Advanced Statistics: Investments test
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 | 0.023 | ||||
| SD | 1.069 | ||||
| Sharpe ratio (Glass type estimate) | 0.022 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.021 | ||||
| df | 37.000 | ||||
| t | 0.038 | ||||
| p | 0.485 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.080 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.123 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.080 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.122 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.039 | ||||
| Upside Potential Ratio | 0.898 | ||||
| Upside part of mean | 0.526 | ||||
| Downside part of mean | -0.503 | ||||
| Upside SD | 0.877 | ||||
| Downside SD | 0.586 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 38.000 | ||||
| Mean of predictor | 0.537 | ||||
| Mean of criterion | 0.023 | ||||
| SD of predictor | 0.269 | ||||
| SD of criterion | 1.069 | ||||
| Covariance | -0.053 | ||||
| r | -0.185 | ||||
| b (slope, estimate of beta) | -0.733 | ||||
| a (intercept, estimate of alpha) | 0.417 | ||||
| Mean Square Error | 1.134 | ||||
| DF error | 36.000 | ||||
| t(b) | -1.128 | ||||
| p(b) | 0.867 | ||||
| t(a) | 0.601 | ||||
| p(a) | 0.276 | ||||
| Lowerbound of 95% confidence interval for beta | -2.051 | ||||
| Upperbound of 95% confidence interval for beta | 0.585 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.989 | ||||
| Upperbound of 95% confidence interval for alpha | 1.822 | ||||
| Treynor index (mean / b) | -0.031 | ||||
| Jensen alpha (a) | 0.417 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -3.680 | ||||
| SD | 6.807 | ||||
| Sharpe ratio (Glass type estimate) | -0.541 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.530 | ||||
| df | 37.000 | ||||
| t | -0.962 | ||||
| p | 0.829 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.645 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.571 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.638 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.578 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.543 | ||||
| Upside Potential Ratio | 0.048 | ||||
| Upside part of mean | 0.328 | ||||
| Downside part of mean | -4.008 | ||||
| Upside SD | 0.530 | ||||
| Downside SD | 6.780 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 38.000 | ||||
| Mean of predictor | 0.490 | ||||
| Mean of criterion | -3.680 | ||||
| SD of predictor | 0.263 | ||||
| SD of criterion | 6.807 | ||||
| Covariance | -0.047 | ||||
| r | -0.026 | ||||
| b (slope, estimate of beta) | -0.683 | ||||
| a (intercept, estimate of alpha) | -3.345 | ||||
| Mean Square Error | 47.588 | ||||
| DF error | 36.000 | ||||
| t(b) | -0.158 | ||||
| p(b) | 0.562 | ||||
| t(a) | -0.757 | ||||
| p(a) | 0.773 | ||||
| Lowerbound of 95% confidence interval for beta | -9.437 | ||||
| Upperbound of 95% confidence interval for beta | 8.072 | ||||
| Lowerbound of 95% confidence interval for alpha | -12.302 | ||||
| Upperbound of 95% confidence interval for alpha | 5.612 | ||||
| Treynor index (mean / b) | 5.390 | ||||
| Jensen alpha (a) | -3.345 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.971 | ||||
| Expected Shortfall on VaR | 0.984 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.141 | ||||
| Expected Shortfall on VaR | 0.307 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 38.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.561 | ||||
| Mean of quarter 1 | 0.854 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.167 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.105 | ||||
| Mean of outliers low | 0.635 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.053 | ||||
| Mean of outliers high | 1.837 | ||||
| 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) | 1.319 | ||||
| VaR(95%) (regression method) | 0.099 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.307 | ||||
| Quartile 1 | 0.480 | ||||
| Median | 0.654 | ||||
| Quartile 3 | 0.827 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.307 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.346 | ||||
| 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) | -0.316 | ||||
| Compounded annual return (geometric extrapolation) | -0.974 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.974 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.974 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.989 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.330 | ||||
| SD | 0.916 | ||||
| Sharpe ratio (Glass type estimate) | -0.360 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.360 | ||||
| df | 831.000 | ||||
| t | -0.641 | ||||
| p | 0.739 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.460 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.740 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.460 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.740 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.412 | ||||
| Upside Potential Ratio | 1.704 | ||||
| Upside part of mean | 1.364 | ||||
| Downside part of mean | -1.694 | ||||
| Upside SD | 0.445 | ||||
| Downside SD | 0.800 | ||||
| N nonnegative terms | 56.000 | ||||
| N negative terms | 776.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 832.000 | ||||
| Mean of predictor | 0.561 | ||||
| Mean of criterion | -0.330 | ||||
| SD of predictor | 0.328 | ||||
| SD of criterion | 0.916 | ||||
| Covariance | -0.019 | ||||
| r | -0.064 | ||||
| b (slope, estimate of beta) | -0.180 | ||||
| a (intercept, estimate of alpha) | -0.229 | ||||
| Mean Square Error | 0.837 | ||||
| DF error | 830.000 | ||||
| t(b) | -1.854 | ||||
| p(b) | 0.968 | ||||
| t(a) | -0.444 | ||||
| p(a) | 0.671 | ||||
| Lowerbound of 95% confidence interval for beta | -0.370 | ||||
| Upperbound of 95% confidence interval for beta | 0.011 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.242 | ||||
| Upperbound of 95% confidence interval for alpha | 0.784 | ||||
| Treynor index (mean / b) | 1.836 | ||||
| Jensen alpha (a) | -0.229 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -3.669 | ||||
| SD | 5.897 | ||||
| Sharpe ratio (Glass type estimate) | -0.622 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.622 | ||||
| df | 831.000 | ||||
| t | -1.109 | ||||
| p | 0.866 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.722 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.478 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.722 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.479 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.624 | ||||
| Upside Potential Ratio | 0.217 | ||||
| Upside part of mean | 1.275 | ||||
| Downside part of mean | -4.945 | ||||
| Upside SD | 0.408 | ||||
| Downside SD | 5.883 | ||||
| N nonnegative terms | 56.000 | ||||
| N negative terms | 776.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 832.000 | ||||
| Mean of predictor | 0.506 | ||||
| Mean of criterion | -3.669 | ||||
| SD of predictor | 0.329 | ||||
| SD of criterion | 5.897 | ||||
| Covariance | -0.084 | ||||
| r | -0.044 | ||||
| b (slope, estimate of beta) | -0.781 | ||||
| a (intercept, estimate of alpha) | -3.274 | ||||
| Mean Square Error | 34.748 | ||||
| DF error | 830.000 | ||||
| t(b) | -1.255 | ||||
| p(b) | 0.895 | ||||
| t(a) | -0.985 | ||||
| p(a) | 0.838 | ||||
| Lowerbound of 95% confidence interval for beta | -2.002 | ||||
| Upperbound of 95% confidence interval for beta | 0.440 | ||||
| Lowerbound of 95% confidence interval for alpha | -9.797 | ||||
| Upperbound of 95% confidence interval for alpha | 3.248 | ||||
| Treynor index (mean / b) | 4.700 | ||||
| Jensen alpha (a) | -3.274 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.458 | ||||
| Expected Shortfall on VaR | 0.531 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.049 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 832.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.298 | ||||
| Mean of quarter 1 | 0.975 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.021 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 54.000 | ||||
| Percentage of outliers low | 0.065 | ||||
| Mean of outliers low | 0.903 | ||||
| Number of outliers high | 56.000 | ||||
| Percentage of outliers high | 0.067 | ||||
| Mean of outliers high | 1.078 | ||||
| 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) | 0.188 | ||||
| VaR(95%) (regression method) | 0.011 | ||||
| Expected Shortfall (regression method) | 0.062 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.022 | ||||
| Quartile 1 | 0.028 | ||||
| Median | 0.092 | ||||
| Quartile 3 | 0.567 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.025 | ||||
| Mean of quarter 2 | 0.092 | ||||
| Mean of quarter 3 | 0.567 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.539 | ||||
| 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) | -0.315 | ||||
| Compounded annual return (geometric extrapolation) | -0.973 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.973 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.973 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.834 | ||||
| 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 | 1.044 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.515 | ||||
| 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 | 0.909 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.520 | ||||
| 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) | -8748565910506219.000 | ||||
| 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) | -157017892746513422501298099453952.000 | ||||
| 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 | ||||