 | ||||
| Downside SD | 0.172 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.495 | ||||
| Mean of criterion | 0.103 | ||||
| SD of predictor | 0.245 | ||||
| SD of criterion | 0.320 | ||||
| Covariance | 0.002 | ||||
| r | 0.022 | ||||
| b (slope, estimate of beta) | 0.028 | ||||
| a (intercept, estimate of alpha) | 0.089 | ||||
| Mean Square Error | 0.105 | ||||
| DF error | 37.000 | ||||
| t(b) | 0.132 | ||||
| p(b) | 0.448 | ||||
| t(a) | 0.427 | ||||
| p(a) | 0.336 | ||||
| Lowerbound of 95% confidence interval for beta | -0.407 | ||||
| Upperbound of 95% confidence interval for beta | 0.464 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.335 | ||||
| Upperbound of 95% confidence interval for alpha | 0.513 | ||||
| Treynor index (mean / b) | 3.642 | ||||
| Jensen alpha (a) | 0.089 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.055 | ||||
| SD | 0.309 | ||||
| Sharpe ratio (Glass type estimate) | 0.179 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.176 | ||||
| df | 38.000 | ||||
| t | 0.323 | ||||
| p | 0.374 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.910 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.266 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.912 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.263 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.294 | ||||
| Upside Potential Ratio | 1.660 | ||||
| Upside part of mean | 0.312 | ||||
| Downside part of mean | -0.257 | ||||
| Upside SD | 0.241 | ||||
| Downside SD | 0.188 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.456 | ||||
| Mean of criterion | 0.055 | ||||
| SD of predictor | 0.232 | ||||
| SD of criterion | 0.309 | ||||
| Covariance | 0.003 | ||||
| r | 0.045 | ||||
| b (slope, estimate of beta) | 0.060 | ||||
| a (intercept, estimate of alpha) | 0.028 | ||||
| Mean Square Error | 0.098 | ||||
| DF error | 37.000 | ||||
| t(b) | 0.274 | ||||
| p(b) | 0.393 | ||||
| t(a) | 0.140 | ||||
| p(a) | 0.445 | ||||
| Lowerbound of 95% confidence interval for beta | -0.383 | ||||
| Upperbound of 95% confidence interval for beta | 0.503 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.378 | ||||
| Upperbound of 95% confidence interval for alpha | 0.434 | ||||
| Treynor index (mean / b) | 0.923 | ||||
| Jensen alpha (a) | 0.028 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.132 | ||||
| Expected Shortfall on VaR | 0.164 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.061 | ||||
| Expected Shortfall on VaR | 0.122 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 39.000 | ||||
| Minimum | 0.801 | ||||
| Quartile 1 | 0.995 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.267 | ||||
| Mean of quarter 1 | 0.934 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.115 | ||||
| Inter Quartile Range | 0.005 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.179 | ||||
| Mean of outliers low | 0.909 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.154 | ||||
| Mean of outliers high | 1.189 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.831 | ||||
| VaR(95%) (moments method) | 0.040 | ||||
| Expected Shortfall (moments method) | 0.277 | ||||
| Extreme Value Index (regression method) | 0.177 | ||||
| VaR(95%) (regression method) | 0.089 | ||||
| Expected Shortfall (regression method) | 0.161 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.068 | ||||
| Quartile 1 | 0.154 | ||||
| Median | 0.240 | ||||
| Quartile 3 | 0.327 | ||||
| Maximum | 0.413 | ||||
| Mean of quarter 1 | 0.068 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.413 | ||||
| Inter Quartile Range | 0.173 | ||||
| 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) | 0.117 | ||||
| Compounded annual return (geometric extrapolation) | 0.104 | ||||
| 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 | 0.638 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.106 | ||||
| SD | 0.336 | ||||
| Sharpe ratio (Glass type estimate) | 0.315 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.315 | ||||
| df | 859.000 | ||||
| t | 0.571 | ||||
| p | 0.284 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.767 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.397 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.767 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.397 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.634 | ||||
| Upside Potential Ratio | 4.757 | ||||
| Upside part of mean | 0.795 | ||||
| Downside part of mean | -0.689 | ||||
| Upside SD | 0.292 | ||||
| Downside SD | 0.167 | ||||
| N nonnegative terms | 195.000 | ||||
| N negative terms | 665.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 860.000 | ||||
| Mean of predictor | 0.531 | ||||
| Mean of criterion | 0.106 | ||||
| SD of predictor | 0.340 | ||||
| SD of criterion | 0.336 | ||||
| Covariance | -0.002 | ||||
| r | -0.017 | ||||
| b (slope, estimate of beta) | -0.017 | ||||
| a (intercept, estimate of alpha) | 0.115 | ||||
| Mean Square Error | 0.113 | ||||
| DF error | 858.000 | ||||
| t(b) | -0.490 | ||||
| p(b) | 0.688 | ||||
| t(a) | 0.615 | ||||
| p(a) | 0.269 | ||||
| Lowerbound of 95% confidence interval for beta | -0.083 | ||||
| Upperbound of 95% confidence interval for beta | 0.050 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.251 | ||||
| Upperbound of 95% confidence interval for alpha | 0.481 | ||||
| Treynor index (mean / b) | -6.394 | ||||
| Jensen alpha (a) | 0.115 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.054 | ||||
| SD | 0.314 | ||||
| Sharpe ratio (Glass type estimate) | 0.173 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.173 | ||||
| df | 859.000 | ||||
| t | 0.313 | ||||
| p | 0.377 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.909 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.255 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.909 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.255 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.314 | ||||
| Upside Potential Ratio | 4.373 | ||||
| Upside part of mean | 0.758 | ||||
| Downside part of mean | -0.704 | ||||
| Upside SD | 0.262 | ||||
| Downside SD | 0.173 | ||||
| N nonnegative terms | 195.000 | ||||
| N negative terms | 665.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 860.000 | ||||
| Mean of predictor | 0.472 | ||||
| Mean of criterion | 0.054 | ||||
| SD of predictor | 0.343 | ||||
| SD of criterion | 0.314 | ||||
| Covariance | -0.002 | ||||
| r | -0.017 | ||||
| b (slope, estimate of beta) | -0.016 | ||||
| a (intercept, estimate of alpha) | 0.062 | ||||
| Mean Square Error | 0.099 | ||||
| DF error | 858.000 | ||||
| t(b) | -0.512 | ||||
| p(b) | 0.696 | ||||
| t(a) | 0.355 | ||||
| p(a) | 0.361 | ||||
| Lowerbound of 95% confidence interval for beta | -0.077 | ||||
| Upperbound of 95% confidence interval for beta | 0.045 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.280 | ||||
| Upperbound of 95% confidence interval for alpha | 0.404 | ||||
| Treynor index (mean / b) | -3.393 | ||||
| Jensen alpha (a) | 0.062 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.031 | ||||
| Expected Shortfall on VaR | 0.039 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.017 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 860.000 | ||||
| Minimum | 0.867 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.367 | ||||
| Mean of quarter 1 | 0.990 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.012 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 199.000 | ||||
| Percentage of outliers low | 0.231 | ||||
| Mean of outliers low | 0.989 | ||||
| Number of outliers high | 198.000 | ||||
| Percentage of outliers high | 0.230 | ||||
| Mean of outliers high | 1.013 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.236 | ||||
| VaR(95%) (moments method) | 0.007 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.693 | ||||
| VaR(95%) (regression method) | 0.007 | ||||
| Expected Shortfall (regression method) | 0.028 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.021 | ||||
| Median | 0.034 | ||||
| Quartile 3 | 0.092 | ||||
| Maximum | 0.653 | ||||
| Mean of quarter 1 | 0.011 | ||||
| Mean of quarter 2 | 0.029 | ||||
| Mean of quarter 3 | 0.064 | ||||
| Mean of quarter 4 | 0.411 | ||||
| Inter Quartile Range | 0.072 | ||||
| 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 | 0.653 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.014 | ||||
| VaR(95%) (moments method) | 0.270 | ||||
| Expected Shortfall (moments method) | 0.392 | ||||
| Extreme Value Index (regression method) | 1.687 | ||||
| VaR(95%) (regression method) | 0.974 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.116 | ||||
| Compounded annual return (geometric extrapolation) | 0.103 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.158 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.252 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.647 | ||||
| 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 | 0.987 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.511 | ||||
| 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 | 0.504 | ||||
| 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) | -8751003833407731.000 | ||||
| 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) | 981920960475418648298305970241536.000 | ||||
| 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 | ||||