Advanced Statistics: Apeiron Short Term
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 | -0.021 | ||||
| SD | 0.032 | ||||
| Sharpe ratio (Glass type estimate) | -0.647 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.643 | ||||
| df | 109.000 | ||||
| t | -1.959 | ||||
| p | 0.617 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.299 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.007 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.296 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.010 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.877 | ||||
| Upside Potential Ratio | 1.217 | ||||
| Upside part of mean | 0.029 | ||||
| Downside part of mean | -0.050 | ||||
| Upside SD | 0.022 | ||||
| Downside SD | 0.024 | ||||
| N nonnegative terms | 24.000 | ||||
| N negative terms | 86.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 110.000 | ||||
| Mean of predictor | 0.111 | ||||
| Mean of criterion | -0.021 | ||||
| SD of predictor | 0.244 | ||||
| SD of criterion | 0.032 | ||||
| Covariance | -0.001 | ||||
| r | -0.102 | ||||
| b (slope, estimate of beta) | -0.014 | ||||
| a (intercept, estimate of alpha) | -0.019 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 108.000 | ||||
| t(b) | -1.067 | ||||
| p(b) | 0.551 | ||||
| t(a) | -1.805 | ||||
| p(a) | 0.586 | ||||
| Lowerbound of 95% confidence interval for beta | -0.039 | ||||
| Upperbound of 95% confidence interval for beta | 0.012 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.041 | ||||
| Upperbound of 95% confidence interval for alpha | 0.002 | ||||
| Treynor index (mean / b) | 1.545 | ||||
| Jensen alpha (a) | -0.019 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.021 | ||||
| SD | 0.032 | ||||
| Sharpe ratio (Glass type estimate) | -0.664 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.659 | ||||
| df | 109.000 | ||||
| t | -2.009 | ||||
| p | 0.620 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.315 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.009 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.312 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.006 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.890 | ||||
| Upside Potential Ratio | 1.193 | ||||
| Upside part of mean | 0.029 | ||||
| Downside part of mean | -0.050 | ||||
| Upside SD | 0.022 | ||||
| Downside SD | 0.024 | ||||
| N nonnegative terms | 24.000 | ||||
| N negative terms | 86.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 110.000 | ||||
| Mean of predictor | 0.082 | ||||
| Mean of criterion | -0.021 | ||||
| SD of predictor | 0.235 | ||||
| SD of criterion | 0.032 | ||||
| Covariance | -0.001 | ||||
| r | -0.110 | ||||
| b (slope, estimate of beta) | -0.015 | ||||
| a (intercept, estimate of alpha) | -0.020 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 108.000 | ||||
| t(b) | -1.149 | ||||
| p(b) | 0.555 | ||||
| t(a) | -1.886 | ||||
| p(a) | 0.589 | ||||
| Lowerbound of 95% confidence interval for beta | -0.041 | ||||
| Upperbound of 95% confidence interval for beta | 0.011 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.041 | ||||
| Upperbound of 95% confidence interval for alpha | 0.001 | ||||
| Treynor index (mean / b) | 1.418 | ||||
| Jensen alpha (a) | -0.020 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.021 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.020 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 110.000 | ||||
| Minimum | 0.964 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.002 | ||||
| Maximum | 1.035 | ||||
| Mean of quarter 1 | 0.995 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.013 | ||||
| Inter Quartile Range | 0.002 | ||||
| Number outliers low | 9.000 | ||||
| Percentage of outliers low | 0.082 | ||||
| Mean of outliers low | 0.984 | ||||
| Number of outliers high | 24.000 | ||||
| Percentage of outliers high | 0.218 | ||||
| Mean of outliers high | 1.015 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.127 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.596 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | 0.017 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.004 | ||||
| Median | 0.009 | ||||
| Quartile 3 | 0.019 | ||||
| Maximum | 0.071 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.008 | ||||
| Mean of quarter 3 | 0.018 | ||||
| Mean of quarter 4 | 0.045 | ||||
| Inter Quartile Range | 0.015 | ||||
| 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 | 0.143 | ||||
| Mean of outliers high | 0.071 | ||||
| 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) | 0.023 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.325 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.511 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.110 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.012 | ||||
| SD | 0.140 | ||||
| Sharpe ratio (Glass type estimate) | -0.083 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.083 | ||||
| df | 2405.000 | ||||
| t | -0.251 | ||||
| p | 0.599 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.730 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.564 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.730 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.564 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.125 | ||||
| Upside Potential Ratio | 2.635 | ||||
| Upside part of mean | 0.245 | ||||
| Downside part of mean | -0.256 | ||||
| Upside SD | 0.105 | ||||
| Downside SD | 0.093 | ||||
| N nonnegative terms | 315.000 | ||||
| N negative terms | 2091.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2406.000 | ||||
| Mean of predictor | 0.171 | ||||
| Mean of criterion | -0.012 | ||||
| SD of predictor | 0.465 | ||||
| SD of criterion | 0.140 | ||||
| Covariance | -0.021 | ||||
| r | -0.315 | ||||
| b (slope, estimate of beta) | -0.095 | ||||
| a (intercept, estimate of alpha) | 0.005 | ||||
| Mean Square Error | 0.018 | ||||
| DF error | 2404.000 | ||||
| t(b) | -16.298 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.107 | ||||
| p(a) | 0.457 | ||||
| Lowerbound of 95% confidence interval for beta | -0.107 | ||||
| Upperbound of 95% confidence interval for beta | -0.084 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.082 | ||||
| Upperbound of 95% confidence interval for alpha | 0.091 | ||||
| Treynor index (mean / b) | 0.122 | ||||
| Jensen alpha (a) | 0.005 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.021 | ||||
| SD | 0.139 | ||||
| Sharpe ratio (Glass type estimate) | -0.153 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.153 | ||||
| df | 2405.000 | ||||
| t | -0.464 | ||||
| p | 0.679 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.800 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.494 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.800 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.494 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.217 | ||||
| Upside Potential Ratio | 2.431 | ||||
| Upside part of mean | 0.240 | ||||
| Downside part of mean | -0.261 | ||||
| Upside SD | 0.099 | ||||
| Downside SD | 0.099 | ||||
| N nonnegative terms | 315.000 | ||||
| N negative terms | 2091.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2406.000 | ||||
| Mean of predictor | 0.065 | ||||
| Mean of criterion | -0.021 | ||||
| SD of predictor | 0.461 | ||||
| SD of criterion | 0.139 | ||||
| Covariance | -0.020 | ||||
| r | -0.317 | ||||
| b (slope, estimate of beta) | -0.096 | ||||
| a (intercept, estimate of alpha) | -0.015 | ||||
| Mean Square Error | 0.017 | ||||
| DF error | 2404.000 | ||||
| t(b) | -16.413 | ||||
| p(b) | 1.000 | ||||
| t(a) | -0.347 | ||||
| p(a) | 0.636 | ||||
| Lowerbound of 95% confidence interval for beta | -0.107 | ||||
| Upperbound of 95% confidence interval for beta | -0.084 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.101 | ||||
| Upperbound of 95% confidence interval for alpha | 0.070 | ||||
| Treynor index (mean / b) | 0.223 | ||||
| Jensen alpha (a) | -0.015 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.018 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2406.000 | ||||
| Minimum | 0.810 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.235 | ||||
| Mean of quarter 1 | 0.997 | ||||
| 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 | 383.000 | ||||
| Percentage of outliers low | 0.159 | ||||
| Mean of outliers low | 0.995 | ||||
| Number of outliers high | 373.000 | ||||
| Percentage of outliers high | 0.155 | ||||
| Mean of outliers high | 1.006 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.025 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| 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 | 5.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.032 | ||||
| Median | 0.047 | ||||
| Quartile 3 | 0.085 | ||||
| Maximum | 0.215 | ||||
| Mean of quarter 1 | 0.017 | ||||
| Mean of quarter 2 | 0.047 | ||||
| Mean of quarter 3 | 0.085 | ||||
| Mean of quarter 4 | 0.215 | ||||
| Inter Quartile Range | 0.054 | ||||
| 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 | 0.200 | ||||
| Mean of outliers high | 0.215 | ||||
| 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) | 0.023 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.106 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.106 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.296 | ||||
| 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 | 0.834 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.538 | ||||
| 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 | 0.689 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.541 | ||||
| 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) | -8772498842057918.000 | ||||
| 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) | 386241289642670004291161720619008.000 | ||||
| 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 | ||||