Advanced Statistics: LBTI
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 | -0.055 | ||||
| SD | 0.043 | ||||
| Sharpe ratio (Glass type estimate) | -1.266 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.255 | ||||
| df | 83.000 | ||||
| t | -3.350 | ||||
| p | 0.999 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.028 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.497 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.020 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.490 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.342 | ||||
| Upside Potential Ratio | 0.256 | ||||
| Upside part of mean | 0.010 | ||||
| Downside part of mean | -0.065 | ||||
| Upside SD | 0.021 | ||||
| Downside SD | 0.041 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 82.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 84.000 | ||||
| Mean of predictor | 0.226 | ||||
| Mean of criterion | -0.055 | ||||
| SD of predictor | 0.306 | ||||
| SD of criterion | 0.043 | ||||
| Covariance | 0.001 | ||||
| r | 0.089 | ||||
| b (slope, estimate of beta) | 0.013 | ||||
| a (intercept, estimate of alpha) | -0.058 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 82.000 | ||||
| t(b) | 0.813 | ||||
| p(b) | 0.209 | ||||
| t(a) | -3.439 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.018 | ||||
| Upperbound of 95% confidence interval for beta | 0.044 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.091 | ||||
| Upperbound of 95% confidence interval for alpha | -0.024 | ||||
| Treynor index (mean / b) | -4.326 | ||||
| Jensen alpha (a) | -0.058 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.056 | ||||
| SD | 0.044 | ||||
| Sharpe ratio (Glass type estimate) | -1.263 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.252 | ||||
| df | 83.000 | ||||
| t | -3.342 | ||||
| p | 0.999 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.025 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.495 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.017 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.487 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.325 | ||||
| Upside Potential Ratio | 0.243 | ||||
| Upside part of mean | 0.010 | ||||
| Downside part of mean | -0.066 | ||||
| Upside SD | 0.020 | ||||
| Downside SD | 0.042 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 82.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 84.000 | ||||
| Mean of predictor | 0.179 | ||||
| Mean of criterion | -0.056 | ||||
| SD of predictor | 0.299 | ||||
| SD of criterion | 0.044 | ||||
| Covariance | 0.001 | ||||
| r | 0.090 | ||||
| b (slope, estimate of beta) | 0.013 | ||||
| a (intercept, estimate of alpha) | -0.058 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 82.000 | ||||
| t(b) | 0.819 | ||||
| p(b) | 0.208 | ||||
| t(a) | -3.427 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.019 | ||||
| Upperbound of 95% confidence interval for beta | 0.045 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.092 | ||||
| Upperbound of 95% confidence interval for alpha | -0.024 | ||||
| Treynor index (mean / b) | -4.202 | ||||
| Jensen alpha (a) | -0.058 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.025 | ||||
| Expected Shortfall on VaR | 0.030 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 84.000 | ||||
| Minimum | 0.928 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.054 | ||||
| Mean of quarter 1 | 0.993 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.004 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.060 | ||||
| Mean of outliers low | 0.969 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.083 | ||||
| Mean of outliers high | 1.012 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -125.681 | ||||
| VaR(95%) (moments method) | -200684344755491.938 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -1.826 | ||||
| VaR(95%) (regression method) | -0.010 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.072 | ||||
| Quartile 1 | 0.075 | ||||
| Median | 0.077 | ||||
| Quartile 3 | 0.080 | ||||
| Maximum | 0.083 | ||||
| Mean of quarter 1 | 0.072 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.083 | ||||
| Inter Quartile Range | 0.005 | ||||
| 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) | -0.011 | ||||
| Compounded annual return (geometric extrapolation) | -0.012 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.141 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.141 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.382 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.050 | ||||
| SD | 0.110 | ||||
| Sharpe ratio (Glass type estimate) | -0.452 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.452 | ||||
| df | 1846.000 | ||||
| t | -1.200 | ||||
| p | 0.514 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.190 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.287 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.190 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.287 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.639 | ||||
| Upside Potential Ratio | 1.517 | ||||
| Upside part of mean | 0.118 | ||||
| Downside part of mean | -0.167 | ||||
| Upside SD | 0.078 | ||||
| Downside SD | 0.078 | ||||
| N nonnegative terms | 40.000 | ||||
| N negative terms | 1807.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1847.000 | ||||
| Mean of predictor | 0.333 | ||||
| Mean of criterion | -0.050 | ||||
| SD of predictor | 0.526 | ||||
| SD of criterion | 0.110 | ||||
| Covariance | -0.004 | ||||
| r | -0.068 | ||||
| b (slope, estimate of beta) | -0.014 | ||||
| a (intercept, estimate of alpha) | -0.045 | ||||
| Mean Square Error | 0.012 | ||||
| DF error | 1845.000 | ||||
| t(b) | -2.918 | ||||
| p(b) | 0.543 | ||||
| t(a) | -1.087 | ||||
| p(a) | 0.516 | ||||
| Lowerbound of 95% confidence interval for beta | -0.024 | ||||
| Upperbound of 95% confidence interval for beta | -0.005 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.126 | ||||
| Upperbound of 95% confidence interval for alpha | 0.036 | ||||
| Treynor index (mean / b) | 3.509 | ||||
| Jensen alpha (a) | -0.045 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.056 | ||||
| SD | 0.110 | ||||
| Sharpe ratio (Glass type estimate) | -0.506 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.505 | ||||
| df | 1846.000 | ||||
| t | -1.343 | ||||
| p | 0.516 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.244 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.233 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.244 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.233 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.687 | ||||
| Upside Potential Ratio | 1.419 | ||||
| Upside part of mean | 0.115 | ||||
| Downside part of mean | -0.170 | ||||
| Upside SD | 0.075 | ||||
| Downside SD | 0.081 | ||||
| N nonnegative terms | 40.000 | ||||
| N negative terms | 1807.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1847.000 | ||||
| Mean of predictor | 0.195 | ||||
| Mean of criterion | -0.056 | ||||
| SD of predictor | 0.524 | ||||
| SD of criterion | 0.110 | ||||
| Covariance | -0.004 | ||||
| r | -0.068 | ||||
| b (slope, estimate of beta) | -0.014 | ||||
| a (intercept, estimate of alpha) | -0.053 | ||||
| Mean Square Error | 0.012 | ||||
| DF error | 1845.000 | ||||
| t(b) | -2.911 | ||||
| p(b) | 0.543 | ||||
| t(a) | -1.278 | ||||
| p(a) | 0.519 | ||||
| Lowerbound of 95% confidence interval for beta | -0.024 | ||||
| Upperbound of 95% confidence interval for beta | -0.005 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.134 | ||||
| Upperbound of 95% confidence interval for alpha | 0.028 | ||||
| Treynor index (mean / b) | 3.921 | ||||
| Jensen alpha (a) | -0.053 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.014 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1847.000 | ||||
| Minimum | 0.883 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.133 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.002 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 81.000 | ||||
| Percentage of outliers low | 0.044 | ||||
| Mean of outliers low | 0.989 | ||||
| Number of outliers high | 77.000 | ||||
| Percentage of outliers high | 0.042 | ||||
| Mean of outliers high | 1.011 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.433 | ||||
| VaR(95%) (moments method) | -0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.454 | ||||
| VaR(95%) (regression method) | -0.003 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.145 | ||||
| Quartile 1 | 0.145 | ||||
| Median | 0.145 | ||||
| Quartile 3 | 0.145 | ||||
| Maximum | 0.145 | ||||
| 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) | -0.011 | ||||
| Compounded annual return (geometric extrapolation) | -0.012 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.079 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.817 | ||||
| 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 | 1.084 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.490 | ||||
| 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 | 0.962 | ||||
| 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) | -8735852376764058.000 | ||||
| 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) | 167566271116271472367936957579264.000 | ||||
| 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 | ||||