Advanced Statistics: Kubera
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 | -0.064 | ||||
| SD | 0.180 | ||||
| Sharpe ratio (Glass type estimate) | -0.357 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.350 | ||||
| df | 38.000 | ||||
| t | -0.643 | ||||
| p | 0.738 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.444 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.736 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.440 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.740 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.439 | ||||
| Upside Potential Ratio | 0.608 | ||||
| Upside part of mean | 0.089 | ||||
| Downside part of mean | -0.153 | ||||
| Upside SD | 0.103 | ||||
| Downside SD | 0.147 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.516 | ||||
| Mean of criterion | -0.064 | ||||
| SD of predictor | 0.290 | ||||
| SD of criterion | 0.180 | ||||
| Covariance | 0.015 | ||||
| r | 0.278 | ||||
| b (slope, estimate of beta) | 0.173 | ||||
| a (intercept, estimate of alpha) | -0.153 | ||||
| Mean Square Error | 0.031 | ||||
| DF error | 37.000 | ||||
| t(b) | 1.760 | ||||
| p(b) | 0.043 | ||||
| t(a) | -1.398 | ||||
| p(a) | 0.915 | ||||
| Lowerbound of 95% confidence interval for beta | -0.026 | ||||
| Upperbound of 95% confidence interval for beta | 0.371 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.376 | ||||
| Upperbound of 95% confidence interval for alpha | 0.069 | ||||
| Treynor index (mean / b) | -0.373 | ||||
| Jensen alpha (a) | -0.153 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.081 | ||||
| SD | 0.192 | ||||
| Sharpe ratio (Glass type estimate) | -0.424 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.416 | ||||
| df | 38.000 | ||||
| t | -0.765 | ||||
| p | 0.775 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.513 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.670 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.507 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.675 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.494 | ||||
| Upside Potential Ratio | 0.510 | ||||
| Upside part of mean | 0.084 | ||||
| Downside part of mean | -0.165 | ||||
| Upside SD | 0.096 | ||||
| Downside SD | 0.165 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.466 | ||||
| Mean of criterion | -0.081 | ||||
| SD of predictor | 0.276 | ||||
| SD of criterion | 0.192 | ||||
| Covariance | 0.015 | ||||
| r | 0.293 | ||||
| b (slope, estimate of beta) | 0.204 | ||||
| a (intercept, estimate of alpha) | -0.176 | ||||
| Mean Square Error | 0.035 | ||||
| DF error | 37.000 | ||||
| t(b) | 1.862 | ||||
| p(b) | 0.035 | ||||
| t(a) | -1.533 | ||||
| p(a) | 0.933 | ||||
| Lowerbound of 95% confidence interval for beta | -0.018 | ||||
| Upperbound of 95% confidence interval for beta | 0.425 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.409 | ||||
| Upperbound of 95% confidence interval for alpha | 0.057 | ||||
| Treynor index (mean / b) | -0.400 | ||||
| Jensen alpha (a) | -0.176 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.093 | ||||
| Expected Shortfall on VaR | 0.114 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.042 | ||||
| Expected Shortfall on VaR | 0.090 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 39.000 | ||||
| Minimum | 0.762 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.142 | ||||
| Mean of quarter 1 | 0.963 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.030 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.077 | ||||
| Mean of outliers low | 0.878 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.077 | ||||
| Mean of outliers high | 1.100 | ||||
| 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) | 0.296 | ||||
| VaR(95%) (regression method) | 0.074 | ||||
| Expected Shortfall (regression method) | 0.241 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.035 | ||||
| Quartile 1 | 0.097 | ||||
| Median | 0.159 | ||||
| Quartile 3 | 0.221 | ||||
| Maximum | 0.284 | ||||
| Mean of quarter 1 | 0.035 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.284 | ||||
| Inter Quartile Range | 0.125 | ||||
| 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) | -0.035 | ||||
| Compounded annual return (geometric extrapolation) | -0.037 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.129 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.129 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.322 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.073 | ||||
| SD | 0.124 | ||||
| Sharpe ratio (Glass type estimate) | -0.592 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.591 | ||||
| df | 859.000 | ||||
| t | -1.072 | ||||
| p | 0.858 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.674 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.490 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.674 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.491 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.791 | ||||
| Upside Potential Ratio | 2.081 | ||||
| Upside part of mean | 0.193 | ||||
| Downside part of mean | -0.266 | ||||
| Upside SD | 0.082 | ||||
| Downside SD | 0.093 | ||||
| N nonnegative terms | 32.000 | ||||
| N negative terms | 828.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 860.000 | ||||
| Mean of predictor | 0.545 | ||||
| Mean of criterion | -0.073 | ||||
| SD of predictor | 0.336 | ||||
| SD of criterion | 0.124 | ||||
| Covariance | 0.002 | ||||
| r | 0.041 | ||||
| b (slope, estimate of beta) | 0.015 | ||||
| a (intercept, estimate of alpha) | -0.082 | ||||
| Mean Square Error | 0.015 | ||||
| DF error | 858.000 | ||||
| t(b) | 1.203 | ||||
| p(b) | 0.115 | ||||
| t(a) | -1.187 | ||||
| p(a) | 0.882 | ||||
| Lowerbound of 95% confidence interval for beta | -0.010 | ||||
| Upperbound of 95% confidence interval for beta | 0.040 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.216 | ||||
| Upperbound of 95% confidence interval for alpha | 0.053 | ||||
| Treynor index (mean / b) | -4.849 | ||||
| Jensen alpha (a) | -0.082 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.081 | ||||
| SD | 0.125 | ||||
| Sharpe ratio (Glass type estimate) | -0.649 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.649 | ||||
| df | 859.000 | ||||
| t | -1.176 | ||||
| p | 0.880 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.731 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.433 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.731 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.433 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.847 | ||||
| Upside Potential Ratio | 1.981 | ||||
| Upside part of mean | 0.189 | ||||
| Downside part of mean | -0.270 | ||||
| Upside SD | 0.080 | ||||
| Downside SD | 0.096 | ||||
| N nonnegative terms | 32.000 | ||||
| N negative terms | 828.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 860.000 | ||||
| Mean of predictor | 0.486 | ||||
| Mean of criterion | -0.081 | ||||
| SD of predictor | 0.341 | ||||
| SD of criterion | 0.125 | ||||
| Covariance | 0.002 | ||||
| r | 0.039 | ||||
| b (slope, estimate of beta) | 0.014 | ||||
| a (intercept, estimate of alpha) | -0.088 | ||||
| Mean Square Error | 0.016 | ||||
| DF error | 858.000 | ||||
| t(b) | 1.141 | ||||
| p(b) | 0.127 | ||||
| t(a) | -1.272 | ||||
| p(a) | 0.898 | ||||
| Lowerbound of 95% confidence interval for beta | -0.010 | ||||
| Upperbound of 95% confidence interval for beta | 0.039 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.224 | ||||
| Upperbound of 95% confidence interval for alpha | 0.048 | ||||
| Treynor index (mean / b) | -5.698 | ||||
| Jensen alpha (a) | -0.088 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.013 | ||||
| Expected Shortfall on VaR | 0.016 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.008 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 860.000 | ||||
| Minimum | 0.895 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.078 | ||||
| Mean of quarter 1 | 0.997 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.003 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 33.000 | ||||
| Percentage of outliers low | 0.038 | ||||
| Mean of outliers low | 0.978 | ||||
| Number of outliers high | 32.000 | ||||
| Percentage of outliers high | 0.037 | ||||
| Mean of outliers high | 1.020 | ||||
| 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) | 0.262 | ||||
| VaR(95%) (regression method) | -0.002 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.006 | ||||
| Quartile 1 | 0.011 | ||||
| Median | 0.093 | ||||
| Quartile 3 | 0.105 | ||||
| Maximum | 0.313 | ||||
| Mean of quarter 1 | 0.009 | ||||
| Mean of quarter 2 | 0.093 | ||||
| Mean of quarter 3 | 0.105 | ||||
| Mean of quarter 4 | 0.313 | ||||
| Inter Quartile Range | 0.094 | ||||
| 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 | 0.200 | ||||
| Mean of outliers high | 0.313 | ||||
| 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) | -0.035 | ||||
| Compounded annual return (geometric extrapolation) | -0.036 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.116 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.116 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.260 | ||||
| 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 | 1.098 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.451 | ||||
| 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 | 0.994 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.452 | ||||
| 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) | -8719179774218742.000 | ||||
| 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) | -83675948838355790851936694042624.000 | ||||
| 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 | ||||