Advanced Statistics: K
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 | -0.070 | ||||
| SD | 0.041 | ||||
| Sharpe ratio (Glass type estimate) | -1.682 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.642 | ||||
| df | 32.000 | ||||
| t | -2.790 | ||||
| p | 0.996 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.922 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.419 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.891 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.394 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.532 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.070 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.045 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 33.000 | ||||
| Mean of predictor | 0.604 | ||||
| Mean of criterion | -0.070 | ||||
| SD of predictor | 0.287 | ||||
| SD of criterion | 0.041 | ||||
| Covariance | 0.001 | ||||
| r | 0.126 | ||||
| b (slope, estimate of beta) | 0.018 | ||||
| a (intercept, estimate of alpha) | -0.081 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 31.000 | ||||
| t(b) | 0.708 | ||||
| p(b) | 0.242 | ||||
| t(a) | -2.728 | ||||
| p(a) | 0.995 | ||||
| Lowerbound of 95% confidence interval for beta | -0.034 | ||||
| Upperbound of 95% confidence interval for beta | 0.071 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.141 | ||||
| Upperbound of 95% confidence interval for alpha | -0.020 | ||||
| Treynor index (mean / b) | -3.825 | ||||
| Jensen alpha (a) | -0.081 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.070 | ||||
| SD | 0.043 | ||||
| Sharpe ratio (Glass type estimate) | -1.643 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.604 | ||||
| df | 32.000 | ||||
| t | -2.724 | ||||
| p | 0.995 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.879 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.383 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.849 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.358 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.503 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.070 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.047 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 33.000 | ||||
| Mean of predictor | 0.550 | ||||
| Mean of criterion | -0.070 | ||||
| SD of predictor | 0.281 | ||||
| SD of criterion | 0.043 | ||||
| Covariance | 0.001 | ||||
| r | 0.119 | ||||
| b (slope, estimate of beta) | 0.018 | ||||
| a (intercept, estimate of alpha) | -0.080 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 31.000 | ||||
| t(b) | 0.666 | ||||
| p(b) | 0.255 | ||||
| t(a) | -2.674 | ||||
| p(a) | 0.994 | ||||
| Lowerbound of 95% confidence interval for beta | -0.037 | ||||
| Upperbound of 95% confidence interval for beta | 0.073 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.142 | ||||
| Upperbound of 95% confidence interval for alpha | -0.019 | ||||
| Treynor index (mean / b) | -3.896 | ||||
| Jensen alpha (a) | -0.080 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.026 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.020 | ||||
| Expected Shortfall on VaR | 0.038 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 33.000 | ||||
| Minimum | 0.931 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.992 | ||||
| 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 | 2.000 | ||||
| Percentage of outliers low | 0.061 | ||||
| Mean of outliers low | 0.965 | ||||
| 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) | 4.507 | ||||
| VaR(95%) (regression method) | 0.001 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.070 | ||||
| Quartile 1 | 0.070 | ||||
| Median | 0.070 | ||||
| Quartile 3 | 0.070 | ||||
| Maximum | 0.070 | ||||
| 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) | -0.025 | ||||
| Compounded annual return (geometric extrapolation) | -0.026 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.372 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.843 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.069 | ||||
| SD | 0.041 | ||||
| Sharpe ratio (Glass type estimate) | -1.683 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.681 | ||||
| df | 732.000 | ||||
| t | -2.815 | ||||
| p | 0.997 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.858 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.508 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.856 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.506 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.675 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.069 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.041 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 733.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 733.000 | ||||
| Mean of predictor | 0.644 | ||||
| Mean of criterion | -0.069 | ||||
| SD of predictor | 0.358 | ||||
| SD of criterion | 0.041 | ||||
| Covariance | 0.000 | ||||
| r | 0.013 | ||||
| b (slope, estimate of beta) | 0.002 | ||||
| a (intercept, estimate of alpha) | -0.070 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 731.000 | ||||
| t(b) | 0.360 | ||||
| p(b) | 0.359 | ||||
| t(a) | -2.836 | ||||
| p(a) | 0.998 | ||||
| Lowerbound of 95% confidence interval for beta | -0.007 | ||||
| Upperbound of 95% confidence interval for beta | 0.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.119 | ||||
| Upperbound of 95% confidence interval for alpha | -0.022 | ||||
| Treynor index (mean / b) | -45.251 | ||||
| Jensen alpha (a) | -0.070 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.070 | ||||
| SD | 0.043 | ||||
| Sharpe ratio (Glass type estimate) | -1.645 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.644 | ||||
| df | 732.000 | ||||
| t | -2.752 | ||||
| p | 0.997 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.820 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.470 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.818 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.469 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.638 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.070 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.043 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 733.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 733.000 | ||||
| Mean of predictor | 0.576 | ||||
| Mean of criterion | -0.070 | ||||
| SD of predictor | 0.370 | ||||
| SD of criterion | 0.043 | ||||
| Covariance | 0.000 | ||||
| r | 0.013 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | -0.071 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 731.000 | ||||
| t(b) | 0.339 | ||||
| p(b) | 0.367 | ||||
| t(a) | -2.770 | ||||
| p(a) | 0.997 | ||||
| Lowerbound of 95% confidence interval for beta | -0.007 | ||||
| Upperbound of 95% confidence interval for beta | 0.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.121 | ||||
| Upperbound of 95% confidence interval for alpha | -0.021 | ||||
| Treynor index (mean / b) | -48.601 | ||||
| Jensen alpha (a) | -0.071 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.006 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.002 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 733.000 | ||||
| Minimum | 0.931 | ||||
| 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 | 2.000 | ||||
| Percentage of outliers low | 0.003 | ||||
| Mean of outliers low | 0.965 | ||||
| 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) | 4.507 | ||||
| VaR(95%) (regression method) | -0.000 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.070 | ||||
| Quartile 1 | 0.070 | ||||
| Median | 0.070 | ||||
| Quartile 3 | 0.070 | ||||
| Maximum | 0.070 | ||||
| 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) | -0.025 | ||||
| Compounded annual return (geometric extrapolation) | -0.026 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.366 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -4.518 | ||||
| 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 | 1.039 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.482 | ||||
| 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 | 0.920 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.485 | ||||
| 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) | -8739570093258832.000 | ||||
| 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) | -100570654026378683586665663954944.000 | ||||
| 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 | ||||