Advanced Statistics:
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 | -0.229 | ||||
| SD | 0.251 | ||||
| Sharpe ratio (Glass type estimate) | -0.914 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.900 | ||||
| df | 51.000 | ||||
| t | -1.902 | ||||
| p | 0.969 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.867 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.049 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.858 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.057 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.949 | ||||
| Upside Potential Ratio | 0.353 | ||||
| Upside part of mean | 0.085 | ||||
| Downside part of mean | -0.314 | ||||
| Upside SD | 0.088 | ||||
| Downside SD | 0.242 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 44.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 52.000 | ||||
| Mean of predictor | 0.423 | ||||
| Mean of criterion | -0.229 | ||||
| SD of predictor | 0.226 | ||||
| SD of criterion | 0.251 | ||||
| Covariance | -0.006 | ||||
| r | -0.100 | ||||
| b (slope, estimate of beta) | -0.111 | ||||
| a (intercept, estimate of alpha) | -0.182 | ||||
| Mean Square Error | 0.064 | ||||
| DF error | 50.000 | ||||
| t(b) | -0.710 | ||||
| p(b) | 0.759 | ||||
| t(a) | -1.320 | ||||
| p(a) | 0.904 | ||||
| Lowerbound of 95% confidence interval for beta | -0.425 | ||||
| Upperbound of 95% confidence interval for beta | 0.203 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.459 | ||||
| Upperbound of 95% confidence interval for alpha | 0.095 | ||||
| Treynor index (mean / b) | 2.063 | ||||
| Jensen alpha (a) | -0.182 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.267 | ||||
| SD | 0.281 | ||||
| Sharpe ratio (Glass type estimate) | -0.948 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.934 | ||||
| df | 51.000 | ||||
| t | -1.974 | ||||
| p | 0.973 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.903 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.015 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.893 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.024 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.963 | ||||
| Upside Potential Ratio | 0.294 | ||||
| Upside part of mean | 0.081 | ||||
| Downside part of mean | -0.348 | ||||
| Upside SD | 0.083 | ||||
| Downside SD | 0.277 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 44.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 52.000 | ||||
| Mean of predictor | 0.391 | ||||
| Mean of criterion | -0.267 | ||||
| SD of predictor | 0.217 | ||||
| SD of criterion | 0.281 | ||||
| Covariance | -0.006 | ||||
| r | -0.096 | ||||
| b (slope, estimate of beta) | -0.125 | ||||
| a (intercept, estimate of alpha) | -0.218 | ||||
| Mean Square Error | 0.080 | ||||
| DF error | 50.000 | ||||
| t(b) | -0.685 | ||||
| p(b) | 0.752 | ||||
| t(a) | -1.419 | ||||
| p(a) | 0.919 | ||||
| Lowerbound of 95% confidence interval for beta | -0.493 | ||||
| Upperbound of 95% confidence interval for beta | 0.242 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.526 | ||||
| Upperbound of 95% confidence interval for alpha | 0.091 | ||||
| Treynor index (mean / b) | 2.130 | ||||
| Jensen alpha (a) | -0.218 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.144 | ||||
| Expected Shortfall on VaR | 0.172 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.083 | ||||
| Expected Shortfall on VaR | 0.168 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 52.000 | ||||
| Minimum | 0.702 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.156 | ||||
| Mean of quarter 1 | 0.908 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.031 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 11.000 | ||||
| Percentage of outliers low | 0.212 | ||||
| Mean of outliers low | 0.891 | ||||
| Number of outliers high | 12.000 | ||||
| Percentage of outliers high | 0.231 | ||||
| Mean of outliers high | 1.033 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -41.294 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.485 | ||||
| VaR(95%) (regression method) | 0.109 | ||||
| Expected Shortfall (regression method) | 0.149 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.670 | ||||
| Quartile 1 | 0.670 | ||||
| Median | 0.670 | ||||
| Quartile 3 | 0.670 | ||||
| Maximum | 0.670 | ||||
| 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) | -0.143 | ||||
| Compounded annual return (geometric extrapolation) | -0.200 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.298 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.158 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.193 | ||||
| SD | 0.378 | ||||
| Sharpe ratio (Glass type estimate) | -0.512 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.512 | ||||
| df | 1135.000 | ||||
| t | -1.066 | ||||
| p | 0.520 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.453 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.430 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.453 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.430 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.674 | ||||
| Upside Potential Ratio | 3.205 | ||||
| Upside part of mean | 0.919 | ||||
| Downside part of mean | -1.112 | ||||
| Upside SD | 0.246 | ||||
| Downside SD | 0.287 | ||||
| N nonnegative terms | 157.000 | ||||
| N negative terms | 979.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1136.000 | ||||
| Mean of predictor | 0.446 | ||||
| Mean of criterion | -0.193 | ||||
| SD of predictor | 0.335 | ||||
| SD of criterion | 0.378 | ||||
| Covariance | 0.004 | ||||
| r | 0.032 | ||||
| b (slope, estimate of beta) | 0.036 | ||||
| a (intercept, estimate of alpha) | -0.210 | ||||
| Mean Square Error | 0.143 | ||||
| DF error | 1134.000 | ||||
| t(b) | 1.087 | ||||
| p(b) | 0.484 | ||||
| t(a) | -1.152 | ||||
| p(a) | 0.517 | ||||
| Lowerbound of 95% confidence interval for beta | -0.029 | ||||
| Upperbound of 95% confidence interval for beta | 0.102 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.567 | ||||
| Upperbound of 95% confidence interval for alpha | 0.147 | ||||
| Treynor index (mean / b) | -5.318 | ||||
| Jensen alpha (a) | -0.210 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.267 | ||||
| SD | 0.386 | ||||
| Sharpe ratio (Glass type estimate) | -0.690 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.690 | ||||
| df | 1135.000 | ||||
| t | -1.437 | ||||
| p | 0.527 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.632 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.252 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.631 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.252 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.867 | ||||
| Upside Potential Ratio | 2.896 | ||||
| Upside part of mean | 0.891 | ||||
| Downside part of mean | -1.157 | ||||
| Upside SD | 0.234 | ||||
| Downside SD | 0.308 | ||||
| N nonnegative terms | 157.000 | ||||
| N negative terms | 979.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1136.000 | ||||
| Mean of predictor | 0.387 | ||||
| Mean of criterion | -0.267 | ||||
| SD of predictor | 0.347 | ||||
| SD of criterion | 0.386 | ||||
| Covariance | 0.004 | ||||
| r | 0.032 | ||||
| b (slope, estimate of beta) | 0.036 | ||||
| a (intercept, estimate of alpha) | -0.281 | ||||
| Mean Square Error | 0.149 | ||||
| DF error | 1134.000 | ||||
| t(b) | 1.078 | ||||
| p(b) | 0.484 | ||||
| t(a) | -1.508 | ||||
| p(a) | 0.522 | ||||
| Lowerbound of 95% confidence interval for beta | -0.029 | ||||
| Upperbound of 95% confidence interval for beta | 0.101 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.645 | ||||
| Upperbound of 95% confidence interval for alpha | 0.084 | ||||
| Treynor index (mean / b) | -7.480 | ||||
| Jensen alpha (a) | -0.281 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.039 | ||||
| Expected Shortfall on VaR | 0.049 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.013 | ||||
| Expected Shortfall on VaR | 0.030 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1136.000 | ||||
| Minimum | 0.756 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.162 | ||||
| Mean of quarter 1 | 0.984 | ||||
| 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 | 181.000 | ||||
| Percentage of outliers low | 0.159 | ||||
| Mean of outliers low | 0.974 | ||||
| Number of outliers high | 164.000 | ||||
| Percentage of outliers high | 0.144 | ||||
| Mean of outliers high | 1.024 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.147 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.007 | ||||
| Extreme Value Index (regression method) | 0.374 | ||||
| VaR(95%) (regression method) | 0.015 | ||||
| Expected Shortfall (regression method) | 0.040 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.005 | ||||
| Quartile 1 | 0.019 | ||||
| Median | 0.065 | ||||
| Quartile 3 | 0.126 | ||||
| Maximum | 0.694 | ||||
| Mean of quarter 1 | 0.008 | ||||
| Mean of quarter 2 | 0.044 | ||||
| Mean of quarter 3 | 0.086 | ||||
| Mean of quarter 4 | 0.417 | ||||
| Inter Quartile Range | 0.107 | ||||
| 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 | 0.167 | ||||
| Mean of outliers high | 0.694 | ||||
| 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) | -0.143 | ||||
| Compounded annual return (geometric extrapolation) | -0.200 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.287 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.479 | ||||
| Compounded annual return / Expected Shortfall lognormal | -4.076 | ||||
| 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 | 1.218 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.361 | ||||
| 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 | 1.151 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.359 | ||||
| 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) | -8631028593111865.000 | ||||
| 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) | -103968641723591730905713362337792.000 | ||||
| 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 | ||||