Advanced Statistics: BelieveOrNotButThisIsNotWorking
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 | 0.463 | ||||
| SD | 2.503 | ||||
| Sharpe ratio (Glass type estimate) | 0.185 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.181 | ||||
| df | 31.000 | ||||
| t | 0.302 | ||||
| p | 0.382 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.017 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.385 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.020 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.382 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.530 | ||||
| Upside Potential Ratio | 1.847 | ||||
| Upside part of mean | 1.616 | ||||
| Downside part of mean | -1.152 | ||||
| Upside SD | 2.307 | ||||
| Downside SD | 0.875 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 28.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.618 | ||||
| Mean of criterion | 0.463 | ||||
| SD of predictor | 0.273 | ||||
| SD of criterion | 2.503 | ||||
| Covariance | -0.020 | ||||
| r | -0.030 | ||||
| b (slope, estimate of beta) | -0.272 | ||||
| a (intercept, estimate of alpha) | 0.632 | ||||
| Mean Square Error | 6.468 | ||||
| DF error | 30.000 | ||||
| t(b) | -0.163 | ||||
| p(b) | 0.564 | ||||
| t(a) | 0.338 | ||||
| p(a) | 0.369 | ||||
| Lowerbound of 95% confidence interval for beta | -3.684 | ||||
| Upperbound of 95% confidence interval for beta | 3.139 | ||||
| Lowerbound of 95% confidence interval for alpha | -3.185 | ||||
| Upperbound of 95% confidence interval for alpha | 4.448 | ||||
| Treynor index (mean / b) | -1.702 | ||||
| Jensen alpha (a) | 0.632 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -3.216 | ||||
| SD | 4.851 | ||||
| Sharpe ratio (Glass type estimate) | -0.663 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.647 | ||||
| df | 31.000 | ||||
| t | -1.083 | ||||
| p | 0.856 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.869 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.554 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.858 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.564 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.675 | ||||
| Upside Potential Ratio | 0.162 | ||||
| Upside part of mean | 0.770 | ||||
| Downside part of mean | -3.986 | ||||
| Upside SD | 0.974 | ||||
| Downside SD | 4.766 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 28.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.567 | ||||
| Mean of criterion | -3.216 | ||||
| SD of predictor | 0.265 | ||||
| SD of criterion | 4.851 | ||||
| Covariance | 0.166 | ||||
| r | 0.129 | ||||
| b (slope, estimate of beta) | 2.364 | ||||
| a (intercept, estimate of alpha) | -4.557 | ||||
| Mean Square Error | 23.913 | ||||
| DF error | 30.000 | ||||
| t(b) | 0.713 | ||||
| p(b) | 0.241 | ||||
| t(a) | -1.289 | ||||
| p(a) | 0.896 | ||||
| Lowerbound of 95% confidence interval for beta | -4.410 | ||||
| Upperbound of 95% confidence interval for beta | 9.137 | ||||
| Lowerbound of 95% confidence interval for alpha | -11.779 | ||||
| Upperbound of 95% confidence interval for alpha | 2.665 | ||||
| Treynor index (mean / b) | -1.361 | ||||
| Jensen alpha (a) | -4.557 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.924 | ||||
| Expected Shortfall on VaR | 0.953 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.309 | ||||
| Expected Shortfall on VaR | 0.624 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 32.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 4.751 | ||||
| Mean of quarter 1 | 0.629 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.540 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.188 | ||||
| Mean of outliers low | 0.505 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.125 | ||||
| Mean of outliers high | 2.081 | ||||
| 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) | -0.051 | ||||
| VaR(95%) (regression method) | 0.503 | ||||
| Expected Shortfall (regression method) | 0.822 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.778 | ||||
| Quartile 1 | 0.834 | ||||
| Median | 0.889 | ||||
| Quartile 3 | 0.944 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.778 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.111 | ||||
| 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) | -0.375 | ||||
| Compounded annual return (geometric extrapolation) | -0.958 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.958 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.958 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.006 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.664 | ||||
| SD | 2.189 | ||||
| Sharpe ratio (Glass type estimate) | 0.303 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.303 | ||||
| df | 709.000 | ||||
| t | 0.499 | ||||
| p | 0.309 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.888 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.494 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.888 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.494 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.548 | ||||
| Upside Potential Ratio | 4.603 | ||||
| Upside part of mean | 5.581 | ||||
| Downside part of mean | -4.917 | ||||
| Upside SD | 1.822 | ||||
| Downside SD | 1.213 | ||||
| N nonnegative terms | 85.000 | ||||
| N negative terms | 625.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 710.000 | ||||
| Mean of predictor | 0.655 | ||||
| Mean of criterion | 0.664 | ||||
| SD of predictor | 0.350 | ||||
| SD of criterion | 2.189 | ||||
| Covariance | 0.051 | ||||
| r | 0.066 | ||||
| b (slope, estimate of beta) | 0.414 | ||||
| a (intercept, estimate of alpha) | 0.393 | ||||
| Mean Square Error | 4.779 | ||||
| DF error | 708.000 | ||||
| t(b) | 1.766 | ||||
| p(b) | 0.039 | ||||
| t(a) | 0.294 | ||||
| p(a) | 0.384 | ||||
| Lowerbound of 95% confidence interval for beta | -0.046 | ||||
| Upperbound of 95% confidence interval for beta | 0.875 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.232 | ||||
| Upperbound of 95% confidence interval for alpha | 3.018 | ||||
| Treynor index (mean / b) | 1.603 | ||||
| Jensen alpha (a) | 0.393 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -3.166 | ||||
| SD | 4.259 | ||||
| Sharpe ratio (Glass type estimate) | -0.743 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.742 | ||||
| df | 709.000 | ||||
| t | -1.223 | ||||
| p | 0.889 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.934 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.448 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.934 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.449 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.779 | ||||
| Upside Potential Ratio | 1.120 | ||||
| Upside part of mean | 4.548 | ||||
| Downside part of mean | -7.714 | ||||
| Upside SD | 1.289 | ||||
| Downside SD | 4.061 | ||||
| N nonnegative terms | 85.000 | ||||
| N negative terms | 625.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 710.000 | ||||
| Mean of predictor | 0.592 | ||||
| Mean of criterion | -3.166 | ||||
| SD of predictor | 0.352 | ||||
| SD of criterion | 4.259 | ||||
| Covariance | 0.111 | ||||
| r | 0.074 | ||||
| b (slope, estimate of beta) | 0.896 | ||||
| a (intercept, estimate of alpha) | -3.696 | ||||
| Mean Square Error | 18.069 | ||||
| DF error | 708.000 | ||||
| t(b) | 1.975 | ||||
| p(b) | 0.024 | ||||
| t(a) | -1.424 | ||||
| p(a) | 0.923 | ||||
| Lowerbound of 95% confidence interval for beta | 0.005 | ||||
| Upperbound of 95% confidence interval for beta | 1.787 | ||||
| Lowerbound of 95% confidence interval for alpha | -8.793 | ||||
| Upperbound of 95% confidence interval for alpha | 1.401 | ||||
| Treynor index (mean / b) | -3.533 | ||||
| Jensen alpha (a) | -3.696 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.359 | ||||
| Expected Shortfall on VaR | 0.423 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.060 | ||||
| Expected Shortfall on VaR | 0.132 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 710.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.846 | ||||
| Mean of quarter 1 | 0.926 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.085 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 120.000 | ||||
| Percentage of outliers low | 0.169 | ||||
| Mean of outliers low | 0.890 | ||||
| Number of outliers high | 85.000 | ||||
| Percentage of outliers high | 0.120 | ||||
| Mean of outliers high | 1.178 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.683 | ||||
| VaR(95%) (moments method) | 0.007 | ||||
| Expected Shortfall (moments method) | 0.008 | ||||
| Extreme Value Index (regression method) | 0.289 | ||||
| VaR(95%) (regression method) | 0.067 | ||||
| Expected Shortfall (regression method) | 0.158 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.013 | ||||
| Quartile 1 | 0.075 | ||||
| Median | 0.240 | ||||
| Quartile 3 | 0.430 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.035 | ||||
| Mean of quarter 2 | 0.202 | ||||
| Mean of quarter 3 | 0.388 | ||||
| Mean of quarter 4 | 0.978 | ||||
| Inter Quartile Range | 0.355 | ||||
| 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 | 0.111 | ||||
| Mean of outliers high | 1.000 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -694.756 | ||||
| VaR(95%) (moments method) | 0.784 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -4.611 | ||||
| VaR(95%) (regression method) | 1.912 | ||||
| Expected Shortfall (regression method) | 1.912 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.369 | ||||
| Compounded annual return (geometric extrapolation) | -0.956 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.956 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.977 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.259 | ||||
| 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 | 1.013 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.543 | ||||
| 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 | 0.867 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.537 | ||||
| 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) | -8756099416699473.000 | ||||
| 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) | -1289775213119153859163956178845696.000 | ||||
| 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 | ||||