Advanced Statistics: BT - Bundle
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 | -0.043 | ||||
| SD | 0.036 | ||||
| Sharpe ratio (Glass type estimate) | -1.209 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.194 | ||||
| df | 60.000 | ||||
| t | -2.726 | ||||
| p | 0.996 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.100 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.309 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.089 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.299 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.385 | ||||
| Upside Potential Ratio | 0.349 | ||||
| Upside part of mean | 0.011 | ||||
| Downside part of mean | -0.054 | ||||
| Upside SD | 0.021 | ||||
| Downside SD | 0.031 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 59.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.331 | ||||
| Mean of criterion | -0.043 | ||||
| SD of predictor | 0.286 | ||||
| SD of criterion | 0.036 | ||||
| Covariance | -0.004 | ||||
| r | -0.383 | ||||
| b (slope, estimate of beta) | -0.048 | ||||
| a (intercept, estimate of alpha) | -0.028 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 59.000 | ||||
| t(b) | -3.186 | ||||
| p(b) | 0.999 | ||||
| t(a) | -1.756 | ||||
| p(a) | 0.958 | ||||
| Lowerbound of 95% confidence interval for beta | -0.078 | ||||
| Upperbound of 95% confidence interval for beta | -0.018 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.059 | ||||
| Upperbound of 95% confidence interval for alpha | 0.004 | ||||
| Treynor index (mean / b) | 0.903 | ||||
| Jensen alpha (a) | -0.028 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.036 | ||||
| Sharpe ratio (Glass type estimate) | -1.213 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.198 | ||||
| df | 60.000 | ||||
| t | -2.735 | ||||
| p | 0.996 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.104 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.313 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.093 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.303 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.368 | ||||
| Upside Potential Ratio | 0.333 | ||||
| Upside part of mean | 0.011 | ||||
| Downside part of mean | -0.055 | ||||
| Upside SD | 0.021 | ||||
| Downside SD | 0.032 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 59.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.286 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.289 | ||||
| SD of criterion | 0.036 | ||||
| Covariance | -0.004 | ||||
| r | -0.418 | ||||
| b (slope, estimate of beta) | -0.053 | ||||
| a (intercept, estimate of alpha) | -0.029 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 59.000 | ||||
| t(b) | -3.538 | ||||
| p(b) | 1.000 | ||||
| t(a) | -1.891 | ||||
| p(a) | 0.968 | ||||
| Lowerbound of 95% confidence interval for beta | -0.082 | ||||
| Upperbound of 95% confidence interval for beta | -0.023 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.060 | ||||
| Upperbound of 95% confidence interval for alpha | 0.002 | ||||
| Treynor index (mean / b) | 0.838 | ||||
| Jensen alpha (a) | -0.029 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.025 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.015 | ||||
| Expected Shortfall on VaR | 0.027 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 61.000 | ||||
| Minimum | 0.939 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.050 | ||||
| Mean of quarter 1 | 0.996 | ||||
| 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 | 3.000 | ||||
| Percentage of outliers low | 0.049 | ||||
| Mean of outliers low | 0.980 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.082 | ||||
| Mean of outliers high | 1.013 | ||||
| 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 | 1.000 | ||||
| Minimum | 0.061 | ||||
| Quartile 1 | 0.061 | ||||
| Median | 0.061 | ||||
| Quartile 3 | 0.061 | ||||
| Maximum | 0.061 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.040 | ||||
| SD | 0.088 | ||||
| Sharpe ratio (Glass type estimate) | -0.454 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.454 | ||||
| df | 1351.000 | ||||
| t | -1.032 | ||||
| p | 0.518 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.317 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.409 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.317 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.409 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.698 | ||||
| Upside Potential Ratio | 2.033 | ||||
| Upside part of mean | 0.117 | ||||
| Downside part of mean | -0.157 | ||||
| Upside SD | 0.067 | ||||
| Downside SD | 0.058 | ||||
| N nonnegative terms | 40.000 | ||||
| N negative terms | 1312.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1352.000 | ||||
| Mean of predictor | 0.387 | ||||
| Mean of criterion | -0.040 | ||||
| SD of predictor | 0.407 | ||||
| SD of criterion | 0.088 | ||||
| Covariance | -0.008 | ||||
| r | -0.214 | ||||
| b (slope, estimate of beta) | -0.047 | ||||
| a (intercept, estimate of alpha) | -0.022 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 1350.000 | ||||
| t(b) | -8.061 | ||||
| p(b) | 0.607 | ||||
| t(a) | -0.582 | ||||
| p(a) | 0.508 | ||||
| Lowerbound of 95% confidence interval for beta | -0.058 | ||||
| Upperbound of 95% confidence interval for beta | -0.035 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.097 | ||||
| Upperbound of 95% confidence interval for alpha | 0.053 | ||||
| Treynor index (mean / b) | 0.862 | ||||
| Jensen alpha (a) | -0.022 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.088 | ||||
| Sharpe ratio (Glass type estimate) | -0.503 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.502 | ||||
| df | 1351.000 | ||||
| t | -1.142 | ||||
| p | 0.520 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.366 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.360 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.365 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.361 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.750 | ||||
| Upside Potential Ratio | 1.955 | ||||
| Upside part of mean | 0.115 | ||||
| Downside part of mean | -0.159 | ||||
| Upside SD | 0.065 | ||||
| Downside SD | 0.059 | ||||
| N nonnegative terms | 40.000 | ||||
| N negative terms | 1312.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1352.000 | ||||
| Mean of predictor | 0.300 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.423 | ||||
| SD of criterion | 0.088 | ||||
| Covariance | -0.009 | ||||
| r | -0.235 | ||||
| b (slope, estimate of beta) | -0.049 | ||||
| a (intercept, estimate of alpha) | -0.029 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 1350.000 | ||||
| t(b) | -8.877 | ||||
| p(b) | 0.617 | ||||
| t(a) | -0.785 | ||||
| p(a) | 0.511 | ||||
| Lowerbound of 95% confidence interval for beta | -0.059 | ||||
| Upperbound of 95% confidence interval for beta | -0.038 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.103 | ||||
| Upperbound of 95% confidence interval for alpha | 0.044 | ||||
| Treynor index (mean / b) | 0.905 | ||||
| Jensen alpha (a) | -0.029 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.011 | ||||
| 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 | 1352.000 | ||||
| Minimum | 0.945 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.104 | ||||
| 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 | 73.000 | ||||
| Percentage of outliers low | 0.054 | ||||
| Mean of outliers low | 0.992 | ||||
| Number of outliers high | 67.000 | ||||
| Percentage of outliers high | 0.050 | ||||
| Mean of outliers high | 1.009 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.954 | ||||
| VaR(95%) (moments method) | -0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.127 | ||||
| VaR(95%) (regression method) | -0.002 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.032 | ||||
| Median | 0.064 | ||||
| Quartile 3 | 0.096 | ||||
| Maximum | 0.128 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.128 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.000 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.001 | ||||
| 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 | 1.329 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.349 | ||||
| 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 | 1.265 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.349 | ||||
| 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) | -8585427672997845.000 | ||||
| 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) | -79396450034224222659146233675776.000 | ||||
| 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 | ||||